Copyright by Ajay Suri 2005

Copyright

by

Ajay Suri

2005

The Dissertation Committee for Ajay Suri Certifies that this is the approved version

of the following dissertation:

CLEANUP OF INTERNAL FILTER CAKE DURING FLOWBACK

Committee:

Mukul M. Sharma, Supervisor

Roger T. Bonnecaze

Daniel A. Hill

Carlos Torres-Verdin

Martin E. Chenevert

Steven L. Bryant


by

Ajay Suri, B. Tech., M.S.

Dissertation

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

The University of Texas at Austin

December 2005

Dedication

This dissertation is dedicated to

The Supreme Spirit

The Ocean of Knowledge, Peace, Purity, Love, Happiness, Bliss, and Power

v

Acknowledgements

I would like to express my sincere gratitude to Dr. Mukul M. Sharma for

constantly inspiring, guiding and supporting me during the course of my research. I

found him very caring during my entire stay here at the university.

I would also like to thank Dr. Roger T. Bonnecaze, Dr. A. D. Hill, Dr. Steven L.

Bryant, Dr. Carlos Torres-Verdin, and Dr. Martin E. Chenevert for serving on the

committee.

Thanks to some of my colleagues, Jagan, Phani, Zongyu, Liu, and Baosheng for

their company and friendship.

Thanks to Reynaldo Casanova for providing the office supplies, to Roger

Terzian for providing the computer accessories and software, to Glenn Baum, Bob

Savicki and Tony Bermudez for setting the lab and for the friendship.

Lastly I would like to thank my brothers and sisters of my Brahmin family,

Sister Hansa, Brother Mark, Brother Mahesh, Brother Sachin and Brother Janardhan for

their constant love and support.

vi


Publication No._____________

Ajay Suri, Ph.D.

The University of Texas at Austin, 2005

Supervisor: Mukul M. Sharma

The flow initiation pressure (FIP) is used as an estimate of the differential

pressure (between the reservoir and the well) required to initiate production. The

standard practice to measure FIP uses a constant flowback rate. This method is shown

to be inadequate to measure the FIP. An improved flowback method, which uses a

series of constant differential pressures, is used instead to measure the FIP. This method

closely represents the constant drawdown experienced between the reservoir and the

wellbore. In addition the permeability during flowback is measured at increasing

differential pressures, resulting in a spectrum of return permeability values.

Two types of drilling fluids (sized calcium carbonate and bentonite) are used for

conducting the filtration and flowback experiments for porous media ranging in

permeability from 4 to 1500 md. Both single-phase and two-phase experiments are

conducted in lab-simulated open-hole and perforated completions to better understand

the factors affecting the FIP and the return permeability spectra.

vii

We observe small values for FIP in all the experiments (considerably smaller

than those measured using the constant flowback method). The values of FIP yield

pressure gradients that are achievable in vertical wells but may not be easily achieved

in horizontal wells. The FIP and the return permeability spectra are controlled by the

cleanup of the internal filter cake. A Bingham fluid in a network of pores is used to

model the cleanup of the internal filter cake during flowback. The results indicate that

very large pressure gradients are required during flowback to cleanup the entire internal

filter cake. However, a pressure gradient of 10 psi / inch is found to yield a skin factor

< 1 for most open-hole completions. For perforated completions, pressure gradients up

to 20 psi / inch and flow rates up to 0.3 bbl/day/perf yield skin factors < 2.

viii

Table of Contents

List of Tables ..................................................................................................................xiii

List of Figures .................................................................................................................xvi

Chapter 1: Introduction ..................................................................................................1 1.1 Background...................................................................................................... 1 1.2 Definition of the Problem ................................................................................ 5 1.3 Outline of the Chapters .................................................................................... 7 References................................................................................................................. 8

Chapter 2: An Improved Laboratory Method to Estimate Flow Initiation Pressures and Return Permeabilities During Flowback ...................................11 2.1 Inroduction..................................................................................................... 11 2.2 Literature Review........................................................................................... 11

2.2.1 Flow Initiation Pressure ........................................................................ 11 2.2.2 Return Permeability .............................................................................. 15

2.3 Problem Description and Motivation............................................................. 17 2.4 Experimental Design...................................................................................... 18

2.4.1 Test Equipment ..................................................................................... 18 2.4.2 Core and Fluid Sample.......................................................................... 20 2.4.3 Test Procedure ...................................................................................... 21

2.5 Test Objectives............................................................................................... 26 2.6 Discussion of Experimental Results .............................................................. 26

2.6.1 Single-phase (Brine) Experiments ........................................................ 27 2.6.2 Two-phase (Brine + Oil) Experiments.................................................. 30 2.6.3 Comparison between Single-phase and Two-phase Flow Experiments33

2.7 Effect of Different Parameters on FIP and Return Permeability ................... 35 2.7.1 Effect of Flowback Condition (Constant Flow Rate vs. Constant

Pressure)................................................................................................ 36 2.7.2 Effect of External Filter Cake ............................................................... 36 2.7.3 Effect of Drill-in or Completion Fluid Type......................................... 37 2.7.4 Effect of Core Length ........................................................................... 38

ix

2.7.5 Effect of Back Pressure......................................................................... 38 2.7.6 Effect of Median Particle Size of the Bridging Agent.......................... 39

2.8 Application of Results To Estimate Skin Around Wells ............................... 39 2.9 Conclusions.................................................................................................... 44 References............................................................................................................... 81

Chapter 3: Role of Drill-in Fluid Components during Filtration and Flowback ....84 3.1 Introduction.................................................................................................... 84 3.2 Drill-in and Completion Fluid Components .................................................. 84

3.2.1 Bridging Additive ................................................................................. 86 3.2.2 Fluid Loss Control Additive ................................................................. 86 3.2.3 Rheology Control Additive................................................................... 87

3.3 Research Objective ........................................................................................ 87 3.4 Experimental Design...................................................................................... 88

3.4.1 Test Description and Fluid Design ....................................................... 88 3.4.2 Test Equipment ..................................................................................... 89 3.4.3 Test Procedure ...................................................................................... 89

3.5 Discussion of Experimental Results .............................................................. 90 3.5.1 Flow Initiation Pressure ........................................................................ 90 3.5.2 Return Permeability Ratio..................................................................... 91 3.5.3 Filtrate Loss .......................................................................................... 94

3.6 Effect of Drill Solids...................................................................................... 95 3.7 Comparison of Experimental Results with UTDamage................................. 96 3.8 Conclusions.................................................................................................... 96 References............................................................................................................. 108

Chapter 4: Filter Cake Yield Strength.......................................................................109 4.1 Introduction.................................................................................................. 109 4.2 Literature Review......................................................................................... 109 4.3 Motivation.................................................................................................... 111 4.4 Constant Strain Rheometer .......................................................................... 112

4.4.1 Principle of Measurement ................................................................... 113

x

4.4.2 Parallel Plate Geometry ...................................................................... 113 4.4.3 Theoretical Equations ......................................................................... 114 4.4.4 Sample Preparation ............................................................................. 115

4.5 Results and Discussion ................................................................................ 115 4.5.1 Dynamic Strain Sweep Test................................................................ 116 4.5.2 Linear Strain Test................................................................................ 117

4.6 Experimental Issues and Concerns .............................................................. 119 4.7 Conclusions.................................................................................................. 121 References............................................................................................................. 135

Chapter 5: Modeling the Cleanup of Internal Filter Cake during Flowback ........136 5.1 Introduction.................................................................................................. 136 5.2 Background and Literature Review ............................................................. 136 5.3 Model Development..................................................................................... 138

5.3.1 Bundle of Tubes Model ...................................................................... 139 5.3.2 Discussion on Bundle of Tubes Model Results .................................. 143 5.3.3 Comparison of Bundle of Tubes Model Results with Experimental

Results................................................................................................. 145 5.3.4 Three Dimensional Network Model with Effective Medium

Approximation .................................................................................... 148 5.3.5 Results and Discussion on Network Model ........................................ 156

5.4 Slow Cleanup of the Internal Filter Cake .................................................... 159 5.5 Conclusions.................................................................................................. 161 References............................................................................................................. 181

Chapter 6: Cleanup of Lab-Simulated Perforation Tunnels during Flowback .....183 6.1 Introduction.................................................................................................. 183 6.2 Background and Literature Review ............................................................. 183 6.3 Problem Description .................................................................................... 186 6.4 Objectives .................................................................................................... 186 6.5 Test Design .................................................................................................. 187

6.5.1 Lab-simulated Perforated Core and Core Holder ............................... 187 6.5.2 Rock Type and Fluid Type ................................................................. 187

xi

6.5.3 Test Procedure .................................................................................... 188 6.6 Discussion of Experimental Results ............................................................ 189

6.6.1 Single-phase Experiments................................................................... 189 6.6.2 Two-phase Experiments...................................................................... 194

6.7 Effect of Different Parameters ..................................................................... 196 6.7.1 Single-phase vs. Two-phase Flow ...................................................... 197 6.7.2 Effect of Completion Fluid Type........................................................ 197 6.7.3 Open-hole Completion vs. Perforated Completion............................. 198 6.7.4 Effect of Overbalance Pressure........................................................... 200 6.7.5 Effect of Perforation Dimensions ....................................................... 201 6.7.6 Single vs. Multiple Perforations ......................................................... 201

6.8 Application of Results To Estimate Skin In Perforated Completions ......... 201 6.9 Conclusions.................................................................................................. 202 References............................................................................................................. 225

Chapter 7: UTDamage: An Application to Model Both Filtration and Flowback and To Design Fluids ..........................................................................................226 7.1 Introduction.................................................................................................. 226 7.2 Background and Literature Review ............................................................. 226 7.3 Model Development..................................................................................... 227 7.4 UTDamage Vs. Experimental Results ......................................................... 243 7.5 Erosion Factor Model Vs. Bingham Model................................................. 244

Chapter 8: Conclusions ...............................................................................................255 8.1 Recommendations........................................................................................ 258 8.2 Future Work ................................................................................................. 258

xii

Appendix-A: Photograph of the lab-setup used in conducting the experiments ........... 260

Appendix-B: Plots for single-phase constant pressure flowback experiments simulating open-hole completion............................................................................................ 262

Appendix-C: Plots of two-phase constant pressure flowback experiments simulating open-hole condition .............................................................................................. 288

Appendix-D: Plots for experiments with flow back at constant rate to study the role of individual drill-in fluid components on formation damage .................................. 307

Appendix-E: Plots of single-phase filtration experiments conducted on cores with lab-simulated perforations with constant pressure flowback condition...................... 341

Appendix-F: Plots for two-phase constant pressure flowback experiments conducted on lab-simulated perforated cores.............................................................................. 369

Appendix-G: Detailed information of all the fluid filtration experiments with constant pressure flowback condition ................................................................................. 375

Appendix-H: Detailed information of all the fluid filtration experiments with constant rate flowback condition......................................................................................... 377

Nomenclature................................................................................................................. 379

Bibliography .................................................................................................................. 382

Vita ............................................................................................................................... 389

xiii

List of Tables

Table 2-1: Short and long core dimensions ........................................................................47

Table 2-2: Different core types used in the study ...............................................................47

Table 2-3: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb)......................48

Table 2-4: Rheology of CaCO3 drill-in mud using Fann viscometer .................................48

Table 2-5: Formulation of bentonite mud (10 ppg) ............................................................49

Table 2-6: Rheology of bentonite mud using Fann viscometer..........................................49

Table 2-7: Flow initiation pressure for single-phase flow and constant pressure

flowback experiments simulating open hole conditions. ................................50

Table 2-8: Summary of return permeability ratio for single-phase constant pressure

flowback tests simulating open hole conditions..............................................51

Table 2-9: API filtrate loss for single-phase flow and constant pressure flowback

experiments simulating open-hole conditions .................................................52

Table 2-10: Flow initiation pressure for two-phase flow experiments with constant

pressure flowback condition simulating open-hole conditions .......................53

Table 2-11: Summary of return permeability ratio for two-phase constant pressure

flowback tests simulating open-hole conditions .............................................54

Table 2-12: API filtrate loss for two-phase flow and constant pressure flowback

experiments simulating open-hole conditions .................................................55

Table 2-13: Comparison of FIP for single-phase vs. two-phase experiments with

constant pressure flowback conditions............................................................56

Table 2-14: Comparison of return permeability ratio for single-phase vs. two-phase

experiments with constant pressure flowback conditions ...............................57

Table 2-15: Comparison of FIP for constant rate vs. constant pressure flowback

condition for two-phase flow experiments ......................................................58

Table 2-16: Comparison of FIP, return permeability ratio and API filtrate loss for

bentonite mud and UltraCarb drill-in fluid......................................................59

Table 3-1: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb) .....................99

Table 3-2: Drill-in fluid formulation matrix .......................................................................99

xiv

Table 3-3: FIP, return permeability ratio and API filtrate loss for different drill-in fluid

formulations on Berea sandstone (Overbalance: 100 psi)...............................100

Table 3-4: Comparison of FIP, return permeability ratio and API filtrate loss for drill-in

fluid with and without revdust.........................................................................101

Table 3-5: Erosion factors used to fit the return permeability ratio obtained from

experiments with UTDamage for different drill-in fluids ...............................101

Table 4.1: Comparison of yield stress measurements done using dynamic strain sweep

test and linear strain test for different filter cake samples...............................123

Table 5-1: Depth of invasion of solids and polymers calculated from UTDamage for

different rocks used in conducting the experiments ........................................163

Table 6-1: Flow initiation pressure for single-phase flow and constant pressure

flowback experiments simulating perforated completion ...............................204

Table 6-2: Summary of return permeability ratio for single-phase constant pressure

flowback tests simulating open-hole completion ............................................205

Table 6-3: Summary of 30 minute fluid loss for lab simulated perforated cores with

single phase flow and constant pressure flowback condition..........................206

Table 6-4: Summary of FIP for lab simulated perforated cores with two phase flow and

constant pressure flowback condition .............................................................207

Table 6-5: Summary of return permeability ratio for two-phase constant pressure

flowback tests simulating open hole completion ............................................207

Table 6-6: Comparison of FIP for single phase vs. two phase experiments with constant

pressure flowback condition in lab-simulated perforated completions...........208

Table 6-7: Comparison of FIP and return permeability ratio between bentonite mud and

UltraCarb completion fluid in lab-simulated perforated completions.............208

Table B.1: List of all the single-phase, constant pressure flowback experiments,

simulating open-hole completion ....................................................................263

Table C.1: List of all the two-phase, constant pressure flowback experiments,

simulating open-hole completion ....................................................................289

xv

Table D.1: List of experiments with constant rate flowback condition to study the effect

of individual drill-in fluid components on FIP, return permeability and API

filtrate loss .......................................................................................................308

Table E.1: List of all the single-phase, constant pressure flowback experiments,

simulating perforated completions ..................................................................342

Table F.1: List of all the two-phase, constant pressure flowback experiments,

simulating lab-simulated perforated completion.............................................370

xvi

List of Figures

Figure 2-1: Flowback pressure profile with constant flow rate boundary condition to

calculate flow initiation pressure (FIP) ...........................................................60

Figure 2-2: Flow-back pressure profile with constant pressure boundary condition

(incremental pressure differentials) to calculate FIP.......................................60

Figure 2-3: Apparatus for fluid filtration and flowback test...............................................61

Figure 2-4: Apparatus for long core holder ........................................................................62

Figure 2-5: Steps used during mud filtration and flowback tests .......................................63

Figure 2-6: Pore volume distribution for different rocks obtained from mercury

penetrometer ....................................................................................................64

Figure 2-7: Top view of a limestone core after flowback at constant pressure (Mud

used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flowLS-

12)....................................................................................................................64

Figure 2-8: Top view of a Berea core after flowback at constant pressure (Mud used:

UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 2-phase flow, BS-17).....65

Figure 2-9: Nugget sandstone core after flowback at constant pressure (Mud used:

UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow, NS-2).......65

Figure 2-10: Top view of an Aloxide core after flowback at constant pressure (Mud

used: UltraCarb-20 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow,

AL-2) ...............................................................................................................66

Figure 2-11: Return permeability spectra for different permeability cores (single-phase

flow and constant flowback pressure). ............................................................66

Figure 2-12: Spurt loss vs. absolute permeability of different cores for single-phase

experiments simulating open hole conditions .................................................67

Figure 2-13: API Filtrate loss vs. absolute permeability of different cores for single-

phase experiments simulating open hole conditions .......................................67

Figure 2-14: Return permeability spectra for different permeability cores (two-phase

flow and constant flowback pressure) .............................................................68

Figure 2-15: Return permeability spectra for different permeability cores (two-phase

flow and constant flowback pressure) .............................................................68

xvii

Figure 2-16: Spurt loss vs. absolute permeability of different cores for two-phase


Figure 2-17: API Filtrate loss vs. absolute permeability of different cores for two-phase


Figure 2-18: Return permeability spectra in Nugget sandstone for single-phase flow and

two-phase flow ................................................................................................70

Figure 2-19: Comparison of return permeability spectra in Texas limestone for single-

phase vs. two-phase flow (constant pressure B.C.) .........................................70

Figure 2-20: Comparison of return permeability spectra in Berea sandstone for single-


Figure 2-21: Comparison of return permeability spectra in Aloxide (synthetic cores) for

single-phase vs. two-phase flow (constant pressure B.C.) ..............................71

Figure 2-22: Comparison of return permeability spectra in Boise sandstone for single-


Figure 2-23: Comparison of FIP between constant rate boundary condition (B.C.) and

constant pressure B.C. during flowback for Berea sandstone.........................72

Figure 2-24: Comparison of FIP and return permeability spectra for Berea sandstone

with and without external filter cake...............................................................73

Figure 2-25: Return permeability vs. differential pressure during flowback in short and

long Berea cores ..............................................................................................73

Figure 2-26: Return permeability vs. average flowback velocity for experiments

conducted on short and long Berea cores ........................................................74

Figure 2-27: Comparison of return permeability spectra for Berea sandstone with and

without back pressure (O.B. = 500 psi)...........................................................74

Figure 2-28: Comparison of return permeability spectra for Aloxide cores with

UltraCarb drill-in fluids with two different median sizes ...............................75

Figure 2-29: Comparison of return permeability spectra for Berea cores with UltraCarb

drill-in fluids with two different median sizes ................................................75

Figure 2-30: Skin with varying return permeability ratio of the near wellbore region.......76

xviii

Figure 2-31: Return permeability ration vs. average pressure gradients in Texas

limestone and Berea during flowback .............................................................76

Figure 2-32: Return permeability ratio vs. average pressure gradient in Boise sandstone

and Aloxide core during flowback ..................................................................77

Figure 2-33: Return permeability ration vs. average pressure gradients in Texas

limestone and Berea during flowback (Semi-log plot) ...................................77


and Aloxide core during flowback (Semi-log plot).........................................78

Figure 2-35: Pressure gradient at the wellbore face at different steady state flow rates ....78

Figure 2-36: Return permeability ratio of inch long Texas limestone and Berea

sandstone core at different flowback rates (semi-log plot) .............................79

Figure 2-37: Return permeability ratio of Boise sandstone and Aloxide core at different

flowback rates (semi-log plot).........................................................................79

Figure 2-38: Return permeability ratio of Texas limestone and Berea sandstone core at

different flowback velocities (semi-log plot) ..................................................80


flowback velocities (semi-log plot) .................................................................80


calculate flow initiation pressure (FIP) ...........................................................102

Figure 3-2: Flow initiation pressure (constant rate flow back) for Berea sandstone with

varying composition of the drill-in fluid .........................................................102

Figure 3-3: Return permeability ratio for Berea sandstone with varying median size of

bridging agents (bridging agent with no xanthan and no starch) ....................103


bridging agents (bridging agent with xanthan but no starch) ..........................104


bridging agents (bridging agent with xanthan and starch) ..............................104

Figure 3-7: Comparison of return permeability ratio at flow back rate = 1 cc/min for

Berea sandstone with varying drill-in fluid composition ................................105

xix





Figure 3-10: Comparison of API filtrate loss for different drill-in fluid compositions on

Berea sandstone...............................................................................................106

Figure 3-11: Comparison of return permeability ratio obtained from experiments and

from UTDAMAGE simulations......................................................................107

Figure 3-12: Comparison of API filtrate loss obtained from experiments and from

UTDAMAGE simulations...............................................................................107

Figure 4.1: Lifting up of the external filter cake during flowback. The internal filter

cake (roots holding the external filter cake) has cleaned up at point A ..........123

Figure 4.2: Lifting up and formation of pin-holes and cracks in the external filter cake

during flowback...............................................................................................123

Figure 4.3a: Photograph of ARES constant strain rheometer.............................................124

Figure 4.3b: Close up photograph of ARES constant strain rheometer with a parallel

plate (25 mm) apparatus ..................................................................................124

Figure 4.3c: Schematic of parallel plate apparatus in ARES constant strain rheometer ....125

Figure 4.4: Plot of visco-elastic parameters using dynamic strain sweep test in a

constant strain rheometer for UltraCarb-2 drill-in fluid filter cake.................125

Figure 4.5: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-2 drill-

in fluid filter cake ............................................................................................126


constant strain rheometer for UltraCarb-12 drill-in fluid filter cake...............126







xx



Figure 4.11: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-20

drill-in fluid filter cake ....................................................................................129

Figure 4.12: Plot of stress vs. strain in a linear strain test using constant strain

rheometer for UltraCarb-2 drill-in fluid filter cake .........................................129


rheometer for UltraCarb-12 drill-in fluid filter cake .......................................130








rheometer for bentonite mud filter cake ..........................................................132





Figure 4.20: Plot of stress vs. strain at a normal force equal to 500 gms in a linear strain

test for bentonite mud filter cake.....................................................................133

Figure 4.21: Yield strength of different muds using dynamic strain sweep test and linear

strain test..........................................................................................................134

Figure 5.1: Schematic of invasion of particles (solids and polymers) in porous medium

representing internal and external filter cake ..................................................164

Figure 5.2: Schematic of filter cake (internal and external) as a Bingham fluid ................165

Figure 5.3: Schematic of filter cake conceived as a Bingham fluid in a porous medium

represented by a bundle of tubes model ..........................................................166

xxi

Figure 5.4: Flow initiation pressure (FIP) as a function of the largest pore throat

diameter of the pores with varying thickness of the internal filter cake .........167

Figure 5.5: Pore volume distribution obtained from mercury penetrometer for Texas

limestone .........................................................................................................167

Figure 5.6: Pore volume distribution obtained from mercury penetrometer for Berea

sandstone .........................................................................................................168

Figure 5.7: Pore volume distribution obtained from mercury penetrometer for Boise

sandstone .........................................................................................................168

Figure 5.8: Plot comparing the pore volume distribution for different rocks obtained

from mercury penetrometer.............................................................................169

Figure 5.9: Return permeability ratio for Berea sandstone using bundle of tubes model

with varying thickness of the internal filter cake ............................................169


with varying cake yield strength .....................................................................170

Figure 5.11: Return permeability spectra for different rocks obtained from the bundle of

tubes model......................................................................................................170

Figure 5.12: Comparison of return permeability ratio obtained from bundle of tubes

model and experimental results for single phase flow in Texas limestone .....171


model and experimental results for single phase flow in Berea sandstone .....171


model and experimental results for single phase flow in Boise sandstone .....172

Figure 5.15: Schematic of a core before flowback for calculating differential pressure

across the internal filter cake (damaged zone) ................................................172

Figure 5.16: Return permeability in the damaged zone with different depths for Nugget

sandstone (NS-2) .............................................................................................173

Figure 5.17: Schematic of a porous medium represented by a two-dimensional network

of pore throats plugged with internal filter cake. Please note that in the

actual network model the pore throats are of varied sizes. .............................174

xxii

Figure 5.18: A schematic of the distribution of the internal filter cake (as a Bingham

fluid) and the flowback fluid (brine) in the pores during flowback ................175

Figure 5.19: Accessible fraction of pore throats for a Bethe tree with Z = 5 to represent

the accessibility fraction of a three dimensional network with Z = 6 .............176

Figure 5.20: Probability function for pore throat radius for Berea sandstone calculated

from volume size distribution obtained from mercury penetrometer..............176

Figure 5.21: Return permeability for a network model with varying coordination

number (without accessibility function)..........................................................177

Figure 5.22: Return permeability for a network model with varying coordination

number (with accessibility function) ...............................................................177

Figure 5.23: Comparison of bundle of tubes model with the network model (the

network model approaches the bundle of tubes model when z approaches

infinity) ............................................................................................................178

Figure 5.24: Return permeability for a network model with varying pore throat length....178

Figure 5.25: Return permeability obtained from experiments conducted on Berea

sandstone and from the network model...........................................................179

Figure 5.26: Pressure gradients across the internal filter cake with different thickness

(calculated from NS-2 return permeability data and the two zone model) .....179

Figure 5.27: Pressure gradients vs. return permeability ratio of the damaged zone

(calculated for NS-2 using the two zone model) .............................................180

Figure 5.28: Ratio of the flow rate of the flowback fluid (Newtonian) to the flow rate of

the internal filter cake (Bingham fluid) ...........................................................180

Figure 6-1: Schematic of a lab-simulated single perforation in a core ...............................209

Figure 6-2: Schematic of the long core holder with a lab-simulated single perforation.....210

Figure 6-3: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2

in.) before flowback at constant pressure (LS-9) ............................................211

Figure 6-4: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2

in.) after flowback at constant pressure (LS-9) ...............................................211

Figure 6-5: Top view of a long Berea core with lab simulated perforation (1/8 X 1 in.)

after flowback at constant pressure (BS-long-#11) .........................................212

xxiii








after flowback at constant pressure (BS-6-13-04-#8) .....................................214

Figure 6-10: Return permeability spectra for Berea with different perforation

dimensions (single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......214

Figure 6-11: Semi-log plot for return permeability in Berea with different perforation

dimensions (single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......215

Figure 6-12: Return permeability ratio in the first 2 inches of Berea cores (single-phase

flow, O.B: 100 psi, UltraCarb-2 drill-in fluid) ................................................215

Figure 6-13: Semi-log plot for return permeability for the first 2 inches in Berea cores

(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)..........................216

Figure 6-14: Return permeability spectra for Berea with varying flowback rate (single-

phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......216

Figure 6-15: Semi-log plot for return permeability for Berea with flowback rate (single-




Figure 6-17: Semi-log plot for return permeability in 1st 2 inches of the Berea core

(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)..........................218

Figure 6-18: Top and side view of a short Berea core with three drilled holes to

represent lab-simulated perforations ...............................................................218

Figure 6-19: Return permeability spectra for lab-simulated open-hole completion vs.

lab-simulated perforated completions in long Berea cores (6 inch long)........219

Figure 6-20: Return permeability vs. flowback pressure for open-hole and perforated

completions (lab-simulated) in short Berea sandstone cores (1 inch long).....219

xxiv

Figure 6-21: Return permeability vs. flowback velocity for open-hole and perforated

completions (lab-simulated) in short Berea sandstone cores (1 inch long).....220


completions (lab-simulated) in short Texas limestone cores (1 inch long).....220

Figure 6-23: Return permeability vs. flowback rate for open-hole and perforated




Figure 6-25: Return permeability with varying flowback pressure in Boise sandstone

with lab-simulated perforations at two different O.B. pressures (Mud used:

UltraCarb-20) ..................................................................................................222

Figure 6-26: Return permeability spectra for two different perforated completions (lab-

simulated) with different lengths.....................................................................222


simulated) with different diameter ..................................................................223

Figure 6-28: Return permeability spectra for the first two inches of cores with different

perforated completions as a function of average pressure gradient ................223

Figure 6-29: Estimate of skin factor for perforated completions with a depth of damage

equal to 2 inches ..............................................................................................224

Figure 6-30: Return permeability spectra for perforated completions in the first 2 inches

as a function of flow rate through the perforation tunnels ..............................224


representing internal and external filter cake ..................................................246

Figure 7.2: Happel 's Sphere-in-cell porous media model representing the grain and the

pore throat........................................................................................................247

Figure 7.3 (a): Initial saturation of fluids in the core..........................................................248

Figure 7.3 (b): Fluid saturations after invasion of mud filtrate...........................................248

Figure 7.4: Erosion factors used in UTDamage to match the experimental data (BS-4-2-

04-I: UltraCarb-2 drill-in fluid on a short Berea core) ....................................249

xxv


04-#5: UltraCarb-2 drill-in fluid on a long Berea core) ..................................249

Figure 7.6: Erosion factors used in UTDamage to match the experimental data (All

single-phase experiments using Berea sandstone and UltraCarb-2 drill-in

fluid) ................................................................................................................250

Figure 7.7: Plot of erosion factor used in UTDamage to match the return permeability

data for Texas limestone (LS-1: 1-P flow with UltraCarb-2 drill-in fluid).....250


data for Texas limestone (LS-12: Two-phase flow with UltraCarb-2 drill-in

fluid) ................................................................................................................251

Figure 7.9: Erosion factors for single-phase flow and two-phase flow return

permeabilities for Texas limestone cores (LS-1: 1-P, LS-12: 2-P

experiment)......................................................................................................251

Figure A.1: Photograph of the filtration and flow back apparatus .....................................261

Figure B-1: Flowback rate at incremental differential pressures after filtration with

UltraCarb-2 on Nugget sandstone (NS-2) .......................................................264

Figure B-2: Return permeability spectra with incremental differential pressures for

Nugget sandstone (NS-2) ................................................................................264

Figure B-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole

completion (NS-2) ...........................................................................................265


UltraCarb-2 on Texas limestone (LS-1) ..........................................................266


Texas limestone (LS-1) ...................................................................................266

Figure B-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole

completion (LS-1) ...........................................................................................267


UltraCarb-2 on Texas limestone (LS-13) ........................................................268


Texas limestone (LS-13) .................................................................................268

xxvi

Figure B-9: Static filtration of UltraCarb-2 on Texas limestone simulating open hole

completion (LS-13) .........................................................................................269


bentonite on Texas limestone (LS-5) ..............................................................270


Texas limestone (LS-5) ...................................................................................270

Figure B-12: Static filtration of bentonite mud on Texas limestone simulating open hole

completion (LS-5) ...........................................................................................271


UltraCarb-2 on Berea sandstone (BS-4-2-04-I) ..............................................272


Berea sandstone (BS-4-2-04-I)........................................................................272

Figure B-15: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole

completion (BS-4-2-04-I)................................................................................273


UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-3) ........................274

Figure B-17: Return permeability spectra for incremental differential pressures in a

long Berea core (BS-long-3) ...........................................................................274

Figure B-18: Static filtration of UltraCarb-2 on a long Berea core simulating open hole

completion (BS-long-3)...................................................................................275


UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-4) ........................276


long Berea core (BS-4-29-04-long-4) .............................................................276

Figure B-21: Static filtration of UltraCarb-2 on a long Berea sandstone simulating open

hole completion (BS-4-29-04-long-4).............................................................277

Figure B-22: Flowback rate at incremental differential pressures after filtration on a

long Berea sandstone with external filter cake removed (BS-4-29-04-long-

5)......................................................................................................................278

xxvii


long Berea core with external filter cake removed (BS-4-29-04-long-5) .......278


completion (BS-4-29-04-long-5).....................................................................279


UltraCarb-20 on a Boise sandstone (Bo-1) .....................................................280


Boise sandstone (Bo-1) ...................................................................................280

Figure B-27: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole

completion (Bo-1) ...........................................................................................281


bentonite mud on Boise sandstone (Bo-2) ......................................................282



Figure B-30: Static filtration of bentonite mud on Boise sandstone simulating open hole

completion (Bo-2) ...........................................................................................283


UltraCarb-2 on Aloxide core (Al-1) ................................................................284


Aloxide core (Al-1) .........................................................................................284

Figure B-33: Static filtration of UltraCarb-2 on Aloxide core simulating open hole

completion (Al-1) ............................................................................................285


UltraCarb-20 on Aloxide core (Al-2) ..............................................................286


Aloxide core (Al-2) .........................................................................................286

Figure B-36: Static filtration of UltraCarb-20 on Aloxide core simulating open hole

completion (Al-2) ............................................................................................287

Figure C-1: Flowback rate at incremental differential pressures after filtration with

UltraCarb-2 on Nugget sandstone (NS-3) .......................................................290

xxviii

Figure C-2: Return permeability spectra with incremental differential pressures for

Nugget sandstone (NS-3) ................................................................................290

Figure C-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole

completion (NS-3) ...........................................................................................291


UltraCarb-2 on Texas limestone (LS-12) ........................................................292


Texas limestone (LS-12) .................................................................................292

Figure C-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole

completion (LS-12) .........................................................................................293


UltraCarb-2 on Berea sandstone (BS-11-11-03-I) ..........................................294

Figure C-8: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole

completion (BS-11-11-03-I)............................................................................294


UltraCarb-20 on Berea sandstone (BS-21)......................................................295


Berea sandstone (BS-21) .................................................................................296


completion (BS-21) .........................................................................................296


UltraCarb-2 on Berea sandstone (BS-17)........................................................297




completion (BS-17) .........................................................................................298


UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-19).........299



xxix

Figure C-17: Static filtration of UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea

sandstone simulating open hole completion (BS-19)......................................300


UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-20).........301




sandstone simulating open hole completion (BS-20)......................................302


UltraCarb-20 on Aloxide core (AL-3).............................................................303


Aloxide core (AL-3)........................................................................................304

Figure C-23: Static filtration of UltraCarb-20 on Aloxide core simulating open hole

completion (AL-3)...........................................................................................304


UltraCarb-20 on Boise sandstone (Bo-7) ........................................................305



Figure C-26: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole

completion (Bo-7) ...........................................................................................306

Figure D-1: Differential pressure profile during flowback on Berea sandstone after

filtration with UltraCarb-2 (BS-4-16-03-II) ....................................................310

Figure D-2: Static filtration of UltraCarb-2 on Berea sandstone simulating open-hole

completion (BS-4-16-03-II) ............................................................................310


filtration with UltraCarb-2 (BS-8-27-03-III)...................................................311

Figure D-4: Return permeability spectra with varying flowback rates for Berea

sandstone (BS-8-27-03-III) .............................................................................312


completion (BS-8-27-03-III) ...........................................................................312

xxx


filtration with UltraCarb-2 (no starch) (BS-4-21-03-II)..................................313

Figure D-7: Static filtration of UltraCarb-2 (no starch) on Berea sandstone simulating

open-hole completion (BS-4-21-03-II) ...........................................................314


filtration with UltraCarb-2 (no xanthan) (BS-4-21-03-III) .............................314

Figure D-9: Static filtration of UltraCarb-2 (no xanthan) on Berea sandstone simulating

open-hole completion (BS-4-21-03-III) ..........................................................315


filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-IV)..............315

Figure D-11: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea

sandstone simulating open-hole completion (BS-6-8-03-IV) .........................316


filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-V) ...............316

Figure D-13: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea

sandstone simulating open-hole completion (BS-6-8-03-V)...........................317


filtration with UltraCarb-12 (BS-6-8-03-VI) ..................................................318


completion (BS-6-8-03-VI) .............................................................................318


filtration with UltraCarb-12 without starch (BS-6-8-03-IX)...........................319


sandstone (BS-6-8-03-IX) ...............................................................................319

Figure D-18: Static filtration of UltraCarb-12 without starch on Berea sandstone

simulating open-hole completion (BS-6-8-03-IX) ..........................................320


filtration with UltraCarb-12 without xanthan (BS-6-8-03-VIII) .....................321


sandstone (BS-6-8-03-VIII) ............................................................................321

xxxi

Figure D-21: Static filtration of UltraCarb-12 without xanthan on Berea sandstone

simulating open-hole completion (BS-6-8-03-VIII) .......................................322


filtration with UltraCarb-12 without xanthan and starch (BS-6-8-03-VII) .....323

Figure D-24: Static filtration of UltraCarb-12 without xanthan and starch on Berea

sandstone simulating open-hole completion (BS-6-8-03-VII) ........................324


filtration with UltraCarb-12 with RevDust (BS-10-2-03-I) ............................325


sandstone (BS-10-2-03-I) ................................................................................325

Figure D-27: Static filtration of UltraCarb-12 with RevDust on Berea sandstone

simulating open-hole completion (BS-10-2-03-I) ...........................................326


filtration with UltraCarb-20 (BS-8-27-03-II) ..................................................327

Figure D-29: Return permeability on Berea sandstone at different flowback rates after

filtration with UltraCarb-20 (BS-8-27-03-II) ..................................................327




filtration with UltraCarb-20 without starch (BS-8-11-03-IX).........................329


sandstone (BS-8-11-03-IX) .............................................................................329

Figure D-33: Static filtration of UltraCarb-20 without starch on Berea sandstone

simulating open-hole completion (BS-8-11-03-IX) ........................................330


filtration with UltraCarb-20 without xanthan (BS-8-11-03-XII) ....................331


sandstone (BS-8-11-03-XII)............................................................................331


simulating open-hole completion (BS-8-11-03-XII).......................................332

xxxii


filtration with UltraCarb-20 without xanthan and starch (BS-8-11-03-X)......333


sandstone (BS-8-11-03-X) ..............................................................................333


simulating open-hole completion (BS-8-11-03-X) .........................................334


filtration with UltraCarb-20 with RevDust (BS-10-7-03-I) ............................335


sandstone (BS-10-7-03-I) ................................................................................335




filtration with Brine (BS-8-27-03-I)................................................................337


sandstone (BS-8-27-03-I) ................................................................................337

Figure D-45: Static filtration of Brine on Berea sandstone simulating open-hole

completion (BS-8-27-03-I)..............................................................................338


filtration with Brine and pH buffer (BS-8-11-03-XIII)...................................339


sandstone (BS-8-11-03-XIII) ..........................................................................339

Figure D-48: Differential pressure profile during flowback on Boise sandstone after

filtration with UltraCarb-20 (Bo-3) .................................................................340

Figure D-49: Static filtration of UltraCarb-20 on Boise sandstone simulating open-hole

completion (Bo-3) ...........................................................................................340

Figure E-1: Flowback rate at incremental differential pressures after filtration with

UltraCarb-2 on Texas limestone with lab simulated perforation (LS-9).........343

Figure E-2: Return permeability spectra with incremental differential pressures for

Texas limestone with lab simulated perforation (LS-9) ..................................343

xxxiii

Figure E-3: Static filtration of UltraCarb-2 on Texas limestone simulating open hole

completion (LS-9) ...........................................................................................344


UltraCarb-2 on Berea core with lab simulated perforation (BS-2-2-04-I) ......345


Berea sandstone with lab simulated perforation (BS-2-2-04-I) ......................345

Figure E-6: Static filtration of UltraCarb-2 on Berea sandstone with lab simulated

perforation (BS-2-2-04-I) ................................................................................346


UltraCarb-2 on Berea sandstone (BS-6-5-04-long-6) .....................................347


Berea sandstone (BS-6-5-04-long-6)...............................................................347

Figure E-9: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole

completion (BS-6-5-04-long-6).......................................................................348

Figure E-10: Flowback rate at incremental differential pressures on Berea sandstone

with a lab simulated perforation (BS-6-5-04-long-7)......................................349


Berea sandstone with a lab simulated perforation (BS-6-5-04-long-7) ..........349

Figure E.12: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated

perforation (BS-6-5-04-long-7) .......................................................................350


with a lab simulated perforation (BS-6-13-04-long-8)....................................351


Berea sandstone with a lab simulated perforation (BS-6-13-04-long-8).........351

Figure E-15: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated

perforation (BS-6-13-04-long-8) .....................................................................352


with a lab simulated perforation (BS-6-13-04-long-9)....................................353


Berea sandstone with a lab simulated perforation (BS-6-13-04-long-9).........353

xxxiv

Figure E-18: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated

perforation (BS-6-13-04-long-9) .....................................................................354


with a lab simulated perforation (BS-6-29-04-long-10)..................................355


Berea sandstone with a lab simulated perforation (BS-6-29-04-long-10).......355

Figure E-21: Static filtration of UltraCarb-2 on a long Berea core simulating open hole

completion (BS-6-29-04-long-10)...................................................................356


with a lab simulated perforation (BS-long-11)................................................357


Berea sandstone with a lab simulated perforation (BS-long-11) ....................357


completion (BS-long-11).................................................................................358

















xxxv




UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-4) ....365


Boise sandstone with a lab simulated perforation (Bo-4) ...............................365


completion (Bo-4) ...........................................................................................366


UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-6) ....367


Boise sandstone with a lab simulated perforation (Bo-6) ...............................367


completion (Bo-6) ...........................................................................................368

Figure F-1: Flowback rate at incremental differential pressures after filtration with

bentonite mud on Berea sandstone (BS-12-22-03-I).......................................371

Figure F-2: Return permeability spectra with incremental differential pressures for

Berea sandstone (BS-12-22-03-I)....................................................................371

Figure F-3: Static filtration of bentonite mud on Berea sandstone simulating open hole

completion (BS-12-22-03-I)............................................................................372


bentonite mud on Berea sandstone (BS-12-15-03-I).......................................373


UltraCarb-2 on Berea sandstone (BS-12-08-03) .............................................374

1

Chapter 1: Introduction

1.1 BACKGROUND

Fluids are used in oil and gas wells for various well operations such as drilling,

completion and stimulation. According to the nature of the operation these fluids are

classified as drilling fluids, completion fluids, or stimulation fluids. In the early history of

the oil industry, the major focus was mainly on drilling and hence most of the

advancement took place on drilling fluids 1, 2. Drilling fluids have many functions, such

as: 1) clean the broken rock fragments beneath the bit, 2) carry those cuttings to the

surface, and 3) exert sufficient pressure against the formation fluids to prevent them from

flowing into the well bore.

Because of an overbalance pressure, wellbore fluids invade the formation during

drilling, completion or stimulation operations. The invasion of fluids and solids into the

formation is a multi-component filtration problem studied and presented by Suri 3.

Invasion of solids, polymer and filtrate into the formation reduces the ability of the

formation to produce. This is because the pores are plugged by the solids and polymers

from the wellbore fluids. The different mechanisms of formation damage can be

summarized as follows 4, 5 :

1. Mechanically Induced:

a. Solids and Polymer Invasion

b. Fines Migration

c. Phase Trapping (water block, gas breakout, condensate banking)

d. Stress Induced

2. Chemically Induced

a. Rock – Fluid Incompatibility

2

i. Clay Swelling

ii. Clay Deflocculation

iii. Formation Dissolution

iv. Chemical Adsorption

b. Fluid – Fluid Incompatibility

i. Solids Precipitation

ii. Wettability Alteration

iii. Wax Deposition

iv. Asphaltene Formation

3. Biologically Induced

4. Thermally Induced

It is believed that the predominant form of near wellbore formation damage is the

invasion of solids and polymers into the formation 6, 7. The invasion of the fluid leads to

the formation of an internal filter cake and an external filter cake. To minimize the

formation damage caused by fluid invasion, Suri and Sharma 8 presented strategies for

sizing solids in the drilling and completion fluids. The filter cake (internal and external)

that can restrict the production during flowback, strengthens the well bore 9 as well.

One of the strategies adopted to prevent formation damage caused by drilling and

completion fluids is to operate the well with an under-balanced mud column which

prevents any invasion of the well bore fluid into the formation. Unfortunately, this

operation is risky in high pressure wells. This method requires the use of special

equipment and trained crews, and may not be economically feasible. Using low density

drill-in fluids can cause severe washouts and bit-balling. In most wells, an overbalanced

column must be maintained in the well, and thus complete prevention of impairment due

3

to solids and filtrate invasion seems impossible. Another strategy to prevent any invasion

of solids into the formation is to use “clear” brines which, in theory, have no solids and,

therefore, cannot damage the formation due to the internal and external filter cake

deposition. But in practice, all field brines contain solids, although the amount may be

very small. The particles contaminating the brine may come from the source water or

from the sacked salt, or they may be picked up in tank trucks or rig pits. Even if extreme

care is taken to remove the contaminating solids at the surface, enough solids may be

picked up on the way down the tubing to cause considerable impairment. Therefore, there

is always going to be some invasion of solids and filtrate into the formation from the

wellbore fluids leading to a build-up of an internal and an external filter cake.

To design drilling and completion fluids for the pay-zone, both the drilling and

the productivity objectives need to be considered. The drilling and productivity objectives

are summarized as follows:

1. Drilling objectives:

• Well-bore stability

• Shale inhibition

• Hole cleaning

• Good lubricity

• Drag and torque mitigation

• High rate of penetration subject to safety, environmental and cost constraints

2. Productivity objectives:

• Minimum invasion of the well-bore fluid (solids and filtrate) into the

formation

4

• Thin, tough and ultra-low permeable external filter cake build up for

minimum fluid leak-off

• Low flow initiation pressure and large return permeabilities during production

In recent years, a new class of drilling fluids has been developed (drill-in fluids)

with special consideration for the productivity objectives. These drill-in fluids form filter

cakes that can be dissolved in acids. Sized CaCO3 and sized salt drill-in fluids are two of

the most commonly used fluids of this kind. Another advantage in using these fluids is

that the size of the solids in these fluids can be designed according to the formation pore

size distribution which would result in more effective bridging of the particles at the

formation face resulting in minimum invasion of the solids and polymers into the

formation. Polymers are added to these drill-in fluids to meet the drilling objectives and

for building an ultra-low permeable external filter cake to minimize the filtrate loss.

A fluid used in a well during completion or work-over operations is called a

completion fluid. Completion fluids remain in contact with the productive pay-zone for

days in a static and an overbalanced condition. The completion fluids used today are

broadly categorized into water-based fluids, oil-based fluids, foams, and emulsions. A

detailed overview of completion fluids is provided by Al-Riyamy 10. Water-based fluids

(brines) are the most commonly used completion fluids.

In the past, the use of oil-based drilling fluids had simplified many drilling

operations that involve water sensitive shales, hole stability issues, friction related

problems etc. However, disposal of the used oil-mud and the oil-soaked cuttings has

become a challenge because of environmental concerns 11, 12.

5

1.2 DEFINITION OF THE PROBLEM

Zain and Sharma 13 clearly showed that the external filter cake does not play any

role during flowback and that it is the solids and polymer invasion which determines the

flow initiation pressure and the return permeability. Therefore, it is expected that after the

well is drilled, completed and put back on production, the internal filter cake be

completely removed leaving behind a formation with clean pores. Breakers such as

hydrochloric acid or an oxidative solution can be used to remove the filter cakes.

However the use of breakers has resulted only in a marginal improvement in the return

permeability. Some of the reasons for the ineffectiveness of the breakers are:

1. The breakers usually have an insufficient contact time with the filter cakes to dissolve

them completely.

2. The breakers can be partially spent with other downhole materials such as tubing,

hydrocarbons, and other components in the well-bore and as a result may not come in

contact with the target zone.

3. The breakers might be ineffective in dissolving the polymers (starch, xanthan etc.)

which cause the most damage.

Some of the concerns in using the breakers are:

1. The breakers may lead to the damage of the downhole materials.

2. The breakers may lead to formation damage.

3. The use of breakers might be uneconomical.

4. The breakers (acids and oxidizers) could be unsafe and hazardous to handle.

5. The breakers could be unfriendly to the environment.

Recently environmentally friendly breakers are formulated which can attack the

polymer in the muds 14. These polymer linkage-specific enzymes offer a safe, effective

alternative to conventional cleanup methods that usually consist of oxidizers such as

6

bleach and acid. These enzymes has none of the “side effects” associated with non-

specific reactants such as premature reaction, corrosive damage to down hole tools and

tubular goods, and disposal problems. Enzyme such as α-amylase targets the starch in the

filter cake as starch acts as a binder for the calcium carbonate and other solids in the

fluid15.

However, even if the breakers can dissolve both the external and the internal filter

cake completely, and be environmentally friendly, there is a significant risk of invasion

of these breakers into the formation which can lead to more damage to the formation.

Therefore, it is still common to flow the wells back naturally (by reducing the well bore

pressure to a value lower than the average reservoir pressure) than to use special acids,

breakers or enzymes to cleanup the filter cakes. Hence, in this dissertation we intend to

look at the cleanup of the near wellbore region during production without the use of

breakers. The motivation behind the research can be listed as follows:

1. There is no exhaustive study available that quantifies the damage caused by the more

commonly used drill-in and completion fluids on cores with a wide range of

permeability. This quantification of the damage can aid in determining if breakers are

required or not in a particular situation.

2. The standard practice is to use a constant rate during flowback to estimate the FIP and

the return permeability to quantify the damage, with the goal of determining the

drawdown requirements for a well (to initiate production) and to determine the flow

rate of the hydrocarbons into the well for a given drawdown. However, this method is

inadequate in representing the wellbore condition during flowback since flow into a

wellbore occurs at constant drawdown. Chapter 2 discusses this inadequacy in more

detail.

7

3. There is no study data in the literature to evaluate the formation damage caused by

the more commonly used water-based completion fluids in perforated completions.

4. There is no model for the cleanup of the formation damage (internal filter cake)

during flowback (when the well is put on production).

The cleanup of the internal filter cake is postulated to be the controlling factor in

determining the flow initiation pressure (FIP) and the return permeability during

flowback. We intend to find the key parameters which determine the cleanup of the

internal filter cake and using these key parameters make recommendations for designing

less damaging drill-in and completion fluids.

1.3 OUTLINE OF THE CHAPTERS

In this work, cleanup of the internal filter cake during flowback is studied.

Chapter 2 presents an improved laboratory method to estimate the FIP and return

permeabilities during flowback (which is used to quantify the damage caused by the

formation of an internal filter cake into the porous medium). This improved flowback

method is used to measure the FIP and return permeabilities in cores with a wide range of

permeability and for commonly used drill-in and completion fluids. Chapter 3 evaluates

the different components used in the drill-in and completion fluids from the formation

damage stand point. Chapter 4 presents yield strength measurements for filter cakes for

two more commonly used water-based muds. These yield strength measurements are

used to model the cleanup of the internal filter cake and to make recommendations to

better design the drill-in and completion fluids. Chapter 5 presents models for cleanup of

the internal filter cake during flowback. Chapter 6 presents an experimental study on the

cleanup of the filter cakes in the lab-simulated perforated completions. Chapter 7 presents

UTDamage, a filtration and flowback simulator to design drill-in and completion fluids.

8

Finally chapter 8 presents the overall conclusions and recommendations to design drill-in

and completion fluids to minimize formation damage and to maximize well productivity.

REFERENCES

1. Gray, George R., Darley, H.C.H., and Rogers, Walter F.: “Composition and

Properties of Oil Well Drilling Fluids,” Fourth edition, Gulf Publishing Company,

Book Division, Houston, London, Paris, Tokyo.

2. Chilingarian, G. V., and Vorabutr, P.: “Drilling and drilling fluids,” updated textbook

edition, Elsevier, Amsterdam-Oxford-New York, 1983.

3. Suri, A.: “A Model for Multi-Component Filtration” MS Thesis, The University of

Texas at Austin, December 2000.

4. Qutob, Hani, et al.: “Underbalanced Drilling; Remedy for Formation Damage, Lost

Circulation, and Other Related Conventional Drilling Problems,” paper 88698

presented at the 11th Abu Dhabi International Petroleum Exhibition and Conference

held in Abu Dhabi, U.A. E., 10-13 October 2004

5. Kruger, R. F.: “An Overview of Formation Damage and Well Productivity in Oil

Field Operations,” JPT, February 1986, 131-152, SPE 10029

6. Browne, S. V., and Smith, P. S.: “Mud cake Clean up to Enhance the Productivity of

Horizontal Wells,” paper SPE 27350 presented at the SPE Formation Damage

Control Symposium held in Lafayette, 9-10 Feb., 1994

7. Browne, S. V., et al.: “Simple Approach to the Cleanup of Horizontal Wells With

Prepacked Screen Completions,” paper SPE 30116 presented at the SPE Formation

Damage Control Symposium held in The Hague, The Netherlands, 15-16 May, 1995

8. Suri, A., and Sharma, M.M.: “Strategies for Sizing Particles in Drilling and

Completion Fluids,” paper SPE 87676 published in SPEJ, March 2004

9

9. Aston, M. S., et al.: “Drilling Fluids for Wellbore Strengthening,” paper IADC/SPE

87130 presented at the IADC/SPE Drilling Conference held in Dallas, Texas, U.S.A.,

2-4 March, 2004

10. Al-Riyamy, K.: “Synthesis and Characterization of Reversible Emulsions:

Application to Completion Fluids,” dissertation presented to the faculty of the

graduate school of The University of Texas at Austin, May 2000

11. Davidson, E., et al.: “Challenging Reservoir Drilling Conditions Overcome by

Engineered Water Based Drill-In Fluids,” paper AADE-04-DF-HO-03 presented at

AADE 2004 Drilling Fluids Conference, held at the Radisson Astrodome in Houston,

Texas, U.S.A., April 6-7, 2004

12. Cameron, C., et al.: “Water-Based Drilling Fluid Helps Achieve Oil-Mud

Performance,” paper AADE-04-DF-HO-03 presented at AADE 2004 Drilling Fluids

Conference, held at the Radisson Astrodome in Houston, Texas, U.S.A., April 6-7,

2004

13. Zain, M. Z., and Sharma, M. M.: “Mechanisms of Mud Cake Removal During

Flowback,” SPE Drilling and Completion, December 2001

14. Sanders, M. W., et al.: “A Quantitative Method for Estimating a-Amylase-Based

Enzyme Concentrations in Wellsite Field Samples and its Application on a Gravel

Pack Completion,” paper AADE-04-DF-HO-35 presented at the 2004 AADE Drilling

Fluids Conference, held at the Radisson Astrodome in Houston, Texas, April 6-7,

2004

15. Suhy, Thomas, et al.: “Application of Polymer Specific Enzymes To Cleanup Drill-In

Fluids,” paper SPE 51094 presented at the SPE Eastern Regional Meeting held in the

Pittsburgh, PA, 9-11 November 1998

10

16. Bailey et al.: “Particulate Invasion From Drilling Fluids,” paper SPE 51094 presented

at the SPE Eastern Regional Meeting held in the Pittsburgh, PA, 9-11 November

1998


Field Operations,” JPT, February 1986, 131-152, SPE 10029

11

Chapter 2: An Improved Laboratory Method to Estimate Flow Initiation Pressures and Return Permeabilities During Flowback

2.1 INRODUCTION

This chapter presents an improved laboratory method, to estimate the flow

initiation pressure (FIP), needed to initiate flow of hydrocarbons from the reservoir into

the wellbore during production. Using this method, a spectrum of return permeabilities

during flowback is also calculated, at increasing flowback pressures.

First a background on the importance of the FIP and the return permeabilities is

presented. Then a literature review on the standard practices used to estimate the FIP and

the return permeability is presented. The motivation behind improving the standard

practices is discussed. The improved flowback test method is presented in detail,

followed by a list of test objectives. Results are discussed for both single-phase and two-

phase flow experiments in cores with a wide range of permeabilities and with more

commonly used muds. The effect of different parameters on the FIP and the return

permeability is discussed. Finally the tests results are applied to vertical and horizontals

wells for field recommendations.

2.2 LITERATURE REVIEW

2.2.1 Flow Initiation Pressure

In 1994 Browne et al.1 presented data on several British Petroleum operated non-

perforated horizontal wells in the North Sea that did not produce from the entire

completed interval. They believed that geological variation and partial cleanup of the

drilling-mud filter cake were the two main reasons for the reduced production. Based on

12

their hypothesis of partial cleanup of filter cakes they suggested laboratory based mud-

cake cleanup tests. Their objectives for formulating mud-cake lift-off tests were:

1) To design filter cakes which need low differential pressure to lift-off,

2) To find out if the filter cakes can be readily removed by fluids,

3) To maximize productivity from horizontal or high angle well bore sections.

The term “lift-off pressure” was first used for estimating the minimum differential

pressure required to initiate flow in a well. More recently “flow initiation pressure” has

been used instead 2. It was not made clear 1 whether the cake lift-off tests were done

under constant flowback rate or constant flowback pressure. I assume that the tests were

done at constant flowback rates based on their subsequent paper 2 in which they used

constant flowback rate for measuring the flow initiation pressure.

Figure 2.1 shows a typical differential pressure profile during a cake lift-off /

flowback test done at a constant flowback rate. It shows ∆P readings recorded as oil is

injected in the reverse direction at an injection rate of 5 ml/min after mud filtration was

conducted at 100 psi on Berea sandstone. As the fluid is flowed back (after mud

filtration), a peak injection pressure, ∆Pmax, is quickly reached, followed by a gradual

decrease until a stabilized pressure ∆Pfinal is obtained. The difference between the peak

pressure and the stabilized pressure is defined as the flow initiation pressure (FIP), ∆Pfi

(equation 2.1). The purpose of determining this laboratory-measured FIP was to estimate

the magnitude of the minimum drawdown pressure required to lift the external filter cake

off and thereby initiate production in a well.

∆Pfi = ∆Pmax - ∆Pfinal (2.1)

13

Browne et al.1, 2 showed that the lift-off pressure depends on the permeability of

the rock and the type of mud used. Their laboratory studies showed that low permeability

reservoirs have significantly larger lift-off pressures than larger permeability sections.

Bailey et al 3 used the term flow initiation pressure (FIP) instead of lift-off

pressure to estimate differential pressure required to initiate flow during flowback. They

presented laboratory data on filter cake strength and its relation to cleanup by back

production for typical reservoir drilling fluids. They showed that FIP is linearly

dependent on filter cake yield strength irrespective of the composition of the water-base

mud.

Ryan et al. 4 indicated that oil-based muds have smaller FIP than water-based

muds. They found that complete external filter cake removal is not necessary to produce

oil through the cake.

Zain and Sharma 5 studied external filter cake behavior by measuring the

flowback pressure profile after mud filtration at constant flow rate. They found that the

external filter cake plays no role in determining the FIP and return permeability. Rather it

is solids and filtrate invasion, which determine the flowback pressure profile during

production.

Rana and Sharma 6 worked on finding the relative importance of solids and

filtrate invasion on the FIP. They showed that for low permeability rocks and small

mobility ratios, relative permeability effects play a dominant role in determining the

flowback pressure profile while for high permeability rocks (>100 md) and large mobility

ratios, both the internal filter cake and relative permeability effects play a significant role.

Alfenore et al. 7 suggested using an ultra low flow rate (0.1 cm3/min) for the

flowback rate to measure FIP. Their results show that oil-based muds have smaller FIP

values than those obtained with water-based muds.

14

Ladva et al. 8 studied the effect of permeability, core length, mud type, and

flowback rate on FIP and provided possible explanations for why FIP is found to be

larger in low permeability cores as compared to high permeability cores in constant

flowback experiments. They used a very small flowback rate of 0.1 cm3/min for

determining the FIP. Their results suggested that the external filter cake does not play a

significant role in determining FIP and that two-phase flow results in larger FIP

compared to single-phase flow. They concluded that core length and velocity of the

flowback fluid will alter the value of FIP and that a drawdown test method is preferred

which will better approximate the conditions observed at the onset of production in a real

well.

Gruber et al. 9 recommended a constant pressure flowback method over a constant

rate flowback method to be consistent with the application of a drawdown in a well. They

found that a minimum “threshold pressure” was required for the fluid to start flowing

upon imposing a differential pressure and measuring the resultant flow rate. Regain

permeability was found to improve with increasing pressure differentials and with

increasing volumetric throughput. They found the maximum threshold pressure to be

approximately 6 psi for cores with an absolute permeability of 30 md using two different

muds. In their subsequent paper 10 they found the “threshold pressure” to have a well

defined inverse relationship with permeability, especially in carbonate cores. In this paper

they found threshold pressures as high as 30 psi for cores with an absolute permeability

of 1 md. They suggested capillary pressure to be the cause of these larger threshold

pressures.

To date almost all the studies for determining FIP have used a constant rate

flowback procedure 1-7 rather than a constant pressure flowback condition 9, 10 to estimate

the drawdown required to initiate production in a well.

15

2.2.2 Return Permeability

Return permeability is defined as the effective permeability to hydrocarbons

during production. The return permeability determines the oil flow rate into a well for a

given drawdown (pressure difference between the reservoir and the well). The standard

practice for measuring return permeability uses a constant flowback rate. Oil is flowed in

the reverse direction to mud filtration at a constant rate while the pressure profile is

recorded until a stable pressure drop across the core is obtained. Figure 2.1 shows a

typical flowback pressure profile at a constant flowback rate used in laboratory studies.

The return permeability ratio is calculated at a specific flowback rate and signifies the

extent of cleanup at a particular flow rate. The return permeability ratio is calculated by

dividing the stabilized ∆P reading before filtration by the stabilized ∆P reading during

flowback (after filtration) at a given flow rate:

Return permeability ratio = ∆P initial / ∆P final (2.2)

The return permeability calculated by the above method is flow rate dependent 5.

However, oil wells in the field are usually produced at fixed drawdowns that approximate

a constant pressure boundary condition. This suggests the use of constant pressure

differentials across the core during flowback instead of using a constant flow rate to

determine the return permeability ratio. Figure 2.2 shows a typical flowback profile for a

constant pressure flowback condition.

Today horizontal wells are increasingly used in oilfield developments to

maximize well productivity, access widely spread reserves, or reduce water and gas

coning by reducing drawdown. Browne and Smith11 showed that these benefits require

the horizontal well sections to be flowing without significant near well bore damage.

16

Ryan et al.12 presented a major joint industry project to study the effectiveness of

different mud cleanup techniques (acids, breakers, solvents) for horizontal wells. The

results of their studies indicate that there is no single best technique for the cleanup of

uncemented / open hole horizontal wells. They concluded that a ‘universally’ non-

damaging mud system or cleanup technique is unlikely to exist. Reservoir specific testing

is required to establish damage levels. They also concluded that:

1. Complete external filter cake removal is not necessary to produce oil through the

cake.

2. High solids loadings in the mud system were found not to adversely effect oil

production through the mud cake.

3. Aggressive breakers (acid) effectively clean the well bore and screens but can

generate increases in fluid losses.

4. Whole mud has a greater impact on sand control screen damage than filter cake back

production.

6. Oil-based muds show smaller breakthrough pressures (FIP) and lower damage levels

(larger return permeability) than water-based muds.

7. Most of the breakers were found to increase the breakthrough pressure (FIP) than to

reduce them.

8. Breakers behaved differently for different mud systems with significant reductions in

damage levels found in many cases but, conversely some mud breaker combinations

increased damage.

Marshall et al.13 presented a detailed comparative study on return permeability.

Their objective was to standardize formation damage testing to select the appropriate

drilling fluid and/or cleanup technique. They presented an extensive laboratory study,

17

based on a refined recommended practice for the determination of return permeability.

They found a wide variation in the results from different laboratories which didn’t allow

for a good level of repeatability and reproducibility.

Alfenore et al.15 have shown that the flowing area ratio between a typical vertical

perforated well and a horizontal open hole completion is ~50/1, resulting in a fluid

velocity ratio to be ~13/1. This would suggest using a 13 times smaller flowback rate for

determining the return permeability ratio for horizontal wells compared to the flowback

rate used for determining return permeability ratio for vertical wells. Assessing return

permeability ratios at elevated drainage rates for horizontal open hole situations would be

irrelevant. Their results showed that oil-based muds (OBM) clean-up faster and easier as

compared to water-based muds (WBM).

Various authors16, 17 have shown the importance of designing drilling and

completion fluids for minimum formation damage. Some authors18, 19 have also presented

models for particulate invasion from drilling fluids into the formation. Suri and Sharma20

presented a rigorous multi-component model to predict the invasion of solids and

considered build-up of both the external and internal filter cake. Their model can be used

to design the mean particle size of the bridging agents to effectively bridge the formation

pores and also filter the polymers in the external filter cake.

2.3 PROBLEM DESCRIPTION AND MOTIVATION

The term flow initiation pressure (FIP) is defined in the literature as the difference

between the peak differential pressure and the stabilized differential pressure across a

core during flowback. The standard practice for estimating FIP is to flowback at a

constant rate after mud filtration. Figure 2.1 shows a typical flowback pressure profile at

constant rate that is used to determine FIP.

18

It is also found that at different flowback rates, different FIP values are observed,

resulting in a non-unique value for estimating flow initiation in a well during production.

There should be a unique value of drawdown required to initiate flow for a given

formation, mud, overbalance pressure and flowback fluid. Various authors have

suggested using a very small flowback rate to estimate FIP. Even a very small flowback

rate would give an approximate FIP that would be rate dependent.

Since flowback in oil and gas wells occurs at constant drawdown (constant

differential pressure between the reservoir and the wellbore), it is more reasonable to

measure the flow initiation at constant differential pressures. Therefore, to estimate the

flow initiation pressure, we conduct constant pressure flowback experiments instead of

constant rate flowback experiments. The constant pressure flowback experiment better

approximates the conditions observed at the onset of production in a real well than the

constant rate flowback experiment. Figure 2.2 shows measured flowback rates at a series

of increasing pressure differentials to determine the FIP and to measure the return

permeability spectra.

2.4 EXPERIMENTAL DESIGN

2.4.1 Test Equipment

A schematic of the experimental setup is shown in Figure 2.3. Two different sized

core holders were used in the apparatus to accommodate for two different core plug sizes.

The short core holder accommodates a 2.5 inches diameter, 1.0 inch core long core plug,

and approximately 110 ml of fluid inside the filter cell. The filtration unit can be heated

up to 350oF and can withstand a maximum filtration pressure of 1300 psi. The long core

holder can accommodate a core plug 2.0 inch in diameter, and up to 12 inches in length.

A hollow cylindrical sleeve with 2.0 inch diameter and ¼ inch thickness was specially

19

designed to hold fluid (drill-in or completion fluid) in the long core holder. The main

purpose behind setting up a long core apparatus was to be perform filtration experiments

on cores having long simulated perforations. It also enabled us to study the depth of

damage caused by solids and polymers (internal filter cake) and filtrate invasion by

recording pressure readings at 2 inch intervals along the length of the core. Figure 2.4

shows a schematic of the long core apparatus. In the short core holder the cores are

epoxied on the sides to restrict any flow between the core and the sides of the cell. The

long core holder uses confining pressure on a rubber sleeve around the core to restrict

flow between the core and the sides of the sleeve. The following is a list of items used to

conduct the mud filtration and flowback experiments:

1. Short HPHT core holder

2. Long HPHT core holder

3. Beckman pump (constant rate condition)

4. Highly sensitive pressure reducing regulator (constant drawdown condition)

5. Accumulators

6. Back pressure regulator

7. Pressure gauges

8. 1/8 inch tubing

9. 2 way valves

10. 3 way valves

11. Pressure transducers

12. Validyne interface

13. Data acquisition computer

14. Data acquisition software (Softwire, Sartoconnect)

15. Electronic balance

16. Dessicator

17. Vacuum pump

18. High pressure source (compressed N2 gas cylinder)

20

Actual photographs of the main equipment and tools used to conduct the

experiments are shown in Appendix-A.

2.4.2 Core and Fluid Sample

Table 2.1 shows the dimensions of the two different sized core plugs used in the

experiments. The dimensions for the shorter core were 2.5 inch diameter and 1 inch

length and the dimensions for the longer core were 2 inch diameter and 6 inch length.

Table 2.2 shows five different rock types used in the study with a permeability range of 4

md to 1500 md. The five rock types used are:

1. Nugget sandstone (4 md),

2. Texas limestone (25 md),

3. Berea sandstone (200 md),

4. Synthetic Aloxide (1000 md), and

5. Boise sandstone (1000 md).

Figure 2.6 shows the pore volume distribution obtained from mercury

penetrometer for some of the rocks used. The larger permeability rocks have a larger

median pore diameter. Texas limestone has a median pore diameter of 0.711 microns,

Berea sandstone has a median pore diameter of 13.5 microns, and Boise sandstone has a

median pore diameter of 17.6 microns.

Two types of fluids were used for the filtration experiments. Table 2.3 shows the

fluid components and their concentration used in formulating the UltraCarb drill-in fluid.

Table 2.4 shows the fluid rheology for the UltraCarb fluid. Table 2.5 shows the fluid

components for the bentonite mud while Table 2.6 shows its rheology.

21

Fluids used for the flowback were: 1) 3% brine solution for single-phase flow

experiments, 2) a non-corrosive and non-reactive oil distillate (Exxsol D110) was used

for the two-phase flow experiments.

2.4.3 Test Procedure

Figure 2.5 shows a schematic of the experimental procedure used for the mud

filtration and flowback test. The detailed procedure is explained step by step as follows:

1. Obtain core plugs of desired dimensions. Clean and dry them in an oven (at 100oC)

for at least 24 hours.

2. Apply a thin layer of epoxy on the side of the short core plug to avoid flow through

the sides of the plug. The epoxy layer is necessary for the small core filtration unit as

it does not have the option of confining pressure but depends only on the two rubber

O-rings each set on the top and bottom of the plug for sealing the sides. The long core

plugs don’t need epoxy as the long core apparatus uses a Viton sleeve confining

pressure to seal the sides of the core.

3. Vacuum the core plugs with 3 % NaCl brine for at least 12 hours.

4. Install the fully saturated core plug in the filter cell followed by the fluid distribution

end cap. Tightly set all cap-locking screws to ensure complete sealing of the side of

the plug while using the short core holder.

5. Inject brine (3 % NaCl) from bottom to top of the core plug at rates from 1 to 10

ml/min as seen in Step 1 of Figure 2.5 (simulating flow from the formation to the well

22

bore). Record differential pressures readings (∆P) continuously until a stabilized ∆P is

reached for the different injection rates.

6. Plot the injected flow rate vs. the measured stabilized differential pressure across the

core. Fit a straight line through all the data points assuming Darcy’s law:

Pmq ∆= (2.3)

where q is the flow rate in cc/min, ∆P is the differential pressure in psi and m is

the slope given by the following equation

1 96.456

k AmLµ

= (2.4)

where k is the permeability in md, A is the area in inch2, µ is the viscosity of the

injected fluid in cp and L is the length of the core in inch.

7. For two-phase experiments inject Exxsol D110 (oil) at a injection rate of 1 ml/min

from top to bottom of the core for piston like displacement of water with oil. After 3-

4 hours of injection increase the flow rate to 10 ml/min and continue flowing for an

hour or so until the pressure drop across the core is stabilized. After that the plug is

assumed to be at irreducible water saturation.

8. Inject Exxsol from bottom to top at rates from 1 to 10 ml/min as seen in Step 1 of

Figure 2.5 (simulating flow from the formation to the well bore). Record differential

pressures readings (∆P) continuously until a stabilized ∆P is reached for the different

23

injection rates. Calculate effective permeability to oil assuming linear Darcy flow

(step 6).

9. Dismantle the filter cell. Pour mud out of the cell. Please note that to pour the mud

out of the filtration cell, the core plug has to be taken out from the filtration cell. This

exposes the core plug to atmosphere. Therefore, it is important to perform this step as

quickly as possible to avoid any drying of the core.

10. Apply a desired filtration (overbalance) pressure using a nitrogen line (Step 2). Open

the valve at the bottom of the cell to allow fluid loss. Collect and record mud filtrate

volume every minute for 30 minutes and every hour for 16 hrs using an electronic

balance connected to a PC.

11. Slowly bleed off the filtration pressure inside the filter cell to atmospheric pressure.

12. Use Exxsol D110 for two-phase flowback experiments and 3 % brine solution for

single-phase flowback experiments. Details of the flowback procedure are provided

in Sub-Sections 2.4.3.1 and 2.4.3.2 below.

2.4.3.1 Constant Pressure Flow-back Procedure

1. Make sure all the lines are liquid filled, specially the outlet line which is open to

atmosphere in case of no back flow pressure. Apply a constant pressure (~ 1 psi) at

the bottom of the core using a sensitive pressure regulator. Monitor the outlet to

check if there is any flow. Keep the flowback differential pressure constant at 1 psi

for 10 minutes and keep monitoring any flow at the outlet.

24

2. In case of no flow, slowly increment the pressure at the bottom of the core using the

pressure regulator to 2 psi and hold it constant for 10 minutes while monitoring the

outlet. Repeat the above step by incrementing the flowback differential pressure by 1

psi until there is some measurable flow.

3. The differential pressure at which there is flow observed at the outlet is recorded as

the flow initiation pressure (FIP). The fluid from the outlet is collected using a

balance and the data is transferred from the balance to a computer electronically to

calculate the flowback rate. The pressure is held constant until the flowback rate

becomes constant.

4. Increment the flowback differential pressure in small steps (1-2 psi) to study the

cleanup behavior of the internal and external filter cake. Figure 2.2 shows a plot of

incremental flowback differential pressures and measured flow rates with time.

Increment ∆P slowly (1-5 psi) until 20 psi is reached and keep recording the flow rate

until rates are stabilized. Apply larger increments of about 10-20 psi after reaching a

flowback differential pressure of 20 psi. Keep incrementing the ∆P up to a maximum

desired flowback differential pressure. In most of our experiments we applied a

maximum of 100 psi flowback differential pressure.

5. Calculate the return permeability spectra using the following steps:

• Tabulate the flowback results as follows: The applied flowback differential

pressure values (∆Pflowback) and the corresponding measured flowback rates (q

flowback). Calculate the ideal differential pressure for the different recorded

flowback rates as given by:

25

m

flowbackideal

qP∆ = (2.5)

where m is given by Equation 2.4.

• Calculate return permeability ratio for different applied flowback differential

pressures by using the following equation:

Return Permeability Ratio ideal

flowback

PP∆

=∆

(2.6)

• Plot the return permeability ratios vs. the applied differential pressures. This plot

provides return permeability spectra for incrementing drawdowns.

2.4.3.2 Constant Rate Flowback Procedure

1. Inject fluid (oil for two-phase and brine for single-phase) from the bottom of the cell

at a constant rate of 1 ml/min. Monitor and record ∆P readings until stabilized

readings are observed.

2. Increase the flowback rate to 3 ml/min and then 5 ml/min and record the flowback

differential pressures until stabilized readings are observed for each rate.

3. Calculate the return permeability ratio for the different flowback rates using equation

3.1.

Finally, dismantle the filter cell and record observations for the external filter

cake such as thickness, rupture, cracks, and partial or total removal. Photograph the filter

cake and the core.

26

2.5 TEST OBJECTIVES

1. Study the effect of core permeability on FIP and return permeability spectra.

2. Study the effect of flowback condition (constant rate vs. constant pressure) on FIP

and return permeability spectra.

3. Study the effect of different fluids (sized CaCO3 drill-in fluid and bentonite mud) on

FIP and return permeability spectra.

4. Study the effect of single vs. two-phase flow on FIP and return permeability spectra.

5. Compare FIP and return permeability spectra for constant pressure flowback

experiments with constant rate flowback experiments.

6. Study the leak-off behavior of different drill-in fluids on different permeability cores.

7. Study the effect of overbalance pressure on FIP and return permeability spectra.

8. Study the effect of back pressure on the removal of internal and external filter cake

(FIP and return permeability spectra).

2.6 DISCUSSION OF EXPERIMENTAL RESULTS

We conducted single-phase and two-phase filtration and flowback experiments on five

different cores and with two different fluids. We measured and reported the following

parameters for all the experiments:

1. Flow initiation pressure

2. Return permeability ratio vs. flowback differential pressure

3. Filtrate loss during mud overbalance

27

2.6.1 Single-phase (Brine) Experiments

The motivation behind conducting single-phase experiments was to obtain results

that would help us understand the flowback problem better. Some factors which can

determine the FIP and the return permeability spectra are:

1. External filter cake properties.

2. Internal filter cake properties.

3. Capillary pressure curves for the rock.

4. Relative permeability curves for the rock.

In this set of experiments the flowback problem is simplified by having to

understand the effect of only the external and internal filter cake in determining the FIP

and return permeability as there are no capillary pressure and relative permeability effects

due to two-phase flow.

Table B.1 in Appendix-B shows a list of all the single-phase constant-pressure

flowback experiments conducted, together with a summary of results. Subsequently,

three plots are shown for each of the experiments conducted:

1) Applied differential pressure and measured flow rates vs. time during

flowback,

2) Return permeability ratio vs. applied differential pressure, and

3) Filtrate loss vs. square root of time.

A brief discussion is also presented in Appendix-B for some of the experiments

after the plots.

28

2.6.1.1 Flow Initiation Pressure

Table 2.7 shows a summary of flow initiation pressures (FIP) for single-phase

constant pressure flowback experiments. Five different types of cores with permeability

ranging from 4 md to 1500 md (Nugget sandstone (4 md), Texas limestone (25 md),

Berea sandstone (200 md), Boise sandstone (1000 md), and Aloxide (1500 md)) were

used with UltraCarb drill-in fluid and bentonite mud. An overbalance pressure of 100 psi

and static filtration time equal to 16 hrs was used for most of the experiments. The

maximum FIP for all the single-phase flow experiments with short cores (1 inch in

length) and appropriate sized fluids resulted in a value of 4 psi. However, upon using

UltraCarb-2, the FIP for Aloxide core (1500 md) resulted in a much larger value of 8 psi.

This suggests that larger FIP values are obtained if the bridging solids are not correctly

sized for the porous medium. The bridging additive particle size was changed from

median size of 2 microns to 20 microns to minimize the invasion of solids and polymers

into the core. Using UltraCarb-20 for Aloxide and Boise sandstone, resulted in a FIP

value smaller than 4 psi. The results indicate that the FIP values are independent of the

rock permeability if the solids are sized properly.

Figures 2.7 to 2.10 show photographs of cores (Texas limestone, Berea sandstone,

Nugget sandstone and Aloxide) after flowback at constant pressure. It can be seen that

the external filter cake detaches from the surface of the cores but doesn’t break into

pieces while allowing flow.

2.6.1.2 Return Permeability Spectra

Table 2.8 shows return permeability ratios for four different flowback differential

pressures (FIP, 20 psi, 50 psi, and 100 psi) for most of the single-phase constant pressure

flowback experiments simulating open-hole conditions. For larger permeability cores

29

(Aloxide, and Boise sandstone), the maximum flowback differential pressure applied was

equal to 50 psi. The flow rates for larger permeability rocks were so high that the

accumulators holding the flowback fluid emptied out very quickly. It is observed in the

table that most of the return permeability improvement is at or below 20 psi of applied

flowback differential pressure. Appendix-B shows return permeability spectra for all the

single-phase flowback tests. A return permeability spectra is a plot between return

permeability ratios vs. applied differential pressures during flowback. All return

permeability spectra are found to be S-shaped.

Figure 2.11 compares the return permeability spectra for all the single-phase

flowback experiments on different rocks using UltraCarb-2 drill-in fluid. The return

permeability ratios for cores with absolute permeability less than 200 md (Nugget

sandstone, Texas limestone and Berea sandstone) are found to reach values above 50% at

larger differential pressures. This suggests a significant amount of natural cleanup of the

damage in cores with permeability less than 60 md at larger differential pressures. But for

Aloxide core with an absolute permeability of more than a Darcy, the return permeability

ratios are found to be quite poor (< 10 %). This indicates that the solids were not sized

correctly for the larger permeability cores which resulted in large invasion of solids and

polymers. In such cases acidizing may be required to improve the return permeability. In

general, the return permeability ratios are found to be larger for cores with smaller

permeability. This indicates that the cores with small absolute permeability were less

damaged than the cores with large absolute permeabilities. The return permeability ratios

are observed to attain an asymptotic value with increasing flowback differential pressures

for all the experiments.

30

2.6.1.3 Filtrate Loss

Table 2.9 shows spurt loss and 30 minute API filtrate loss for single-phase

filtration experiments simulating an open-hole completion. The API filtrate loss is based

on a 3 inch diameter filter paper for standard reporting. Figure 2.12 and 2.13 show plots

of spurt loss and API filtrate loss vs. the absolute permeability of the cores used to

conduct the single-phase experiments. It can be seen that the cores with larger

permeability show larger spurt loss and filtrate loss than cores with smaller permeability

for the same filtration fluid. Bentonite muds result in larger filtrate loss than UltraCarb

drill-in fluids.

Appendix-B contains plots for cumulative filtrate loss with square root of time for

all the single-phase filtration experiments. The plot shows a linear increase of cumulative

filtrate loss with square root of time that can be expressed as:

w spQ C t Q= + (2.8)

Where Qsp is called the spurt loss and Cw the leak-off coefficient.

2.6.2 Two-phase (Brine + Oil) Experiments

The motivation behind conducting two-phase experiments was to closely

represent the actual flow conditions around a wellbore where there are at least two-phases

(water and oil) present during production.

Table C.1 in Appendix-C shows the list of all the two-phase constant pressure

flowback experiments simulating open-hole completion with results summarized. shown

Three plots are shown for each of the experiments conducted: 1) applied differential

pressure and measured flow rates vs. time during flowback, 2) return permeability ratio

31

vs. applied differential pressure, and 3) filtrate loss vs. square root of time. A brief

discussion is also presented for some of the experiments after their plots.


Table 2.10 shows a summary of flow initiation pressures (FIP) for two-phase

constant pressure flowback experiments. Five different types of cores with permeability

ranging from 4 md to 1500 md (Nugget sandstone (4 md), Texas limestone (25 md),

Berea sandstone (200 md), Boise sandstone (1000 md), and Aloxide (1500 md)) were

used with UltraCarb drill-in fluid. An overbalance pressure of 100 psi and static filtration

time equal to 16 hrs was used for most of the experiments. The maximum FIP observed

for the two-phase flow experiments was 7 psi. The FIP for two-phase flow experiments

were slightly larger than the FIP found for similar single-phase flow experiments. This

indicates that an additional differential pressure is required to initiate flow because of

capillary pressure and relative permeability effects in two-phase flow. As in the single-

phase flow experiments, the two-phase flow experiments did not show any correlation

between rock permeability and the FIP.


Table 2.11 shows the return permeability ratios at four different flowback

differential pressures (FIP, 20 psi, 50 psi, and 100 psi) for the two-phase constant

pressure flowback experiments simulating open-hole conditions. For larger permeability

cores (Aloxide, and Boise sandstone), the maximum flowback differential pressure

applied was 50 psi. It can be observed in the table that the return permeability

improvement is more gradual as compared to single-phase experiments. We still observe

that most of the permeability improvement occurs at or below 20 psi of applied flowback

32

differential pressure. Appendix-C shows the return permeability spectra for all the two-

phase flowback tests. The return permeability spectra for the two-phase experiments are

also found to be S-shaped.

Figure 2.14 compares the return permeability spectra for the two-phase flowback

experiments conducted on Texas limestone and Berea sandstone one inch cores with

UltraCarb-2 drill-in fluid. It is observed that the return permeability improvement is more

gradual as compared to the return permeability spectra for single-phase experiments.

However, the return permeability ratios are found to be larger for cores with smaller

permeability as observed in the single-phase experiments. Similar trend is observed in

experiments conducted on Boise sandstone and Aloxide cores with UltraCarb-20 drill-in

fluid as shown in Figure 2.15. The return permeability spectra are S-shaped and are

asymptotic with increasing flowback differential pressures for all the experiments.


Table 2.12 shows spurt loss and 30 minute API filtrate loss for two-phase

filtration experiments simulating open-hole conditions. Figure 2.16 and 2.17 show plots

of spurt loss and API filtrate loss vs. the absolute permeability of the cores used to

conduct the two-phase experiments. Similar observations to single-phase filtration

experiments are seen where larger permeability cores show larger spurt loss and filtrate

loss than smaller permeability cores when using the same filtration fluid. Appendix-C

contains plots for cumulative filtrate loss with square root of time for all the two-phase

filtration experiments. The plots again show a linear increase of cumulative filtrate loss

with square root of time. This indicates the formation of an external filter cake early in

the filtration process.

33

2.6.3 Comparison between Single-phase and Two-phase Flow Experiments

Table 2.13 shows comparison of FIP between single-phase and two-phase flow

experiments. We observe that the FIP is larger for smaller permeability cores in two-

phase flow tests than single-phase flow tests. This is attributed to the additional capillary

pressure required to initiate flow in two-phase flow experiments. However, for larger

permeability cores the FIP is either equal or slightly larger for single-phase flow

experiments than two-phase flow experiments. This is attributed to deeper invasion of

internal filter cake in single-phase flow experiments during mud filtration. The shallower

invasion of the internal filter cake in two-phase flow experiments especially in large

pores is attributed to the resistance imposed by oil in the core to filtrate invasion.

Table 2.14 shows a comparison of return permeability ratios for single-phase and

two-phase flow experiments. We observe that the return permeabilities are larger for two-

phase flow tests than single-phase flow tests. Figure 2.18 to Figure 2.22 show plots

comparing return permeability spectra for single-phase vs. two-phase flow experiments

conducted on cores with different permeability.

Figure 2.18 shows plots of return permeability spectra for single-phase flow and

two-phase flow experiments conducted on Nugget sandstone cores. The single-phase

flow experiment resulted larger return permeability ratios than two-phase flow

experiments for the entire applied differential pressure range. The mud overbalance

during filtration in the two-phase experiment was equal to 140 psi as compared to 100 psi

used in the single-phase experiment. Also while conducting the two-phase experiment,

the bottom of the core came in contact with the drill-in fluid while pouring the mud out

from the filter cell. These two reasons might have caused smaller return permeability

ratios in the two-phase flow experiment than single-phase flow experiment.

34


two-phase flow experiments conducted on Texas limestone cores. The single-phase flow

experiment had larger return permeability ratios than two-phase flow experiments up to

about 10 psi of applied differential pressure during flowback. For differential pressures

larger than about 10 psi, the return permeability ratios were observed to be larger for two-

phase flow experiment than single-phase flow experiment. The single-phase return

permeability did not improve after a differential pressure of about 10 psi or larger. This

indicated significant damage in the core used in for the single-phase flow experiment. I

repeated the single-phase flow experiment to confirm the results and obtained nearly

identical spectrum as shown in the figure. This confirmed that significant damage is

caused in Texas limestone cores in single-phase flow experiments. The reasons behind

this large damage in single-phase experiments are unclear.


two-phase flow experiments conducted on Berea sandstone cores. From the figure we

observe that the two return permeability spectrums obtained from single-phase and two-

phase flow experiments are very similar.


two-phase flow experiments conducted on Aloxide cores. As we can see in the figure, the

two-phase flow experiment yielded larger return permeability ratios than single-phase

flow experiments for the entire applied differential pressure range. The following could

be one of the possible reasons behind larger return permeability in two-phase flow

experiment than single-phase flow experiment. In two-phase flow experiment, most of

the large pores are filled with oil while the smaller pores are filled with brine before

filtration. In single-phase flow experiments both the large and small pores are filled with

brine before filtration. During filtration the water based mud tries to invade the pores due

35

to the overbalance pressure. In single-phase experiments all the pores are invaded by the

filtration fluid. But in two-phase experiments, due to capillary pressure the larger pores

still remain filled with oil while the smaller pores are invaded with the fluid containing

solids and polymers. The large pores in two-phase flow experiments are not invaded to

the extent they are invaded in the single-phase flow experiments. Hence the return

permeability which is more governed by the flow through the large pores is larger in two-

phase flow experiments than in single-phase flow experiments.


two-phase flow experiments conducted on Boise sandstone cores. As we can see in the

figure, the two-phase flow experiment yielded larger return permeability ratios than

single-phase flow experiments for the entire applied differential pressure range.

2.7 EFFECT OF DIFFERENT PARAMETERS ON FIP AND RETURN PERMEABILITY

The effect of the following different parameters on FIP and return permeability spectra

are analyzed for the single and two-phase flow experiments:

1. Flow-back condition (constant pressure vs. constant rate)

2. External filter cake

3. Fluid type (drill-in fluid vs. bentonite mud)

4. Core length (1 inch core vs. 6 inch core)

5. Back pressure (No back pressure vs. 500 psi back pressure)

6. Median particle size of the bridging agent

36

2.7.1 Effect of Flowback Condition (Constant Flow Rate vs. Constant Pressure)

Figure 2.23 shows a comparison of FIP for constant flow rate and constant

pressure conditions during flowback in Berea sandstone cores. We can see that the FIP is

larger for the constant flow rate test than for the constant pressure flowback test. The FIP

is equal to 14 psi for the test with constant flow rate while the FIP is equal to only 7 psi

for the constant pressure case.

Table 2.15 shows a comparison of FIP for the constant flow rate tests and

constant pressure flowback tests for two-phase flow experiments. We can see that the

constant flow rate tests yield much larger FIP values than constant pressure tests. These

large FIP values are not valid and would give a very high estimate of the drawdown

required to initiate flow from the reservoir into a well. This would require the use of

artificial cleaning methods if the reservoir is depleted and is not able to provide the

required estimated drawdown. It is, therefore, recommended that constant rate

experiments not be used to estimate FIP since they can yield unreasonably high values.

2.7.2 Effect of External Filter Cake

Zain and Sharma showed that the external filter cake plays no role in determining

the flow initiation pressure. However, they conducted tests using a constant rate condition

during flowback. Tests with constant pressure flowback condition are conducted to verify

if there is any effect of external filter cake on FIP and return permeability.

Two long core experiments are conducted to study the effect of external filter

cake on FIP. In one of the experiments the flowback is done with the external filter cake

while in the other the external filter cake is mechanically scraped before flowback. For

both the experiments, the FIP value is found to be equal to 2 psi. Figure 2.24 shows FIP

and return permeability ratios during flowback for Berea cores with and without external

37

filter cake. It can be seen clearly that the two return permeability spectras are very

similar. Hence, the external filter cake is found to have no effect on the FIP and return

permeability spectrum. The presence of the external filter cake can have a large impact

on plugging of screens and liners and on the injectivity of injection wells. It should be

noted that for the acid or solvents to come into contact with the internal filter cake, either

the external filter cake should be mechanically removed or it should be dissolved

completely.

2.7.3 Effect of Drill-in or Completion Fluid Type

Table 2.16 shows a comparison of FIP, maximum return permeability ratio, and

API filtrate loss for UltraCarb drill-in fluid and a bentonite mud.

Flow initiation pressure: We found FIP equal to 1 psi for both UltraCarb-2 drill-in

fluid and bentonite mud on Texas limestone cores (~ 25 md). However, bentonite mud

gave a smaller FIP value equal to 1 psi for Boise sandstones (~ 1 Darcy) as compared to

the FIP value of 3 psi for UltraCarb-20 drill-in fluid. In conclusion, we observed an

insignificant effect of mud type on FIP on different permeability cores.

Return permeability spectra: The return permeability ratios are found to be better

for bentonite mud as compared to UltraCarb drill-in fluids for both Texas limestone cores

and Boise sandstone. This result was surprising considering the fact that drill-in fluids are

so much more expensive than bentonite muds and are supposed to be less damaging. One

advantage offered by drill-in fluids is that they are easier to remove by stimulation fluids.

Fluid loss: Bentonite muds have a larger fluid loss as compared to UltraCarb drill-

in fluids. As a result, the thickness of the external filter cake formed by bentonite muds

was much larger compared to the thickness of the external filter cake formed by the

UltraCarb drill-in fluid.

38

2.7.4 Effect of Core Length

We used a 6 inch long and 2 inch in diameter Berea core to find out if there is any

effect of core length on FIP. We found the FIP to be equal to 3 psi for the 6 inch long

core, which is comparable to the FIP value of 4 psi for the short Berea core. Hence, no

effect of core length was observed on FIP. This was because FIP depends on the depth of

the internal filter cake, yield strength of the internal filter cake and the pore size

distribution of the rock. All the factors mentioned above are expected to be

approximately equal in the both the short and long core experiments.

Figure 2.25 compares return permeability spectra for experiments conducted on

short and long Berea cores. We can see that the return permeability spectra are quite

different for the two cases. But if we plot the return permeability for the first 2 inches of

the long core the plot shifts toward the short core return permeability spectra. We need to

compute the permeability of the top one inch of the longer core to be able to compare its

return permeability spectra with the short 1 inch core. Unfortunately, we only made

measurements at every two inch intervals in long core experiments. Figure 2.26 shows a

plot comparing the return permeability spectra for the short and long Berea cores with

average flowback velocity on the x-axis. We observe similar trends as in Figure 2.25

showing very little overlap between the short and long core return permeabilities. The

two spectra come close to each other when the permeability of the first 2 inches of the

long core is plotted as seen in Figures 2.25 and 2.26.

2.7.5 Effect of Back Pressure

Figure 2.27 shows a comparison of return permeability spectra for Berea cores

with and without back pressure during flowback. We can observe an insignificant

difference between the two spectra. Hence, we conclude that back pressure has no

39

measurable effect on FIP and return permeability. This means that lab-experiments can

be done without applying any back pressure to characterize formation damage due to

drill-in and completion fluids, which would ease in setting up and conducting the

experiments.

2.7.6 Effect of Median Particle Size of the Bridging Agent

Figure 2.28 shows a comparison of return permeability spectra for UltraCarb drill-

in fluids with two different median size particles on Aloxide core samples. We can

observe larger FIP and smaller return permeability ratios when UltraCarb-2 (median size

= 2 microns) is used than when UltraCarb-20 (median size = 20 microns) is used on

Aloxide cores. Similar trend is seen in Figure 2.29 which shows the return permeability

spectra for UltraCarb-2 and UltraCarb-20 drill-in fluids on Berea core samples.

The external filter cake didn’t lift-off at all when UltraCarb-2 drill-in fluid was

used but it lifted-off completely when UltraCarb-20 drill-in fluid was used. We attribute

this lift-off in the case of UltraCarb-2 drill-in fluid to a much deeper and denser internal

filter cake. The external filter cake is being held to the rock surface by roots (internal

filter cake) which penetrate much deeper into the pores of the rock as compared to the

UltraCarb-20. As a result pin holes are formed in UltraCarb-2 filter cake during flowback

while the external filter cake is still held in place by the internal roots.

2.8 APPLICATION OF RESULTS TO ESTIMATE SKIN AROUND WELLS

The return permeability spectra can be used to estimate the skin around the

wellbores due to the damage caused by the drill-in and completion fluids. The skin is

calculated using the Hawkin’s formula:

40

( 1)(ln )d

d w

rkSkink r

= − (2.9)

where kd/k is taken equal to the return permeability ratio and rd is taken equal to

the sum of the wellbore radius and the length of the core (which was equal to 1 inch for

the short core experiments). We make two approximations in using the return

permeability data to calculate skin around wellbores: 1) The return permeability ratio

(kd/k) in a radial well is approximately equal to the return permeability ratio in the

flowback experiments with linear flow geometry; 2) The depth of damage in a radial well

is approximately equal to the depth of damage in the flowback experiments with linear

flow (which is equal to 1 inch). The approximations will hold well if the depth of damage

is small. Substituting k/kd with the return permeability ratio (RPR) and depth of damage

equal to the length of the core (1 inch), we obtain:

11( 1)(ln )w

w

rSkinRPR r

+= − (2.10)

where RPR is the return permeability ratio and rw is the radius of the well in

inches. Figure 2.30 shows a plot of skin with varying return permeability ratios for a

damaged depth of 1 inch for different well radii. We can see in the above figure that

below a return permeability ratio of 20 % the skin values becomes large.

Figures 2.31 and 2.32 show return permeability ratios at increasing pressure

gradients during flowback in one inch cores with different absolute permeabilities. The

average pressure gradients were calculated by dividing the applied differential pressures

during flowback by the length of the core. Figures 2.33 and 2.34 show the above plots of

return permeability ratio as a function of the log of the average pressure gradient applied

during flowback. We observe in the above figures that a minimum pressure gradient

equal to 10 psi/inch during flowback yields a return permeability ratio larger than 20 %

41

for all the four different types of cores with different permeabilities. Therefore, wells

flowing below a pressure gradient of 10 psi/inch are most likely to be damaged (with skin

factor > 1) and need artificial cleaning methods (acids, mutual solvents, enzymes) to

further improve the return permeability of the near wellbore region.

The following equation is used to calculate the pressure gradient at the wellbore

face for a single well located at the center of a cylindrical, homogeneous and isotropic

reservoir and which is produced instantaneously at a constant rate, q:

2173.94 exp( )

2 4t w

w wr

c rdp q Bdr kh r kt

φµµπ

−= (2.11)

The above equation is the solution of the diffusivity equation for radial flow in an

infinite acting reservoir. It can be observed that the exponential term in the Eq. (2.11) is

smaller than 1, therefore the maximum pressure gradient at the wellbore face is given by:

173.942w wr

dp q Bdr kh r

µπ

= (2.12)

The above equation is essentially Darcy’s law for radial flow at steady state. The

term dp/dr is the pressure gradient in psi/inch, q is the flow rate in STB/day, µ is the

viscosity of the flowing phase in cp, B is the formation volume factor for the flowing

phase in RB/STB, k is the permeability of the near wellbore region in md, and rw is the

radius of the well in ft. For a vertical well h is the thickness of the pay zone while for a

horizontal well h is equal to the length of the horizontal well, both in ft. The pressure

gradient at the wellbore face is directly proportional to the flow rate, viscosity of the

flowback fluid, and the formation volume factor and is inversely proportional to the

42

permeability, wellbore radius, and the thickness of the pay zone in a vertical well or the

length in the horizontal wells.

Figure 2.35 shows a plot of the pressure gradient at the wellbore face for a typical

vertical and a horizontal well with varying flow rates at steady state. The above plot

suggests that the near wellbore region can experience a wide range of pressure gradients

depending upon the flow rate. However, we can observe that the pressure gradients are

between 0.5 to 50 psi/inch in a vertical well (the rates are considered in the range of 100-

10000 STB/day) and 0.1 to 10 psi/inch in a horizontal well (the rates are considered in

the range of 1000-100000 STB/day). Typical values for permeability, viscosity, radius of

the well, formation volume factor, thickness of the pay zone in the vertical well and

length of the horizontal well were chosen as shown in the Figure 2.35 to calculate the

pressure gradients at the wellbore face.

We consider the average pressure gradients applied in the flowback experiments

to closely represent the pressure gradients in a radial well at the wellbore face. The

minimum average pressure gradient (10 psi/inch) which is needed to establish a good

return permeability (> 20 %) of the near wellbore region is in the range of the steady state

pressure gradients (0.5 – 50 psi/inch) for vertical wells. This means that there can be a

significant amount of damage present in the near wellbore region depending upon the

flow rates / pressure gradients in these wells. For the horizontal wells the average

pressure gradient (10 psi/inch) is the upper limit of the approximate pressure gradients

(0.1 to 10 psi/inch) which is required for low skin (return permeability ratio >20%).

Therefore, horizontal wells are most likely damaged even at large flow rates.

Eq. (2.12) assumes a constant permeability of the reservoir to calculate the

pressure gradients at the wellbore face. However the near wellbore permeability is not

constant during production because of the internal filter cake. Therefore, the pressure

43

gradients calculated using Eq. (2.12) will be different from the actual pressure gradients

at the wellbore face during production.

Another approach is to use the flow rate instead of the pressure gradient to

estimate the skin factor. The flow rates can be measured at the wellbore and therefore can

be used to estimate the amount of cleanup for a given flowrate. Figures 2.36 and 2.37

show the average return permeability ratios for inch long cores (Texas limestone, Berea

sandstone, Boise sandstone and Aloxide) at different steady state flowback rates. These

plots can be used to estimate return permeability of the near wellbore region instead of

using the pressure gradient values. For Texas limestone a flowback rate of 1 ml/min

yields a return permeability ratio larger than 20 %, while for Berea sandstone a flowback

rate of 10 ml/min is needed to achieve a return permeability ratio larger than 20 %. For

Boise sandstone a flowback rate of 10 ml/min yields a return permeability ratio larger

than 20 %, while for Aloxide core a flowback rate of 100 ml/min is needed to achieve a

return permeability ratio larger than 20 %.

Figures 2.38 and 2.39 show average return permeability ratios for inch long cores

(Texas limestone, Berea sandstone, Boise sandstone and Aloxide) at different steady state

flowback velocities. The flowback velocities were computed by dividing the flowback

rates by the total area of the top face of the cores. To achieve a return permeability ratio

larger than 20 %, an average flowback velocity of 0.02 cm/min is needed for Texas

limestone, 0.2 cm/min for Berea sandstone, 0.2 cm/min for Boise sandstone and 1

cm/min for Aloxide.

For a specific formation, drill-in fluid and an over-balance pressure, a constant

pressure flowback experiment should be conducted to obtain the return permeability

spectra as a function of average pressure gradient or the average flow rate. The return

44

permeability spectra will give us an estimate of the average pressure gradient needed for

a good return permeability of the near wellbore region.

2.9 CONCLUSIONS

1. Constant pressure flowback experiments result in much smaller FIP values than

constant rate flowback experiments. Constant rate flowback experiments yield

artificially large FIP values that are not representative of values relevant to the field.

2. No correlation is found between FIP and rock permeability for both single-phase and

two-phase flow experiments. However, the FIP for two-phase flow experiments in

small permeability rocks is found to be slightly larger than the FIP values obtained for

single-phase flow experiments because of capillary pressure and relative permeability

effects.

3. Flow initiation pressure (FIP) depends upon the extent and depth of internal damage

(internal filter cake) and does not depend on the external filter cake. FIP will be larger

if the particles in the drill-in fluid are not sized according to the rock permeability

(pore throat size). This causes deeper invasion of solids (larger thickness of the

internal filter cake).

4. Permanent damage to the core is dominated by the internal filter cake, a thin layer of

cake residue inside the porous medium. The return permeability spectra obtained

from the two-phase experiments is similar to the return permeability spectra obtained

from the single-phase experiments. For cores with large permeabilities (Aloxide and

Boise sandstone) the return permeabilities in two-phase experiments are found to be

larger than the single-phase return permeabilities. For cores with small permeabilities

(Texas limestone) and at small flowback pressures the return permeabilities in two-

45

phase flow experiments are found to be smaller than the single-phase return

permeabilities. However at large flowback pressures the single-phase return

permeabilities are found to be smaller than the two-phase return permeabilities. For

Berea sandstone the two spectra (single-phase and two-phase) are found to be very

similar indicating that the cleanup is controlled by the internal filter cake.

5. We recommend using a median size for the bridging additive equal to the median

pore-throat size of the formation for optimizing the return permeability and fluid loss.

If the pore throat size distribution of the formation is very broad then we recommend

using a combination of two or three different median sized bridging agents.

6. Core length plays insignificant role in determining the FIP. However the return

permeability ratios should be calculated at equal intervals in cores with different

lengths to compare the return permeabilities.

7. Back pressure on the external filter cake plays no role in determining the FIP and

return permeability.

8. The return permeability spectra, when plotted as a function of applied differential

pressure during flowback are consistently S-shaped. Return permeability spectrum is

a more meaningful measure of the formation damage than the FIP value. The return

permeability spectra can be used to evaluate the formation damage potential of

different drill-in and completion fluids.

9. The return permeability spectra can be used to estimate the skin in vertical and

horizontal wells as a function of the pressure gradient at the wellbore face or the flow

velocity of the hydrocarbons into the well. A pressure gradient of approximately 10

46

psi/inch or a flowback velocity of 1 cm/min is needed at the wellbore face to obtain a

skin factor < 1 for most formations completed open-hole provided the solids are

correctly sized according to the formation permeability or pore size distribution.

47

Table 2-1: Short and long core dimensions

Core type Core length (inch)

Core diameter (inch)

Short core 1 2.5

Long core 6 2

Table 2-2: Different core types used in the study

No. Core name Average porosity (%)

Av. absolute permeability

(md)

1 Nugget sandstone 14 4

2 Texas Limestone 29 25

3 Berea sandstone 20 200

4 Boise sandstone 28 1000

5 Aloxide 44 1500

48

Table 2-3: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb)

Composition

Field units

Laboratory units

Brine 0.98 bbl of9.7 ppg NaCl brine

343 ml of 16.4% NaCl brine

Viscosifier (Xanthan) 1 ppb

1 gram / 350 ml

FL-7 Plus (Starch) 7 ppb

7 grams / 350 ml

pH buffer 2 ppb

2 grams / 350 ml

Sized CaCO3 with median size of particles (2, 5, 12, 20 microns)

22 ppb

22 grams / 350 ml

Table 2-4: Rheology of CaCO3 drill-in mud using Fann viscometer

Rotational speed

(rpm)

Dial reading

(lbf / 100 sq. ft.)

600 43

300 32

200 24

100 18

6 8

3 7

Plastic viscosity

11 cp

Yield point

21 lbf/100 sq. ft.

pH 9.5

49

Table 2-5: Formulation of bentonite mud (10 ppg)

Composition

Field units

Laboratory units

NaCl 10.5 ppb

(10.5 gms) / 350 ml (3% by wt.)

Bentonite 22 ppb

22 gram / 350 ml

Ligno-sulfonate 3.5 ppb

3.5 grams / 350 ml (1% by wt.)

pH buffer 2 ppb

2 grams / 350 ml

Table 2-6: Rheology of bentonite mud using Fann viscometer

Rotational speed

(rpm)

Dial reading

(lbf / 100 sq. ft.)

600 23

300 13

Plastic viscosity

10 cp

Yield point

5 lbf/100 sq.ft.

pH 9

50

Table 2-7: Flow initiation pressure for single-phase flow and constant pressure flowback experiments simulating open hole conditions.

Core Type

Mud used

Core Dimensions (Dia. X Len.)

[inches]

Completion type simulated

FIP

[psi]

Nugget sandstone

(4 md)

UltraCarb-2*

Short core 2.5 X 1

Open hole 2

UltraCarb-2*

Open hole 1

UltraCarb-2* (Repeat

experiment)

Open hole 2

Texas limestone

(25 md)

Bentonite

Short core 2.5 X 1

Open hole 1

Short core 2.5 X 1

Open hole 4

Long core 2 X 6

Open hole 2

Berea sandstone

(200 md)

UltraCarb-2*

Long core 2 X 6

Open hole (external filter cake removed)

2

UltraCarb-20*

Open hole 3 Boise sandstone

(1000 md) Bentonite

Short core 2.5 X 1

Open hole 1

UltraCarb-2*

Open hole 8 Aloxide (Synthetic)

(1500 md) UltraCarb-20*

Short core 2.5 X 1

Open hole 4

* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.

51

Table 2-8: Summary of return permeability ratio for single-phase constant pressure flowback tests simulating open hole conditions

Return permeability ratio (%)

Core Type

Mud used

Core Dimensions

(Dia. X Len.)

[inches]

Lab Simulated

Completion type At

(FIP) At 20 psi

At 50 psi

At 100 psi

Nugget sandstone

(4 md)

UltraCarb-2*

Short core 2.5 X 1

Open hole 2.5 (2)

60.8 68.8 72.3

UltraCarb-2*

Open hole 33.88(1)

54.3 56.5 56.6


experiment)

Open hole 30.39 (2)

54 55 55

Texas Limestone

(25 md)

Bentonite

Short core 2.5 X 1

Open hole 38.1 (1)

100 100 100

Short core2.5 X 1

Open hole 0.9 (4)

50.4

Open hole 36.3 (3)

58 64.1 70

Berea Sandstone (200 md)

UltraCarb-2*

Long core 2 X 6

Open hole (w/o filter

cake)

34.3 (2)

60.7 68.2 73

UltraCarb-20*

17 (3)

18.8 13.2 Boise sandstone (1000 md)

Bentonite

Short core 2.5 X 1

Open hole

1.41 (1)

12 (2)

22 (10)

UltraCarb-2*

0.003 (8)

1.2 (16)

1.7 (20)

5.2 (50)

Aloxide (1000 md)

UltraCarb-20*

Short core 2.5 X 1

Open hole

.04 (4)

2.3 (7)

7 (20)

7.3 (50)


52

Table 2-9: API filtrate loss for single-phase flow and constant pressure flowback experiments simulating open-hole conditions

Core Type

Mud used

Core Dimensions

(Dia. X Len.)

[inches]

Completion type

simulated

API Spurt loss

[ml]

API filtrate

[ml] Nugget

sandstone (4 md)

UltraCarb-2*

Short core 2.5 X 1

Open hole 0 3.74

UltraCarb-2*

Open hole 0.23 4.79


experiment)

Open hole 0.2 4.55

Texas limestone

(25 md)

Bentonite

Short core 2.5 X 1

Open hole 0.7 22.4

Short core 2.5 X 1

Open hole 0.2 4.65 Berea sandstone

(200 md)

UltraCarb-2*

Long core 2 X 6

Open hole 0.8 6.37

UltraCarb-20*

Open hole 0.47 4.16 Boise sandstone

(1000 md) Bentonite

Short core 2.5 X 1

Open hole 0.71 31.1

UltraCarb-2*

Open hole 3.62 14.9 Aloxide (Synthetic)

(1500 md) UltraCarb-20*

Short core 2.5 X 1

Open hole 1.04 8.04


53

Table 2-10: Flow initiation pressure for two-phase flow experiments with constant pressure flowback condition simulating open-hole conditions

Core Type

Mud used


[inches]

Completion type simulated

FIP

[psi]

Nugget sandstone

(4 md)

UltraCarb-2*

Short core 2.5 X 1

Open hole 6

Texas limestone

(25 md)

UltraCarb-2*

Short core 2.5 X 1

Open hole

2

UltraCarb-2*

Open hole 7


experiment)

Open hole 4

Berea sandstone

(200 md)

UltraCarb-20*

Short core 2.5 X 1

Open hole 4

Boise sandstone

(1000 md)

UltraCarb-20*

Short core 2.5 X 1

Open hole 2

Aloxide (Synthetic)

(1500 md)

UltraCarb-20*

Short core 2.5 X 1

Open hole 3


54

Table 2-11: Summary of return permeability ratio for two-phase constant pressure flowback tests simulating open-hole conditions


Core Type

Mud used

Core Dimensions

(Dia. X Len.)

[inches]

Lab Simulated

Completion type At

(FIP) At 20 psi

At 50 psi

At 100 psi

Nugget sandstone

(4 md)

UltraCarb-2*

Short core 2.5 X 1

Open hole 1 (6)

18 38 48

Texas Limestone

(25 md)

UltraCarb-2*

Short core 2.5 X 1

Open hole 1 (2)

63 82 93

UltraCarb-2*

Open hole 25 (7)

>29


experiment as above)

Open hole 0.452(4)

46 62 72

Berea Sandstone

(200 md)

UltraCarb-20*

Short core 2.5 X 1

Open hole 3.64 (4)

69 82

Boise sandstone (1000 md)

UltraCarb-20*

Short core 2.5 X 1

Open hole 35 (2)

84 96

Aloxide

(1500 md)

UltraCarb-20*

Short core 2.5 X 1

Open hole 2.1 (3)

25 26.5


55

Table 2-12: API filtrate loss for two-phase flow and constant pressure flowback experiments simulating open-hole conditions

Core Type and

Permeability

Mud used


[inches]

API Spurt loss

[ml]

API filtrate

[ml]

Nugget sandstone

(4 md)

UltraCarb-2*

Short core 2.5 X 1

0 3.82

Texas limestone

(25 md)

UltraCarb-2*

Short core 2.5 X 1

0.18 4.83

UltraCarb-2*

0.26 5.47


experiment for above)

0.57 4.6

Berea sandstone

(200 md)

UltraCarb-20*

Short core 2.5 X 1

0.13 3.02

Boise sandstone

(1000 md)

UltraCarb-20*

Short core 2.5 X 1

0.65 3.23

Aloxide (Synthetic)

(1500 md)

UltraCarb-20*

Short core 2.5 X 1

1.1 5.6


56

Table 2-13: Comparison of FIP for single-phase vs. two-phase experiments with constant pressure flowback conditions

FIP [psi]

Core Type

Mud used


[inches] Single-phase

(Flowback fluid: 3 % brine)

Two-phase (Flowback

fluid: Exxsol)

Nugget Sandstone

(4 md)

UltraCarb-2

2.5 X 1 (Short core)

2 6

Texas limestone

(25 md)

UltraCarb-2


1 2

Berea sandstone

(200 md)

UltraCarb-2


7 7

Aloxide

(1000 md)

UltraCarb-20


4 3

Boise sandstone

(1000 md)

UltraCarb-20


3 2

57

Table 2-14: Comparison of return permeability ratio for single-phase vs. two-phase experiments with constant pressure flowback conditions

Return permeability ratio at the maximum applied differential

pressure [%]

Core Type

Mud used


[inches]

Single-phase (Flowback fluid:

3 % brine)

Two-phase (Flowback

fluid: Exxsol)

Nugget Sandstone

(4 md)

UltraCarb-2


72.3 (100 psi)

48.4* (100 psi)

Texas limestone

(25 md)

UltraCarb-2


56.6 (100 psi)

93 (100 psi)

Berea sandstone

(200 md)

UltraCarb-2


50.4 (20 psi)

72 (100 psi)

Aloxide

(1000 md)

UltraCarb-20


7.3 (50 psi)

26.5 (50 psi)

Boise sandstone

(1000 md)

UltraCarb-20


13.2 (50 psi)

96 (50 psi)

* The overbalance pressure was equal to 140 psi for this experiment. For rest of the experiments the mud overbalance pressure was equal to 100 psi.

58

Table 2-15: Comparison of FIP for constant rate vs. constant pressure flowback condition for two-phase flow experiments

FIP [psi]

Core Type

Mud used


[inches] Constant Rate

Flowback condition

(Rate: ml/min)

Constant Pressure

Flowback condition

Nugget Sandstone

(4 md)

Ultra-Carb


121 (5 ml/min)* 6

Texas limestone

(25 md)

Ultra-Carb


5.5 (1 ml/min)*

44 (5 ml/min)*

78 (20 ml/min)*

2

Berea sandstone

(200 md)

Ultra-Carb


14 (5 ml/min)* 7

Aloxide

(1000 md)

Ultra-Carb


21 (5 ml/min)*

38 (20 ml/min)*

3

* Reference: Zain and Sharma 5 Note: The mud overbalance pressure was equal to 100 psi for all the experiments.

59

Table 2-16: Comparison of FIP, return permeability ratio and API filtrate loss for bentonite mud and UltraCarb drill-in fluid

FIP [psi]


30 minute API filtrate loss [ml]

Core Dimensions (Dia.X Len.)

and Type Bentonite UltraCarb Bentonite UltraCarb Bentonite UltraCarb

Short (2.5”X 1”)

Texas Limestone

(25 md)

1 1 38.1 33.8 22.37 4.79

Short (2.5”X 1”)


1

3 22 19 31.1 4.16

60

0

2

4

6

8

10

12

14

16

18

20

0 20 40 60 80 100 120 140Time (min)

Mea

sure

d P

ress

ure

Diffe

rent

ial (

psi)

∆P peak = 18.4 psi

∆P f inal = 4.8 psi

FIP = ∆P peak - ∆P final = 13.6 psi

Flowrate = 5 ml/min


calculate flow initiation pressure (FIP)

0

2

4

6

8

10

12

0 20 40 60 80 100 120 140Time (min)

Appl

ied

Pre

ssur

e D

iffer

entia

l (ps

i)

0

2

4

6

8

10

12

14

16

Mea

sure

d Ra

te (m

l/min

)

Const Pressure Flowback rate

FIP = 7 psi

kreturn = 25%

kreturn = 29%

Figure 2-2: Flow-back pressure profile with constant pressure boundary condition

(incremental pressure differentials) to calculate FIP.

61

Figure 2-3: Apparatus for fluid filtration and flowback test

Pressure transducer

Data acquisition

systems

Liquid pump 0.1 - 28 ml/min

Graduated cylinder for static filtration

High pressure gas line

o-ring Core plug (2.5” x 1”)

Fluid distribution end

Fluid Space

Fluid outlet during flow back

Pressure bleed off line

Electronic Balance

Pressure regulator

Fluid accumulator

Constant pressure flow back line

Constant rate flow back line

Modified HPHT Filtration Cell

62

Pressure taps

Borehole sleeve

Core

Confining liquid

Rubber sleeve

Completion fluid

Stationary end cap

End spacer

Dynamic end cap

End spacer

2 in.

Min

imum

: 1.3

5 in

.

.97

in.

17 in

.

1.35

in. 1

in.

2.15

in.

2 in

. 1.

85 in

.

Max

imum

: 6.3

in.

6 in

.

Perforation

Figure 2-4: Apparatus for long core holder

63

Flow-back with oil for 2-phase experiments Brine flow for single-phase exp.

Step 3: FIP & Return permeability

Flow oil for two-phase experiments Flow brine for single-phase experiments

Step 1: Initial permeability

Over-balance pressure

Fluid

Step 2: Static filtration

External filter cake

Boundary Condition: Constant pressure / Constant rate

Record fluid loss for 16 hours

Record differential pressure & flow rate during flow-back

Figure 2-5: Steps used during mud filtration and flowback tests

64

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.01 0.1 1 10 100 1000Pore diameter (µm)

Nor

mal

ized

Intr

usio

n Vo

lum

e (m

l/g)

Berea sandstone Median = 13.5 µm

Boise sandstone Median = 17.6 µm

Texas Limestone Median = 0.7 µm

Figure 2-6: Pore volume distribution for different rocks obtained from mercury

penetrometer

Figure 2-7: Top view of a limestone core after flowback at constant pressure (Mud used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flowLS-12)

65

Figure 2-8: Top view of a Berea core after flowback at constant pressure (Mud used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 2-phase flow, BS-17)

Figure 2-9: Nugget sandstone core after flowback at constant pressure (Mud used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow, NS-2)

66

Figure 2-10: Top view of an Aloxide core after flowback at constant pressure (Mud used: UltraCarb-20 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow, AL-2)

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100Flowback Pressure (psi)

Ret

urn

Perm

eabi

lity

Rat

io (%

)

Aloxide, kabs = 1313 md

Berea sandstone, kabs = 60 md

Texas limestone, kabs = 24 md

Nugget sandstone, kabs = 4 md

UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiSingle-phase flow (brine)

Figure 2-11: Return permeability spectra for different permeability cores (single-phase

flow and constant flowback pressure).

67

0

1

2

3

4

0 250 500 750 1000 1250 1500

Absolute Permeability (md)

Spur

t los

s (m

l)

UltraCarb-2 Bentonite UltraCarb-20

Figure 2-12: Spurt loss vs. absolute permeability of different cores for single-phase

experiments simulating open hole conditions

0

5

10

15

20

25

30

35

0 250 500 750 1000 1250 1500

Absolute Permeability (md)

30 M

inut

e AP

I Filt

rate

Los

s (m

l)

UltraCarb-2 Bentonite UltraCarb-20

Figure 2-13: API Filtrate loss vs. absolute permeability of different cores for single-phase


68

0

20

40

60

80

100

0 20 40 60 80 100 120 140Flowback Pressure (psi)

Retu

rn P

erm

eabi

lity

Rat

io (%

)

Berea sandstone, kef f (oil) = 129 md

Texas limestone, kef f (oil) = 15 md

UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow

Figure 2-14: Return permeability spectra for different permeability cores (two-phase flow

and constant flowback pressure)

0

10

20

30

40

50

60

70

80


Retu

rn P

erm

eabi

lity

Ratio

(%)

Aloxide, kabs = 1313 md

Berea sandstone, kabs = 60 md

Texas limestone, kabs = 24 md

Nugget sandstone, kabs = 4 md

UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiSingle-phase flow (brine)

Figure 2-15: Return permeability spectra for different permeability cores (two-phase flow

and constant flowback pressure)

69

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Effective Permeability to Oil (md)

Spur

t los

s (m

l)

UltraCarb-2 (OB=100 psi) UltraCarb-20 (OB=100 psi)

Figure 2-16: Spurt loss vs. absolute permeability of different cores for two-phase


0

1

2

3

4

5

6

0 200 400 600 800 1000

Effective Permeability to Oil (md)

30 M

inut

e A

PI F

iltra

te L

oss

(ml)

UltraCarb-2 (OB=100 psi) UltraCarb-20 (OB=100 psi)

Figure 2-17: API Filtrate loss vs. absolute permeability of different cores for two-phase


70

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100

Applied Differential Pressure During Flowback (psi)

Retu

rn P

erm

eabi

lity

Ratio

(%)

Two-phase flow (O.B. = 140 psi)

Single-phase flow(O.B. = 100 psi)

Figure 2-18: Return permeability spectra in Nugget sandstone for single-phase flow and

two-phase flow

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)

Ret

urn

Per

mea

bilit

y R

atio

(%)

Two-phase flow

Single-phase flow

Figure 2-19: Comparison of return permeability spectra in Texas limestone for single-

phase vs. two-phase flow (constant pressure B.C.)

71

0

10

20

30

40

50

60

70

80

90


Retu

rn P

erm

eabi

lity

Ratio

(%)

Single-phase flow (UltraCarb-2)

Two-phase flow (UltraCarb-2)

Two-phase flow (UltraCarb-20)

Figure 2-20: Comparison of return permeability spectra in Berea sandstone for single-


0

5

10

15

20

25

30

0 10 20 30 40 50 60Applied Differential Pressure During Flowback (psi)

Ret

urn

Per

mea

bilit

y R

atio

(%)

Two-phase flow

Single-phase flow

Figure 2-21: Comparison of return permeability spectra in Aloxide (synthetic cores) for

single-phase vs. two-phase flow (constant pressure B.C.)

72

0

10

20

30

40

50

60


Retu

rn P

erm

eabi

lity

Rat

io (%

)

Two-phase flow

Single-phase flow

Figure 2-22: Comparison of return permeability spectra in Boise sandstone for single-


0

2

4

6

8

10

12

14

16

18

20

0 20 40 60 80 100 120 140

Time (min)

∆p

(psi

)

0

2

4

6

8

10

12

14

16

Rat

e (m

l/min

)

Const Pressure Const Rate

FIP (constant pressure b.c.) = 7 psi

kreturn = 25%

kreturn = 29%

kreturn = 26% at q = 5 ml / min

FIP (constant rate b. c.) = 14 psi

Figure 2-23: Comparison of FIP between constant rate boundary condition (B.C.) and

constant pressure B.C. during flowback for Berea sandstone

73

0

10

20

30

40

50

60

70

80


Ret

urn

Perm

eabi

lity

Rat

io (%

)

with external filter cakewithout external filter cakewith external filter cake (repeat experiment)

Figure 2-24: Comparison of FIP and return permeability spectra for Berea sandstone with

and without external filter cake

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80Differential Pressure During Flowback (psi)

Retu

rn P

erm

eabi

lity

Ratio

(%)

Berea long core (diameter = 2 in., length = 6 in.)

Berea short core (dia. = 2.5 in., length = 1 in.)

Berea long core with K calculated for the first two inches of the core

Figure 2-25: Return permeability vs. differential pressure during flowback in short and

long Berea cores

74

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3Average Flowback Velocity (cm/min)

Retu

rn P

erm

eabi

lity

Rat

io (%

)Berea long core (diameter = 2 in., length = 6 in.)

Berea short core (dia. = 2.5 in., length = 1 in.)

Berea long core with K calculated for the first two inches of the core

Figure 2-26: Return permeability vs. average flowback velocity for experiments

conducted on short and long Berea cores

0

10

20

30

40

50

60

70

80


Ret

urn

Perm

eabi

lity

Rat

io (%

)

No back pressure

Back pressure = 500 psi

Figure 2-27: Comparison of return permeability spectra for Berea sandstone

with and without back pressure (O.B. = 500 psi)

75

0

1

2

3

4

5

6

7

8


Ret

urn

Perm

eabi

lity

Rat

io (%

)

UltraCarb-20 (Median size = 20 microns)

UltraCarb-2 (Median size = 2 microns)

Figure 2-28: Comparison of return permeability spectra for Aloxide cores with UltraCarb

drill-in fluids with two different median sizes

0

10

20

30

40

50

60

70

80

90


Ret

urn

Perm

eabi

lity

Ratio

(%)

UltraCarb-2* drill-in fluid

UltraCarb-20* drill-in fluid

* Median size of the bridging agent

Figure 2-29: Comparison of return permeability spectra for Berea cores with UltraCarb

drill-in fluids with two different median sizes

76

0

1

2

3

4

5

6

0 20 40 60 80 100Return Permeability Ratio (%)

Skin

Depth of damage = 1 inch

radius of well (rw) = 3 inch

rw = 4 inch

rw = 6 inch

Figure 2-30: Skin with varying return permeability ratio of the near wellbore region

0

20

40

60

80

100

0 20 40 60 80 100 120 140Average Pressure Gradient During Flowback (psi/inch)

Retu

rn P

erm

eabi

lity

Ratio

(%)




Figure 2-31: Return permeability ration vs. average pressure gradients in Texas limestone

and Berea during flowback

77

0

20

40

60

80

100

0 10 20 30 40 50 60Average Pressure Gradient During Flowback (psi/inch)

Retu

rn P

erm

eabi

lity

Ratio

(%)

Aloxide, kef f (oil) = 965 md

Boise sandstone, kef f (oil) = 600 md


Error = -20%

Error = 20%


and Aloxide core during flowback

0

20

40

60

80

100

1 10 100 1000Average Pressure Gradient During Flowback (psi/inch)

Retu

rn P

erm

eabi

lity

Rat

io (%

)




Figure 2-33: Return permeability ration vs. average pressure gradients in Texas limestone

and Berea during flowback (Semi-log plot)

78

0

20

40

60

80

100

1 10 100Average Pressure Gradient During Flowback (psi/inch)

Retu

rn P

erm

eabi

lity

Rat

io (%

)




Error = -20%

Error = -20%


and Aloxide core during flowback (Semi-log plot)

0.01

0.1

1

10

100

10 100 1000 10000 100000Flow Rate (bpd)

dp/d

r (ps

i/inc

h) a

t the

Wel

lbor

e Fa

ce

Radial well Horizontal well

ko = 200 mdµ = 0.74 cpBo = 1.3 RB/STBrw = 0.25 fth (radial well) = 50 ftlength of hor. well = 2000 ft

Figure 2-35: Pressure gradient at the wellbore face at different steady state flow rates

79

0

20

40

60

80

100

0.001 0.01 0.1 1 10 100 1000Flowback Rate (ml/min)

Ret

urn

Perm

eabi

lity

Ratio

(%)




Figure 2-36: Return permeability ratio of inch long Texas limestone and Berea sandstone

core at different flowback rates (semi-log plot)

0

20

40

60

80

100

1 10 100 1000Flowback Rate (ml/min)

Ret

urn

Perm

eabi

lity

Rat

io (%

)




Error = -20%

Error = 20%


flowback rates (semi-log plot)

80

0

20

40

60

80

100

0.0001 0.001 0.01 0.1 1 10Flowback Velocity (cm/min)

Retu

rn P

erm

eabi

lity

Rat

io (%

)




Figure 2-38: Return permeability ratio of Texas limestone and Berea sandstone core at

different flowback velocities (semi-log plot)

0

20

40

60

80

100

0.01 0.1 1 10 100Flowback Velocity (cm/min)

Ret

urn

Perm

eabi

lity

Ratio

(%)




Error = -20%

Error = 20%


flowback velocities (semi-log plot)

81

REFERENCES






Damage Control Symposium held in The Hague, The Netherlands, 15-16 May, 1995

3. Bailey, L., et al.: “Filter cake Integrity and Reservoir Damage,” paper SPE 39429

presented at the 1998 SPE International Symposium on Formation Damage Control

held in Lafayette, 18-19 February, 1998

4. Ryan, D. F., et al.: “Mud Clean-Up in Horizontal Wells: A Major Joint Industry

Study,” paper SPE 30528 presented at the SPE Annual Technical Conference and

Exhibition held in Dallas, USA, 22-25 October, 1995

5. Zain, M. Z., and Sharma, M. M.: “Cleanup of Wall-Building Filter Cakes,” paper

SPE 56635 presented at the SPE Annual Technical Conference and Exhibition held in

Houston, Texas, 3-6 October, 1999

6. Roy, S. R., and Sharma, M. M.: “The Relative Importance of Solids and Filtrate

Invasion on the Flow Initiation Pressure,” paper SPE 68949 presented at the

European Formation Damage Conference held in The Hague, The Netherlands, 21-22

May, 2001

7. Alfenore, J., et al.: “What really Matters In our Quest of Minimizing Formation

Damage In Open Hole Horizontal Wells,” paper SPE 54731 presented at the

European Formation Damage Conference held in The Hague, The Netherlands, 31

May – 1 June, 1999

82

8. Ladva, J. K. H., et al.: “Multiphase Flow and Drilling-Fluid Filtrate Effects on the

Onset of Production,” paper SPE 58795 presented at the SPE International

Symposium on Formation Damage Control, Lafayette, Louisiana, 23-24 Feb., 2000

9. Gruber, N. G., and Adair, K. L.: “New Laboratory Procedures for Evaluation of

Drilling Induced Formation Damage and Horizontal Well Performance,” paper JCPT

Volume 34, No. 5, May 1995


Drilling Induced Formation Damage and Horizontal Well Performance: An Update,”

paper SPE 37139 presented at the SPE International Conference on Horizontal Well

Technology held in Calgary, Canada, 18-20 November, 1996






Exhibition held in Dallas, USA, 22-25 October, 1995

13. Marshall, S. D., et al,: “Return Permeability: A Detailed Comparative Study,” paper

SPE 54763 presented at the SPE European Formation Damage Conference held in

The Hague, The Netherlands, 31 May - 1 June 1999






83




May – 1 June, 1999

17. Smith, P. S., et al.: “Drilling Fluid Design to Prevent Formation Damage in High

Permeability Quartz Arenite Sandstones,” paper SPE 36430 presented at the Annual

Technical Conference and Exhibition held in Denver, Colorado, U.S.A., 6-9 October

1996

18. Kalpakci, B., et al.: “A Systematic Approach for Selection of Drill-in Fluids and

Cleanup Options for Minimum Formation Damage in Horizontal Well: A Case Study

for Paloma Field, Bolivia,” paper SPE 53948 presented at the SPE Latin American

and Caribbean Petroleum Engineering Conference held in Caracas, Venezuela, 21-23

April, 1999

19. Bailey, L., et al.: “Particulate Invasion From Drilling Fluids,” paper SPE 54762

presented at the SPE European Formation Damage Conference held in The Hague,

The Netherlands, 31 May -1 June, 1999


Completion Fluids,” paper SPE 68964 presented at the SPE European Formation

Damage Conference held in The Hague, The Netherlands, 21–22 May 2000

84

Chapter 3: Role of Drill-in Fluid Components during Filtration and

Flowback

3.1 INTRODUCTION

In this chapter, we evaluate the formation damage potential of different

components used in water-based drill-in and completion fluids. First a literature review of

past studies on the major components used in water-based drill-in and completions fluids

(starch, xanthan and calcium carbonate) is presented. A total of 12 fluid formulations are

designed to study the formation damage potential of individual components. Results are

presented and discussed for each of these formulations. UTDamage is used to simulate

the experiments. A quantitative match for the return permeabilities and a qualitative

match for the filtrate loss is found between the two. Finally, conclusions are presented

and recommendations are provided to better design drill-in and completion fluids for

minimizing formation damage.

3.2 DRILL-IN AND COMPLETION FLUID COMPONENTS

The components used in drilling and completion fluids have been changing since

the beginning of the oil industry. In the early years water was used as the only component

in the fluid to clean the bore hole by circulating it through the drill pipe and out through

the annulus. Gray and Darley 1 have presented a detailed history on the development of

drilling fluids technology. Drilling muds on the broadest level can be classified as: water-

based muds, oil-based muds, and gas-based muds. They can be further classified into sub

categories according to the specific components used in the mud for a desired purpose.

85

After the advent of horizontal drilling technology and multi-lateral drilling

through the pay-zone, careful thought was given to mud formulations based on

productivity concerns. A new class of drilling fluids was developed for use when drilling

through the pay-zone. These fluids were called drill-in fluids. A drill-in fluid (DIF) is

defined as a drilling / completion fluid, specially formulated to optimize well

productivity. Like standard drilling fluids, DIF’s provide lubricity, inhibition, solids

suspension, and borehole stability. Additionally, they are also formulated to protect

producing intervals by: (1) mechanically sealing exposed pore space openings in

boreholes by forming thin, tough and impermeable filter cakes; (2) stabilizing the

wellbore during completion by strengthening the wellbore; (3) allowing easy cleanup

after drilling and completion.

Most DIF’s contain solid materials such as sized calcium carbonate or sized salt.

Solids are used as bridging agents to plug the surface of a formation matrix and as

weighting material to control formation pressure. Drill-in fluids use viscosifiers such as

biopolymers to provide gel strength and to improve the carrying of the drill solids to the

surface. They also use fluid loss control agents to reduce the fluid loss from the well bore

to the formation. The important components of the more commonly used water based

DIF’s are as follows:

1. Base brines (Na, Ca, K, and cesium chlorides, bromides, halides and formates) to

meet the density and formation compatibility requirements.

2. Sized salt/CaCO3 as bridging additives.

4. Modified starch for controlling fluid loss.

3. Polymers (usually Xanthan) for desired rheology and viscosity behavior.

5. pH buffer for desired alkalinity requirements.

86

The three main additives (bridging additive, fluid loss control additive, and the

rheology control additive) are discussed in more detail below:

3.2.1 Bridging Additive

Sized calcium carbonate and sized salt are the two most common bridging

additives used in drill-in fluids. Sized calcium carbonate is used even more widely than

sized salt. The use of calcium carbonate was proposed as a weighting material because it

can be dissolved in hydrochloric acid. It is readily available as ground limestone or oyster

shell. It can also be used as a substitute for barite in oil-based muds as it disperses more

readily in oil than barite. Its specific gravity is between 2.6 and 2.8 which limit the

maximum density of drill-in fluid to about 12 lb/gal. There are two advantages of using

sized calcium carbonate particles in drill-in fluids: 1) the particles are acid soluble which

provides an option of dissolving the filter cake using acids before production, and 2) the

particles are available with different median sizes which can be used to match the pore

throat or permeability of the formation to be drilled for minimizing invasion.

3.2.2 Fluid Loss Control Additive

Starch is the most common fluid loss control additive used in drilling or drill-in

fluids. It was the first organic polymer used in substantial quantities in mud. The

widespread use of starch decreased as other polymers (notably CMC) were introduced.

Starch is still the most economical filtration loss control additive for strongly alkaline and

salt saturated muds. However starch is subject to fermentation by many microorganisms

(yeasts, molds, bacteria). To avoid this, the mud is saturated with salt or the pH is kept

around 12. A biocide needs to be added if the mud with starch is to be used for several

days. Starch can also break down at high temperatures and at high circulation rates.

87

Numerous modifications and derivatives of starch are proposed and used in drill-in fluids.

For example a fermentation-resistant starch is prepared by blending moist starch (about

20 % water) with 3 % bis (2-hydroxy, 3,5-dichlorophenyl) sulfide, and passing the

mixture under pressure through a heated extruder1. Gums, polyanionic cellulose, sodium

polyacrylonitrile, oil are some other additives which are also used to control fluid loss

from the well into the formation.

3.2.3 Rheology Control Additive

Xanthan polymer is used as the most common rheology control additive in drill-in

fluids. It was introduced as a drilling fluids component in the mid 1960s under the name

“XC polymer” and its use has increased noticeably since 1970. It is a water soluble

polysaccharide produced by bacterial action (genus Xanthomonas) on carbohydrates. The

most important property of xanthan in its application to drill-in fluids is that it builds

viscosity at low concentrations as compared to gums or other viscosifiers. It acts as an

excellent suspending agent for drill cuttings and surpasses any other polymer used in

drilling or drill-in fluids. It displays excellent shear thinning properties with apparent

viscosity markedly lower at high shear rates than measured at low shear rates. Cross

linking with chromic ion significantly increases viscosity. There is a small effect of pH

on viscosity in the range of 7 -11. It shows negligible sign of degradation at high

temperatures. Other rheology control additives used in drilling fluids are CMC, gums,

and HEC.

3.3 RESEARCH OBJECTIVE

There has been no study done in evaluating the effect of individual components in

drill-in fluids from a productivity stand point. The main idea behind studying the role of

88

individual components in drill-in fluids was to have a clear picture of how each

component affects production and if we can design drill-in fluids better using that

understanding. The research objective is to experimentally evaluate the effect of the

following drilling fluid components on FIP and return permeability ratio: Bridging

additive, fluid loss control additive, and rheology control additive.

3.4 EXPERIMENTAL DESIGN

3.4.1 Test Description and Fluid Design

Table 3.1 shows the composition of UltraCarb drill-in fluid with all the

components. For studying the effect of individual components we formulated the drill-in

fluid with different combinations of components by taking out one of the three main

components in one formulation. Table 3.2 shows the different drill-in fluid formulations

used in evaluating the effect of different components. The different drill-in fluid

formulations are described below in detail:

1. Drill-in fluid with no fluid loss control agent (starch) and no rheology control agent

(xanthan polymer). Only sized calcium carbonate was added to brine with the pH

buffer (see Table 3.1).

2. Drill-in fluid with no rheology control agent (xanthan polymer). Sized calcium

carbonate along with fluid loss control agent (starch) was added to brine with the pH


3. Drill-in fluid with no fluid loss control agent (starch). Sized calcium carbonate along

with the rheology control agent (xanthan polymer) was added to brine with the pH


4. Drill-in fluid with all the components.

89

Each of the above 4 formulations were made for three different median sizes (2

micron, 12 micron, and 20 micron) of bridging additive. Hence a total of 12 drill-in fluid

formulations were made to study the effect of these components on FIP and return

permeability. Two more experiments were also conducted: 1) with only brine and 2) with

brine and pH buffer to measure FIP and return permeability ratio.

3.4.2 Test Equipment

The experimental set up used in conducting the experiments was the same as

presented in Chapter 2. Figure 2.3 in Chapter 2 shows the schematic of the experimental

set up. Berea cores with diameter 2.5 inch and length equal to 1 inch were used in the

modified HPHT API filtration cell. The temperature used in the early experiments was

equal to 150 oF to simulate reservoir conditions but later, after we found that the effect of

high temperature on filter cake removal to be negligible, experiments were conducted at

room temperature (75 oF).


The test procedure used in conducting the experiments is outlined in Chapter 2,

Section 2.3.5. In brief, Berea cores were first vacuum saturated in 3% brine and then

Exxsol D-110 (oil distillate) was flowed until an irreducible water saturation was

achieved. The initial effective permeability to oil for the core was calculated. A static

filtration test at an overbalance of 100 psi was conducted with the drill-in fluid on top of

the core for a filtration time of 16 hours. The fluid loss was recorded during that time to

calculate the standard API 30 minute fluid loss for each drill-in fluid formulation. After

filtration, a flow back test was conducted at a constant rate and the differential pressure

profile was recorded across the core. Figure 3.1 shows a typical plot of the differential

90

pressure profile across the core during flowback after filtration. The flow initiation

pressure (FIP) is defined as the difference between the peak pressure and the stabilized

pressure.


We measure and report the following parameters for all the two-phase (brine and

Exxsol D-110) filtration and flow back experiments:


2. Return permeability ratio

3. API filtrate loss

Table 3.3 shows the results for peak pressure during flow back, FIP, return

permeability ratio, and API filtrate loss for all the experiments. Appendix D shows plots

of differential pressure profile across the core during flowback and filtrate loss vs. square

root of time during static filtration for all the tests. The FIP, return permeability ratio, and

the filtrate loss for all the experiments are discussed below.

3.5.1 Flow Initiation Pressure

Figure 3.2 shows a bar graph comparing the FIP for four different compositions of

drill-in fluids: (1) only bridging additive, (2) bridging additive and fluid loss control

additive (starch), (3) bridging additive and rheology control additive (xanthan), (4)

bridging additive, fluid loss control additive (starch), and rheology control additive

(xanthan). Each of these four compositions was formulated for three median sizes (2 µm,

12 µm, 20 µm) of bridging additive, with a total of 12 fluid formulations. We can see that

the largest FIP is found for drill-in fluid formulations (3) and (4) which have xanthan

91

polymer. Drill-in fluid formulation number (2), which is made up of bridging additive

and starch, shows the smallest FIP in comparison to the rest of the drill-in fluid

formulations. We attribute this small FIP to minimum invasion of particles/polymers for

this formulation into Berea cores. It could also be that the internal filter cake formed from

this drill-in fluid formulation has the lowest yield strength, which would also result in a

small FIP. Most likely the product of depth of invasion of solids and the yield strength of

the internal filter cake is minimum for this fluid formulation. Because FIP is directly

proportional to the product of the yield strength of the internal filter cake and the depth of

the internal filter cake. The dependence of FIP on the yield strength and the depth of

internal filter cake is discussed in detail in Chapter 5.

3.5.2 Return Permeability Ratio

The return permeability ratio is defined in equation 2.6 of Chapter 2. Return

permeability ratio depends on the flow rate in flow back experiments done at constant

rate. The following sections present return permeability ratios for different drill-in fluid

formulations.

3.5.2.1 Drill-in Fluid Formulation 1 (Only Bridging Additive)

Figure 3.3 shows a bar graph for return permeability ratio for drill-in fluid

formulation (1) for the three different median sizes (2 µm, 12 µm, 20 µm) of bridging

additive and at three different flow rates (1ml/min, 3 ml/min, 5 ml/min). The graph

clearly shows that the drill-in fluid with a median size equal to 12 microns results in the

largest return permeability ratio. The fluid with median size equal to 12 microns is closest

in size to the median pore throat size of Berea sandstone (13.5 microns) than the median

sizes (2 µm and 20 µm) of the other two formulations. This would have led to the most

92

effective bridging with fluid with median size equal to 12 microns with minimum

invasion of solids and filtrate into the rock. As a result the return permeability ratio was

the largest for the fluid with median size equal to 12 microns.

It can also be seen in Figure 3.3 that the return permeability ratios are larger with

larger flowback rates for all fluid formulations. This observation is consistent with the

earlier observations presented by Zain and Sharma 2.

3.5.2.2 Drill-in Fluid Formulation 2 (Bridging Additive + Fluid Loss Control Additive)




clearly shows that the drill-in fluid with bridging agents with a median size equal to 20

microns results in the largest return permeability ratio. I assume that the addition of

starch to sized CaCO3 particles with a fixed median size must have reduced the overall

median size of the mixture. This reduction in an overall median size of the particles might

have approached a median size closer to the median pore throat size of Berea sandstone.

As a result there was minimum invasion of the fluid into the Berea core which led to the

largest return permeability ratio compared to the return permeability ratios obtained using

other fluid formulations.

3.5.2.3 Drill-in Fluid Formulation 3 (Bridging Additive + Rheology Control Additive)




93

clearly shows that the drill-in fluid with bridging agents with a median size of 20 microns

results in the largest return permeability ratio. Addition of xanthan polymer (size of few

microns) to calcium carbonate particles with a median size of 20 microns reduced the

median size of the overall mixture. This reduction in an overall median size might have

approached a median size very close to the median pore throat size of Berea sandstone.

As a result there was minimum invasion of the fluid into the Berea core which led to the

largest return permeability ratio compared to the return permeability ratios obtained using

other fluid formulations.

3.5.2.4 Drill-in Fluid Formulation 4 (Bridging Additive + Fluid Loss Control Additive + Rheology Control Additive)



additive and at three different flow rates (1ml/min, 3 ml/min, 5 ml/min). The graph shows

that the drill-in fluid with bridging agents with a median size equal to 12 microns results

in the largest return permeability ratio. The drill-in fluid with a median size equal to 20

microns results in a slightly smaller return permeability ratio than the fluid with bridging

agents with a median size equal to 12 microns. This result was different from the results

obtained when only one of the additives (xanthan or starch) was added to the sized

CaCO3 particles. This suggests that addition of both the additives to the sized CaCO3

particles with a median size of 12 microns did not reduce the median size of the overall

mixture but kept the median size close to the median pore throat size of Berea sandstone.

It could be that the two polymers when mixed together results in a larger median size

than their individual median sizes because of some form of linking or interaction.

94

3.5.2.5 Comparison of Return Permeability Ratio for the Different Drill-in Fluid Formulations

Figure 3.7, 3.8, and 3.9 show bar graphs of return permeability ratio for the four

different drill-in fluid formulations at three different flow back rates (1ml/min, 3 ml/min,

and 5 ml/min). All the three figures clearly indicate that drill-in fluid formulation number

3 (bridging additive + xanthan) has the smallest return permeability ratio. This indicates

that xanthan polymer is the most damaging of all the constituents and must have invaded

the most into the rock compared to the other components during filtration. This deep

invasion is assumed to be because of the small size of xanthan polymer. It could also be

that the xanthan polymer forms an internal filter cake with large yield strength which

would make the cleanup of the internal filter cake difficult. Drill-in fluid formulation

number 2 (bridging additive + starch) shows large return permeability ratio which is

approximately the same as drill-in fluid formulation 4 (bridging additive + starch +

xanthan). This suggests that starch is very less damaging and doesn’t invade much into

the formation. Not only it doesn’t invade into the formation but it also restricts xanthan to

invade into the formation. The drill-in fluid formulation number 1 (only bridging

additive) shows the largest return permeability ratio with a median size of 12 µm

compared to all the other drill-in fluid formulations. This is because there are no

polymers in this fluid which can invade deep into the rock which can cause significant

permanent damage to the rock.

3.5.3 Filtrate Loss

Figure 3.10 shows a bar graph comparing API filtrate loss for the four different

compositions of drill-in fluids as presented in Table 3.2 for three median sizes of bridging

additive. The largest API filtrate loss is found for drill-in fluid formulation number 1 with

95

only sized CaCO3 particles and no additives, while the smallest API filtrate loss is found

for the drill-in fluid formulation number 4 with all the components. This is because the

drill-in fluid formulation number 1 resulted in the thickest and largest permeability filter

cake while the drill-in fluid formulation number 4 made the thinnest and smallest

permeability filter cake. The polymer additives can fit into the pores of the filter cake

made from the bigger sized CaCO3 particles which will lower the porosity and the

permeability of the filter cake resulting in a reduced leak-off. Appendix D shows plots for

filtrate loss vs. square root of time for all the twelve tests. The filtrate loss shows a linear

fit with square root of time.

3.6 EFFECT OF DRILL SOLIDS

10 ppb RevDust was added to UltraCarb drill-in fluid to simulate drill solids in a

clean mud to represent the mud in a wellbore. Static filtration experiments with an

overbalance of 100 psi on Berea sandstone were conducted with UltraCarb-12 and

UltraCarb-20 drill-in fluids with and without RevDust. Table 3.4 compares the FIP,

return permeability ratio and API filtrate loss for both the cases (with and without

RevDust) for both the drill-in fluids. It can be seen in the table that the FIP is larger for

the drill-in fluids with RevDust than for the drill-in fluids without RevDust. However, the

return permeability ratio is found to be also slightly larger for drill-in fluid with RevDust

than for drill-in fluid without RevDust. The 30 minute API filtrate loss is found to be

approximately the same for both the cases. Hence there is not much effect of addition of

RevDust to clean drill-in fluids.

96

3.7 COMPARISON OF EXPERIMENTAL RESULTS WITH UTDAMAGE

A multi-component filtration model developed by Suri and Sharma 3 was used to

simulate the filtration and flowback experiments. The model needs an empirical constant

called erosion factor to determine the return permeability ratio during flow back. The

erosion factor is defined as the ratio of fractional volume of the particles resuspended at

the onset of flowback from the total volume of the deposited particles in the porous

medium after filtration. If all the deposited particles remain deposited at the onset of

flowback then erosion factor is equal to zero. If all the deposited particles are

resuspended at the onset of flowback then erosion factor is equal to 1. Table 3.5 shows

the erosion factors used in fitting the model results with the experimental results. I have

chosen one erosion factor for one kind of fluid formulation to fit the return permeability

ratio data. Figure 3.11 shows a bar graph of return permeability ratio obtained from

UTDamage and from the experiments. The model results match quite well with the

experimental results for return permeability ratios.

Figure 3.12 shows a bar graph of API filtrate loss obtained from UTDamage and

from the experiments. The model results match quite well with the experimental results

for return permeability ratios but match the filtrate loss only qualitatively. Hence,

UTDamage needs to be improved estimating the external filter cake permeability to

match the fluid loss during filtration.

3.8 CONCLUSIONS

1. UltraCarb-12 drill-in fluid resulted in the smallest FIP, largest return permeability

ratio and smallest API filtrate volume in comparison to UltraCarb-2 and UltraCarb-20

drill-in fluids for Berea sandstone. Therefore, a median size of the bridging additive

equal to the median pore throat size of the formation is recommended rather than

97

using the 1/3rd rule (which says the median size of the bridging additive should be

equal to the 1/3rd of the median size of the pore throat of the rock).

2. Xanthan polymer is the most damaging component among all the drill-in fluid

components tested. The drill-in fluid with xanthan shows the smallest return

permeability ratio among all the formulations.

3. Starch is a relatively less damaging component. It not only invades very little into the

formation but it also seems to restrict xanthan polymer from damaging the formation.

Therefore to minimize damage, it is recommended that within acceptable rheological

parameter requirements, more starch and less xanthan should be used in drill-in and

completion fluids.

4. Drill-in fluids with no starch and no xanthan polymer result in a smaller FIP and a

larger return permeability ratio than using the whole mud. However the API filtrate

loss is 50-100 times larger than the API filtrate loss with the whole mud.

5. Addition of RevDust to the drill-in fluid results in larger FIP than the FIP from the

clean drill-in fluid. However, the return permeability is also found to be larger as

compared to the clean fluid.

6. A quantitative match is found between UTDamage and the experimental results for

return permeability ratio. However, a value for erosion factor, an empirical constant is

needed to fit the results. A qualitative match is found between UTDamage and the

experimental results for API filtrate loss. The model to estimate the external filter

cake permeability in UTDamage needs to be modified to better fit the fluid loss

results.

99

Table 3-1: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb)

Composition

Field Scale

Laboratory Scale

Brine 0.98 bbl of9.7 ppg NaCl brine

343 ml of 16.4% NaCl brine

Viscosifier (Xanthan) 1 ppb

1 gram / 350 ml

FL-7 Plus (Starch) 7 ppb

7 grams / 350 ml

pH buffer 2 ppb

2 grams / 350 ml

Sized CaCO3 with median size of particles (2, 5, 12, 20 microns)

22 ppb

22 grams / 350 ml

Table 3-2: Drill-in fluid formulation matrix

Drill-in Fluid

Formulation

Drill-in Fluid Composition

1

Only bridging additive (no xanthan and no starch)

(Brine + pH buffer + Sized CaCO3)

2

Bridging additive with starch (no xanthan)

(Brine + pH buffer + Sized CaCO3 + starch)

3

Bridging additive with xanthan (no starch)

(Brine + pH buffer + Sized CaCO3 + xanthan)

4

Bridging additive with starch and xanthan

(Brine + pH buffer + Sized CaCO3 + starch + xanthan)

100

Table 3-3: FIP, return permeability ratio and API filtrate loss for different drill-in fluid formulations on Berea sandstone (Overbalance: 100 psi)

Test No. Mud Used

Av. Brine Perm (md)

Av. oil Perm (md)

Av. Porosity

Core Sample Name

Peak pressure

(psi)

FIP (psi)

Return perm (%)

API filtrate (ml)

1 UltraCarb-2 (all components) 60 N/A 0.17 BS-4-16-03-II 11.9 8.95 N/A 6.15

2 UltraCarb-2 (all components) 247 217 0.19 BS-8-27-03-III 18.27 13.9 26 6

3 UltraCarb-2 (no starch) 60 N/A 0.20 BS-4-21-03-II 13.3 10.8 14 25.3

4 UltraCarb-2 (no xanthan) 60 N/A 0.19 BS-4-21-03-III 6.2 3.57 13.1 17.2

5 UltraCarb-2

(no starch and no xanthan) 186 129 0.20 BS-6-8-03-IV 2.1 0.3 29 321

6 UltraCarb-2

(no starch and no xanthan) 130 87 0.20 BS-6-8-03-V 2.5 0 22 304

7 UltraCarb-12 (all components) 190 134 0.19 BS-6-8-03-VI 9.52 7.33 33.9 3.62

8 UltraCarb-12 (no starch) 128 92 0.17 BS-6-8-03-IX 29 20 29 48.9

9 UltraCarb-12 (no xanthan) 252 162 0.19 BS-6-8-03-VIII 7.47 4.07 47 23.7

10 UltraCarb-12

(no starch and no xanthan) 85 70.5 0.20 BS-6-8-03-VII 12.53 6.53 70 435.7

11 UltraCarb-12 + RevDust 233 214 0.21 BS-10-2-03-I 13.47 10.2 36 3.98

12 UltraCarb-20 (all components) 247 199 0.20 BS-8-27-03-II 13.44 9.97 33.4 4.5

13 UltraCarb-20 (no starch) 535 287 0.19 BS-8-11-03-XI 7.01 4.71 41.2 25.13

14 UltraCarb-20 (no xanthan) 291 166 0.19 BS-8-11-03-XII 7.59 4.36 53.1 27.7

15 UltraCarb-20

(no starch and xanthan) 142 128 0.20 BS-8-11-03-X 9.39 5 44.8 515

16 UltraCarb-20 + RevDust 272 184 0.21 BS-10-7-03-I 15 11.5 39 4.44

17 Brine 223 188 0.19 BS-8-27-03-I 5.71 2.51 52 951

18 Brine + pH Buffer 231 176 0.19 BS-8-11-03-

XIII 4.95 2.35 72

101

Table 3-4: Comparison of FIP, return permeability ratio and API filtrate loss for drill-in fluid with and without revdust

FIP [psi]


30 minute API filtrate loss [ml]

Drill-in fluid

Without RevDust

With RevDust

Without RevDust

With RevDust

Without RevDust

With RevDust

UltraCarb-12*

7.33 10.2 33.9 36 3.62 3.98

UltraCarb-20*

9.97

11.53 33.4 39 4.5 4.44

* The number denotes the median size of the bridging agent (calcium carbonate)

Table 3-5: Erosion factors used to fit the return permeability ratio obtained from experiments with UTDamage for different drill-in fluids

Drill-in fluid formulations Erosion factor

All formulations with UltraCarb-2

0.9


0.3


0.1

102

0

2

4

6

8

10

12

14

16

18

20

0 20 40 60 80 100 120 140Time (min)

Mea

sure

d P

ress

ure

Diffe

rent

ial (

psi)

∆P peak = 18.4 psi

∆P f inal = 4.8 psi

FIP = ∆P peak - ∆P final = 13.6 psi

Flowrate = 5 ml/min


calculate flow initiation pressure (FIP)

0

5

10

15

20

25

Only UltraCarb UltraCarb +Starch

UltraCarb +Xanthan

UltraCarb +Starch +XanthanVarying Composition of Drill-in Fluid

Flow

Initi

atio

n Pr

essu

re (p

si)

UltraCarb-2 UltraCarb-12 UltraCarb-20

Figure 3-2: Flow initiation pressure (constant rate flow back) for Berea sandstone with

varying composition of the drill-in fluid

103

0

10

20

30

40

50

60

70

80

2 12 20Median Size of Bridging Additive (microns)

Ret

urn

Perm

eabi

lity

Rat

io (%

)

1 ml/min 3 ml/min 5 ml/min


bridging agents (bridging agent with no xanthan and no starch)

0

10

20

30

40

50

60


Ret

urn

Perm

eabi

lity

Rat

io (%

)



bridging agents (bridging agent with starch but no xanthan)

104

0

10

20

30

40

50

2 12 20

Median Size of Bridging Additive (microns)

Ret

urn

Perm

eabi

lity

Rat

io (%

)



bridging agents (bridging agent with xanthan but no starch)

0

10

20

30

40

50


Ret

urn

Perm

eabi

lity

Rat

io (%

)



bridging agents (bridging agent with xanthan and starch)

105

0

10

20

30

40

50

60

70


UltraCarb +Xanthan


Ret

urn

Perm

eabi

lity

Rat

io (%

)



Berea sandstone with varying drill-in fluid composition

0

10

20

30

40

50

60

70

80


UltraCarb +Xanthan


Ret

urn

Perm

eabi

lity

Rat

io (%

)




106

0

10

20

30

40

50

60

70

80


UltraCarb +Xanthan


Ret

urn

Perm

eabi

lity

Rat

io (%

)




1

10

100

1000


UltraCarb +Xanthan


API

Filt

rate

Los

s (c

u. c

ms)


Figure 3-10: Comparison of API filtrate loss for different drill-in fluid compositions on

Berea sandstone

107

0

20

40

60

80

100

Exp Model Exp Model Exp Model


Ret

urn

Perm

eabi

lity

Rat

io (%

)

Only UltraCarb UltraCarb + StarchUltraCarb + Xanthan UltraCarb + Starch + Xanthan

Figure 3-11: Comparison of return permeability ratio obtained from experiments and

from UTDAMAGE simulations

0.01

0.1

1

10

100

1000

Exp Model Exp Model Exp Model


API

Filt

rate

Los

s (c

u.cm

s)

Only UltraCarb UltraCarb + StarchUltraCarb + Xanthan UltraCarb + Starch + Xanthan

Figure 3-12: Comparison of API filtrate loss obtained from experiments and from

UTDAMAGE simulations

108

REFERENCES

1. Darley, H. C. H. and Gray, George R.: “Composition and Properties of Drilling and

Completion Fluids,” fifth edition, Gulf Publishing Company




3. Suri, A. and Sharma, M. M.: “Strategies for Sizing Particles in Drilling and

Completion Fluids,” paper SPE 87676 published in March 2004 SPE Journal

109

Chapter 4: Filter Cake Yield Strength

4.1 INTRODUCTION

This chapter reports the yield strength measurements of filter cake samples

prepared using UltraCarb drill-in fluids and bentonite muds. A constant strain rheometer

with parallel plate geometry is used to conduct both linear strain tests and dynamic strain

sweep tests. Complementary results are obtained from the two tests. The yield strength

values obtained in this chapter are used in Chapter 5 to model the cleanup of the internal

filter cake during flowback. A list of issues faced is discussed to provide guidance for the

future use of the rheometer to measure the filter cake yield strength.

4.2 LITERATURE REVIEW

The external filter cake formed should be thin, tough and highly impermeable to

seal the well bore during drilling, completion and work over operations. During

production we require the external filter cake to let the well flow freely without the need

for expensive cleanup treatments. The external filter cake either detaches from the

formation (lifts-off) or ruptures (blistering and pin holing) during production 1. Figures

4.1 and 4.2 show cartoons of external filter cake lifting-up and having pin holes and

cracks. Although the ultimate productivity is determined by the residual damage of the

near well bore region, the lift-off pressure is crucial to bringing the well on-stream; if it

exceeds the expected drawdown breakers will be required.

Very high flow initiation pressures (FIP) were observed 1 for carbonate mud with

ultra-fine particles and a mean size of 3.9 microns as compared to other carbonate muds

with larger particle sizes. The terms lift-off pressure and FIP are used interchangeably in

the literature. Bailey et al. 1 presented laboratory data on filter cake yield strength for

110

bentonite, polymer, and mixed metal hydroxide-bentonite (MMH) muds with barite and

carbonate as weighting agents. It was found that FIP is linearly dependent on filter cake

yield strength irrespective of water-based mud type or the nature and size of the

weighting agent and its concentration. A hole punch method was used for measuring the

filter cake yield strength.

Cerasi et al.2 presented a more detailed explanation of external filter cake failure.

According to them the filter cake’s initial failure is characterized by localized loss of

adhesion between the cake and the rock substrate. At low differential pressures, pinholes

appear directly above these detached areas whereas at high drawdowns, the deformed

zones grow in size and merge, leading to complete or partial cake lift-off. A parallel plate

configuration in a constant stress rheometer from Bohlin instruments was used to

measure the filter cake yield strength. They also measured the visco-elastic properties of

the filter cake such as the elastic modulus G’ (storage modulus), viscous modulus G”

(loss modulus) and phase angle. The cross over point between G’ and G” was used as a

means to calculate an approximate yield stress value. The main method used to measure

the yield strength was to apply a stress ramp and measure the shear rate. At stresses

smaller than the yield stress the shear rates will be vanishingly small indicating very high

viscosity values but on reaching the yield point (yield stress) the instantaneous viscosity

will drop by a few orders of magnitude indicating yielding of the filter cake. Oil-based

muds were found to have lower yield stress values as compared to water based muds.

Zain et al.3, 4 conducted filtration and constant rate flow back experiments to study

the behavior of filter cakes by measuring the flowback pressure profile after mud

filtration. They found similar flow back pressure profiles with and with out the external

filter cake. They concluded that the external filter cake plays no role in determining the

FIP and return permeability ratio but rather the solids and filtrate invasion into the pores

111

of the rock, which determine the flowback pressure profile during production. They

proposed a simple mathematical model for determining FIP based on Bingham fluid flow

as shown in equation 4.1.

(4.1)

p y2

p p

vdP dL 18000 d 2700 d

µ τ= +

where dp/dL is the pressure gradient, µp is the viscosity, v is the velocity, dp is the pore

diameter, and τy is the yield stress. As we can see from Equation 4.1, if there is no flow

then the pressure gradient required to initiate flow depends directly on the yield stress of

the internal filter cake and inversely on the pore diameter. The invaded polymer and

solids inside the pores of a rock forming the internal filter cake is assumed to behave as a

Bingham fluid with yield strength. The pores are assumed to be cylindrical tubes with

diameter equal to the mean pore throat diameter of the rock.

To conclude, two very different views have been presented above by authors (1-2)

and authors (3-4) to understand the mechanisms behind the flow initiation pressure (FIP).

The first view suggests that cake-rock adhesion and cake-cake adhesion control the

flowback behavior and looked at the failure of the external filter cake while the second

view suggested solids and filtrate invasion into the pores to control the flowback

behavior.

4.3 MOTIVATION

The experiments conducted by Zain and Sharma 4 clearly show that the external

filter cake does not play any role in determining the flowback pressure profile. We have

also shown the same in Chapter 2 by conducting flowback experiments with constant

pressure boundary conditions. We are convinced that it is the internal filter cake and not

the external filter cake which determines the flow initiation pressure and return

112

permeability. Therefore, to estimate the FIP and return permeability spectra,

understanding the cleanup of the internal filter cake is more important than understanding

the break down of the external filter cake. The breaking down of the external filter cake is

important from the stand point that removal of the external filter cake may lead to

plugging of screens or other flow devices in the well. In that case, pinholes or formation

of blisters in the external filter cake would be better than complete lifting up of the

external filter cake. Understanding the formation of pinholes and blistering is less

relevant to the scope of this work. However, Cerasi et al.2 have presented the mechanism

and modeling of external filter cake failure.

To determine FIP and return permeability the author assumes the invaded solids

and polymers to be represented as an internal filter cake similar to the external filter cake

but squeezed into the pores of the rock. It is assumed that the internal filter cake will

behave like a Bingham fluid with a shear yield strength. This shear yield strength can

then be related to FIP using Equation 4.1 and also to the return permeability which is

discussed in detail in Chapter 5. Hence the objective in this Chapter is to quantify the

shear yield strength of the external filter cake as an approximation for the shear yield

strength of the internal filter cake to predict the FIP and return permeability.

4.4 CONSTANT STRAIN RHEOMETER

A constant strain rheometer from TA Instruments is used to measure the yield

strength of external filter cakes produced by sized CaCO3 drill-in fluid (UltraCarb) and

bentonite muds on API filter press. As mentioned before the motivation behind making

these measurements is to find a relationship (if any), between flow initiation pressure,

return permeability and the yield strength of the external filter cake. The yield stress is

113

defined as the stress which marks the transition between the elastic region where the cake

behaves like a solid and plastic flow where the cake will behave more like a thick liquid.

4.4.1 Principle of Measurement

The constant strain rheometer can subject a sample to either dynamic (sinusoidal)

or steady (linear) shear strain (deformation), and measure the resultant torque exerted by

the sample in response to the shear strain. Shear strain is applied by a motor and torque is

measured by a transducer. Figure 4.3a shows a picture of the instrument. Figure 4.3b

shows a close up picture of the parallel plate assembly used in the experiments to

measure the yield strength of filter cakes.

In the dynamic mode (sinusoidal strain) the motor begins all tests at the motor

zero position and drives symmetrically about motor zero position to the strain

commanded by the user using RHIOS software. The motor is labeled with graduations

indicating 0.1, 0.25 and 0.5 radians from motor zero position. The maximum angular

deflection of the motor is 0.5 radians from either side of motor zero.

In the steady mode the motor can begin a test from any position, rotating either

clockwise or counter clockwise, as specified by the user, to apply linear strain to the

sample.

4.4.2 Parallel Plate Geometry

A parallel plate geometry was used to measure the yield stress of the filter cake

samples. Two different pairs of circular plates were available for the parallel plate

geometry, one with 25 mm diameter and the other with 50 mm diameter. We chose the 25

mm diameter plates so that we require smaller filter cake samples. Figure 4.3c shows a

114

schematic of the parallel plate apparatus with a description of the functionality of the

plates.

4.4.3 Theoretical Equations

The average shear stress on the top plate is given by the following equation:

(4.2)( ) ( )( ) stress k Mττ =

where M is the torque measured by the transducer connected to the top plate in g-

cm and kτ is a stress constant as given below

3

2 (4.3)

10

cGR

kτ

π=

⎛ ⎞⎜ ⎟⎝ ⎠

where Gc is the gravitational constant which is equal to 98.07 (SI units) and 980.7

in cgs units, and R is the radius of the plates in mm.

The strain applied to the sample through the bottom plate is given by the

following equation:

(4.4)( ) ( )( ) strain kγγ θ=

where θ is the angle of the bottom plate with respect to its initial position in

radians and kγ is a strain constant as given below

(4.5) R

Hkγ =

115

where R is the radius of the plates and Η is the gap between the plates.

The visco-elastic parameters G’ and G” are given by the following equations. G’

is called the elastic (storage) modulus while G” is called the viscous (loss) modulus.

cos ( ) (4.6) G τδγ

′ =

sin ( ) (4.7) G τδγ

′′ =

where δ is the phase angle (phase shift between stress and strain vectors).

4.4.4 Sample Preparation

API filter cells were used to prepare the filter cake samples. An overbalance of

100 psi was applied for a filtration time equal to 16 hours. 3 1/2" (9 cm) diameter, and 2.7

micron pore size filter papers (OFITE brand, part number: 140-55) were used to prepare

the external filter cakes. UltraCarb drill-in fluid and bentonite muds were used as the

filtration fluids with composition given in Table 2.2 of chapter 2.

4.5 RESULTS AND DISCUSSION

The following subsections provide and discusses the results obtained using the

dynamic strain sweep test and the linear strain test to measure the filter cake yield

strength.

116

4.5.1 Dynamic Strain Sweep Test

In the dynamic strain sweep test the sample was strained sinusoidally with

increasing amplitude (strain) at a constant frequency. The sample was kept between the

two parallel and circular plates. The top plate was used to apply a normal force and to

create a static boundary condition at the top of the sample. The bottom plate was used to

apply the strain to the sample by rotating back and forth sinusoidally at a specified

frequency. The minimum strain and maximum strain were specified in the RHIOS

software as the lower and upper limit for the strain. It was assumed that there was no

slippage between the top and bottom surface of the filter cake samples and the plates.

Figure 4.4 shows a plot of visco-elastic parameters (elastic modulus and viscous

modulus) for a dynamic strain test on a filter cake sample prepared from UltraCarb-2

drill-in fluid at a frequency of 0.1 rad/sec. The plot shows a higher elastic modulus than

viscous modulus at early strain values indicating the filter cake behave predominantly

elastically at small strains. After increasing the strain amplitude to a certain value the

elastic modulus falls sharply and becomes smaller than the viscous modulus. This clearly

shows a transition of filter cake behavior from elastic to plastic at well-defined yield

strength. It is assumed that the filter cake predominantly behaves as an elastoplastic

material with a well defined yield point at the transition point between the elastic and

plastic regimes. At sufficiently small strain it behaves predominantly elastically, and after

the yield point the filter cake behaves predominantly as a plastic material. Figure 4.5

shows a plot of stress vs. strain for the same experiment with the maximum stress

denoting the yield stress of the filter cake. The yield stress for the filter cake sample was

found to be equal to 418 Pascals as shown in Figure 4.5.

Figures 4.6 - 4.9 show results for two dynamic strain sweep tests done on filter

cake samples prepared using UltraCarb-12 (Median particle size: 12 microns) drill-in

117

fluid. The yield stress values were found to be equal to 353 Pascals and 248 Pascals in the

two tests. The yield stress values for UltraCarb-12 filter cakes are lower than, the yield

stress values for UltraCarb-2 filter cakes.

Figure 4.10 and 4.11 show results for a dynamic strain sweep test done on filter

cake samples prepared using UltraCarb-20 (median particle size: 20 microns) drill-in

fluid. The yield stress was found to be equal to 268 Pascals as seen in Figure 4.11. The

yield stress value for UltraCarb-20 is lower than the yield stress value of UltraCarb-12

samples. The yield stress varied as follows: UltraCarb-2 > UltraCarb-12 > UltraCarb-20.

The filter cake samples with smallest median particle size had the largest yield stress.

4.5.2 Linear Strain Test

In the linear strain test the sample was sheared linearly with time (either

clockwise or counter clockwise). The parallel plate geometry used in this test had plates

with diameter equal to 25 mm. A normal force approximately equal 100 gram force was

applied on the filter cake samples through the top plate.

Figure 4.12 shows a plot of measured stress vs. applied linear strain on a filter

cake sample prepared from UltraCarb-2 drill-in fluid. The gap between the two plates

was 1.31 mm. The applied linear strain with time is given by the following equation:

-41 * 10 t where 0 t 1000 (4.8)γ = ≤ ≤

where unit of strain is % and time is in seconds. A linear rise in stress can be seen in the

plot with applied linear strain indicating elastic behavior of the sample up to the yield

point. Considering the sample to be elastic and obeying Hook’s law of elasticity in this

region the maxima is taken to be equal to the yield or tensile strength of the filter cake.

The yield stress for the UltraCarb-2 drill-in fluid filter cake sample was found to equal to

118

439 Pascals. This value is comparable to the yield stress value of 418 Pascals measured

using the dynamic strain sweep test.

Figure 4.13 and 4.14 show results of two linear strain tests performed on

UltraCarb-12 drill-in fluid filter cake samples. The yield stress values were found to be

equal to 243 Pascals and 194 Pascals in the two tests. Figure 4.15 and 4.16 show results

of two linear strain tests performed on UltraCarb-20 drill-in fluid filter cake samples. The

yield stress values were found to be equal to 236 Pascals and 288.5 Pascals in the two

tests. Figure 4.17 - 4.19 show results of three linear strain tests performed on bentonite

mud filter cake samples. The yield stress values were found to be equal to 738 Pascals,

835 Pascals and 807 Pascals. The bentonite mud filter cake samples were much thicker

than the UltraCarb-2, 12, 20 drill-in fluid filter cake samples. The gap between the

parallel plates varied between 6.4 and 6.6 mm for the bentonite filter cake tests. The plot

shows a maxima or a turning point at 738 Pascals. The terms yield strength and yield

stress are used synonymously here. Figure 4.20 shows the effect of higher applied normal

force (500 grams) on bentonite filter cake samples. The yield stress is found to be equal

to 944 Pascals which is larger than the yield stress values with 100 grams of applied

normal force.

Figure 4.21 shows average yield strength of different filter cake samples prepared

from bentonite mud and the UltraCarb drill-in fluids. It can be seen that the filter cakes

made from bentonite muds have much higher yield strength than filter cakes made from

UltraCarb drill-in fluids. The figure also compares the yield strength values obtained

from the dynamic strain sweep test and the linear strain test. It can be seen that the two

different measurement techniques (dynamic strain sweep test and linear strain test) yield

approximately the same values. Hence the two tests can be used as complimentary tests.

Table 4.1 presents the yield strength values of the filter cakes from different muds.

119

4.6 EXPERIMENTAL ISSUES AND CONCERNS

The following experimental issues were encountered in conducting the tests:

1) Did the shear occur inside the filter cake, i.e. at the cake/cake interface or did it occur

at the cake/metal interface (slipping of the filter cake)?

The shear at the cake/metal interface means slipping between the filter cake and

the metal plates. This condition is unwanted as the objective is to measure the shear yield

stress of the filter cake which requires shearing to occur at the cake/cake interface. To our

advantage, the filter cake samples were found to adhere well to the metal plates. However

the bottom plate which was used to apply strain to the filter cake samples was doubted for

some slippage between the filter cake and the plate. To minimize slipping between the

filter cake sample and the bottom metal plate, multiple tests were conducted by varying

the normal force applied on top of the filter cake samples. A normal force of 100 grams

was found to minimize the slipping between the filter cake samples and the metal plates

without damaging the sample. A particle depleted zone between the filter cake samples

and the plates is postulated especially for the filter cake samples prepared using

UltraCarb drill-in fluids. This is because the UltraCarb fluid filter cakes can bend which

might lead to no contact zones at some places between the filter cakes samples and the

metal plates. Therefore, the actual shear strength of the filter cake samples obtained from

UltraCarb drill-in fluid could be slightly larger than the measured yield strength.

To further check for slipping between the filter cake and the metal plates, tests

were conducted on filter cake samples with and without the filter paper attached to the

samples. Similar results for the yield stress measurements were found for samples with

and without the filter paper attached to the filter cake. Tests were also conducted using

different filter papers and again similar results were obtained for the filter cake samples

120

with different filter papers. Therefore it was concluded that the filter cake samples were

mostly sheared in the bulk i.e. at the cake/cake interface and may have slipped minimally

at some places because of a particle depleted zone between the filter cake and the metal

plates.

2) Removal of filter cake sample from the filter paper. Is it necessary?

Tests were performed with and without filter paper and similar results were

obtained. Hence filter cake samples were not removed from the filter paper to avoid any

damage to the filter cake samples. It is recommended that the filter paper may not be

removed for measuring the yield strength of the filter cake samples using the rheometer.

3) Drying of the filter cake sample.

Tests were designed so as to finish in the minimum time to minimize the effect of

drying on the filter cake samples. A trial-and-error method was used for this.

a. Dynamic strain sweep test: An optimum frequency for the dynamic sweep was

found to avoid drying of the sample (which needed higher frequency) and to

avoid slipping between the sample and the plates (which needed lower

frequency). Initial tests were done at a frequency of 10 radians/sec but consistent

results were not found because of slipping. Finally a frequency of 0.1 radians/sec

was found to give consistent results for all the samples. The maximum time was

about 30 minutes for the sample to yield with minimum effect of drying and to

avoid any slipping.

b. Linear strain test: Similarly for the linear strain test, a maximum time of about 30

minutes was chosen initially to minimize the effect of drying. With trial-and-

error, the time was reduced to about 5 minutes for the samples to yield.

121

4) Yield stress measurements are sensitive to the applied normal force.

A trial-and-error method was used to find the optimum normal force that needs to

be applied to the filter cake samples to satisfy the following two conditions. First, there

should be complete contact between the sample’s top surface and the top plate. Secondly,

the sample should not be extruded with the application of the normal force.

5) Filter cake preparation requires that the excess mud left from the filtration test on top

of the filter cake be removed.

The excess mud from the top of each cake sample was carefully removed by

dabbing the cake samples with a paper towel. The excess mud was soaked repeatedly into

fresh paper towels until no more liquid is visible on top of the sample.

4.7 CONCLUSIONS

1. The yield strength of different filter cake samples obtained from bentonite muds and

UltraCarb drill-in fluids are successfully measured using a constant strain rheometer.

2. Two different methods (dynamic strain sweep test and linear strain test) are found to

compliment the yield strength measurements. The linear strain test is recommended

over the dynamic strain sweep test to measure the filter cake yield strength. This is

because the time required to finish the linear strain test is found less than the dynamic

strain sweep test which minimizes the drying of the filter cake sample. If other visco-

elastic properties are required to be measured then the dynamic strain sweep test is

recommended.

3. The yield strength of bentonite mud filter cakes is found to be larger than the yield

strength of the filter cake samples prepared using UltraCarb drill-in fluid.

122

4. Filter cake samples prepared from calcium carbonate drill-in fluid with the smallest

median particle size (2 microns) resulted in larger yield strength values as compared

to CaCO3 drill-in fluids with larger median particle size. This is consistent with the

experimental results obtained in Chapter 2 for the return permeabilities using drill-in

fluids with two different sizes. The drill-in fluid with a median size of two microns

resulted in smaller return permeabilities than the drill-in fluid with a median size of

20 microns. This supports the hypothesis that the cleanup of the internal filter cake

depends strongly on the yield strength of the filter cake.

5. The yield strength measurement values obtained can be used to estimate the FIP and

the return permeability spectra for different drill-in and completion fluids. Drill-in

and completion fluids with small yield strength values are recommended because a

large yield strength value suggests a large pressure gradient needed to cleanup the

internal filter cake.

123

Table 4.1: Comparison of yield stress measurements done using dynamic strain sweep test and linear strain test for different filter cake samples

Yield Stress (Pascals) Mud used to form the

filter cake sample Dynamic strain

sweep test

Linear strain

test

Bentonite mud 800*

UltraCarb-2 418 439*

UltraCarb-12 300* 225*

UltraCarb-20 268 263*

* Mean values calculated using two repeated experiments

Figure 4.1: Lifting up of the external filter cake during flowback. The internal filter cake

(roots holding the external filter cake) has cleaned up at point A

Figure 4.2: Lifting up and formation of pin-holes and cracks in the external filter cake

during flowback

Rock Flow-back

External filter cake with pin holes and cracks

Rock Flow-back

Lifted external filter cake

124

Figure 4.3a: Photograph of ARES constant strain rheometer

Figure 4.3b: Close up photograph of ARES constant strain rheometer with a parallel plate

(25 mm) apparatus

125

Figure 4.3c: Schematic of parallel plate apparatus in ARES constant strain rheometer

10

100

1000

10000

0.1 1 10 100 1000Strain (%)

(Pas

cals

)

G' (Elastic modulus) G" (Viscous Modulus)

Frequency = 0.1 rad/s

Figure 4.4: Plot of visco-elastic parameters using dynamic strain sweep test in a constant

strain rheometer for UltraCarb-2 drill-in fluid filter cake

Filter cake (sample)

Top plate is kept stationary and the torque is measured by the transducer

Bottom plate is rotated to apply a strain to the sample

Normal force is applied

126

10

100

1000

1 10 100 1000Strain (%)

Stre

ss (P

a)

Frequency = 0.1 rad/sYield stress = 418 Pascals

Figure 4.5: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-2 drill-in

fluid filter cake

10

100

1000

10000

0.1 1 10 100 1000Strain (%)

(Pas

cals

)

G' Pa G" Pa

Frequency = 0.1 rad/sStress at cross-over = 374 Pa



127

10

100

1000

1 10 100 1000Strain (%)

Stre

ss (P

a)

Frequency = 0.1 rad/sYield stress = 353 PascalsStrain at yield point = 6.34 %


fluid filter cake

10

100

1000

10000

0.1 1 10 100 1000Strain (%)

(Pas

cals

)

G' Pa G" Pa

Frequency = 0.1 rad/sStress at cross over point = 232 Pa



128

10

100

1000

1 10 100 1000Strain (%)

Stre

ss (P

a)

Frequency = 0.1 rad/sYield stress = 248 PascalsStrain at yield point = 20 %


fluid filter cake

10

100

1000

10000

0.1 1 10 100Strain (%)

(Pas

cals

)

G' Pa G" Pa

Frequency = 0.1 rad/sCross over stress = 262 Pa



129

10

100

1000

1 10 100Strain (%)

Stre

ss (P

a)

Frequency = 0.1 rad/sYield stress = 268 PaStrain at yield point = 20 %


in fluid filter cake

0

100

200

300

400

500

0 20 40 60 80 100 120Strain (%)

Stre

ss (P

asca

ls)

Yield stress: 439 PascalsStrain at yield point: 30%Normal force = 100 gramsGap = 1.31 mm

Figure 4.12: Plot of stress vs. strain in a linear strain test using constant strain rheometer

for UltraCarb-2 drill-in fluid filter cake

130

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120Strain (%)

Stre

ss (P

asca

ls)

Yield stress: 243 PascalsStrain at yield point: 12.85%Normal force = 100 gramsGap = 1.096 mm



0

50

100

150

200

250

0 50 100 150Strain (%)

Stre

ss (P

asca

ls)




131

0

50

100

150

200

250

0 50 100 150 200Strain (%)

Stre

ss (P

asca

ls)




0

50

100

150

200

250

300

350

0 50 100 150 200Strain (%)

Stre

ss (P

asca

ls)

Yield stress: 288.5 PascalsStrain at yield point: 34.2%Normal force = 100 gramsGap = 1.22 mm



132

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10 12Strain (%)

Stre

ss (P

asca

ls)

Yield Strength = 738 PascalsStrain at yield point = 3.6%Normal force = 100 gmsGap = 6.551 mm


for bentonite mud filter cake

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12Strain (%)

Stre

ss (P

asca

ls)

Yield Strength = 835 PascalsStrain at yield point = 2.4 %Normal force = 100 gmsGap = 6.466 mm



133

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6

Strain (%)

Stre

ss (P

asca

ls)

Yield Strength = 807 PaStrain at yield point = 3%Normal force = 100 gmsGap = 6.414 mm



0

100

200

300

400

500

600

700

800

900

1000

0 2 4 6 8 10 12 14Strain (%)

Stre

ss (P

asca

ls)

Yield Strength = 944 PascalsStrain at break point = 2.8%Normal force = 500 gmsGap = 3.685 mm

Figure 4.20: Plot of stress vs. strain at a normal force equal to 500 gms in a linear strain

test for bentonite mud filter cake

134

0

200

400

600

800

1000

Bentonite UltraCarb-2 UltraCarb-12 UltraCarb-20

Yiel

d St

reng

th (P

asca

ls)

Dynamic Strain Sweep Test Linear Strain Test

Error = 20%For all the bars

Figure 4.21: Yield strength of different muds using dynamic strain sweep test and linear

strain test

135

REFERENCES



held in Lafayette, 18-19 February, 1998

2. Cerasi, P., et al.: “Measurement of the Mechanical Properties of Filtercakes,” paper

SPE 68948 presented at the 2001 SPE European Formation Damage Conference held

in The Hague, The Netherlands, 21-22 May, 2001






5. Lakes S. R.: “Viscoelastic solids,” published by CRC press.

136

Chapter 5: Modeling the Cleanup of Internal Filter Cake during Flowback

5.1 INTRODUCTION

A literature review of the existing models for flowback (with a focus on cleanup

of the formation damage) is presented. The motivation behind developing a new model

for the cleanup of the internal filter cake is discussed. A bundle of tubes model is

presented to calculate the FIP and the return permeabilities during flowback. Results

from the bundle of tubes model are presented along with a parametric study. The model

results are compared with the experimental results presented in Chapter 2. The

motivation behind developing a network model is presented. A parametric study for the

network model is also presented. The network model results are compared with the

experimental results.

5.2 BACKGROUND AND LITERATURE REVIEW

When a well is put back on production, there is usually an external filter cake on

the wellbore face and an internal filter cake (invaded solids and polymer) in the rock

matrix. These filter cakes are formed because of the excess pressure in the wellbore

during drilling and completion operations. To produce hydrocarbons from the formation

into the well, the pressure in the wellbore is reduced to below the formation pressure.

How do these filter cakes cleanup? What is the return permeability as a function of

applied drawdown (pressure difference between the well and the reservoir). Chapter 2

presented experimental data on return permeabilities as a function of differential

pressures across different permeability rocks during flowback. In this chapter we model

the return permeability spectra as a function of differential pressure for different

137

permeability cores during flowback. Below is a brief review of the literature on the

modeling of the cleanup of formation damage during production.

Ding et al.1 presented a numerical model to simulate a) fluid invasion and

permeability damage during filtration and b) natural cleanup of damage during flowback

when the well is put on production. Their objective was to predict well performance of

horizontal wells as a function of pressure drawdown. They conducted laboratory tests to

obtain data for external filter cake permeability, damaged permeability during invasion

and final return permeability during flowback. For two-phase flow, their model also

requires the reservoir oil/fluid filtrate relative permeability curves for both the drilling

mud filtrate phase and flowback production phase. They used the model to investigate the

influence of different parameters such as relative permeability curves, external filter cake

permeability, flow initiation pressure, depth of internal filter cake, overbalance pressure,

and drilling fluid circulation rate. They found the end point relative permeability for oil

during drainage to be the most influential parameter on horizontal well performance.

However, the model did not include the cleanup of the internal filter cake which we

believe is a crucial factor in determining the return permeability as a function of applied

drawdown during production.

Suri and Sharma 2 presented a model to predict the permeability reduction in the

near wellbore region during mud filtration and the improvement in permeability during

production. Figure 5.1 shows a schematic of their conceptual model. Their model

accounted for both the internal filtration and the external filtration of particles. Internal

filtration led to deposition of particles on the surface of the grains, while external

filtration led to the development of an external filter cake consisting of filtered particles

of different sizes. For flowback, they defined a parameter, the “erosion factor”, for

simulating resuspension of deposited particles from the rock grains. The “erosion factor”

138

was defined as the ratio of the volume of particles resuspended during flowback to the

total volume of particles deposited during mud filtration. If all the particles are eroded

from the surface of the grains and are resuspended in the fluid then the erosion factor is

equal to one. An erosion factor equal to zero means that all the particles remain deposited

on the grain surface during flowback and that there will be no improvement in the

permeability during flowback. However, they did not present any method to predict or

estimate the erosion factor for a given mud, formation, and flowback conditions.

Zain and Sharma 3 proposed a simplified model for cleanup of the internal filter

cake. This model can be used to estimate the flow initiation pressure. However, they did

not extend the model to predict the return permeability spectra.

Rana and Sharma 4 also presented a flowback model based entirely on relative

permeability effects and did not consider cleanup of the internal filter cake. Their model

considers flowback at constant rate and can be used to predict the FIP at constant rate.

No model is found which focuses on the cleanup of the damage (internal filter

cake) as a function of applied drawdown during flowback. Below is a simple model

presented which considers the cleanup of the internal filter cake and computes the return

permeability as a function of the applied drawdown.

5.3 MODEL DEVELOPMENT

The invasion of solids and polymers into the porous medium can be thought of as

occurring in two zones: 1) an internal filter cake which consists of solids, polymers and

filtrate from the mud as a homogenous pore-filling paste, 2) loose particles (solids and

polymers) and fluid filtrate that penetrates deeper into the formation but does not fill up

the entire pore space. Figure 5.2 shows a schematic of this conceptual model representing

the external filter cake, internal filter cake, and loose solids and polymers ahead of the

139

internal filter cake. The depth of the internal filter cake is usually a few millimeters while

the fine particles and mud filtrate penetrate much deeper into the formation. We focus on

the removal of the pore-filling internal filter cake since it offers a much larger flow

resistance than the dispersed fines that penetrate deeper into the formation.

We assume the internal filter cake to behave like a Bingham fluid with a finite

yield stress. The cleanup of the internal filter cake is controlled by the removal of this

Bingham fluid out of the pores during flowback. We consider the following two models

to represent the porous medium: 1) a bundle of tubes model, and 2) 3-D network of pore

throats model. The pore size distribution of the porous medium is represented by the pore

size distribution data obtained from mercury penetrometer data for three different rock

samples: 1) Texas Limestone, 2) Berea sandstone, and 3) Boise sandstone.

5.3.1 Bundle of Tubes Model

In the bundle of tubes model the porous medium is represented by cylindrical

tubes with varying diameter. In this simple model of the porous medium the tubes are

parallel to each other and are connected only at the two ends (inlet and outlet). Figure 5.3

shows a schematic of the bundle of tubes representation of the porous medium with the

external filter cake and the internal filter cake. The following assumptions are made in

representing the structure of the internal filter cake: 1) the internal filter cake is a

homogeneous paste, 2) the rhelogical properties of the internal filter cake are the same or

proportional to the properties of the external filter cake so that the yield strength of the

internal filter cake is taken to be approximately equal to the yield strength of the external

filter cake, and 2) the depth of the internal filter cake is the same for tubes of all sizes.

The flow rate (q) of a Newtonian fluid in a tube of radius r is given by Hagen

Poisuellie’s law as followed:

140

4

8r Pq

Lπ

µ∆

= (1)

where r is the radius of the tube, µ is the viscosity of the fluid, L is the length of

the tube and ∆P is the pressure gradient across the tube. The flow rate for a bundle of

tubes with a continuous distribution of diameter from 0 to infinity can be given by the

following equation:

4

0( )

8r Pq f r dr

Lπ

µ∞ ∆

= ∫ (2)

where f (r) is the number/frequency distribution of the radius of the tubes. Note

that the boundary condition is that the pressure difference across the bundle of tubes is a

constant.

For a real porous medium (rock matrix), the flow rate is given by Darcy’s law as

followed:

kA Pq

Lµ∆

= (3)

Comparing Eq. 2 and Eq. 3, we obtain the permeability for the bundle of tubes

model:

4

0( )

8rk f r drA

π∞= ∫ (4)

141

where f (r) is the number frequency distribution of the radius of the tubes, k is the

permeability of the porous medium, and A is the area of the porous medium, which is

given by the following equation:

2

0( )A r f r drπ

φ∞

= ∫ (5)

We assume that before a differential pressure is applied across the core during

flowback, all the tubes are filled with the internal filter cake up to a fixed distance d and

beyond that the tubes are filled with a Newtonian fluid (brine/oil). The internal filter cake

in a tube of radius r, is assumed to flow (internal filter cake is assumed to behave like a

Bingham fluid) if the pressure difference across the tube is more than a minimum

pressure gradient. The minimum pressure gradient for a tube of radius r filled with a

Bingham fluid is given by the following equation:

2

f

dPrτ

∆ = (6)

where τ is the yield strength of the Bingham fluid, d is the thickness of the

internal filter cake, and rf is the radius of the tube. The Bingham fluid will flow in the

tubes whose radius is larger than rf and will not flow in tubes whose radius is smaller than

rf. There will be a transient period during which the Bingham fluid will be flowing out

through the tubes till the tube is completely cleaned up of the internal filter cake. Finally,

the flow will reach a steady state when the flowing Bingham fluid is pushed completely

out of the porous medium in tubes with radius larger than rf. At steady state the flowback

fluid, which is assumed as a Newtonian fluid will be flowing through tubes with radius

larger than rf and the tubes with radius smaller than rf will not allow any flow through

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them. The return permeability for the bundle of tubes, at a fixed applied pressure gradient

is, therefore, given by the following equation:

4

4

0

( )( )

( )return

frr f r dr

k Pr f r dr

∞

∞∆ =∫

∫ (7)

where 2f

LrP

τ=

∆ (8)

Eq. 7 is the ratio of the total flow rate through tubes with radius rf to R (the tubes

which have cleaned up) to the total possible flow rate if all the tubes were cleaned up.

The flow initiation pressure for the bundle of tubes model is given by the pressure

gradient which results in initiating flow in the pore with the largest radius. The flow

initiation pressure (FIP) can be calculated using the following equation:

2 dFIPRτ

= (9)

where R is the radius of the largest pore in a media. Figure 5.4 shows the FIP as a

function of the largest pore throat diameter for different thickness of the internal filter

cake. The FIP increases with increasing thickness of the internal filter cake and decreases

with the increasing largest pore diameter of a rock. The yield strength of the internal filter

cake was taken equal to 400 Pascals (for UltraCarb-2 drill-in fluid) as presented in

Chapter 4.

We used the mercury penetrometer to obtain the pore size distribution of the

different rock samples. The mercury penetrometer gives the volume size distribution of

the pores for a given rock sample rather than its number size distribution of the pores. To

convert the volume size distribution to number distribution data, we need a relation

143

between the volume and the number of the pores. We assume that the relation between

the volume and the number of pores for the actual rock samples to be the same as for a

bundle of tubes. For a bundle of tubes, the volume of a tube is proportional to the square

of its radius, and is independent of the length of the tubes (because all the tubes are of

constant length). Equation (7) is modified to include the volume size distribution in the

equation as followed:

2

2

0

( )( )

( )return

frr V r dr

k Pr V r dr

∞

∞∆ =∫

∫ (10)

where V(r) is the volume distribution of the rock sample. We can see in the above

equation that the return permeability is a function of pressure drop across the bundle of

tubes. Figures 5.5, 5.6, and 5.7 show plots of volume distribution for Texas limestone,

Berea sandstone and Boise sandstone obtained from mercury injection data. Figure 5.8

shows the above three plots together for a comparison. The Texas limestone has a median

volume pore size of 0.71 microns, the Berea sandstone has a median volume pore size of

13.5 microns, and the Boise sandstone has a median volume pore size of 17.6 microns.

5.3.2 Discussion on Bundle of Tubes Model Results

The three factors which determine the return permeability in a bundle of tubes

model are: 1) the thickness of the internal filter cake, 2) the filter cake yield strength, and

3) the pore size distribution of the rock.

5.3.2.1 Effect of Depth of Internal Filter Cake

Figure 5.9 shows the calculated return permeability with varying pressure drop for

a bundle of tubes representation of Berea sandstone. The three return permeability curves

144

shown in the figure are for three different assumed thicknesses of the internal filter cake.

Larger internal filter cake thickness results in smaller return permeabilities at a fixed

pressure drop across the bundle of tubes. The yield strength of the internal filter cake is

assumed to be equal to 400 pascals (approximate yield strength of UltraCarb drill-in

fluids as presented in Chapter 4).

5.3.2.2 Effect of Filter Cake Yield Strength

Figure 5.10 shows return permeability vs. pressure drop across a bundle of tubes

model for Berea sandstone with varying yield strength of the internal filter cake. Larger

filter cake yield strength results in smaller return permeabilities at a fixed pressure drop.

The thickness of the internal filter cake is equal to 2 mm (approximate depth of damage

calculated using UTDamage) for all the three plots.

5.3.2.3 Effect of Pore Size Distribution

Figure 5.11 shows return permeability vs. pressure drop across a bundle of tubes

model for three different rock samples with varying pore size distribution. The three rock

samples chosen were Texas limestone, Berea sandstone, and Boise sandstone for which

we have measured the pore size distribution. We can see that for a pore size distribution

with a larger median, larger return permeabilities are obtained at a fixed pressure drop.

The filter cake yield strength is taken equal to 400 pascals and the thickness of the

internal filter cake is taken equal to 2 mm in calculating the return permeability spectra

using the bundle of tubes model. The pore size distribution for Texas limestone shows the

minimum cleanup and requires very higher pressure drops for complete cleanup.

145

5.3.3 Comparison of Bundle of Tubes Model Results with Experimental Results

Bailey et al. presented that the most of the damage due to invasion of particulate

from drilling fluids is approximately 15 mm deep in from the surface of the rock. The

amount of particulate invasion decreases exponentially with distance in the rock. The

volume of solids deposited / trapped is very high within the first few mms and is reduced

to very small values at large depths into the core.

UTDamage calculates the depth of invasion of solids and polymers in cores

during filtration. We used UTDamage to estimate the thickness of the internal filter cake

for different rocks with different drill-in fluids. Table 5.1 shows range of the depth of

solids and polymer invasion in rocks with different permeability (calculated using

UTDamage). This range of invasion of solids and polymer invasion was taken as an

estimate of the range of thickness of the internal filter cake.

The yield strength of the internal filter cake is taken to be approximately 400

pascals which was estimated using a constant strain rheometer for filter cake samples

prepared from UltraCarb drill-in fluids (presented in Chapter 4).

After obtaining an estimate for the three parameters needed in the bundle of tubes

model (thickness of the internal filter cake, yield strength of the internal filter cake, and

the pore size distribution of the rock), we computed the return permeability ratio for the

different rock samples to compare with the experimental results. Figures 5.12, 5.13 and

5.14 show return permeability obtained from the bundle of tubes model and from the

flowback experiments conducted on Texas limestone, Berea sandstone and Boise

sandstone cores. The comparison between the model results and the experimental results

show a good match for Berea sandstone and Texas limestone cores but not for Boise

sandstone cores. The large permanent damage in Boise sandstone (small return

permeability ratio) was quite different from the model prediction. The bundle of tubes

146

model predict 100 % return permeability ratio at large differential pressures. However

the experimental results do not show complete clean up (i.e. 100% return permeability) at

large pressures. It should be noted that the return permeability calculated is an average

return permeability for the entire one inch core. But actually the return permeability

would vary with distance in the core. The return permeability would be very small in the

first few millimeters and would increase with increasing distance into the core. However,

the return permeability for a bundle of tubes is independent of the length of the tubes.

In conducting the experiments, the pressures are recorded at the two ends of the

short core (1 inch in length) and at intervals of 2 inches in using the long cores (6 inch in

length). We do not have the return permeability data with varying distance in the core. I

believe that to compare the return permeability ratio calculated from the bundle of tubes

model with the return permeability ratio obtained from the experiments, we should

consider the return permeability of the front end of the core (which would have the

internal filter cake) and not the average return permeability of the whole core.

To estimate the return permeability of the first few millimeters of the core, we

hypothesized two zones in the core. Figure 5.15 shows a schematic of a core with two

zones: 1) a zone with the internal filter cake (damaged zone), and 2) an undamaged zone.

In reality there will be some damage in the undamaged zone as well (due to solids,

polymers and filtrate). But most of the damage would be due to the internal filter cake

(which is plugging the entire pore space of the rock) as compared to the solids and

polymers penetrating deep into the formation and plugging only some part of the pore

space. Therefore, we assume that there is no damage in the undamaged zone and that the

permeability of the undamaged zone is equal to the initial permeability of the rock. The

pressure drop across the damaged zone can be calculated by subtracting the pressure drop

147

across the undamaged zone from the pressure drop across the whole core during

flowback and can be written as:

D FB U DP P P∆ = ∆ − ∆ (11)

where ∆PFB is the differential pressure across the core during flowback. ∆PUD is

the pressure drop across the undamaged zone, which can be calculated using the

following equation:

96.456 ( )U D FB

UD

L dP qk A

µ −∆ = (12)

where qFB is the measured flow rate in cc/min at a specific applied differential

pressure ∆PFB (in psi) during flowback, KUD is the initial undamaged permeability of the

core in md, µ is the viscosity of the flowback fluid in cp, L is the length of the core in

inches, and d is the thickness of the damaged zone in inches. We assume that the

thickness of the damaged zone is the same as the thickness of the internal filter cake. The

return permeability of the damaged zone (with the internal filter cake) can be calculated

using the following equation:

96.456/ (%) *100D FBD

dk k qA P

µ=

∆ (13)

Figure 5.16 shows the return permeability ratio of the damaged zone with varying

depths of damage (thickness of the internal filter cake). We can see that the return

permeability ratio of the damaged zone is much smaller than the average return

permeability of the whole core. Hence the two zone model suggests even smaller return

permeability ratios for the damaged zone (across the internal filter cake) as compared to

148

the return permeability of the entire core during flowback. This suggests even lesser clean

up of the cores closer to the rock face during flowback.

We now present a three dimensional network model to represent the porous

medium. This model is more generic than the bundle of tubes model.

5.3.4 Three Dimensional Network Model with Effective Medium Approximation

The network model used to represent the porous medium consists of a regular

array of variable sized pore throats and pore bodies interconnected to each other as shown

in Figure 5.17. The figure shows the pore bodies and pore throats with uniform size for

ease of presentation. However the pore throats sizes in the network model are considered

to be distributed according to a certain pore size distribution. The flow is considered in

the pore throats with a varied size distribution. Koplik3 applied the effective medium

theory (E.M.T.) to flow in porous media and showed that the E.M.T. provides an

excellent approximation to flow in two-dimensional (2-D) networks. Rossen et al.4

applied the E.M.T. to predict the single and two-phase flow of Bingham fluids in natural

fractures. They found the minimum pressure gradient for flow of Bingham fluid in a

fracture with an aperture distribution to depend primarily on the widest portion of the

aperture distribution. Fractures with narrow aperture distribution are easily plugged by

Bingham fluids as compared to fractures with broad aperture distribution.

The basic idea of E.M.T. in its application to flow in porous medium is to replace

the random microscopic flow conductances (which depends on a pore throat chosen

randomly from a distribution) with a certain mean flow conductance value so that the

mean field produced by the random flow conductances is the same as that produced when

all parameters have this mean value. By integrating local fluctuations and equating them

to zero, Kirkpatrick showed that sufficiently away from the percolation threshold, the

149

effective medium flow conductance (average flow conductance) of a network symbolized

as gm can be obtained by solving the following equation:

0( ) 0

( 1)2

m

m

g g G g dgZg g

∞ −=

+ −∫ (14)

where the network of pore throats is represented by randomly distributed

cylindrical tubes with varying radius but a constant length. G (g) dg is the probability of a

pore throat having a flow conductance between g and g + dg which is equal to f (r) dr ,

the probability of a pore throat having a radius between r and r + dr, i.e. ( ) = ( )G g dg f r dr (the fundamental transformation law of probabilities).

All the pore throats are completely filled by the Bingham fluid, which is used to

represent the internal filter cake before flowback. We consider modeling cleanup of the

internal filter cake in single-phase flow experiments, where brine is the displacing fluid

while the Bingham fluid (internal filter cake) is the displaced fluid.

A pore throat in the network can only allow flow if the pressure difference across

it is more than the pressure difference given by the following equation:

2

f

LPrτ

∆ = (15)

where τ is the yield stress of the Bingham fluid in the pore throat, L is the length

of the pore throat and ∆P is the pressure difference across the pore throat. The fraction of

pores with radius >= rf can allow flow while the other pore throats with radius < rf can

not allow flow. The fraction of pore throats which can allow flow is denoted by Xf, which

can be calculated by the following equation:

150

( )f

frX f r dr

∞

= ∫ (16)

However, in the network model, the above fraction of pore throats, Xf which can

allow flow are not completely accessible by the displacing fluid as opposed to the bundle

of tubes model. The fraction of pore throats which are accessible from this allowed

fraction of pores is given by the accessibility function for a network:

, ( )ad f fX X X= (17)

where Xa (Xf) is the accessibility function and Xd,f is the fraction of accessible

pore throats which can flow. The accessibility function gives the fraction of pore throats

which are accessible from the total number of pore throats which can allow flow. Figure

5.18 shows a schematic of the fluid (internal filter cake and brine) distribution in the

pores with a size distribution during flowback. To compute the accessibility function for

a three dimensional pore throat network, Monte Carlo simulations on computer generated

samples would be needed. This would be a very tedious and involved task, which we

wish to omit. Moreover, the accessibility function calculated would depend on the

computer generated sample networks and would change each time the sample network is

changed. The reason behind using E.M.T. was to avoid performing computer simulations

but to use a quick and easy semi-analytical model for flow of a Bingham fluid in a

network to model internal cake cleanup. To simplify the problem, we are going to use the

accessibility function for a Bethe tree for the accessibility function of a network with

same percolation thresholds. It has been shown by Heiba et al. 5 that Bethe trees with

same percolation thresholds as of a network gives very similar accessibility functions. A

Bethe tree is an endlessly branching structure similar to the branches of a tree that lack

151

reconnections. The accessibility function for a Bethe tree with local coordination Z is

given by the following equation5:

( )a fX X = (18)

where X* is the root of the following equation:

( 2) ( 2)*(1 *) (1 ) 0b b

f fZ ZX X X X− −− − − = (19)

The above eq. (18) vanishes as Xf approaches 0 or 1. The bond percolation

threshold for the Bethe tree is given by:

1

( 1)cb

XZ

=−

(20)

The local coordination number for a Bethe tree (ZB) and the average coordination

number of the three-dimensional network (Z) are related as followed:

11.5bZZ = + (21)

Heiba et al.5 have shown that aside from the shift in the bond percolation

threshold Xc, the accessibility function Xa (X) and the normalized conductivity K (X) / K

(1) of three dimensional networks and Bethe trees are qualitatively similar. They

illustrated the above similarity by comparing Xa (X) and K (X) / K (1) for a Bethe tree of

(2 2)( 2)*1 , f f c

f

bb

ZZXX X X

X

−−⎡ ⎤

− ≥⎢ ⎥⎢ ⎥⎣ ⎦

0 , f cX X<

152

local coordination number (Zb = 5) and the six-coordinated three dimensional simple

cubic network (Z = 6). The percolation threshold (Xc) for the Bethe tree with (Zb = 5) is

equal to 0.25, while Xc for the simple cubic network (Z = 6) was taken close to 0.25 for

the comparison. Their results showed a very good match for the accessibility function Xa

(X) and the normalized conductivity K (X) / K (1) between the cubic network and the

Bethe tree. Figure 5.19 shows a plot between accessibility fraction of pore throats and the

allowable fraction of pore throats. The allowable fraction of pore throats was calculated

using eq. (16) and the corresponding accessibility fraction of pore throats was calculated

using eqs. (18-21). The figure shows that the accessibility fraction of pore throats is zero

until the allowable fraction of pore throats reaches a certain threshold (minimum fraction

of allowable fraction of pore throats).

The flow conductance (g) of a pore throat is defined as follows:

q g P= ∆ (22)

where ∆P is the pressure difference across the pore throat, q is the flow rate of the

phase whose flow conductance is to be evaluated and g is the flow conductance for the

pore throat. Relating eq. (1) and eq. (12), we calculate the flow conductance for the pore

throat, which is given as followed:

4

4

8rg Cr

lπ

µ= = (23)

In the above eq. (13), r is the radius of the pore throat, l is the length of the pore

throat, µ is the viscosity of the phase whose flow conductance is to be evaluated, and C is

a constant. The pore throats in the network are assumed to have a size distribution f (r)

153

with random connectivity. We are considering brine as one phase and the Bingham fluid

(internal filter cake) as the second phase. Brine is displacing the Bingham fluid from the

pore throats.

The flow conductivity distribution function for the displacing phase (brine) during

flow back is given by the following equation:

d, f , ,G (g) ( ) (1 ) ( )d f d f fX G g X gδ= + − (24) The first term , , ( )d f d fX G g denotes the conductance distribution of the displacing

fluid through the pore throats which allow flow and are accessible. The second term (1 ) ( )fX gδ− denotes the conductance distribution of the displacing fluid through the

pore throats which don’t allow flow. All the inaccessible pore throats will be filled with

the Bingham fluid, while all the accessible pores will be filled with brine. ( )gδ is the

Dirac delta function, whose value is equal to 1 when g is equal to 0 and is equal to 0

when g is not equal to 0. The probability of allowed conditional flow conductance of the

displacing phase (brine) used in eq. (24) can be written as following:

, , ( )d f d fdrG f rdg

= (25)

, ( )d ff r = (26)

,1 ( )d f

f

drG f rX dg

= (27)

1 ( ) ff

f r r rX

≥

0 fr r<

154

d, f ,1G (g) ( ) (1 ) ( )d f f

f

drX f r X gX dg

δ= + − (28)

Substituting eq. (28) into eq. (14), we get the following equation:

,0

1 ( ) (1 ) ( ) 0( 1)2

md f f

fm

g g drX f r X g dgz X dgg gδ

∞ ⎡ ⎤−+ − =⎢ ⎥

⎢ ⎥⎣ ⎦+ −∫ (29)

,

0

( ) (1 ) ( ) 0( 1)2

d fmf

fm

Xg g f r dr X g dgz Xg gδ

∞ ⎡ ⎤−+ − =⎢ ⎥

⎢ ⎥⎣ ⎦+ −∫ (30)

, ,0

( ) (1 ) ( ) 0( 1) ( 1)2 2

f

fm m

d f d f fr

m m

rg g g gX f r dr X g dgz zg g g g

δ∞ − −

+ − =+ − + −

∫ ∫ (31)

,0

( ) (1 ) ( ) 0( 1) ( 1)2 2

f

fm m

d f ffr

m m

rg g g gf rX dr X g dgz zXg g g g

δ∞ − −

+ − =+ − + −

∫ ∫ (32)

( )g r = (33)

Substituting g from eq. (33) into eq. (32), we get the following:

, (1 )

( ) 0( 1) ( 1)2 2

f

d f fm

f rm

X Xg g f r drz zX g g

∞ −−− =

+ − −∫ (34)

4 fCr r r≥

0 fr r<

155

The flow of Bingham fluid starts when the network reaches its percolation

threshold, i.e. the accessible fraction of pore throats which can allow flow and are

connected will become greater than zero. The displacement of the Bingham fluid

(internal filter cake) by the displacing fluid (brine) would continue until the pore throats

containing the Bingham fluid allow flow and are connected. This would mean cleaning

up of the damage (internal filter cake) and gain in return permeability of the network. At

some point, the pore throats containing the Bingham fluid will become isolated and hence

inaccessible to the flow paths. The inaccessible fraction of pore throats containing the

Bingham fluid will also be given by a threshold fraction as followed:

,n f cX X= (35)

where X c is the percolation threshold of the network given by eq. (19) and Xn,f is

the inaccessible fraction of pore throats containing the Bingham fluid.

Discretizing eq. (33) to include the measured discrete pore radii distribution of

different rocks obtained from mercury penetrometer and to fit the experimental data, we

obtain the following equation:

4

,1

4

(1 )( )( ) 0

( 1) ( 1)2 2

Nd f fi m

i i ii nff

i m

X XCr g f r r rz zX Cr g+

=

−−− − =

+ − −∑ (36)

If we take the coordination number (z) for the network equal to 6, then the above

equation is reduced to:

4

,14

(1 )( )( ) 0

2 2

Nd f fi m

i i ii nff i m

X XCr g f r r rX Cr g +

=

−−− − =

+∑ (37)

where fX is also discretized and is given by the following equation:

156

1( )( )N

f i i ii nf

X f r r r+=

= −∑ (38)

where i = nf gives the pore throat radius equal to rf in the pore throat radii

distribution as given by the following equation:

( ) ( ) [1, ]if r f r where i N= = (39)

The return permeability ratio of the network is the ratio of the conductivity of the

displacing fluid to the total conductivity, when all the pores are conductive and is given

by the following equation:

/ /o m mofbk k g g= (40)

where mog is obtained from the following equation:

4

140

( )( ) 02

Ni mo

i i ii i mo

Cr g f r r rCr g +

=

−− =

+∑ (41)

It is interesting to note that this model is equivalent to flow of water in an oil wet

rock, where water is the conductive phase (representing brine) and oil is the non-

conductive phase (representing the Bingham fluid/internal filter cake).

5.3.5 Results and Discussion on Network Model

Equations (36-41) are solved in Excel using Solver to calculate the return

permeability for a network (representing the porous medium) filled with a Bingham fluid

157

(representing the internal filter cake) as a function of pressure gradient across the

network. A uniform pressure gradient is assumed in the network which means that there

is an equal amount of pressure difference across all the pore throats (as the pore throats

are considered to be of equal length). Figure 5.20 shows the probability distribution

function for the number of pores with varying radius for Berea sandstone. This number

distribution was used to represent the number distribution of the pore throats in the

network model to model the flowback of brine.

Figure 5.21 shows a plot of return permeability ratio calculated with varying

pressure difference across the pore throats (without taking the accessibility function into

account) for networks with different coordination numbers. At large pressure difference

across the pore throats, we find complete cleanup of the Bingham fluid from the network

(100% return permeability ratio). Next we use the accessible fraction instead of the

allowable fraction in calculating the return permeability ratio of the network (using Eq.

17). Figure 5.22 shows return permeability ratio for a network with varying pressure

difference across the pore throats (using accessibility function) for different coordination

numbers. The above figure shows the return permeability ratios to reach an asymptotic

value at large pressure differences across the pore throats. However, both the figures

show return permeabilities to be small for small coordination numbers at equal pressure

difference across the pore throats. Figure 5.23 shows that at very large coordination

numbers the return permeability curve obtained from the network model approach the

return permeability curve obtained from the bundle of tubes model. This is consistent

with the fact that the bundle of tubes model is a network with a coordination number

approaching infinity.

Figure 5.24 shows a plot of return permeability ratio for a network with increasing

pressure difference in pore throats with different lengths. A network with shorter pore

158

throats results in larger return permeabilities as compared to a network with longer pore

throats for the same pressure difference across the pore throats. This trend is consistent

with the fact that pore throats with a larger length need a larger pressure difference to

push a Bingham fluid through it as given by Eq. (15).

Figure 5.25 shows plots of return permeability ratios obtained from experiments

conducted on Berea sandstone and return permeability ratios obtained from the network

model. The model shows a good qualitative match with the experiments, but predicts

much larger FIP and much faster cleanup as compared to the experimental results. The

network model return permeability curve is much narrower than the experimental return

permeability curve which is much broader. However it should be noted that the pressure

difference across the pore throats in the network model is assumed to be equal to the

applied differential pressure across the cores during flowback in obtaining the match

between the model and the experiments.

The network model predicts FIP values in the range of 1 to 20 psi for networks

with pore throats with length equal to 100 microns. The corresponding pressure gradients

for these FIP values would be in the range of 250 – 5000 psi/inch. These pressure

gradients are very large as compared to the steady state pressure gradients in typical

vertical or horizontal wells as shown in Figure 2.26 of Chapter 2. There are two reasons

for this difference. One reason is the poor estimate of E.M.T. for flow in networks near

the percolation threshold and the second reason is that the pressure gradients calculated

for vertical or horizontal wells in Chapter 2 assume uniform permeability around the

wellbore. However, we know that the permeability near the wellbore is very small

(because of the damage) and increases with increasing radius away from the wellbore.

Therefore, we use the two zone model presented earlier in Section 5.2.3, to estimate the

pressure gradients across the internal filter cake with varying thickness. The single-phase

159

return permeability ratio data for Nugget sandstone (NS-2) is taken and the two zone

model is applied to calculate the pressure gradients across the internal filter cake. Figure

5.26 shows a plot of pressure gradients across the damaged zone (internal filter cake)

with varying thickness. It can be clearly seen that the pressure gradients across the

internal filter cake increases with decreasing thickness. The pressure gradients across the

internal filter cake with thickness equal to 100 microns are larger than 1000 psi/inch as

shown in Figure 5.26. These pressure gradients are comparable to the pressure gradients

estimated by the network model across pore throats to initiate flow. However the return

permeability ratios for the damaged zone calculated using the two zone model are very

small as seen in Figure 5.27. If the thickness of the internal filter cake (damaged zone) is

equal to 100 microns then the return permeability ratio of the damaged zone is only about

1% even at a pressure gradient of 7000 psi/inch. This suggests that there is very little

cleanup of the internal filter cake during flowback. To validate these small return

permeabilities, differential pressures need to be recorded for the first few millimeters

while conducting the flowback experiments.

5.4 SLOW CLEANUP OF THE INTERNAL FILTER CAKE

Both the single-phase and two-phase experiments show that the flow rates did not

stabilize instantly when the flowback pressures were incremented but took very long time

to stabilize. Two-phase experiments showed even larger time scale of cleanup than the

single-phase experiments. This is because two-phase experiments had relative

permeability effects along with the cleaning of the pores whereas in single-phase

experiments only the cleaning of the pores was taking place.

For most of the experiments, about 1000 pore volumes of the fluid were flowed

across the thin layer of the core with the internal filter cake during flowback for the flow

160

rates to reach a steady state. We wish to look at the reasons as to why there was slow

cleanup of the internal filter cake in both the single-phase and two-phase experiments to

explain the large amount of pore volumes needed during flowback for the rates to

stabilize. Below is the explanation for the slow cleanup of the internal filter cake.

The volume flow rate of a Bingham fluid which is used to model the cleanup of

the internal filter cake can be calculated using the following equation:

i0 when i oq τ τ= < (42)

4

4i

i i

4 1(1 ( ) ( ) ) when 8 3 3

i o oi o

rq Pl

π τ τ τ τµ τ τ

= − + ∆ > (43)

where qi is the volume flow rate of the Bingham fluid (representing the internal filter

cake), ri is the radius of the capillary tube (representing the pores), ∆P is the differential

pressure across the capillary (representing the flowback differential pressure), and τi is

the shear stress at the wall of the capillary given by:

i 2

i iPrl

τ ∆= (44)

If the shear stress at the wall of a pore is less than the yield strength of the

Bingham fluid then there is no flow as shown in Eq. (42). If the shear stress at the wall of

the pore is larger than the yield strength of the Bingham fluid then the flow is given by

Eq. (43).

The flow rate of a Newtonian fluid (representing the flowback fluid) is given by

the following equation:

161

4

8i

i newtonian

r PqL

πµ

∆= (45)

The ratio of the volume flow rate of a Newtonian fluid (i.e. the flowback fluid) to

the flow rate of a Bingham fluid (i.e. the internal filter cake) for a given pressure drop

across pores with radius ri is calculated using Eq. (43) and Eq. (45) and is given by:

i4

i i

1 when 4 1(1 ( ) ( ) )3 3

i newtoniano

o oi bingham

qq

τ ττ ττ τ

= >− +

(46)

Figure 5.28 shows a plot of the ratio of the flow rate of a Newtonian fluid to the

flow rate of a Bingham fluid as a function of τo/τi (ratio of the yield stress at the wall of a

capillary tube to the yield strength of the Bingham fluid). The figure clearly shows that

for τo/τi values close to 1 (i.e. when the shear stress at the wall is barely equal to the

yield strength of the Bingham fluid), qnewtonian/qbingham is very large (i.e. the flow of

Bingham fluid is very small compared to the flow rate of the Newtonian fluid). This large

difference in the flow rates between the two fluids explains the slow cleaning up of the

internal filter cake (Bingham fluid) as compared to the measured rates for the flowback

fluid (Newtonian fluid).

5.5 CONCLUSIONS

1 The return permeability spectra obtained from the bundle of tubes model compares

qualitatively with the return permeability spectra obtained from the experiments

conducted on inch long Berea sandstone and Texas limestone cores. However, the

bundle of tubes model predicts complete cleanup (100% return permeability) at large

162

differential pressures whereas the experimental results does not show complete

cleanup even at large differential pressures during flowback.

2 A network model is also found to match qualitatively with the experimental results.

The network model can capture the asymptotic values for the return permeabilities

observed in the flowback experiments. The network model indicates the requirement

of very large pressure gradients to cleanup the internal filter cake. Therefore, the

permeability across the first few millimeters in a core during flowback is needed to

further validate the network model.

163

Table 5-1: Depth of invasion of solids and polymers calculated from UTDamage for different rocks used in conducting the experiments

Core type Drill-in fluid Depth of internal filter

cake (mm)

Nugget sandstone (4 md) UltraCarb-2 0.1 - 0.5

Texas limestone (25 md) UltraCarb-2 0.5 - 2.5

Berea sandstone (200 md) UltraCarb-2 1 - 5

Boise sandstone (1000 md) UltraCarb-20 1 - 10

Aloxide (1500 md) UltraCarb-20 1 - 15

164

∆h = Thickness of an external cake layer, k = Permeability of an external cake layer dg = Average grain diameter of an external cake layer


representing internal and external filter cake

∆h1, k1,dg1

∆h2, k2,dg2

Depth of damage

Formation grains

Mud particles and polymers

165

Figure 5.2: Schematic of filter cake (internal and external) as a Bingham fluid

Formation grains

Internal filter cake


Loose particles

Formation grains

Internal filter cake


Loose particles

166

Figure 5.3: Schematic of filter cake conceived as a Bingham fluid in a porous medium

represented by a bundle of tubes model

External Filter Cake

Internal Filter Cake

167

0

1

2

3

4

5

6

7

8

9

10

30 40 50 60 70 80 90 100Largest Pore Throat Diameter (µm)

FIP

(psi

)d = 0.2 mm d = 0.5 mm d = 1 mm

Yield strength of the internal filter cake = 400 Pascals

Figure 5.4: Flow initiation pressure (FIP) as a function of the largest pore throat diameter

of the pores with varying thickness of the internal filter cake

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.001 0.01 0.1 1 10 100 1000Pore Diameter (µm)

Pore

Vol

ume

(ml/g

)

Figure 5.5: Pore volume distribution obtained from mercury penetrometer for Texas

limestone

FIP (Experiments) = 1 – 8 psi FIP (Model) = 0.5 – 8 psi

168

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.001 0.01 0.1 1 10 100 1000Pore Diameter (µm)

Pore

Vol

ume

(ml/g

)

Figure 5.6: Pore volume distribution obtained from mercury penetrometer for Berea

sandstone

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.01 0.1 1 10 100 1000Pore Diameter (µm)

Pore

Vol

ume

(ml/g

)

Figure 5.7: Pore volume distribution obtained from mercury penetrometer for Boise

sandstone

169

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.01 0.1 1 10 100 1000

Pore Diameter (µm)

Nor

mal

ized

Por

e Vo

lum

eBerea sandstone Median = 13.5 µm

Boise sandstone Median = 17.6 µmTexas Limestone

Median = 0.7 µm

Figure 5.8: Plot comparing the pore volume distribution for different rocks obtained from

mercury penetrometer

0

20

40

60

80

100

120

0 20 40 60 80 100∆P (psi)

k/ko

(%)

Thickness of the internal filter cake (d) = 1 mmd = 2.5 mmd = 5 mm

Cake's yield strength = 400 Pascals


with varying thickness of the internal filter cake

170

0

20

40

60

80

100

120

0 50 100 150 200∆P (psi)

k/ko

(%)

Filter cake's yield strength = 100 PaFilter cake's yield strength = 500 PaFilter cake's yield strength = 1000 Pa

Thickness of the internal filter cake = 2 mm


with varying cake yield strength

0

20

40

60

80

100

120

0 50 100 150 200∆P (psi)

k/ko

(%)

Berea sandstone Texas limestone Boise sandstone

Cake's yield strength = 400 PascalsDepth of internal filter cake = 2mm

Figure 5.11: Return permeability spectra for different rocks obtained from the bundle of

tubes model

171

0

20

40

60

80

100

120

0 20 40 60 80 100∆P (psi)

k/ko

(%)

Thickness of the internal filter cake (d) = 0.5 mmd = 1 mmd = 2.5 mmExperimental Results

Cake's yield strength = 400 Pascals


model and experimental results for single phase flow in Texas limestone

0

20

40

60

80

100

120

0 20 40 60 80 100∆P (psi)

k/ko

(%)

Thickness of the internal filter cake (d) = 1 mmd = 2.5 mmd = 5 mmExperimental Results

Filter cake's yield strength = 400 Pascals


model and experimental results for single phase flow in Berea sandstone

172

0

20

40

60

80

100

120

0 50 100 150 200∆P (psi)

k/ko

(%)

Thickness of the internal filter cake (d) = 1 mmd = 5 mmd = 10 mmExperimental Results

Filter cake's yield strength = 400 Pascals


model and experimental results for single phase flow in Boise sandstone

Figure 5.15: Schematic of a core before flowback for calculating differential pressure

across the internal filter cake (damaged zone)

Internal filter cake (Damaged zone)

Undamaged zone

Core length – d

Core length

d

d = thickness of the internal filter cake

∆Pdamage

∆Pundamaged

173

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120


Retu

rn P

erm

eabi

lity

Rat

io (%

)Across the whole core (1 inch)Across first 0.5 mm of the core (d)d = 2.5 mmd = 5 mm

Figure 5.16: Return permeability in the damaged zone with different depths for Nugget

sandstone (NS-2)

174

Figure 5.17: Schematic of a porous medium represented by a two-dimensional network of

pore throats plugged with internal filter cake. Please note that in the actual network model the pore throats are of varied sizes.

Inte

rnal

filte

r ca

ke


175

Figure 5.18: A schematic of the distribution of the internal filter cake (as a Bingham fluid) and the flowback fluid (brine) in the pores during flowback

r f

f ( r )

Small pores occupied by the Bingham fluid (internal filter cake) (1-X d, f)

Large pores drained by the displacing fluid (Brine) (X d, f)

r

Inaccessible pores containing Bingham fluid (X f – X d, f)

X f = Allowable fraction of pore-segments for the displacing fluid

X d, f = Accessible fraction of pore-segments from the allowable fraction for the displacing fluid

176

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1Xf (Allowable Fraction of Pore Throats)

XA

(Acc

essi

ble

Frac

tion

of P

ore

Thro

ats)

Figure 5.19: Accessible fraction of pore throats for a Bethe tree with Z = 5 to represent

the accessibility fraction of a three dimensional network with Z = 6

0

0.5

1

1.5

2

2.5

3

3.5

0.1 1 10 100 1000

Pore Throat Diameter (µm)

Pro

babi

lity

func

tion

f(d)

Figure 5.20: Probability function for pore throat radius for Berea sandstone calculated

from volume size distribution obtained from mercury penetrometer

177

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200∆P Across Pore Throat (psi)

k/ko

z=4 z=6 z=8 z=12

Filter cake yield strength = 400 PaPore throat length = 100 microns

Figure 5.21: Return permeability for a network model with varying coordination number

(without accessibility function)

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100∆P Across Pore Throat (psi)

k/ko

z=4 z=6 z=8 z=12


Figure 5.22: Return permeability for a network model with varying coordination number

(with accessibility function)

178

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60∆P Across Pore Throat (psi)

k/ko


Bundle of tubes model

Network model (z = 12)Network model (z = 6)

Network model (z = 50)

Figure 5.23: Comparison of bundle of tubes model with the network model (the network

model approaches the bundle of tubes model when z approaches infinity)

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100∆P Across Pore Throat (psi)

k/ko

Filter cake yield strength = 400 PaZ (Coordination number) = 6

Pore throat length (L) = 10 microns

L = 50 microns

L = 100 microns

Figure 5.24: Return permeability for a network model with varying pore throat length

179

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80∆P (psi)

Ret

urn

Perm

eabi

lity

Rat

io (%

)

Berea short core (dia. = 2.5 inch, length = 1 inch)

Berea long core (dia. = 2 inch, length = 6 inch)

Berea long core with K and ∆P calculated only at the first two inches of the core

Network model (z=6, Pore throat length = 50 microns, τ = 400 Pa)

Figure 5.25: Return permeability obtained from experiments conducted on Berea

sandstone and from the network model

1

10

100

1000

10000

0 20 40 60 80 100 120


Pres

sure

Gra

dien

t Acr

oss

the

Inte

rnal

Fi

lter C

ake

(psi

/inch

)

Across the whole core (1 inch)Thickness of the internal filter cake (d) = 5 mmd = 1 mmd = 0.1 mm (100 microns)

Figure 5.26: Pressure gradients across the internal filter cake with different thickness

(calculated from NS-2 return permeability data and the two zone model)

180

1

10

100

1000

10000

0.01 0.1 1 10 100

Return Permeability Ratio (%)

Pres

sure

Gra

dien

t Acr

oss

the

Inte

rnal

Fi

lter C

ake

(psi

/inch

)

Across the whole core (1 inch)Thickness of the internal filter cake (d) = 5 mmd = 1 mmd = 0.1 mm (100 microns)

Figure 5.27: Pressure gradients vs. return permeability ratio of the damaged zone

(calculated for NS-2 using the two zone model)

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1 1.1 1.2 1.3 1.4τi/τo

q new

toni

an/q

bing

ham

Figure 5.28: Ratio of the flow rate of the flowback fluid (Newtonian) to the flow rate of

the internal filter cake (Bingham fluid)

181

REFERENCES

1. Ding, Y., et al.: “Modeling of Both Near-Wellbore Damage and Natural Cleanup of

Horizontal Wells Drilled With Water-Based Drilling Fluids,” paper SPE 88807

revised for publication from paper 73733, presented at the SPE Formation Damage

Control Symposium held in Lafayette, Louisiana, 20-21 Feb., 2002



Damage Conference held in The Hague, The Netherlands, 21–22 May 2000






May, 2001

5. Koplik, J.: “Creeping Flow in Two-Dimensional Networks,” Journal of Fluid

Mechanics, v.119, p.219 (1982)

6. Rossen, W. R., and Kumar, Arun T. A.: “Single- and Two-phase Flow in Natural

Fractures,” paper SPE 24915 presented at the 67th Annual Technical Conference and

Exhibition of the Society of Petroleum Engineers, Washington, DC, Oct. 4-7, 1992

7. Heiba, A. A., et al.: “Percolation Theory of Two-phase Relative Permeability,” paper

SPE 11015 presented at the 57th Annual Technical Conference and Exhibition of the

Society of Petroleum Engineers of AIME, held in New Orleans, Lafayette, September

26-29, 1982

182

8. Wang, Y.: “A Three-Dimensional Network Model for Porous Media,” M.S. Thesis,

The University of Texas at Austin, August 1988

183

Chapter 6: Cleanup of Lab-Simulated Perforation Tunnels during Flowback

6.1 INTRODUCTION

This chapter presents a study on the cleanup of lab-simulated perforation tunnels

during flowback. A background and a literature review on the fluids used in perforated

completions are presented first. The motivation for the experimental study and the

objectives of the study are presented thereafter. Both single-phase and two-phase flow

experiments are designed using lab-simulated perforated completions with different

dimensions (length and diameter of the perforation) to understand the cleanup during

flowback in these completions. The results for the FIP and return permeabilities in both

single-phase and two-phase experiments are presented and discussed. The effect of

different parameters on the FIP and return permeability ratio is also presented and

discussed. The results of the experiments are applied for field use and rule of thumbs are

provided for cleanup in perforated completions.

6.2 BACKGROUND AND LITERATURE REVIEW Fluids used during and after perforating a well are usually referred to as kill-pills.

Kill-pills can be water-based or oil-based. A typical water-based kill-pill consists of a

brine that meets density requirements, a xanthan polymer for viscosity control, a starch

polymer for fluid loss control and sized calcium carbonate for bridging at the pore

throats. The water-based kill-pill can have the same ingredients as a water-based drill-in

fluid mentioned in Chapter 2 except of drill-solids. A typical oil-based kill-pill consists of

a base oil, an emulsifier package, brine as an internal phase, barite or sized calcium

184

carbonate to meet density and bridging requirements, and lime and organophilic clay for

alkalinity and viscosity, respectively. In addition fluid loss control additives are also

added in oil-based muds.

Jiang et al.1 conducted formation damage tests using both water-based and oil-

based kill-pills on Clashach sandstone with drilled tunnels (1 cm in diameter and ~3.3 cm

in depth) simulating perforations. The results from all the tests which used oil-based kill-

pills showed return permeability ratios from 52% to 80%. However the return

permeability ratios were greatly reduced to about 10% when zinc debris (to simulate

perforating gun debris) was incorporated into the oil-based kill-pills. Water-based kill-pill

results for return permeability ratio were not affected by the addition of the zinc debris.

All the tests which used water-based kill-pills showed return permeability ratios from

69% to 91%. However, they recommended using low solids oil-based kill-pills with

charges that produce zinc debris. The water-based muds have chemical reactions that

significantly increase the fluid loss due to gas evolution from the mixture with zinc debris

although these interactions have little effect on return permeability.

Chang et al.2 (2003) conducted experiments which simulated the field conditions

when perforating in overbalance in a well. They investigated oil-based muds, low solids

oil-based muds, and water-based kill-pills formulated from formates and bromide brines

to evaluate damage caused by these fluids during overbalanced perforation operations.

Their conclusions were:

1. Oil-based kill fluids are capable of controlling leak-off effectively when perforating

overbalance. The perforation and the adjacent formation is also easily cleaned up

185

when using these oil-based fluids. The filtrate leaking into the formation does not

cause relative permeability reduction.

2. Oil-based kill fluids perform better in preventing productivity impairment than water-

based fluids in oil wells (even when the fluid losses are equal).

3. The productivity impairment from water-based kill-pills is a function of leak off. The

more fluid loss to the formation, the lower the perforation permeability. Therefore,

being able to control fluid loss when using a water-based fluid is a key factor in

minimizing formation damage.

4. There are two major mechanisms of damage to perforations by water-based kill-pills.

The first is the relative permeability damage induced by the brine filtrate, the second

is the tough and elastic filter cake built inside the perforation tunnel. The toughness of

the filter cake is enhanced by increasing polymer, polymer residue, and solids

concentration in the cake when leak-off increases – high leak-off results in the

formation of a thick filter cake.

Chang et al.3 (2005) conducted experiments simulating field conditions to

recommend field practice for overbalanced perforating. They considered the three most

common field practices for perforating in overbalance and investigated the effect of

perforation pressure dynamics on fluid loss, different kill-pills (oil-based mud, low solid

oil-based mud, and water-based kill-pills) and finally provided design guidelines for

production optimization. They concluded that building an effective filter cake is the key

to controlling fluid loss which is the main factor in determining productivity in perforated

completions. They used a constant rate flowback condition rather than constant pressure

186

flowback condition to estimate the flow initiation pressure (FIP) and to measure the

return permeability during flowback.

6.3 PROBLEM DESCRIPTION

All the tests in the literature simulating perforated completions have used a

constant rate flowback condition to estimate FIP. As mentioned in Chapter 2, a constant

pressure flowback condition will better approximate the FIP. In addition, there is no

study in the literature, which shows how return permeability improves with drawdown

for perforated completions. Return permeability spectra, as obtained here, can be used as

a guide for determining if artificial cleanup methods for a given formation, mud system

and field conditions are needed or not.

6.4 OBJECTIVES

The objectives of the experiments conducted on lab-simulated perforated cores

are as follows:

1. Measure FIP and return permeability spectra for lab-simulated perforated cores with

different permeability using a constant pressure flowback condition.

2. Study the effect of single-phase flow vs. two-phase flow in lab-simulated perforated

completion.

3. Study the effect of different parameters such as: perforation dimensions, completion

fluid type (sized CaCO3 fluid vs. bentonite mud), and overbalance on FIP and the

return permeability.

187

6.5 TEST DESIGN

6.5.1 Lab-simulated Perforated Core and Core Holder

To simulate perforations, holes were drilled through the cores before conducting

the experiments. The cores were epoxied on the top to create a no flow boundary before

drilling the hole. Figure 6.1 shows a schematic of a lab-simulated single perforation. The

perforation diameters were varied from 1/8 inch to 3/8 inch, while the lengths were

varied from ½ inch to 2 inches to represent different perforation dimensions.

Two different sized core holders were used to accommodate two different core

sizes. The short core holder accommodates a 2.5 inches diameter, 1.0 inch core long core

plug, and approximately 110 ml of fluid inside the filter cell. The long core holder can

accommodate a core plug 2.0 inch in diameter, and up to 12 inch in length. The main

purpose behind setting up a long core apparatus was to be conduct filtration experiments

on cores having long, lab-simulated, perforations. It also enabled us to study the depth of

damage caused by solids and polymers (internal filter cake) and filtrate invasion by

recording pressure readings at 2 inch intervals along the length of the core. Figure 6.2

shows a schematic of the long core apparatus. In the short core holder the cores are

epoxied on the sides to restrict any flow between the core and the sides of the cell. The

long core holder uses confining pressure on a rubber sleeve around the core to restrict

flow between the core and the sides of the sleeve.

6.5.2 Rock Type and Fluid Type

Three different rock types were used in the study with a permeability range of 25

md to 1000 md. The three rock types used are: 1) Texas limestone (25 md), 2) Berea

sandstone (200 md), and 3) Boise sandstone (1000 md).

188

Two types of fluids were used for the filtration experiments. Table 2.3 in Chapter

2 shows the fluid components and their concentration used in formulating the UltraCarb

drill-in fluid. Table 2.4 in Chapter 2 shows the fluid rheology for the UltraCarb fluid.

Table 2.5 in Chapter 2 shows the fluid components for the bentonite mud and Table 2.6

in Chapter 2 shows its rheology.

Fluids used for the flowback were: 1) 3% brine solution for single-phase flow

experiments, 2) a non-corrosive and non-reactive oil distillate (Exxsol D110) for two-

phase flow experiments.


The test procedure used for conducting the experiments is outlined in detail in

Chapter 2 Section 2.4.3. We used a constant pressure condition during flowback.

The return permeability ratio at different applied flowback differential pressures

was calculated using the following equation:

Return Permeability Ratio ideal

flowback

PP∆

=∆

(6.1)

where ∆Pideal is the pressure drop across the lab-simulated perforated core before

mud filtration and ∆Pflowback is the pressure drop across the lab-simulated perforated core

after mud filtration at a given rate. Plotting return permeability ratio for different

differential pressures across the core during flowback yields a return permeability spectra

curve.

189

The lab-simulated perforated cores were visually examined before and after

flowback to observe the filter cake condition. Photographs of the filter cake along with

the core were taken before and after the flowback.


Single-phase and two-phase filtration experiments on three different types of

cores with permeability ranging from 25 md to 1000 md and two different types of fluids

were conducted on the lab-simulated perforated cores. We measured, reported, and

analyzed the following parameters:


2. Return permeability ratio vs. flowback differential pressure

3. Filtrate loss during mud filtration

6.6.1 Single-phase Experiments

The motivation behind conducting single-phase experiments was to obtain results

that would help us understand the cleanup of perforations better. In this set of

experiments the flowback problem is simplified by having to understand the effect of

only the external and internal filter cake on FIP and return permeability as there are no

capillary pressure and relative permeability effects due to two-phase flow.

Table E.1 in Appendix-E shows a list of all the single phase constant pressure

flowback experiments conducted on lab-simulated perforated completions. Subsequently

three plots are shown for each of the experiments conducted: 1) applied differential

pressure and measured flow rates vs. time during flowback, 2) calculated return

permeability ratio vs. applied differential pressure during flowback, and 3) measured

190

filtrate loss vs. square root of time. A brief discussion is also presented for some of the

experiments after the plots.


Table 6.1 shows a summary of the flow initiation pressures (FIP) for single-phase

constant pressure flowback experiments simulating perforated completions. Three

different types of cores with permeability ranging from 25 md to 1000 md (Texas

limestone (25 md), Berea sandstone (200 md), and Boise sandstone (1000 md)) were

used with UltraCarb drill-in fluid. An overbalance pressure of 100 psi and static filtration

time equal to 16 hrs was used for all the experiments. For Texas limestone and Berea

sandstone the median size of bridging agent in the UltraCarb completion fluid was equal

to 2 microns while for Boise sandstone the median size of bridging agent was equal to 20

microns. The bridging additive particle size was changed from a median size of 2

microns to 20 microns to minimize the invasion of solids and polymers into the cores

with large permeability.

Figure 6.3 shows a photograph of a short (2.5 inch diameter and 1 inch length)

Texas limestone core with a 1/4 inch diameter and ½ inch long lab-simulated perforation

in the middle after mud filtration with UltraCarb-2 completion fluid. It can be seen that

the hole is completely plugged with the external filter cake. Figure 6.4 shows a

photograph of the same core after flowing back with brine. We can see that the external

filter cake is lifted-off partially but still remains in the perforation tunnel after flowback.

Figure 6.5 shows a photograph of a long (2 inch diameter and 6 inch long) Berea

core with a 1/8 inch diameter and 1 inch long, lab-simulated perforation after flowback

with brine. The lab-simulated perforation was plugged by the external filter cake after

mud filtration with UltraCarb-2 completion fluid. However, after flowing back with brine

191

the external filter cake was entirely removed from the hole as seen in Figure 6.5. A

similar observation was made for a long Berea core with a lab-simulated perforation

diameter equal to 1/8 inch and length equal to 2 inches. Figure 6.6 shows a photograph

where the external filter cake is broken into pieces. Figures 6.7 and 6.8 show photographs

of long Berea cores with lab-simulated perforations with diameter equal to ¼ inch and

lengths equal to 1 inch and 2 inch respectively. It can be seen in the figures that the

external filter cake plugs came out from the hole after flowback in both the cores.

However for a long Berea core with a lab-simulated perforation with diameter equal to

3/8 inch, the external filter cake remained in the hole as seen in Figure 6.9.

The maximum FIP for all the single-phase flow experiments on lab-simulated

perforated cores was 14 psi. The FIP was found to be significantly different for lab-

simulated perforations with diameter 1/8 inch as compared to perforations with diameter

larger than 1/8 inch. It was found that for small diameter perforations (up to 1/8 inch) the

FIP values were large. For perforation sizes larger than 1/8 inch, the FIP values were

quite small and ranged between 1 psi and 4 psi. The small FIP values were comparable to

the FIP values for the open-hole case with no perforations. The cake formed in small

diameter perforations completely plugged the tunnel when the thickness of the cake

became equal to the perforation radius. The large FIP values in small diameter

perforations are a result of the additional pressure drop required to push the plug out of

the perforation tunnel to initiate flow. Both internal and external filter cakes played a role

in determining FIP for perforations with small diameter. In the case of larger diameter

perforations, the external filter cake was only formed along the walls of the perforation

tunnel and did not pose any additional resistance during flowback.

In general, perforations with a diameter larger than twice the external filter cake

thickness had small FIP values and that the external filter cake did not play any role in

192

determining the FIP. The flowback through perforations with large diameter is achieved

similar to the open-hole flowback case (pin-holes or partial lift-off of the external filter

cake at small flowback pressures). But perforations with diameter smaller or equal to

twice the external filter cake thickness can have large FIP values and that the external

filter cake will play a significant role in determining the FIP. For perforations with small

diameter the flow is initiated after some part of the plug (external filter cake) is removed

from the tunnel. At large flowback pressures the entire external filter cake lifts off and the

whole plug (external filter cake) is removed from the perforation tunnel.


Table 6.2 shows return permeability ratios at four different flowback differential

pressures (FIP, 20 psi, 50 psi, and 100 psi) for all the single-phase (3% brine) constant

pressure flowback experiments simulating perforated completions at an overbalance of

100 psi. We can see in the table that most of the return permeability improvement is at 20

psi of the applied flowback differential pressure for almost all the experiments.

Figure 6.10 shows the return permeability spectra for all the single-phase

flowback experiments conducted on Berea cores with different dimensions of lab-

simulated perforations. The mud used for all the tests was UltraCarb-2 drill-in fluid at an

overbalance of 100 psi. The plot shows that most of the permeability is recovered within

20 psi of applied differential pressure during flowback. The plot is S-shaped for most of

the cases and the return permeability ratios are asymptotic to a return permeability ratio

ranging between 60 to 70 % except for the case with a ¼ inch diameter and 2 inch long

perforation. The return permeability spectrum for ¼ inch diameter and 2 inch long

perforation was found to be significantly different from the rest of the return permeability

spectra. Figure 6.11 shows a semi-log plot version of the above plot which shows that the

193

return permeability ratios are approximately linear with the log of the differential

pressure. Figure 6.12 shows return permeability ratios for the first 2 inches of the core in

6 inch long Berea cores with different lab-simulated perforations. Figure 6.13 shows a

semi-log plot for the above data. The return permeability ratios for the first two inches of

the core are much smaller than return permeability ratios for the whole core (6 inches

long). This is because most of the damage occurs in the first two inches of the cores (area

around the perforation tunnel).

Figure 6.14 shows a plot of return permeability ratio with measured flowback

rates for Berea with different lab-simulated perforations. The return permeability ratios

approach asymptotic values at larger flowback rates. When plotted as a semi-log plot the

return permeability spectra becomes linear as seen in Figure 6.15. We observe that at a

flowback rate of 2 ml/min the return permeability ratios are larger than 20 % and at a

flowback rate of 10 ml/min the return permeability ratios are larger than 40 % for all the

experiments.

We computed the average velocity of the flowback fluid through the perforations

for all the tests by dividing the total measured flowback rate by the surface area of the

perforation tunnel. Figure 6.16 shows a plot of return permeability ratio with the log of

the average velocity of the flowback fluid. We can observe in the figure that a flowback

velocity of 0.5 cm/min results in return permeability ratios larger than 20 % for all the

experiments. At a flowback velocity of 2 cm/min the return permeability ratios are larger

than 40 % for all the cases. Figure 6.17 shows return permeability spectra for the first two

inches of the perforated cores with varying flowback velocity.

A flow rate of 10 ml/min or an average velocity of 2 cm/min in all the lab-

simulated perforated completions with single-phase flow resulted in a significant

improvement in the return permeability ratio.

194


Table 6.3 shows 30 minute filtrate loss for all the single-phase filtration

experiments simulating perforation completions. It can be seen that the lab-simulated

perforations with large (diameter or length) leading to a larger exposed surface area of the

rock yields larger filtrate loss than in smaller diameter or smaller length perforations.

Appendix-E contains plots for cumulative filtrate loss with square root of time for

all the tests. The plots show a linear increase of cumulative filtrate loss with square root

of time, and can be expressed as:

w spQ C t Q= + (6.1)

Where Qsp is called the spurt loss and Cw, the slope of the line, is called the leak-

off coefficient.

However the volume of filtrate loss is very small and is in the range of 0 to 2 ml

for 30 minutes filtration in all the single-phase experiments (see Table 6.3). This is

because of the small surface area of the rock exposed to the completion fluid during

overbalance. Therefore, the damage caused by the filtrate invasion in perforated

completions should be potentially small.

6.6.2 Two-phase Experiments

The motivation behind conducting two-phase experiments was to closely

represent the actual field conditions where there is usually oil and water both present

during production.

Table F.1 in Appendix-F shows three two-phase constant pressure flowback

experiments conducted on cores with simulated perforations. Subsequently shown are

plots for each of the experiments conducted. All the tests were done on short Berea cores

195

at an overbalance of 100 psi. The third test was done on a core with multiple perforations.

Figure 6.18 shows a schematic of the core with three perforations.


The FIP for two-phase flow filtration experiments with lab-simulated perforations

and done at constant pressure flowback condition are shown in Table 6.4. Small Berea

core plugs with 1/8 inch diameter and ½ inch long holes were used to simulated

perforations. In one of the tests bentonite mud was used as the filtration fluid and in the

other one UltraCarb-2 completion fluid was used. A FIP of 15 psi was observed when

UltraCarb-2 drill-in fluid was used as compared to a FIP of 14 psi when bentonite mud

was used. In case of Berea core plug with 3 lab-simulated perforations, the FIP was found

to be equal to 8 psi, a value less than the FIP values for single perforation.

The FIP values for two-phase flow experiments were larger than the FIP values

for corresponding single-phase flow experiments on Berea cores with lab-simulated

perforations with diameter 1/8 inch and length equal to ½ inch. This suggests the

additional differential pressure required to initiate flow is because of capillary pressure

and relative permeability effects in two-phase flow.


Table 6.5 shows return permeability ratios for the two-phase constant pressure

flowback experiments simulating perforated completion. It is observed that the return

permeability improvement is more gradual in two-phase experiments as compared to

single-phase experiments. For the case of Berea core with three perforations, the return

permeability improvement is even more gradual (Figure F-1 in Appendix F) than single

perforation cases (Figure F-4 and Figure F-5). It is possible that the perforation tunnels

196

were getting cleaned up one by one. Figure F-2 in Appendix-F shows a plot of return

permeability ratio with applied differential pressure for Berea core with 3 lab-simulated

perforations. We can see that the return permeability ratio is increasing linearly with

applied differential pressure and is not S-shaped. Figure F-2 in Appendix-F shows that

the flow rates were still increasing and had not stabilized at the end of each pressure step

change. The maximum unstabilized flow rates at different applied differential pressures

were used to calculate the return permeability ratio. This could be a possible explanation

for the return permeability spectra to be not S-shaped in case of multiple perforations.


Figure F-3 in Appendix-F shows plot for cumulative filtrate loss with square root

of time for two-phase filtration experiments on Berea core with 3 lab-simulated

perforations. The plot shows a linear increase of cumulative filtrate loss with square root

of time. This suggests that the leak-off behavior in perforations is similar to the leak-off

behavior in open-hole completions. Therefore the formation of the filter cake in

perforations is similar to the formation of the filter cake in open-hole completions. The

leak-off volume at large times can therefore be estimated by extending the straight line fit

in the filtrate loss plot.

6.7 EFFECT OF DIFFERENT PARAMETERS

The effect of the following different parameters on FIP and return permeability spectra

are analyzed:

1. Single-phase vs. two-phase flow

2. Completion fluid (sized CaCO3 vs. bentonite mud)

3. Completion type (open hole vs. perforated completion (lab-simulated))

197

4. Overbalance pressure

5. Perforation dimensions (length and diameter of the drilled hole)

6. Single vs. multiple perforations

6.7.1 Single-phase vs. Two-phase Flow

Table 6.6 shows a comparison of FIP observed for single phase flow experiments

and two-phase flow experiments conducted on lab-simulated perforated cores. The FIP

for two-phase flow experiments is larger than the FIP for single-phase flow experiments.

We attribute the reason for larger FIP in two-phase flow than single-phase flow to

additional pressure required to overcome capillary forces and relative permeability effects

in two-phase flow. However the return permeability ratio was found to be larger in the

two-phase experiments than the single-phase experiments at the same flowback pressure.

6.7.2 Effect of Completion Fluid Type

Table 6.7 shows a comparison of FIP and return permeability ratio for UltraCarb-

2 completion fluid and bentonite mud when used on Berea cores with same hole sizes and

similar test conditions. Bentonite mud showed smaller FIP and larger return permeability

ratios as compared to UltraCarb-2 completion fluid. This is a similar result to what was

observed in for lab-simulated open-hole completions that the bentonite mud performed

better than the UltraCarb fluid in terms of both FIP and return permeability ratio.

However the fluid loss is larger for bentonite mud as compared to the fluid loss from

UltraCarb-2.

198

6.7.3 Open-hole Completion vs. Perforated Completion

The flow area in open-hole completions is much larger than the flow area in

perforated completions. Therefore the amount of fluid invasion (solids, polymers, and

filtrate) into the formation in open-hole completions will be much larger than the amount

of fluid invasion in perforated completions. Tables 2.9 and 2.12 in Chapter 2 (filtrate loss

in open-hole completion) and Table 6.3 (filtrate loss in perforated completion) clearly

show that the volume of fluid loss in open-hole completions is much larger than the fluid

loss in lab-simulated perforated completions.

The FIP values for the lab-simulated perforated completions with diameter larger

than 1/8 inch are found to be comparable with the FIP values obtained for the lab-

simulated open-hole completions. The FIP is a function of the diameter of the largest

pore throat of the media, the depth of the internal filter cake and the yield strength of the

internal filter cake assuming that there is no resistance offered by the external filter cake.

All the parameters should be about the same in both the lab-simulated open-hole

completion and lab-simulated perforated completion because the same core type, drill-in

fluid and the overbalance was applied in the two completions. However the FIP values

are found to be much larger in the lab-simulated perforated completions with diameter

equal to 1/8 inch. This is because there is an additional flow resistance offered by the

external filter cake in a form of a plug in addition to the internal filter cake in these small

diameter perforations.

Figure 6.19 shows three return permeability spectra, one for a lab-simulated open-

hole completion and two for the lab-simulated perforated completions (with two different

perforation dimensions). All the experiments were conducted on 6 inch long Berea cores

with UltraCarb-2 drill-in fluid at an overbalance of 100 psi. It can be clearly seen in the

above figure that the return permeability ratios for the lab-simulated perforated

199

completions are smaller than the return permeability ratios obtained for the lab-simulated

open-hole completions at an equal flowback pressure. The smaller return permeabilities

in the perforated completions compared to the return permeabilities in the open-hole

completion suggests less cleanup of the internal filter cake around the perforation tunnels.

We believe that this could be because of the geometry of the perforations. The tip of the

perforation tunnel is closer to the bottom face of the core than the rest of the area around

the perforation tunnel. The pressure is raised at the bottom face (reservoir side) of the

core during flowback. Before the flow is initiated the pressure gradient across the internal

filter cake around the perforation tunnel is the same. Once the flow is initiated at some

part of the perforation (i.e. some part of the internal filter cake is cleaned up around the

tunnel), the pressure gradients around the tunnel are distributed unevenly around the

perforation tunnel. The pressure gradients will be larger near the tip of the tunnel and

smaller away from the tunnel (closer to the top face of the core). Most of the flow will

take place from the tip of the tunnel and therefore the pressure gradients experienced by

the internal filter cake away from the tip of the tunnel will be small. Whereas in the lab-

simulated open-hole completions there will be a much more uniform pressure gradient

across the whole area at the top face of the core even after flow has initiated leading to a

better cleanup of the internal filter cake. This uneven distribution of pressure gradients

around the perforation tunnel during flowback might be one possible explanation of

lower return permeabilities in perforated completions compared to the open-hole

completion.

Figure 6.20 shows return permeability spectra for Berea core with open-hole and

lab-simulated perforated completions. It can be clearly seen in the figure that the FIP is

smaller for the open-hole case than the perforated case. This is because the hole diameter

was equal to 1/8 inch in the perforation completion leading to extra resistance imposed by

200

the external filter cake in the perforation tunnel. However at large flowback pressures the

return permeabilities are approximately the same in the two completions. Figure 6.21

shows the same two return permeability spectra but now as a function of the average

flowback velocity. The flowback velocities are smaller in the open-hole case than the

flowback velocities in the lab-simulated perforated case because of the small flow area in

the later case. However the two spectra show a similar cleanup behavior of the internal

filter cake as a function of the flowback velocity.

Figure 6.22 shows return permeability spectra for Texas limestone core with

open-hole and lab-simulated perforated completions. It can be clearly seen in the figure

that the FIP is small (~ 1 psi) for both the open-hole and the perforated completion.

However the return permeabilities are slightly larger for the open-hole case than the

perforated case initially. However at large flowback pressures the return permeabilities

for the perforated completion is larger than the open-hole completion. This could be

because of permanent damage to the core in the open-hole completion. We do not

understand the reason behind the permanent damage to the core in the open-hole

completion. Figures 6.23 and 6.24 show return permeability spectra for the two

completions as a function of the flowback rate and the average flowback velocities.

6.7.4 Effect of Overbalance Pressure

Figure 6.25 shows a comparison of the return permeability spectra for two

different overbalance pressures (100 psi and 500 psi) in Boise sandstone cores with lab-

simulated perforations (1/8 inch diameter and ½ inch long). It can be clearly seen in the

figure that larger overbalance results in a larger FIP and lower return permeabilities than

smaller overbalance. This suggests that the kill pills or the completion fluids should be

kept at low overbalance pressures in perforated completions.

201

6.7.5 Effect of Perforation Dimensions

Figure 6.26 shows a comparison of return permeability spectra for lab-simulated

perforations with different lengths. The figure shows that the return permeability spectra

are about the same for the two cases which suggests that the length of the perforation

does not play a significant role in the cleanup of the internal filter cake.

Figure 6.27 shows a comparison of return permeability spectra for lab-simulated

perforations with different hole diameter. The figure shows that at small flowback

pressures the perforations with large hole diameter cleanup easily and yield large return

permeabilities but at large flowback pressures the return permeabilities are about the

same for all the perforations with different hole diameter.

6.7.6 Single vs. Multiple Perforations

A lab-simulated single perforation (1/8 inch in diameter and ½ inch long) in Berea

sandstone core resulted in a FIP of 14 psi (see Figure F-4) while a Berea core with three

perforations in parallel (see Figure 6.18) resulted in a FIP of 8 psi (see Figure F-1). Even

though the FIP for the multiple perforation case was smaller than the FIP for the single

perforation case, it took a longer time to clean the 3 perforations than the single

perforation during flowback. The return permeability of the core with a single-perforation

was also larger than the return permeability of the core with 3 perforations at an equal

flowback pressure.

6.8 APPLICATION OF RESULTS TO ESTIMATE SKIN IN PERFORATED COMPLETIONS

Figure 6.29 shows a plot of skin calculated using Hawkin’s formula with a depth of

damage equal to 2 and for different return permeability ratios for the damaged zone. It

can be clearly seen that to obtain a skin factor < 2, the return permeability ratio should be

202

larger than 20 % in the damaged zone. Figure 6.30 shows a plot of the flow rates during

cleanup of the internal filter cake vs. the obtained return permeability ratios. We can

clearly see in Figure 6.30 that to obtain a return permeability ratio of 20 %, the flow rates

should be larger than 0.3 bbl/day/perf for all perforated completions. Therefore, to obtain

a significant cleanup (skin factor < 2) the perforations should flow at a rate mentioned

above. If the flow rates are smaller than 0.3 bbl/day/perf then we can assume that the skin

factor around the perforations is larger than 2. The data can also be used to estimate the

skin factor for perforated completions, if the flow rates are known.

6.9 CONCLUSIONS

1. Lab-simulated perforated completions with perforation diameter larger than 1/8 inch

resulted in FIP values similar to FIP values obtained from experiments conducted on

lab simulated open-hole completions. The external filter cake played a significant role

in case of lab-simulated perforations with diameter equal to 1/8 inch. If the external

filter cake thickness becomes equal or greater than the radius of the perforation

tunnel, additional pressure is required to push the external filter cake plug. Therefore

perforations with large hole diameter are recommended.

2. The FIP’s for two-phase flow experiments are found to be slightly larger than the

single-phase flow experiments for lab-simulated perforated completions. This is

consistent with the experimental results obtained for lab-simulated open-hole

completions as presented in Chapter 2.

3. The average return permeability spectra for lab-simulated perforated cores, when

plotted as a function of applied differential pressure is consistently S-shaped similar

to the results obtained for cores with lab-simulated open-hole completion. Perforated

203

completions are also permanently damaged similar to the open-hole completions

because of the incomplete removal of the internal filter cake leading to asymptotic

values for the return permeabilities at large flowback pressures.

4. Overbalance pressure plays a significant role in determining the FIP and return

permeability spectra in perforated completions. A large overbalance pressure results

in a large FIP and a smaller return permeability ratio compared to a small overbalance

pressure.

5. The perforation tunnel length doesn’t seem to play a significant role in determining

the FIP and the return permeability ratio during flowback in perforated completions.

6. Bentonite mud performed better than UltraCarb-2 drill-in fluid on Berea sandstone in

terms of FIP and return permeability for cores with lab-simulated perforated

completion. However bentonite mud resulted in a much larger fluid loss than

UltraCarb-2 drill-in fluid.

7. The data presented in this chapter can be used to determine the return permeability

ratio in perforated completions for a given perforation size and the drawdown /

average flow velocity / average flow rate. A flowback rate of 0.3 bbl/day/perf yielded

in a skin factor < 2 in all perforated completions.

204

Table 6-1: Flow initiation pressure for single-phase flow and constant pressure flowback experiments simulating perforated completion

Core Type

Mud used


[inches]

Lab-simulated Perforation dimensions

(Dia. X Length)

[inches]

FIP

[psi] Texas

limestone (25 md)

UltraCarb-2*

Short core 2.5 X 1

(1/4 X 1/2) 1

Short core 2.5 X 1

(1/8 X 1/2) 10

(1/8 X 1) 4

(1/8 X 1)** 12

(1/8 X 2) 3

(1/8 X 2)** 14

(1/4 X 1) 4

(1/4 X 1)** 2

(1/4 X 2) 1.5

(1/4 X 2)** 1

Berea sandstone (200 md)

UltraCarb-2*

Long core 2 X 6

(3/8 X 1) 3.5


UltraCarb-20*

Short core 2.5 X 1

(1/8 X ½) 2

* The number represents the median size of CaCO3 particles ** Repeat experiment Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the

experiments.

205

Table 6-2: Summary of return permeability ratio for single-phase constant pressure flowback tests simulating open-hole completion


Core Type

Mud used

Core Dimensions

(Dia. X Len.)

[inches]

Lab-simulated

Perforation dimensions

(Dia.X Len.) [inches]

At (FIP)

At 20 psi

At 50 psi

At 100 psi

Texas Limestone

(25 md)

UltraCarb-2* Short core 2.5 X 1

(1/4 X 1/2) 7.7 (1)

64.3 74.8 78.9

Short core2.5 X 1

(1/8 X 1/2) 41.9 (10)

56.1 77.1 100

(1/8 X 1) 0.2 (4)

46.3 64.7 73

(1/8 X 1)** 1.4 (10)

66.8 91 96

(1/8 X 2) 3.2 (3)

59.7 71.1 74.1

(1/8 X 2)** 55.4 (14)

62.5 76 78.9

(1/4 X 1) 11.4 (4)

42.8 59.4 64

(1/4 X 1)** 0.7 (2)

47.7 61.7 74.4

(1/4 X 2) 56.6 (1)

86.4 86.6 87

(1/4 X 2)** 80 (1.5)

86 93 93


UltraCarb-2* Long core

2 X 6

(3/8 X 1) 13.7 (3.5)

46.5 55.2 63


UltraCarb-20*

Short core 2.5 X 1

(1/8 X 1/2) 1 (2)

38

* The number represents the median size of CaCO3 particles. ** Repeat experiment Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.

206

Table 6-3: Summary of 30 minute fluid loss for lab simulated perforated cores with single phase flow and constant pressure flowback condition

Core Type

Mud used


[inches]

Lab-simulated Perforation dimensions

(Dia. X Length)

[inches]

30 Minute Filtrate Loss

[ml]

Texas limestone (25 md)

UltraCarb-2*

Short core 2.5 X 1

(1/4 X 1/2) 0.16

Short core 2.5 X 1

(1/8 X 1/2) 0.05

(1/8 X 1) 0.5

(1/8 X 1)** 0.46

(1/8 X 2) 0.87

(1/8 X 2)** 1.06

(1/4 X 1) 0.89

(1/4 X 1)** 0.99

(1/4 X 2) 1.92

(1/4 X 2)** 1.72


UltraCarb-2*

Long core 2 X 6

(3/8 X 1) 1.15


UltraCarb-20*

Short core 2.5 X 1

(1/8 X ½) 0.12

* The number represents the median size of CaCO3 particles ** Repeat experiment Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.

207

Table 6-4: Summary of FIP for lab simulated perforated cores with two phase flow and constant pressure flowback condition

Core Type

Mud used


[inches]


(Dia. X Length)

[inches]

FIP

[psi]

UltraCarb-2* (1/8 X 1/2) 15

(1/8 X 1/2) 14


Bentonite

Short core 2.5 X 1

3 Perforations (1/8 X 1/2)

8


Table 6-5: Summary of return permeability ratio for two-phase constant pressure flowback tests simulating open hole completion


Core Type

Mud used

Core Dimensions

(Dia.X Len.)

[inches]

Lab-simulated

Perforation dimensions (Dia.X Len)

[inches]

At (FIP)

At 10 psi

At 12 psi

At 14 psi

UltraCarb-2

Short core 2.5 X 1

(1/8 X 1/2) >*56 (15)

(1/8 X 1/2) >*72 (14)

>*72


Bentonite Short core 2.5 X 1

3 Perforations (1/8 X 1/2)

>*25 (8)

>*33 >*44 >*55

* The > sign represents that the rate during flowback was still increasing and would have resulted in a calculation of a larger return permeability than cited. The overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.

208

Table 6-6: Comparison of FIP for single phase vs. two phase experiments with constant pressure flowback condition in lab-simulated perforated completions

FIP [psi]

Core Type

Mud used

Core Dimensions

(Dia. X Len.)

[inches]


(Dia. X Length)

[inches]

Single phase (Flowback fluid: 3 %

brine)

Two phase (Flowback

fluid: Exxsol)

Berea sandstone

(200 md)

UltraCarb-2


(1/8 X ½) 10 15

Table 6-7: Comparison of FIP and return permeability ratio between bentonite mud and UltraCarb completion fluid in lab-simulated perforated completions

FIP

[psi] Return permeability ratio

(%) Core Type and Permeability

Core dimensions

[inches]


[inches] Bentonite UltraCarb-2 Bentonite UltraCarb-2


(2.5” X 1”)

(1/8” X ½”)

14

15

72

56

209

mud cake

Escaid flow

Measure Flow rate

Apply constant pressure / Constant flow back rate

Top view of the core

Side view of the core

Impermeable Epoxy Perforation

mud cake

Escaid flow

mud cake

Escaid flow

Measure Flow rate

Apply constant pressure / Constant flow back rate

Top view of the core

Side view of the core

Impermeable Epoxy Perforation

mud cake

Escaid flow

Figure 6-1: Schematic of a lab-simulated single perforation in a core

210

Pressure taps

Borehole sleeve

Core

Confining liquid

Rubber sleeve

Completion fluid

Stationary end cap

End spacer

Dynamic end cap

End spacer

2 in.

Min

imum

: 1.3

5 in

.

.97

in.

17 in

.

1.35

in. 1

in.

2.15

in.

2 in

. 1.

85 in

.

Max

imum

: 6.3

in.

6 in

.

Perforation

Figure 6-2: Schematic of the long core holder with a lab-simulated single perforation

211

Figure 6-3: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2 in.) before flowback at constant pressure (LS-9)

Figure 6-4: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2 in.) after flowback at constant pressure (LS-9)

212

Figure 6-5: Top view of a long Berea core with lab simulated perforation (1/8 X 1 in.) after flowback at constant pressure (BS-long-#11)


213


after flowback at constant pressure (BS-long-#13)


214

Figure 6-9: Top view of a long Berea core with lab simulated perforation (3/8 X 1 in.) after flowback at constant pressure (BS-6-13-04-#8)

0

20

40

60

80

100

0 20 40 60 80 100Differential Pressure During Flowback (psi)

Ret

urn

Per

mea

bilit

y R

atio

(%)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1

Perf. Dim. Dia. Len. (in.) (in.)

Figure 6-10: Return permeability spectra for Berea with different perforation dimensions

(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)

215

0

20

40

60

80

100

1 10 100Differential Pressure During Flowback (psi)

Ret

urn

Per

mea

bilit

y R

atio

(%)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1


Figure 6-11: Semi-log plot for return permeability in Berea with different perforation

dimensions (single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)

0

20

40

60

80

100

0 10 20 30 40 50 60Differential Pressure Across First 2 inches of the Core (psi)

Ret

urn

Per

mea

bilit

y R

atio

(%)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1


Figure 6-12: Return permeability ratio in the first 2 inches of Berea cores (single-phase

flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)

216

0

20

40

60

80

100

0.1 1 10 100Differential Pressure Across First 2 inches of the Core (psi)

Ret

urn

Per

mea

bilit

y R

atio

(%)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1


Figure 6-13: Semi-log plot for return permeability for the first 2 inches in Berea cores


0

20

40

60

80

100

0 30 60 90Measured Flow back Rate (ml/min)

Retu

rn P

erm

eabi

lity

Ratio

(%)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1


Figure 6-14: Return permeability spectra for Berea with varying flowback rate (single-

phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid)

217

0

20

40

60

80

100

0.01 0.1 1 10 100Measured Flow back Rate (ml/min)

Ret

urn

Perm

eabi

lity

Ratio

(%)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1




0

20

40

60

80

100

0.01 0.1 1 10 100Average Velocity Through The Perforation (cm/min)

Retu

rn P

erm

eabi

lity

Ratio

(%)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1




218

0

20

40

60

80

100

0.01 0.1 1 10 100Average Velocity Through The Perforation (cm/min)

Ret

urn

Perm

eabi

lity

Ratio

in F

irst T

wo

Inch

es o

f The

Cor

e (%

)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1


Figure 6-17: Semi-log plot for return permeability in 1st 2 inches of the Berea core


1/8 in.

2.5

inch

es

1/2 in

1 in.

Figure 6-18: Top and side view of a short Berea core with three drilled holes to represent lab-simulated perforations

Top view of the coreSide view of the core

Drilled holes to simulate perforations

Epoxy to seal the top of the core

219

0

10

20

30

40

50

60

70

80


k/ko

(%)

Lab-simulated open-hole completionPerf. dimensions: 1/8" diameter, 1" lengthPerf. dimensions: 1/4" diameter, 1" length

Figure 6-19: Return permeability spectra for lab-simulated open-hole completion vs. lab-

simulated perforated completions in long Berea cores (6 inch long)

0

20

40

60

80

100

120


Retu

rn P

erm

eabi

lity

Ratio

(%)

Open-hole

Perforated (1/8"X1/2")

Berea sandstoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi


completions (lab-simulated) in short Berea sandstone cores (1 inch long)

220

0

20

40

60

80

100

120

0.001 0.01 0.1 1 10 100

Average Flowback Velocity (cm/min)

Retu

rn P

erm

eabi

lity

Rat

io (%

)

Open-hole Perforated (1/8"X1/2")

Berea sandstoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi


completions (lab-simulated) in short Berea sandstone cores (1 inch long)

0

10

20

30

40

50

60

70

80

90


Ret

urn

Perm

eabi

lity

Rat

io (%

)

Open-hole

Perforated (1/4"X1/2")

Texas LimestoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi


completions (lab-simulated) in short Texas limestone cores (1 inch long)

221

0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100Measured Flowback Rate (ml/min)

Ret

urn

Perm

eabi

lity

Rat

io (%

)



Figure 6-23: Return permeability vs. flowback rate for open-hole and perforated


0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100Average Flowback Velocity (cm/min)

Retu

rn P

erm

eabi

lity

Ratio

(%)





222

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50 60 70Applied Differential Pressure During Flowback (psi)

Ret

urn

Perm

eabi

lity

Rat

io (%

) O.B. pressure = 100 psi

O.B. pressure = 500 psi

Figure 6-25: Return permeability with varying flowback pressure in Boise sandstone with

lab-simulated perforations at two different O.B. pressures (Mud used: UltraCarb-20)

0

20

40

60

80

100


Ret

urn

Perm

eabi

lity

Rat

io (%

)

1/8 1

1/8 1(Repeat)

1/8 2

1/8 2(Repeat)



simulated) with different lengths

223

0

20

40

60

80

100


Ret

urn

Perm

eabi

lity

Ratio

(%)

1/8 1

1/4 1

3/8 1



simulated) with different diameter

0

20

40

60

80

100

0.1 1 10 100Average Pressure Gradient (psi/inch)

Ret

urn

Perm

eabi

lity

Rat

io (%

)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1


Figure 6-28: Return permeability spectra for the first two inches of cores with different

perforated completions as a function of average pressure gradient

224

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100Return Permeability Ratio (%)

Skin

Depth of damage = 2 inch

radius of well (rw) = 4 inch

rw = 4 inch

rw = 6 inch

Figure 6-29: Estimate of skin factor for perforated completions with a depth of damage

equal to 2 inches

0

20

40

60

80

100

0.001 0.01 0.1 1

Flow rate (bbl/day/perforation)

Ret

urn

Perm

eabi

lity

Rat

io (%

)

1/8 1

1/8 2

1/4 1

1/4 2

3/8 1


Figure 6-30: Return permeability spectra for perforated completions in the first 2 inches

as a function of flow rate through the perforation tunnels

225

REFERENCES

1. Jiang, P., et al.: “New Low-Solids OBM Demonstrates Improved Returns as

Perforating Kill-pill,” paper SPE 73709 presented at the SPE International

Symposium and Exhibition on Formation Damage Control held in Lafayette,

Louisiana, 20-21 February 2002.

2. Chang, F. F., et al.: “Perforating in Overbalance – Is it really sinful?,” paper SPE

82203 presented at the SPE European Formation Damage Conference held in The

Hague, The Netherlands, 13-14 May 2003.

3. Chang, F. F., et al.: “Recommended Practice for Overbalanced Perforating in Long

Horizontal Wells,” paper SPE 94596 presented at the SPE European Formation

Damage Conference held in Scheveningen, The Netherlands, 25-27 May 2005.

226

Chapter 7: UTDamage: An Application to Model Both Filtration and

Flowback and To Design Fluids

7.1 INTRODUCTION

In this chapter, an overview of UTDamage (a multi-component filtration model)

is presented first. The model is used to match with the experimental results presented in

Chapter 2 to develop strategies for designing drill-in and completion fluids. The erosion

factors for the different muds are calculated by matching the model results with the

experimental results. However, no clear trend was found for the erosion factors for

different muds. In the end the erosion factor model in UTDamage is compared with the

Bingham model presented in Chapter 5. A discussion on the pros and cons for the two

flowback models is presented.

7.2 BACKGROUND AND LITERATURE REVIEW

Suri and Sharma1 presented a model to predict the permeability reduction in the

near wellbore region during mud filtration and permeability improvement during

production. Figure 7.1 shows a schematic of their conceptual model. The model accounts

for the development of both the internal and the external filter cakes during filtration.

During flowback, a parameter called “erosion factor” is defined for simulating cleanup of

deposited particles inside the porous medium. The “erosion factor” is defined as the ratio

of the volume of particles resuspended during flowback to the total volume of particles

deposited during mud filtration. If all the particles are eroded from the surface of the

grains and are resuspended in the fluid then the erosion factor is equal to one. An erosion

factor equal to zero means that all the particles remain deposited on the surface of the

227

grains during flowback. As a result, there is no improvement in the permeability during

flowback.

A Visual Basic application called UTDAMAGE 2.0 is developed to design and

evaluate drill-in and completion fluids for minimum formation damage. The application

sizes bridging solids in drill-in fluids to minimize solids invasion into the formation. The

program also evaluates the formation damage potential of a given drill-in or completion

fluid. The porosity and permeability reduction in the formation is estimated both during

filtration and production. The program accounts for both the external filter cake and the

internal filter cake build up. The application can be used for: 1) designing drill-in and

completion fluids and 2) estimating permeability distribution around the wellbore in oil-

wells during mud overbalance and during production.

7.3 MODEL DEVELOPMENT

A filtration model was developed 2 that estimates the reduction in porosity and

permeability due to invasion of particles from the mud into the formation. A description

of the model formulation is given in the following section.

A general conservation equation for particles within a certain size range can be

written as:

0)()..( =+∂∂

+∇−∇ iiiii ct

cDcu σφ (1)

where u is the Darcy velocity, ci is the volume fraction (per unit pore volume) of

suspended particles of the ith species (particles within a certain size range) in the fluid, Di

is the dispersion coefficient of the ith species, φ is the porosity of the formation and σi is

228

the volume fraction of deposited particles of the ith species in the porous medium per unit

bulk volume.

The above equation is simplified with the following approximations:

1 Incompressible flow (for both the fluid and the particles (solids/polymers) in the

mud).

2 Dispersion is neglected (diffusion is negligible for particles larger than 1µm).

3 The porosity of the medium changes due to the deposition of particles and can be

calculated as follows:

tti

∂∂

−=∂∂ σφ (2)

4 The particle deposition term dσi/dt is assumed to follow an empirical relation

proposed by Iwasaki (1937) :

iii uc

dtd λσ

= (3)

where λ is the filtration coefficient with units of (1/length).

The volumetric concentration of particles in the fluid is assumed to be low

(c<<1). With the above assumptions Equation (1) for each species reduces to,

0. =+∂∂

+∇ iii

i uctccu λφ (4)

A semi-empirical equation based on extensive computer simulations conducted by

Rajagopalan and Tien (1976) was used to calculate the filtration coefficient for each

species. The following equation gives an approximate closed form solution for the initial

229

collection efficiency in deep bed filtration by using Happel’s model. Figure 7.2 shows the

Happel's sphere-in-cell porous media model used in the model. The volume of the liquid

shell covering the solid grain is such that the volume of this liquid shell divided by the

total volume of the Happel’s sphere-in-cell is equal to the porosity of the porous medium.

3/23/14.038/158/1 4104.272.0

2.1 −−− +×+= PESRGSRLOSi NANNANNAη (5)

where AS is Happel’s geometric parameter and ηi is the collection efficiency of

the ith species and is given as the ratio of trapped particle concentration to the inlet

particle concentration in an unit bed element and is defined as,

cell sHappel' thecell sHappel' thecell sHappel' the /)( enteringileavingienteringii ccc −=η (6)

and NLO (London group), NR (relative size group), NG (gravity group), and NPE

(Peclet number) are dimensionless groups for the ith species and are defined as,

ua

HNi

LO 29πµ= (7)

µ

ρρu

gaN fii

G 9)(2 2 −

= (8)

BM

gPE D

udN = (9)

g

piR d

dN = (10)

230

The above equation for the collector efficiency is valid for NR<0.18 i.e. when the

mud particles are less than one-fifth the size of the rock grains and when there is no

energy barrier for particle deposition on the rock grains. The difference in the diameter of

the solid grain and the diameter of the Happel’s sphere-in-cell is used to represent the

pore throat diameter of the porous medium.

For a Happel cell, the relation between λi and ηi can be written as

ig

i dηφλ

2)1(3 3/1−

= (11)

Substituting equation (11) in equation (4) and assuming u and φ to be a function

of only space and not time, we get an analytical solution, which is quasi-linear in

concentration. The solution to the above equation for the ith species in linear and radial

flow geometry in one dimension was obtained using Laplace transforms.

7.3.1 Solution for Mud Filtration in Linear Geometry

For linear flow in one dimension, the following initial and boundary conditions

are used for the ith species

( ,0) 0ic x = (Initial condition) (12)

( )(0, )i i inc t c= (Boundary condition) (13)

where ci(in) is the concentration of the ith species at the face of the formation.

The solution obtained for the injection of the ith species is,

231

0),( =txci uxt φ

< (14)

)exp(),( )( xctxc iinii λ−= uxt φ

> (15)

This solution for the concentration of the ith species can be used to calculate the

total deposited concentration (σ) by using the deposition rate of the ith species in the

porous medium:

dttxuctx i

t

ii ),(),(0∫= λσ (16)

∑=

=N

ii txtx

0

),(),( σσ (17)

),()0,(),( txftf o σφφ −= (18)

A permeability reduction model due to particle deposition based on the Kozeny-

Carman equation as proposed by Pang (1996) is used. The permeability reduction can be

broken into three parts; namely reduced porosity (kdp), increased surface area (kds), and

increased tortuosity (kdt). The reduced permeability can then be written as,

dtdsdpo kkkkk =/ (19)

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−=

23

23

)1()1(

φφφφ

o

odpk (20)

232

2

)(0

)/()1(

1

)1/(1

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−+

−+=

∑=

ipgo

iN

i

ods

ddk

φσ

φσ (21)

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=βσ1

1dtk (22)

The damage factor (β) is introduced as an empirical parameter which accounts for

the change in tortuosity as particles deposit on the rock grains. The initial grain diameter ( god ) of the porous medium is calculated using the

Carmen-Kozeny equation as given below

o

ogo

kdφ

200= (23)

where ko is in md and dgo is in microns.

Based on Happel’s sphere-in-cell model, the pore throat diameter ( thd ) of the

porous medium is defined as the difference between the diameter of the Happel cell and

the diameter of the solid grain with deposited particles, if any. This can be seen in Figure

7.2, and is given by,

[ ]3/13/1 ))1/((1(1

)1( dpo

goth

dd φφ

φ−−−

−= (24)

233

where oφ is the initial porosity of the medium, φ is the new porosity of the

medium after deposition of particles and φ dp is the porosity of the deposited particles on

the cake grains.

The constraint for a given species to be allowed to enter the porous medium is

that it’s diameter (di) should be smaller than the pore throat diameter of the porous

medium.

ith dd > (25)

7.3.2 Build-up of an External Filter cake

The process of fluid invasion involves both solids invasion and external cake

filtration, i.e. some particles are trapped inside the porous medium, forming an internal

filter cake and some particles are retained on the face of the porous medium forming an

external filter cake. When the above condition is not met for a given species, then the

species is filtered out and starts to form an external filter cake. The thickness of the

external filter cake formed by the filtering species which are not able to enter into the

core in ∆t time is given by,

∑=

=N

niicake hh (26)

where mciii tuch φ/∆= (27)

where i = n refers to the smallest species filtered out and N refers to the largest

species in the suspension.

234

The initial porosity of the external mud cake is assumed to be of a hexagonal

packing of spheres (φmci=25.6%). The initial permeability of this new layer of external

filter cake is calculated from the modified Carmen-Kozeny equation given by Panda and

Lake (1994) as below,

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

++−

=22

23

2

32

)1(13

)1(72 PD

PDPD

mci

mcipi C

CCdk

γφτ

φ (28)

where CDP is the coefficient of variation of the psd, and the total cake

permeability is given by

∑

=

= N

ni i

icake

kh

hk (29)

Dewan and Chenevert (2000) have shown that the external cake porosity is a

function of the pressure across it. The following equation has been used to account for the

cake compressibility as proposed by them,

ν

φφ

)()(

tPt

mc

mcimc = (30)

where ν is an exponent in the range of 0.1 - 0.2 (based on porosity – permeability

cross plots for shaly sand).

As the species filtering into the core have to first filter through the external filter

cake the constraint imposed by equation (25) also has to be satisfied by these species in

235

the external filter cake if present in order to filter through and deposit in the porous

medium. The ( thd ) used in equation (25) would be of the external filter cake for the

species to filter through.

The boundary for the species filtering into the porous medium is a moving

boundary as the external filter cake is growing. The boundary condition of constant

concentration of any species is given on the face of the external filter cake as,

)(),0( inii ctc = at X = 0 (31)

where cakehxX += (32)

i.e. the origin for the x axis is moved to the face of the external filter cake formed

at each time step.

As the external filter cake also now acts as a porous medium with species filtering

in and depositing in it, equations (33) and (34) will govern the filtration process. The

filtration coefficient will of course be different in the external filter cake because of the

different grain size (which is equal to the mean size of the species being filtered out).

0),( =tXci frontXX > (33)

[ ])(exp),( 1.0

)( jjji

X

jinii XXctXc

front

−−= +=

∏ λ frontXX < (34)

where cakefront hutX += φ/ (35)

236

where i refers to the species number and j refers to the external cake layer number

starting from the face of the external cake. The internal filtration process continues until

no more species can fulfill the pore throat constraint as given by equation (25).

7.3.3 Effect of Relative Permeability on Solids and Filtrate Invasion

The formation is assumed to be at some specified initial water saturation. The

initial saturation of water (Swi) and HC (1-Swi) in the formation is provided as an input

to the program. Invasion of the mud filtrate is assumed to be piston like. The oil

saturation is reduced to the residual oil saturation (Sor) behind the filtrate front (XF). In

front of filtrate front, oil and water saturations remain equal to their initial saturations.

The relative permeability of water at (Swi) and (1-Sor) and relative permeability of oil at

(Soi) is also provided in the program by the user.

Figure 7.3 (a) shows a linear core before the filtrate invasion and Figure 7.3 (b)

shows the core after the filtrate has invaded it. The filtrate front (XF) in a linear core is

calculated using equation (31) and the flow rate is calculated using equation (32).

)1( SwiSorAQ

X LF −−

=φ

(36)

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛++−

⎥⎦

⎤⎢⎣

⎡+∆

=

−Soiroi

o

wSwirwi

Sorrwd

F

cake

cakeF

o

Soiro

w

Swirwi

kkkkkk

XkX

XL

kkPAk

q||

|)(

||

1 µµ

µµ (37)

where XF = distance of the filtrate front from the core inlet.

QL = Cumulative filtrate leak-off.

Sor = Residual oil saturation.

237

Swi = Initial water saturation in the core.

ki = Initial permeability of the core.

krw|Swi = Relative permeability of water at Swi.

kro|Soi = Relative permeability of oil at Soi.

krw|1-Sor = Relative permeability of water at residual oil saturation.

Xcake = Thickness of the external filter cake.

kcake = Average permeability of the external filter cake.

kd = Average permeability of the core behind the filtrate front.

q = filtrate flow rate at a given time.

7.3.4 Solution for Flowback in Linear Geometry

We are ultimately interested in obtaining the return permeability when the well is

put back on production. The return permeability for linear flow is calculated using the

same mass balance approach except that the flow is reversed. The following initial and

boundary conditions, now apply,

φσα /*),()0,( iiibi txxc = (Initial condition) (38)

where cbi is the initial suspended particle concentration of the ith species during

flowback and σi is the trapped/deposited concentration of ith species obtained from the

solution of the inflow case for ith species. *it is the transition time for the ith species

after which it started to build an external filter cake (internal filtration of the ith species

stopped).

As some of the deposited particles from each species are eroded during flowback

of the formation fluids, an empirical erosion factor (αi) is introduced where αi<=1. αi=1

implies that all trapped particles from the ith species are resuspended during flowback,

238

while αi=0 implies that none of the trapped particles from the ith species are resuspended.

Since this profile is found to be well represented by an exponential relation, it is fitted to

the following form:

)exp()0,( xbAxc iibi −= for x < xfi (39)

where Ai and bi are the fitted constants for ith species initial suspended particle

concentration profile ( bic ) and xfi is the depth of invasion of the ith species.

The boundary condition for the suspended particle concentration of the ith species

is specified as,

0),( =txc fibi , (40)

i.e. liquid with no suspended particles is flowed back.

The solution for the back flow case for the ith species can also be obtained by

using Laplace transforms,

0),( =txcbi )( xxu

t fi −>φ (41)

))(exp()exp(),( tbuxbAtxc iiiibi +−−= λφ

)( xxu

t fi −<φ (42)

dttxcutx bi

t

bi ),( ),( i0

λσ ∫= (43)

239

The porosity and flowback permeability is then calculated using the same

equations (equations 18-22) as used for the mud inflow case.

7.3.5 Solution for Mud Filtration in Radial Geometry

For a radial flow geometry, with the following initial and boundary conditions for

each species,

0),( =orci (Initial condition) (44)

)(),( iniwi ctrc = (Boundary condition) (45)

where ci(in) is the concentration of the ith species at the face of the formation.

Both theory and experiments show that λ depends on velocity. Assuming a

power-law dependence of λ upon u as shown below

uua γλ −= (46)

where a and uγ are empirical constants, and in radial flow we know that

u(r) = q/A (47)

For a radial geometry the flow rate (q) is calculated using the following equation.

240

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

++

⎥⎦

⎤⎢⎣

⎡+∆Π

=

−Soiroi

o

wSwirwi

Sorrwd

w

f

cake

cake

w

f

e

o

Soiro

w

Swirwi

kkkkkk

rr

krr

rr

kkPhk

q

|||

lnln)(ln

||2

1 µµ

µµ (48)

where rf = radius of the filtrate front.

re = radius of the drainage boundary.

rw = radius of the well-bore.

rcake = radius of the face of the external filter cake.

h = length of the pay-zone.

The solution obtained for a radial geometry at a constant injection rate is

0),( =trci , ur

rrt w )( 22 −<

φ (49)

⎥⎦

⎤⎢⎣

⎡−

+−

= ++ )()1(

)(exp),( 11

)(uu

uw

u

iinii rr

rr

ctrc γγγγ

λ,

urrrt w )( 22 −

>φ

(50)

The multi-component (species of different sizes) filtration through the external

cake in radial geometry would be given by,

0),( =tRci , frontRR > (51)

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

+

−= ++

+=

∏ )()1(

)(exp),( 11

1,

0)(

uu

u

front

jjju

jjiR

jinii RR

R

RctRc γγ

γγ

λ, frontRR < (52)

241

where cakehrR += (53)

and so, cakefrontfront hrR += (54)

where i refers to the species number and j refers to the external cake layer number

starting from the face of the external cake.

7.3.6 Dynamic Filtration

Jiao and Sharma (1993) have shown that due to cross flow in the annular region

of the well-bore the maximum radius of particles which can be deposited on the well-bore

face forming the external filter cake can be obtained by

( )γφρ

ρ−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛=

1323

1

maxuR

n

f

s (55)

particles larger than Rmax will be removed from the cake surface. This occurs

because there is a competing force between the shear force tending to entrain the particles

in the suspension and the normal drag force holding the particle on the cake surface.

7.3.7 Solution for Flowback in Radial Geometry

The return permeability for radial flow is calculated using the same mass balance

approach as used for the flowback case in linear geometry. The following initial and

boundary conditions, now apply,

φσα /*),()0,( iiibi trrc = (Initial condition) (56)

242

where cbi is the initial suspended particle concentration of the ith species during

flowback and σi is the trapped/deposited concentration of ith species obtained from the

solution of the inflow case for ith species. *it is the transition time for the ith species

after which it started to build an external filter cake (internal filtration of the ith species

was complete and stopped).

As some of the deposited particles from each species are eroded during flowback

of the formation fluids, an empirical erosion factor (αi) is introduced where αi ≤ 1. αi=1

implies that all trapped particles from the ith species are resuspended during flowback,

while αi=0 implies that none of the trapped particles from the ith species are resuspended.

Since this profile is found to be well represented by an exponential relation, it is fitted to

the following form:

)](exp[)0,( 22wiibi rrbArc −−= for r < rfi (57)

where Ai and bi are the fitted constants for ith species initial suspended particle

concentration profile ( bic ) and rfi is the depth of invasion of the ith species.

The boundary condition for the suspended particle concentration of the ith species

is specified as,

0),( =trc fibi , (58)

i.e. liquid with no suspended particles is flowed back. We have assumed ( uγ = 1)

in equation 46 in order to get an analytical solution for flowback in radial geometry.

ua

=λ (59)

243

The solution for the back flow case for the ith species can also be obtained by

using Laplace transforms,

0),( =trcbi )(2

22 rrru

t fiww

−>φ (60)

])2(exp[()0,(),( tbr

rurctrc iiww

bibi +−=λ

φ )(

222 rr

rut fi

ww

−<φ (61)

dttrcutr bi

t

bi ),( ),( i0

λσ ∫= (62)

The porosity and flowback permeability is then calculated using the same

equations (equations 18-22) as used for mud inflow.

7.4 UTDAMAGE VS. EXPERIMENTAL RESULTS

The erosion factor in UTDamage was tuned to match the return permeability

ratios obtained from experiments conducted on Berea sandstone and Texas limestone

cores. Figure 7.4 shows a plot of erosion factors used to match the return permeability

ratios at different flowback differential pressures for a short Berea core. Figure 7.5 shows

a similar plot of erosion factors used to match the return permeability ratios at different

flowback differential pressures for a long Berea core. Figure 7.6 shows a plot of erosion

factors needed to match the return permeability ratios for all the single phase experiments

conducted on Berea sandstone. It can be seen in the plot that the erosion factors are large

at large return permeabilities. Moreover, the plot shows that the erosion factors range

from 0.5 to 0.95 for Berea sandstone and UltraCarb-2 drill-in fluid.

244

Figure 7.7 and 7.8 shows plots of erosion factors tuned to match the return

permeability ratios for single-phase and two-phase experiments conducted on Texas

limestone cores. It can be observed in the plots that the erosion factor curves have a

similar shape as the return permeability curves and that the erosion factors are large at

large return permeabilities similar to the erosion factors trend found for Berea sandstone.

Figure 7.9 shows a comparison of the erosion factor plots for the single and two-phase

experiments. Similar match between UTDamage and other experiments can be obtained

by tuning the erosion factor. However, no clear trend for erosion factors is found for any

specific mud or rock type.

7.5 EROSION FACTOR MODEL VS. BINGHAM MODEL

The erosion factor model assumes the internal filter cake to be composed of

particles which are deposited in the porous media. These particles are eroded and

resuspended in the pore fluid at the onset of flowback. The Bingham model is based on

the assumption that the internal filter cake behaves as a Bingham fluid. The internal filter

cake can flow only if the applied pressure gradient is larger than the yield strength of the

internal filter cake. In applying both the models to cleanup of internal filter cake, it is

assumed that both the erosion factor and the yield strength of the Bingham fluid are

constant with in the damaged zone. In actuality this wouldn’t be the case, the erosion

factor or the yield strength of the Bingham fluid both would vary inside the damaged

zone with distance.

A better representation of the invaded solids would be a combination of both

loose deposited particles and a composite paste as shown in Figure 5.2 of Chapter 5. The

loose deposited particles deeper into the rock formation would be eroded and

resuspended into the flowback fluid while the internal filter cake (close to the rock face)

245

would need a certain threshold pressure gradient to flow. I believe that the Bingham

model can estimate the return permeabilities during flowback better than the erosion

factor model because most of the damage is caused by the internal filter cake and not by

the particles which have penetrated deeper into the formation.

The advantage of the erosion factor model with respect to its implementation is

that it is already incorporated in UTDamage and therefore can be used to fit the

experimental data. It is much simpler to use and has fewer variables than the Bingham

model. The shortcoming of using UTDamage is that it does not include the pore size

distribution of the formation and is only a one dimensional model. Also the return

permeabilities in UTDamage are found not to depend on the flowback pressure gradient

but only on the erosion factor value.

The advantage of the Bingham model presented in this dissertation is that it

includes the pore size distribution of the formation. However, the Bingham model is

currently not been combined with any filtration model. It is only a flowback model and

needs the thickness of the internal filter cake and the yield strength of the Bingham fluid

as input parameters to model flowback. The thickness of the internal filter cake can be

estimated by using UTDamage1 (as used in Chapter 5), X-ray imaging of thin sections of

the damaged cores 9, or by CAT scans. The yield strength of the internal filter cake can

be estimated using a constant strain rheometer (as shown in Chapter 4) or a constant

stress rheometer 10. The Bingham model needs to be combined with UTDamage to better

model the cleanup of the internal filter cake.

246

∆h = Thickness of an external cake layer, k = Permeability of an external cake layer dg = Average grain diameter of an external cake layer

∆h1, k1,dg1

∆h2, k2,dg2

Depth of damage

Formation grains

Mud particles and polymers


representing internal and external filter cake

247

Limiting trajectory

Liquid Shell

Grain

b dg

(b,θS)

(ap+ac , π)

(r,θ)

Flow

Pore throat diameter (dth)

Figure 7.2: Happel 's Sphere-in-cell porous media model representing the grain and the pore throat

248

Figure 7.3 (a): Initial saturation of fluids in the core

XF

LCORE XCAKE

Sw = 1 Sw = 1 - Sor Sw = Swi


Uninvaded zone

Filtrate invaded zone

Figure 7.3 (b): Fluid saturations after invasion of mud filtrate

Where XCAKE = Cake thickness

XF = Distance of the filtrate front from the core inlet

LCORE = Length of the core

Sw = Water saturation

So = Oil saturation

Sor = Residual oil saturation

Swi = Initial water saturation in the formation

LCORE

Sw = SwiSo = 1 - Swi Core Inlet

249

0

10

20

30

40

50

60


Ret

urn

Perm

eabi

lity

Rat

io (%

)

0

0.2

0.4

0.6

0.8

1

Eros

ion

fact

or

Experimental result UTDamage Results Erosion factor


04-I: UltraCarb-2 drill-in fluid on a short Berea core)

0

10

20

30

40

50

60

70

80


Ret

urn

Perm

eabi

lity

Rat

io (%

)

0

0.2

0.4

0.6

0.8

1

Eros

ion

fact

or

Experiment result UTDamage Results Erosion factor


04-#5: UltraCarb-2 drill-in fluid on a long Berea core)

250

0

0.2

0.4

0.6

0.8

1


Eros

ion

Fact

or

Long core exp. 1 Long core exp. 2 Short core exp. 1

Figure 7.6: Erosion factors used in UTDamage to match the experimental data (All

single-phase experiments using Berea sandstone and UltraCarb-2 drill-in fluid)

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100Applied Differential Pressure (psi)

Ret

urn

Perm

eabi

lity

Rat

io (%

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Eros

ion

Fact

or

Experimental Data UTDamage Results Erosion Factor


data for Texas limestone (LS-1: 1-P flow with UltraCarb-2 drill-in fluid)

251

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120 140


Ret

urn

Perm

eabi

lity

Rat

io (%

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Eros

ion

Fact

or

Experimental Results UTDamage Results Erosion Factor


data for Texas limestone (LS-12: Two-phase flow with UltraCarb-2 drill-in fluid)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140


Eros

ion

Fact

or

Single-phase experiment Two-phase experiment

Figure 7.9: Erosion factors for single-phase flow and two-phase flow return

permeabilities for Texas limestone cores (LS-1: 1-P, LS-12: 2-P experiment)

252

Nomenclature

φ : porosity

σ : specific deposit (volume of deposited particles per unit bulk volume)

u : darcy velocity

c : concentration of suspended fluid

λ : filtration coefficient

As : Happel’s geometric parameter

η : collection efficiency

NLO : London group

NR : Relative size group

NG : Gravity group

NPE : Peclet number

H : Hamakar constant for the particle medium system (~ 1*10-13 erg)

µ : plastic viscosity

ap : radius of the injected particle

ρp : injected particle density

ρf : fluid density

dg : grain diameter

DBM : Brownian diffusion coefficient

dp : diameter of the injected particle

fv : volume distribution function

rw : radius of the well

γu : velocity dependence parameter for filtration coefficient

Kdp : reduced porosity fraction

Kds : increased surface area fraction

Kdt : increased tortuosity fraction

P : pressure

dp : pore throat diameter

τy : mud cake yield point

253

Xd : depth of solids invasion, inch

ν : superficial flow velocity

h : cake thickness

φcrit : critical porosity

254

REFERENCES


Texas at Austin, December 2000.


Completion Fluids,” paper SPE 87676 published in SPEJ, March 2004

3. Jiao, D. and Sharma, M.M.: ‘Mechanism of cake buildup in crossflow filtration of

colloidal suspension’, Journal of Colloid and Interfacial Science, 162, pp 454-462,

1994.

4. Khilar, K. C., et. al (1998): "Existence of a Critical Particle Concentration in

Plugging of a Packed Bed," AICHE J, April 1998, Vol. 44, No. 4, 978-81

5. Panda, M.N. and Lake, L.W.: ‘Estimation of single-phase permeability from

parameters of particle-size distribution’, AAPG Bulletin, V.78, No. 7, July 1994.

6. Rajagopalan, R. and Tien, C.: ‘Trajectory analysis of deep bed filtraiotn with sphere-

in cell model’, AIChE J, Vol. 22, No. 3, May 1976.

7. Scheuerman, R.F. and Berensen, B.M.: ‘Injection-water salinity, formation

pretreatment and well-operations fluid-selection guidelines’, JPT, July 1990.

8. Sharma, M.M. and Yortsos, Y.C.: ‘Transport of particulate suspensions in porous

media: Model formulation’, AIChE Journal, October 1987.


at the SPE Eastern Regional Meeting held in the Pittsburgh, PA, 9-11 November,

1998.



in The Hague, The Netherlands, 21-22 May, 2001.

255

Chapter 8: Conclusions

1. Flow initiation pressures (FIP) are found to be considerably smaller with the constant

pressure flowback method compared to the constant rate flowback method. The

constant rate flowback method is found to be inadequate to estimate the FIP because

of two reasons: 1) the method yields FIP values which are rate dependent (which can

lead to very large FIP estimates) and 2) the constant rate flowback method does not

represent the wellbore condition during production.

2. An improved flowback method using constant differential pressures during flowback

is designed and used to estimate the FIP. Differential pressures are incremented in

steps to measure the return permeability spectra. The return permeability spectra,

when plotted as a function of applied differential pressure are consistently S-shaped.

3. Both single-phase (brine) and two-phase (oil and brine) experiments yielded small

and comparable values for the FIP. For very small permeability cores (Nugget

sandstone, 4 md), the FIP value for the two-phase flow experiment was slightly larger

than the FIP value obtained for a similar experiment but with single-phase flow.

4. The return permeability spectra can be used to evaluate the formation damage

potential of drill-in and completion fluids and to screen for the best fluids to use. The

return permeability spectra can be used to estimate the near wellbore permeability and

skin in vertical and horizontal wells.

5. The external filter cake is found to play no role in determining the FIP and the return

permeability spectra. The internal filter cake alone determines the FIP and return

permeabilities during flowback in open-hole completions.

256

6. Lab simulated perforated completions result in similar FIP values as lab simulated

open-hole completions. However, if the external filter cake thickness becomes equal

to or greater than the radius of the perforation tunnel (i.e. if the perforation tunnel is

completely plugged with the external filter cake) then an additional resistance is

imposed by the external filter cake in the form of a plug in the tunnel. This requires

additional pressure (larger FIP) to initiate production through these completely

plugged perforation tunnels. At small flowback pressures the return permeabilities in

lab-simulated perforated completions are found to be smaller than the return

permeabilities for the open-hole completions. This is because of the non-uniform

pressure gradients around the perforation tunnel compared to more uniform pressure

gradients across the internal filter cake in open-hole completions. However, at large

flowback pressures the return permeabilities in perforated completions are

comparable with the return permeabilities obtained in open-hole completions. This is

because a significant amount of internal filter cake is cleaned up at these large

pressure gradients in both the completions leading to similar return permeabilities.

7. A drill-in or a completion fluid with all the components (xanthan, starch, and sized

CaCO3) is the optimum fluid to use for maximizing return permeability and

minimizing fluid loss. Xanthan polymer causes the most damage while starch is

found to lower the FIP by minimizing the invasion of solids and polymers into the

formation and thus yielded larger return permeabilities.

8. Bentonite mud performed better than UltraCarb-2 drill-in fluid on Berea sandstone in

terms of FIP and return permeability. Using the median size of the bridging agent

equal or larger than the median size of the pore throat size of the formation (or mixing

257

two or three different grades of median sized bridging agents) in UltraCarb drill-in

fluids results in a lower FIP and larger return permeabilities. However, in terms of

fluid loss, bentonite mud does poorly (larger fluid losses than UltraCarb). The

external filter cakes formed from bentonite muds are much thicker than the external

filter cakes from UltraCarb drill-in fluids.

9. The yield strength of the external filter cake is measured using a constant strain

rheometer to model the cleanup of the internal filter cake to estimate the FIP and the

return permeabilities during flowback. Two different methods (dynamic strain sweep

test and linear strain test) were found to complement each other and provided

consistent yield strength measurements. However, the linear strain test is preferred

over the dynamic strain sweep test for measuring the yield strength of the filter cake

because it is quicker. Bentonite mud filter cakes are found to have larger shear

strength values than the filter cake samples prepared using UltraCarb drill-in fluids.

10. A bundle of tubes model and a network model with the effective medium

approximation is used to model the cleanup of the internal filter cake. A qualitative

match is found between the experiments and the models. The bundle of tubes model

predicts complete cleanup (100 % return permeability ratio) while the network model

captures the asymptotic values for return permeabilities (< 100 %) found in the

experiments.

11. Both the experimental results and the model results indicate that very large pressure

gradients are required to cleanup the internal filter cake completely. There will

always be some residual damage left in the near wellbore region due to the internal

filter cake. The near wellbore skin due to the internal filter cake is a function of the

258

drawdown or the flow rate. A pressure gradient of 10 psi/inch is required for a skin

factor < 1 in open-hole completions. For perforated completions a minimum

flowback velocity of 2 cm / min, or a flow rate of 0.3 bbl/day/perf or a pressure

gradient of 20 psi / inch is required to yield a skin factor < 2. The data presented can

be used to estimate the pressure gradient needed in wells to optimize production

while not failing the rock matrix and inducing sand production. The pressure

gradients required for small skin factors are achievable in vertical wells but may not

be easily achieved in horizontal wells.

1.1 RECOMMENDATIONS

1. We recommend using a median size for the bridging additive in drill-in and

completion fluids equal to the median pore-throat size of the formation for optimizing

the return permeability and fluid loss. The 1/3rd rule-of-thumb is not recommended

for determining the median size of the bridging agents. If the pore throat size

distribution of the formation is very broad then we recommend using a combination

of two or three different median sized bridging agents.

2. The skin around wells due to the internal filter cake should be calculated as a function

of the flow rate or the drawdown. The data presented (for a wide range of

permeability and for both open-hole and lab-simulated perforated completions) can be

used as a guide to estimate the skin factors in vertical and horizontal wells.

1.2 FUTURE WORK

1. Almost all the experiments in this study were conducted at an overbalance of 100 psi

during filtration. Large overbalance pressures can be applied during filtration in a

259

similar comprehensive experimental study to obtain more data (FIP and return

permeabilities).

2. Pressure measurements should be made at intervals of a few millimeters from the top

of the core to measure the differential pressure across this thin zone. These pressure

measurements can be used to further validate and tune the Bingham fluid model used

to represent the internal filter cake.

3. A similar comprehensive study can be done to estimate the FIP and return

permeability spectra for more commonly used oil-based and emulsion-based drill-in

and completion fluids.

260

Appendix-A: Photograph of the lab-setup used in conducting the experiments

261

Figure A.1: Photograph of the filtration and flow back apparatus

262

Appendix-B: Plots for single-phase constant pressure flowback experiments simulating open-hole completion

263

Table B.1: List of all the single-phase, constant pressure flowback experiments, simulating open-hole completion

Test No. Mud Used Rock Type

Av. Brine Perm (md)

Average Porosity

Overbalance (psi) Phase Core Type

Simulated Completion Type

Core Sample Name

1 UltraCarb-2 Nugget

sandstone 4 0.12 100 Single Short core Open hole NS-2

2 UltraCarb-2 Texas

limestone 24 0.28 100 Single Short core Open hole LS-1

3 UltraCarb-2 Texas

limestone 18 0.28 100 Single Short core Open hole LS-13*

4 Bentonite Texas

limestone 26 0.28 100 Single Short core Open hole LS-5

5 UltraCarb-2 Berea

sandstone 60 0.17 100 Single Short core Open hole BS-4-2-04-I

6 UltraCarb-2 Berea

sandstone 153 0.15 100 Single Long core Open hole BS-4-29-04-long-3

7 UltraCarb-2 Berea


8 UltraCarb-2 Berea


9 UltraCarb-20 Boise

sandstone 885 0.28 100 Single Short core Open hole Bo-1

10 Bentonite Boise

sandstone 982 0.28 100 Single Short core Open hole Bo-2

11 UltraCarb-2 Aloxide 960 0.44 100 Single Short core Open hole AL-1

12 UltraCarb-20 Aloxide 1313 0.44 100 Single Short core Open hole AL-2 * Experiment repeated to verify LS-1 experimental results.

264

Test No. 1

0

20

40

60

80

100

120

0 50 100 150 200 250Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

2

4

6

8

10

12

14

16

Mea

sure

d Ra

te (m

l/min

)

Flowback pressure (psi) Flowback Rate (ml/min)

Flowback started at ∆P = 2 psi


UltraCarb-2 on Nugget sandstone (NS-2)

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120

Applied Differential Pressure (psi)

Ret

urn

Per

mea

bilit

y Ra

tio (%

)


Nugget sandstone (NS-2)

265

0

5

10

15

20

0 10 20 30 40Sqrt of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure B-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole

completion (NS-2)

Discussion on the experiment

Figure B.2 shows a plot of return permeability ratio vs. flowback pressure on short

Nugget core (2.5 in. in diameter and 1 in. in length). There was no flow observed below a

differential pressure of 2 psi during flowback. The flow starts at a flowback pressure of 2

psi, and stabilizes with a return permeability ratio of 2.5% indicating very little cleanup

of the core. Upon increasing the applied differential pressure in small increments, larger

return permeability ratio values are observed as shown in the Figure B.2. At a differential

pressure of 20 psi, the return permeability ratio came up to 60.8%. The plot shows a

linear relationship between differential pressure and return permeability ratio nearly up to

a differential pressure of 20 psi indicating most of the cleanup. At larger drawdowns the

return permeability ratio becomes asymptotic as seen in Figure B.2. At a differential

pressure of 100 psi during flowback the return permeability ratio was 72.3%.

266

Test No. 2

0

20

40

60

80

100

120

0 50 100 150Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-2 on Texas limestone (LS-1)

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100


Ret

urn

Per

mea

bilit

y R

atio

(%)

Figure B-5: Return permeability spectra with incremental differential pressures for Texas

limestone (LS-1)

267

0

5

10

15

20

0 10 20 30 40Sqrt of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure B-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole completion (LS-1)


Figure B.5 shows a plot of return permeability ratio vs. flowback pressure on short Texas

limestone core (2.5 in. in diameter and 1 in. in length). As soon as a differential pressure

of 1 psi was applied, flow was observed. The flow was stabilized after some time with a

return permeability ratio of 33.8% indicating significant cleanup of the internal damage

in the core. Upon increasing the applied differential pressure in small increments, larger

return permeability ratio values are observed as shown in the Figure B.5. At a differential

pressure of 20 psi, the return permeability ratio came up to 54.3%. At larger drawdowns

the return permeability ratio remained nearly constant as can be seen in the Figure B.5.

At a differential pressure of 100 psi the return permeability ratio was 56.6%.

268

Test No. 3

0

20

40

60

80

100

120

0 10 20 30 40 50 60Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

5

10

15

20

25

30

35

40

45

50

Mea

sure

d Ra

te (m

l/min

)





0

20

40

60

80

100

0 20 40 60 80 100 120


Retu

rn P

erm

eabi

lity

Ratio

(%)

Figure B-8: Return permeability spectra with incremental differential pressures for Texas

limestone (LS-13)

269

0

5

10

15

20

0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure B-9: Static filtration of UltraCarb-2 on Texas limestone simulating open hole completion (LS-13)


Figure B.8 shows a plot of return permeability ratio vs. flowback pressure on short Texas

limestone core (2.5 in. in diameter and 1 in. in length). This experiment was conducted to

verify the results of earlier experiment (LS-1). The results indicate that the test results to

be very similar. This suggests that the tests are repeatable.

270

Test No. 4

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

80

90

Mea

sure

d Ra

te (m

l/min

)



bentonite on Texas limestone (LS-5)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60


Retu

rn P

erm

eabi

lity

Rat

io (%

)

Figure B-11: Return permeability spectra with incremental differential pressures for Texas limestone (LS-5)

271

0

20

40

60

80

0 5 10 15 20 25 30 35Sqrt of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure B-12: Static filtration of bentonite mud on Texas limestone simulating open hole

completion (LS-5)



Texas limestone core (2.5 in. in diameter and 1 in. in length). As soon as a differential

pressure of 1 psi was applied, flow was observed. The flow was stabilized after some

time with a return permeability ratio of 33.8% indicating significant cleanup of the

internal damage in the core. Upon increasing the applied differential pressure in small

increments, larger return permeability ratio values are observed as shown in Figure B.11.

At a differential pressure of 20 psi, the return permeability ratio came up to 100%. At

larger drawdowns the return permeability ratio remained nearly constant as can be seen in

the Figure B.11. At a differential pressure of 50 psi the return permeability ratio was

found to be more than 100%.

272

Test No. 5

0

5

10

15

20

25

0 50 100 150 200Time (min)

App

lied

Diff

eren

tial P

ress

ure

(psi

)

0

5

10

15

20

25

30

35

Mea

sure

d Ra

te (m

l/min

)



UltraCarb-2 on Berea sandstone (BS-4-2-04-I)

0

10

20

30

40

50

60

0 5 10 15 20


Ret

urn

Per

mea

bilit

y Ra

tio (%

)


Berea sandstone (BS-4-2-04-I)

273

0

1

2

3

4

0 2 4 6 8

Sqrt of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure B-15: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-4-2-04-I)



Berea core (2.5 in. in diameter and 1 in. in length). There was no flow observed below a

differential pressure of 4 psi during flowback. The flow starts at a flowback pressure of 4

psi, and stabilizes with a return permeability ratio of 0.9% indicating very little cleanup

of the core. Upon increasing the applied differential pressure in small increments, larger

return permeability ratio values are observed as shown in Figure B.14. At a differential

pressure of 20 psi, the return permeability ratio came up to 50.4%. The plot shows a

linear relationship between differential pressure and return permeability ratio. The

increasing linear trend suggests larger return permeabilities at differential pressure larger

than 20 psi during flowback.

274

Test No. 6

0

20

40

60

80

100

0 50 100 150 200 250 300 350 400Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

Mea

sure

d Ra

te (m

l/min

)



UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-3)

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100


Ret

urn

Perm

eabi

lity

Rat

io (%

)

Figure B-17: Return permeability spectra for incremental differential pressures in a long

Berea core (BS-long-3)

275

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35Sqrt of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)


completion (BS-long-3)


Figure B.17 shows results for return permeability ratio vs. flowback pressure in a long

Berea core (2 inch in diameter and 6 inch in length). The mud used was UltraCarb-2 for

the filtration step with an overbalance of 100 psi. The FIP was around 3 psi and the return

permeability ratio was 36.3% at FIP. Compared to the short Berea core experimental

results there was a significant amount of cleanup in the longer core. The short Berea core

showed a return permeability ratio of 0.9% at FIP while the longer core showed 36.3%.

The reason for the difference is not understood. Upon increasing the flowback pressure,

there was an increase in the return permeability ratio reaching an asymptotic value of

70% for the return permeability ratio.

276

Test No. 7

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300Time (min)

App

lied

Diff

eren

tial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

Mea

sure

d R

ate

(ml/m

in)




UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-4)

0

10

20

30

40

5060

70

80

90

100

0 20 40 60 80 100


Retu

rn P

erm

eabi

lity

Rat

io (%

)

For the whole core (0-6 inch)For the top 0-2 inch of the coreFor the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core


Berea core (BS-4-29-04-long-4)

277

0

5

10

15

20

0 10 20 30 40 50 60Sqrt of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

The overbalance pressure got reduced to 20 psi overnight but w as again increased to 100 psi

Figure B-21: Static filtration of UltraCarb-2 on a long Berea sandstone simulating open hole completion (BS-4-29-04-long-4)


Another long core experiment was done on Berea core with additional pressure taps at 2

inch and 4 inch point of the 6 inch long core. The reason was to study how different parts

of the core are cleaned during flowback and to estimate the depth of damage. Figure B.20

shows the results indicating nearly no damage at the far end (4-6 inch) and the middle

part (2-4 inch) of the core with permeability recovery of approximately 100% value.

Most of the damage was observed only at the top of the core (0-2 inch) as can be seen in

Figure B.20. In this experiment also the average permeability recovery for the whole core

was asymptotic reaching approximately a maximum of 70%.

278

Test No. 8

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90 100Time (min)

App

lied

Diff

eren

tial P

ress

ure

(psi

)

0

10

20

30

40

50

60

Mea

sure

d R

ate

(ml/m

in)



Figure B-22: Flowback rate at incremental differential pressures after filtration on a long

Berea sandstone with external filter cake removed (BS-4-29-04-long-5)

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80


Retu

rn P

erm

eabi

lity

Ratio

(%)



Berea core with external filter cake removed (BS-4-29-04-long-5)

279

0

4

8

12

16

0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure B-24: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-4-29-04-long-5)


Another long core experiment was done on Berea core but this time the external filter

cake was mechanically scraped from the top surface of the core before flow back. The

objective behind doing this was to study the role of external filter cake during flow back.

Figure B.23 shows the results of return permeability ratio vs. flow back pressure.

280

Test No. 9

0

10

20

30

40

50

60

0 10 20 30 40 50Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

50

100

150

200

250

300

350

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-20 on a Boise sandstone (Bo-1)

0

5

10

15

20

25

0 10 20 30 40 50 60


Retu

rn P

erm

eabi

lity

Rat

io (%

)


Boise sandstone (Bo-1)

281

0

5

10

15

20

25

30

0 10 20 30 40 50 60Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure B-27: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole completion (Bo-1)

282

Test No. 10

0

2

4

6

8

10

12

0 20 40 60 80 100 120Time (min)

App

lied

Diff

eren

tial P

ress

ure

(psi

)

0

20

40

60

80

100

120

Mea

sure

d R

ate

(ml/m

in)




bentonite mud on Boise sandstone (Bo-2)

0

5

10

15

20

25

30

0 2 4 6 8 10 12


Retu

rn P

erm

eabi

lity

Ratio

(%)


Boise sandstone (Bo-2)

283

0

20

40

60

80

0 5 10 15 20Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure B-30: Static filtration of bentonite mud on Boise sandstone simulating open hole completion (Bo-2)

284

Test No. 11

0

10

20

30

40

50

60

0 50 100 150 200 250 300Time (min)

Appl

ied

Diff

eren

tial P

ress

ure

(psi

)

0

20

40

60

80

100

120

140

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-2 on Aloxide core (Al-1)

0

1

2

3

4

5

6

0 10 20 30 40 50 60


Ret

urn

Per

mea

bilit

y R

atio

(%)


Aloxide core (Al-1)

285

0

10

20

30

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure B-33: Static filtration of UltraCarb-2 on Aloxide core simulating open hole completion (Al-1)

286

Test No. 12

0

10

20

30

40

50

60

0 50 100 150Time (min)

App

lied

Diffe

rent

ial P

ress

ure

(psi

)

0

50

100

150

200

250

300

Mea

sure

d R

ate

(ml/m

in)




UltraCarb-20 on Aloxide core (Al-2)

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60


Retu

rn P

erm

eabi

lity

Ratio

(%)


Aloxide core (Al-2)

287

0

5

10

15

20

0 10 20 30 40Sqrt of time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure B-36: Static filtration of UltraCarb-20 on Aloxide core simulating open hole completion (Al-2)

288

Appendix-C: Plots of two-phase constant pressure flowback experiments simulating open-hole condition

289

Table C.1: List of all the two-phase, constant pressure flowback experiments, simulating open-hole completion


Average Brine Perm. (md)

Average Porosity

Over balance pressure

(psi) Phase Core TypeSimulated

Completion TypeCore Sample

Name

1 UltraCarb-2 Nugget

sandstone 26 0.13 140 Two Short core Open hole NS-3

2 UltraCarb-2 Texas

limestone 15

(keff oil) 0.30 100 Two Short core Open hole LS-12

3 UltraCarb-2 Berea

sandstone 285 0.20 100 Two Short core Open hole BS-11-11-03-I

4 UltraCarb-20 Berea

sandstone 146

(keff oil) 0.20 100 Two Short core Open hole BS-21

5 UltraCarb-2 Berea

sandstone 129

(keff oil) 0.20 100 Two Short core Open hole BS-17

6

UltraCarb-5(20%)

+12(60%) +20(20%)

Berea sandstone

144 (keff oil) 0.20 500 Two Short core Open hole BS-19

7

UltraCarb-5(20%)

+12(60%) +20(20%)

Berea sandstone

138 (keff oil) 0.20

500 (with 500

psi as back pressure Two Short core Open hole BS-20

8 UltraCarb-20 Aloxide 965

(keff oil) 0.42 100 Two Short core Open hole AL-3


sandstone 600

(keff oil) 0.28 100 Two Short core Open hole Bo-7

290

Test No. 1

0

20

40

60

80

100

120

0 50 100 150 200Time (min)

App

lied

Diffe

rent

ial P

ress

ure

(psi

)

0

5

10

15

20

25

30

35

40

45

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-2 on Nugget sandstone (NS-3)

0

10

20

30

40

50

60

0 20 40 60 80 100 120


Ret

urn

Per

mea

bilit

y R

atio

(%)


Nugget sandstone (NS-3)

291

0

5

10

15

20

25

0 10 20 30 40Sqrt of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure C-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole completion (NS-3)

292

Test No. 2

0

20

40

60

80

100

120

140

0 50 100 150 200 250Time (min)

App

lied

Diffe

rent

ial P

ress

ure

(psi

)

0

5

10

15

20

25

30

35

40

45

Mea

sure

d Ra

te (m

l/min

)





0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120 140


Retu

rn P

erm

eabi

lity

Ratio

(%)

Figure C-5: Return permeability spectra with incremental differential pressures for Texas

limestone (LS-12)

293

0

5

10

15

20

0 10 20 30 40Sqrt of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure C-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole

completion (LS-12)

294

Test No. 3

0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

Time (min)

∆p

(psi

)

0

2

4

6

8

10

12

14

16

Rat

e (m

l/min

)

Const Pressure Flowback rate

FIP = 7 psi

kreturn = 25%

kreturn = 29%


UltraCarb-2 on Berea sandstone (BS-11-11-03-I)

0

10

20

30

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure C-8: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-11-11-03-I)

295

Test No. 4

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

50

100

150

200

250

Mea

sure

d R

ate

(ml/m

in)




UltraCarb-20 on Berea sandstone (BS-21)

0

20

40

60

80

100

0 20 40 60 80 100


Ret

urn

Perm

eabi

lity

Rat

io (%

)

296

Figure C-10: Return permeability spectra with incremental differential pressures for Berea sandstone (BS-21)

0

5

10

15

20

0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure C-11: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-21)

297

Test No. 5

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140Time (min)

App

lied

Diff

eren

tial P

ress

ure

(psi

)

0

50

100

150

200

250

Mea

sure

d R

ate

(ml/m

in)




UltraCarb-2 on Berea sandstone (BS-17)

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120


Retu

rn P

erm

eabi

lity

Ratio

(%)

298


0

5

10

15

20

0 10 20 30 40Sqrt of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure C-14: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-17)

299

Test No. 6

0

20

40

60

80

100

120

0 50 100 150 200 250 300Time (min)

App

lied

Diffe

rent

ial P

ress

ure

(psi

)

0

50

100

150

200

250

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-19)

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120


Retu

rn P

erm

eabi

lity

Rat

io (%

)

300


0

5

10

15

20

25

0 10 20 30 40Sqrt of Time (min)1/2

Volu

me

of F

iltra

te (m

l)


sandstone simulating open hole completion (BS-19)

301

Test No. 7

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

Mea

sure

d R

ate

(ml/m

in)




UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-20)

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40


Retu

rn P

erm

eabi

lity

Ratio

(%)

302


0

5

10

15

20

25

0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)


sandstone simulating open hole completion (BS-20)

303

Test No. 8

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120 140 160Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

50

100

150

200

250

300

350

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-20 on Aloxide core (AL-3)

0

5

10

15

20

25

30

0 10 20 30 40 50 60


Retu

rn P

erm

eabi

lity

Ratio

(%)

304

Figure C-22: Return permeability spectra with incremental differential pressures for Aloxide core (AL-3)

0

5

10

15

20

0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure C-23: Static filtration of UltraCarb-20 on Aloxide core simulating open hole

completion (AL-3)

305

Test No. 9

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70Time (min)

App

lied

Diff

eren

tial P

ress

ure

(psi

)

0

50

100

150

200

250

300

350

Mea

sure

d R

ate

(ml/m

in)




UltraCarb-20 on Boise sandstone (Bo-7)

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50


Ret

urn

Per

mea

bilit

y Ra

tio (%

)

306

Figure C-25: Return permeability spectra with incremental differential pressures for Boise sandstone (Bo-7)

0

5

10

15

0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure C-26: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole

completion (Bo-7)

307

Appendix-D: Plots for experiments with flow back at constant rate to study the role of individual drill-in fluid components on formation

damage

308

Table D.1: List of experiments with constant rate flowback condition to study the effect of individual drill-in fluid components on FIP, return permeability and API filtrate loss

Test No. Mud Used Rock

Type

Av. Brine Perm (md)

Average Porosity

Over balance

(psi)

Temp (oF)

Flowback rate

(ml/min)Phase Core

Dim.

Simulated Completion

Type

Core Sample Name

1 UltraCarb-2 Berea

sandstone 60 0.17 100 150 1 Two Short core Open-hole BS-4-16-03-II

2 UltraCarb-2 Berea

sandstone 247 0.19 100 150 5 Two Short core Open-hole BS-8-27-03-III

3 UltraCarb-2 (no starch)

Berea sandstone 60 0.20 100 150 1 Two

Short core Open-hole BS-4-21-03-II

4 UltraCarb-2 (no xanthan)


Short core Open-hole BS-4-21-03-III

5

UltraCarb-2 (no starch and

xanthan) Berea

sandstone 186 0.20 100 75 1 Two Short core Open-hole BS-6-8-03-IV

6


xanthan) Berea

sandstone 130 0.20 100 75 1 Two Short core Open-hole BS-6-8-03-V


sandstone 190 0.19 100 75 1 Two Short core Open-hole BS-6-8-03-VI

8 UltraCarb-12

(no starch) Berea

sandstone 128 0.17 100 75 5 Two Short core Open-hole BS-6-8-03-IX



Short core Open-hole BS-6-8-03-VIII

10


xanthan) Berea

sandstone 85 0.20 100 75 5 Two Short core Open-hole BS-6-8-03-VII

11 UltraCarb-12 +

RevDust Berea

sandstone 233 0.21 100 75 5 Two Short core Open-hole BS-10-2-03-I


sandstone 247 0.20 100 75 5 Two Short core Open-hole BS-8-27-03-II

309

Test No. Mud Used Rock

Type

Av. Brine Perm (md)

Average Porosity

Over balance

(psi)

Temp (oF)

Flowback rate

(ml/min)Phase Core

Dim.


Type

Core Sample Name

13 UltraCarb-20

(no starch) Berea

sandstone 535 0.19 100 75 5 Two Short core Open-hole BS-8-11-03-XI



Short core Open-hole BS-8-11-03-XII

15


xanthan) Berea

sandstone 142 0.20 100 75 5 Two Short core Open-hole BS-8-11-03-X

16 UltraCarb-20 +

RevDust Berea


17 Brine Berea


18 Brine + pH

Buffer Berea

sandstone 231 0.19 100 75 5 Two Short core Open-hole BS-8-11-03-XIII


sandstone 1121 0.29 100 75 5 SingleShort core Open-hole BS-8-11-03-XIII

310

Test No. 1

0

2

4

6

8

10

12

14

0 100 200 300 400Time (min)

Diffe

rent

ial p

ress

ure

durin

g flo

wba

ck

(psi

)

∆P (FIP) = 8.95 psi

Flowback rate = 1 ml/min


filtration with UltraCarb-2 (BS-4-16-03-II)

0

5

10

15

20

25

0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure D-2: Static filtration of UltraCarb-2 on Berea sandstone simulating open-hole completion (BS-4-16-03-II)

311

Test No. 2

0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400 500Time (min)

Diffe

rent

ial P

ress

ure

Dur

ing

Flow

back

(p

si)

3 ml / min

1 ml / min

5 ml / min

∆P (FIP) = 13.93 psi


filtration with UltraCarb-2 (BS-8-27-03-III)

0

5

10

15

20

25

30

0 1 2 3 4 5 6Flowback Rate (ml/min)

Retu

rn P

erm

eabi

lity

Rat

io (%

)

with external filter cake without external filter cake

312

Figure D-4: Return permeability spectra with varying flowback rates for Berea sandstone (BS-8-27-03-III)

0

5

10

15

20

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-5: Static filtration of UltraCarb-2 on Berea sandstone simulating open-hole completion (BS-8-27-03-III)

313

Test No. 3

0

2

4

6

8

10

12

14

0 100 200 300 400 500 600

Time (min)

Diff

eren

tial P

ress

ure

Duri

ng F

low

back

(p

si)

mud cake removed

∆P (FIP) = 10.78 psi

Kret (with mud cake) = 14.1 %Kret (w/o mud cake) = 20.0 %


filtration with UltraCarb-2 (no starch) (BS-4-21-03-II)

0

5

10

15

20

0 2 4 6 8Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

314

Figure D-7: Static filtration of UltraCarb-2 (no starch) on Berea sandstone simulating open-hole completion (BS-4-21-03-II)

Test No. 4

0

1

2

3

4

5

6

7

0 50 100 150 200 250 300 350Time (min)

Diff

eren

tial P

ress

ure

Duri

ng F

low

back

(p

si)

mud cake removed

∆P (FIP) = 3.57 psi

Kret (with mud cake) = 13.1%Kret (w/o mud cake) = 13.8 %


filtration with UltraCarb-2 (no xanthan) (BS-4-21-03-III)

0

10

20

30

40

0 4 8 12 16Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

315

Figure D-9: Static filtration of UltraCarb-2 (no xanthan) on Berea sandstone simulating

open-hole completion (BS-4-21-03-III)

Test No. 5

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300

Time (min)

Diffe

rent

ial P

ress

ure

Dur

ing

Flow

back

(psi

)

∆P (FIP) = 0.3 psi

1 ml/min

Kreturn at 1 ml / min = 29 %Kreturn at 3 ml / min = 74 %



filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-IV)

316

0

20

40

60

80

100

0 1 2 3 4Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure D-11: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea sandstone

simulating open-hole completion (BS-6-8-03-IV) Test No. 6

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80Time (min)

Diff

eren

tial P

ress

ure

Dur

ing

Flow

back

(p

si)

3 ml/min


Kreturn at 1 ml / min = 22 %Kreturn at 3 ml / min = 46 %


filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-V)

317

0

10

20

30

40

50

0 1 2 3Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-13: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea sandstone

simulating open-hole completion (BS-6-8-03-V)

318

Test No. 7

0

2

4

6

8

10

0 20 40 60 80 100Time (min)

Diff

eren

tial P

ress

ure

Duri

ng F

low

back

(psi

)

Kreturn at 3 ml / min = 34 %

∆P (FIP) = 7.33 psi


filtration with UltraCarb-12 (BS-6-8-03-VI)

0

4

8

12

16

20

0 10 20 30 40

Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)


completion (BS-6-8-03-VI)

319

Test No. 8

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400

Time (min)

Diff

eren

tial P

ress

ure

Duri

ng F

low

back

(psi

)

3 ml / min1 ml / min

Flowback rate = 5 ml / min

∆P (FIP) = 20 psi


filtration with UltraCarb-12 without starch (BS-6-8-03-IX)

0

5

10

15

20

25

30

35

0 2 4 6 8 10Flowback Rate (ml/min)

Retu

rn P

erm

eabi

lity

Ratio

(%)


sandstone (BS-6-8-03-IX)

320

0

10

20

30

40

50

60

0 2 4 6 8 10 12Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-18: Static filtration of UltraCarb-12 without starch on Berea sandstone simulating open-hole completion (BS-6-8-03-IX)

321

Test No. 9

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100Time (min)

Diffe

rent

ial P

ress

ure

Durin

g Fl

owba

ck

(psi

)

3 ml / min

1 ml / min


∆P (FIP) = 4 psi


filtration with UltraCarb-12 without xanthan (BS-6-8-03-VIII)

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2 2.5 3 3.5Flowback Rate (ml/min)

Retu

rn P

erm

eabi

lity

Ratio

(%)


sandstone (BS-6-8-03-VIII)

322

0

20

40

60

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-21: Static filtration of UltraCarb-12 without xanthan on Berea sandstone simulating open-hole completion (BS-6-8-03-VIII)

323

Test No. 10

0

2

4

6

8

10

12

14

0 10 20 30 40 50Time (min)

Diffe

rent

ial P

ress

ure

Durin

g Fl

owba

ck (p

si)

3 ml / min

1 ml / min


∆P (FIP) = 6.53 psi


filtration with UltraCarb-12 without xanthan and starch (BS-6-8-03-VII)

0

10

20

30

40

50

60

70

80


Retu

rn P

erm

eabi

lity

Rat

io (%

)


sandstone (BS-6-8-03-VII)

324

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1 1.2


Volu

me

of F

iltra

te (m

l)

Figure D-24: Static filtration of UltraCarb-12 without xanthan and starch on Berea sandstone simulating open-hole completion (BS-6-8-03-VII)

325

Test No. 11

0

2

4

6

8

10

12

14

0 20 40 60 80 100 120Time (min)

Diffe

rent

ial P

ress

ure

Duri

ng F

low

back

(p

si)

3 ml / min

1 ml / min

∆P (FIP) = 10.2 psi



filtration with UltraCarb-12 with RevDust (BS-10-2-03-I)

0

5

10

15

20

25

30

35

40


Ret

urn

Perm

eabi

lity

Rat

io (%

) with external filter cake

without external filter cake


sandstone (BS-10-2-03-I)

326

0

5

10

15

20

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-27: Static filtration of UltraCarb-12 with RevDust on Berea sandstone simulating open-hole completion (BS-10-2-03-I)

327

Test No. 12

0

2

4

6

8

10

12

14

0 25 50 75 100 125 150 175 200 225Time (min)

Diffe

rent

ial P

ress

ure

Dur

ing

Flow

back

(psi

)

3 ml / min

1 ml / min


∆P (FIP) = 9.97 psi



0

5

10

15

20

25

30

35

40


Retu

rn P

erm

eabi

lity

Rat

io (%

)

Figure D-29: Return permeability on Berea sandstone at different flowback rates after


328

0

5

10

15

20

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)


329

Test No. 13

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70Time (min)

Diffe

rent

ial P

ress

ure

Durin

g Fl

owba

ck (p

si)

3 ml / min

1 ml / min


∆P (FIP) = 4.71 psi


filtration with UltraCarb-20 without starch (BS-8-11-03-IX)

0

5

10

15

20

25

30

35

40

45


Ret

urn

Per

mea

bilit

y R

atio

(%)


sandstone (BS-8-11-03-IX)

330

0

10

20

30

40

50

0 4 8 12 16Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-33: Static filtration of UltraCarb-20 without starch on Berea sandstone simulating open-hole completion (BS-8-11-03-IX)

331

Test No. 14

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100Time (min)

Diffe

rent

ial P

ress

ure

Duri

ng F

low

back

(p

si)

3 ml / min

1 ml / min


∆P (FIP) = 4.36 psi


filtration with UltraCarb-20 without xanthan (BS-8-11-03-XII)

0

10

20

30

40

50

60


Ret

urn

Per

mea

bilit

y Ra

tio (%

)


sandstone (BS-8-11-03-XII)

332

0

10

20

30

40

50

0 5 10 15 20Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-36: Static filtration of UltraCarb-20 without xanthan on Berea sandstone simulating open-hole completion (BS-8-11-03-XII)

333

Test No. 15

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100Time (min)

Diff

eren

tial P

ress

ure

Dur

ing

Flow

back

(p

si)

1 ml / min



filtration with UltraCarb-20 without xanthan and starch (BS-8-11-03-X)

0

5

10

15

20

25

30

35

40

45

50


Ret

urn

Per

mea

bilit

y Ra

tio (%

)


sandstone (BS-8-11-03-X)

334

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2


Volu

me

of F

iltra

te (m

l)

Figure D-39: Static filtration of UltraCarb-20 without xanthan on Berea sandstone simulating open-hole completion (BS-8-11-03-X)

335

Test No. 16

0

2

4

6

8

10

12

14

16

0 50 100 150 200Time (min)

Diffe

rent

ial P

ress

ure

Duri

ng F

low

back

(psi

)

3 ml / min

1 ml / min


∆P (FIP) = 11.53 psi


filtration with UltraCarb-20 with RevDust (BS-10-7-03-I)

0

5

10

15

20

25

30

35

40

45

50


Ret

urn

Per

mea

bilit

y Ra

tio (%

)



336

0

5

10

15

20

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)


337

Test No. 17

0

1

2

3

4

5

6

0 10 20 30 40 50 60Time (min)

Diff

eren

tial P

ress

ure

Duri

ng F

low

back

(p

si)

3 ml / min

1 ml / min


∆P (FIP) = 2.51 psi


filtration with Brine (BS-8-27-03-I)

0

10

20

30

40

50

60


Retu

rn P

erm

eabi

lity

Ratio

(%)



338

0

20

40

60

80

0 0.1 0.2 0.3


Volu

me

of F

iltra

te (m

l)

Figure D-45: Static filtration of Brine on Berea sandstone simulating open-hole completion (BS-8-27-03-I)

339

Test No. 18

0

1

2

3

4

5

6

0 10 20 30 40 50Time (min)

Diffe

rent

ial P

ress

ure

Dur

ing

Flow

back

(p

si)


∆P (FIP) = 2.35 psi


filtration with Brine and pH buffer (BS-8-11-03-XIII)

0

10

20

30

40

50

60

70

80


Ret

urn

Perm

eabi

lity

Rat

io (%

)


sandstone (BS-8-11-03-XIII)

340

Test No. 19

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70Time (min)

Diffe

rent

ial P

ress

ure

Durin

g Fl

owba

ck (p

si)

∆PInitial = 0.09 psi

Return Perm = 10 %

∆PFinal = 0.97 psi

∆P(FIP) = 2.8 psi

Figure D-48: Differential pressure profile during flowback on Boise sandstone after

filtration with UltraCarb-20 (Bo-3)

0

5

10

15

20

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure D-49: Static filtration of UltraCarb-20 on Boise sandstone simulating open-hole

completion (Bo-3)

341

Appendix-E: Plots of single-phase filtration experiments conducted on cores with lab-simulated perforations with constant pressure flowback

condition

342

Table E.1: List of all the single-phase, constant pressure flowback experiments, simulating perforated completions


Av. Brine Perm (md)

Average Porosity

Overbalance (psi) Phase Core Type

Simulated Completion Type

Core Sample Name

1 UltraCarb-2 Texas

limestone ~25 0.31 100 Single Short core

Single perforation (1/4" dia., 1/2"

len.) LS-9

2 UltraCarb-2 Berea

sandstone ~200 0.17 100 Single Short core

Single perforation (1/8" dia., 1/2"

len.) BS-2-2-04-I

3 UltraCarb-2 Berea

sandstone 187 0.19 100 Single Long coreSingle perforation

(1/8" * 1") BS-6-5-04-long-6

4 UltraCarb-2 Berea


(1/8" * 2") BS-6-5-04-7

5 UltraCarb-2 Berea


(3/8" * 1") BS-6-13-04-8

6 UltraCarb-2 Berea


(1/4" * 2") BS-6-13-04-9

7 UltraCarb-2 Berea


(1/4" * 1") BS-6-29-04-10

8 UltraCarb-2 Berea


(1/8" * 1") BS-long-11

9 UltraCarb-2 Berea

sandstone 175 0.20 100 Single Long coreSingle perforation.

(1/8" * 2") BS-long-12



(1/4" * 1") BS-long-13



(1/4" * 2") BS-long-14


sandstone ~1000 0.29 100 Single Short coreSingle perforation. (1/8"dia., 1/2"len.) Bo-4


sandstone ~1000 0.28 500 Single Short coreSingle perforation. (1/8"dia., 1/2"len.) Bo-6

343

Test No. 1

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70Time (min)

App

lied

Diffe

rent

ial P

ress

ure

(psi

)

0

5

10

15

20

25

30

35

40

45

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-2 on Texas limestone with lab simulated perforation (LS-9)

0

20

40

60

80

100

0 20 40 60 80


Ret

urn

Per

mea

bilit

y Ra

tio (%

)

Figure E-2: Return permeability spectra with incremental differential pressures for Texas

limestone with lab simulated perforation (LS-9)

344

0

0.4

0.8

1.2

1.6

0 10 20 30 40Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure E-3: Static filtration of UltraCarb-2 on Texas limestone simulating open hole completion (LS-9)

345

Test No. 2

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300 350 400 450 500 550Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-2 on Berea core with lab simulated perforation (BS-2-2-04-I)

0

10

20

30

40

50

60

70

80

90

100


Ret

urn

Per

mea

bilit

y R

atio

(%)

Figure E-5: Return permeability spectra with incremental differential pressures for Berea

sandstone with lab simulated perforation (BS-2-2-04-I)

346

0

0.1

0.2

0.3

0.4

0 10 20 30 40


Volu

me

of F

iltra

te (m

l)

Figure E-6: Static filtration of UltraCarb-2 on Berea sandstone with lab simulated perforation (BS-2-2-04-I)

347

Test No. 3

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500Time (min)

Appl

ied

Diffe

rent

ial

Pres

sure

(psi

)

0

10

20

30

40

50

60

70

80

Mea

sure

d Ra

te (m

l/min

)




UltraCarb-2 on Berea sandstone (BS-6-5-04-long-6)

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120


Retu

rn P

erm

eabi

lity

Ratio

(%)

For the whole core (0-6 inch) For the top 0-2 inch of the coreFor the middle 2-4 inch of the core For the bottom 4-6 inch of the coreFor the top 0-1/8 inch of the core

Figure E-8: Return permeability spectra with incremental differential pressures for Berea

sandstone (BS-6-5-04-long-6)

348

0

0.5

1

1.5

2

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure E-9: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole

completion (BS-6-5-04-long-6)

349

Test No. 4

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400Time (min)

Appl

ied

Diff

eren

tial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

80

90

Mea

sure

d Ra

te (m

l/min

)



Figure E-10: Flowback rate at incremental differential pressures on Berea sandstone with

a lab simulated perforation (BS-6-5-04-long-7)

0

10

20

30

40

50

60

70

80

90

100


Ret

urn

Perm

eabi

lity

Ratio

(%)



Berea sandstone with a lab simulated perforation (BS-6-5-04-long-7)

350

0

1

2

3

4

0 10 20 30 40Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure E.12: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated perforation (BS-6-5-04-long-7)

351

Test No. 5

0

20

40

60

80

100

120

0 20 40 60 80 100 120Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

80

Mea

sure

d Ra

te (m

l/min

)


Flowback started at ∆P = 3.5 psi



0

20

40

60

80

100

120

0 20 40 60 80 100 120


Retu

rn P

erm

eabi

lity

Ratio

(%)

For the whole core (0-6 inch) For the top 1/8-2 inch of the coreFor the middle 2-4 inch of the core For the bottom 4-6 inch of the coreFor the top 0-1/8 inch of the core For the top 0-2 inch of the core



352

0

2

4

6

0 10 20 30 40Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure E-15: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated perforation (BS-6-13-04-long-8)

353

Test No. 6

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120 140Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

20

40

60

80

100

120

Mea

sure

d R

ate

(ml/m

in)


Flowback started at ∆P = 1.5 psi



0

20

40

60

80

100

120

140

160

180

200


Ret

urn

Per

mea

bilit

y Ra

tio (%

)

For the whole core (0-6 inch) For the top 1/8-2 inch of the core

For the middle 2-4 inch of the core For the bottom 4-6 inch of the core



354

0

2

4

6

8

10

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure E-18: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated perforation (BS-6-13-04-long-9)

355

Test No. 7

0

20

40

60

80

100

120

0 50 100 150 200 250 300Time (min)

Appl

ied

Diff

eren

tial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

80

Mea

sure

d Ra

te (m

l/min

)





0

10

20

30

40

50

60

70

80

90

100


Ret

urn

Perm

eabi

lity

Rat

io (%

)

For the w hole core (0-6 inch) For the middle 2-4 inch of the core

For the bottom 4-6 inch of the core For the top 0-2 inch of the core



356

0

1

2

3

4

0 10 20 30 40Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure E-21: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-6-29-04-long-10)

357

Test No. 8

0

20

40

60

80

100

120

0 50 100 150 200 250Time (min)

App

lied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

80

Mea

sure

d Ra

te (m

l/min

)




a lab simulated perforation (BS-long-11)

0

10

20

30

40

50

60

70

80

90

100


Ret

urn

Perm

eabi

lity

Rat

io (%

)

For the whole core (0-6 inch) For the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core For the top 0-2 inch of the core


Berea sandstone with a lab simulated perforation (BS-long-11)

358

0

0.5

1

1.5

2

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure E-24: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-long-11)

359

Test No. 9

0

20

40

60

80

100

120

0 50 100 150 200 250 300Time (min)

Appl

ied

Diff

eren

tial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

80

Mea

sure

d R

ate

(ml/m

in)





0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120


Ret

urn

Per

mea

bilit

y R

atio

(%)




360

0

1

2

3

4

5

0 10 20 30 40Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)


361

Test No. 10

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350 400Time (min)

Appl

ied

Diffe

retia

l Pre

ssur

e (p

si)

0

10

20

30

40

50

60

70

Mea

sure

d Ra

te (m

l/min

)





0

10

20

30

40

50

60

70

80

90

100


Retu

rn P

erm

eabi

lity

Ratio

(%)




362

0

1

2

3

4

5

0 10 20 30 40Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)


363

Test No. 11

0

20

40

60

80

100

120

0 10 20 30 40 50Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

10

20

30

40

50

60

70

80

90

Mea

sure

d Ra

te (m

l/min

)





0

10

20

30

40

50

60

70

80

90

100


Ret

urn

Per

mea

bilit

y Ra

tio (%

)




364

0

2

4

6

8

0 10 20 30 40Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)


365

Test No. 12

0

5

10

15

20

25

30

0 20 40 60 80 100 120Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

20

40

60

80

100

120

140

160

Mea

sure

d Ra

te (m

l/min

)



UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-4)

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30


Ret

urn

Perm

eabi

lity

Rat

io (%

)


Boise sandstone with a lab simulated perforation (Bo-4)

366

0

0.2

0.4

0.6

0.8

0 10 20 30 40Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure E-36: Static filtration of UltraCarb-20 on a long Berea core simulating open hole completion (Bo-4)

367

Test No. 13

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300 350Time (min)

Appl

ied

Diffe

rent

ial P

ress

ure

(psi

)

0

50

100

150

200

250

300

350

Mea

sure

d Ra

te (m

l/min

)

Flowback pressure Flowback rate



UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-6)

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80


Ret

urn

Perm

eabi

lity

Ratio

(%)


Boise sandstone with a lab simulated perforation (Bo-6)

368

0

0.2

0.4

0.6

0.8

0 10 20 30Sqrt. of Time (min)1/2

Vol

ume

of F

iltra

te (m

l)

Figure E-39: Static filtration of UltraCarb-20 on a long Berea core simulating open hole completion (Bo-6)

369

Appendix-F: Plots for two-phase constant pressure flowback experiments conducted on lab-simulated perforated cores

370

Table F.1: List of all the two-phase, constant pressure flowback experiments, simulating lab-simulated perforated completion


Av. Brine Perm (md)

Average Porosity

Over balance pressure

(psi) Phase Core TypeSimulated

Completion TypeCore Sample

Name

1 Bentonite Berea

sandstone Not

available 0.20 100 Two Short core3 Perforations

(1/8"dia.,1/2"len.) BS-12-22-03-I

2 Bentonite Berea

sandstone Not

available 0.20 100 Two Short coreSingle perforation (1/8"dia., 1/2"len.) BS-12-15-03-I

3 UltraCarb-2 Berea

sandstone Not

available 0.20 100 Two Short coreSingle perforation (1/8"dia., 1/2"len.) BS-12-08-03-I

371

Test No. 1

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300 350 400Time (min)

Appl

ied

Diff

eren

tial P

ress

ure

(psi

)

0

2

4

6

8

10

12

14

16

Mea

sure

d Ra

te (m

l/min

)




bentonite mud on Berea sandstone (BS-12-22-03-I)

0

20

40

60

80

100

0 5 10 15 20


Retu

rn P

erm

eabi

lity

Ratio

(%)

Figure F-2: Return permeability spectra with incremental differential pressures for Berea


372

0

2

4

6

8

0 5 10 15 20 25Sqrt. of Time (min)1/2

Volu

me

of F

iltra

te (m

l)

Figure F-3: Static filtration of bentonite mud on Berea sandstone simulating open hole completion (BS-12-22-03-I)

373

Test No. 2

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100 120 140 160Time (min)

App

lied

Diff

eren

tial P

ress

ure

(psi

)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Mea

sure

d R

ate

(ml/m

in)


Kreturn = 72%



bentonite mud on Berea sandstone (BS-12-15-03-I)

374

Test No. 3

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500

Time (min)

App

lied

Diffe

rent

ial P

ress

ure

(psi

)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Mea

sure

d Ra

te (m

l/min

)


kreturn = 56 %



UltraCarb-2 on Berea sandstone (BS-12-08-03)

375

Appendix-G: Detailed information of all the fluid filtration experiments with constant pressure flowback condition

376

Test No.M

ud UsedRock Type

Av. Brine Perm

(md)

Average Porosity

Overbalance (psi)

PhaseCore Type

Simulated Com

pletion TypeCore Sam

ple Name

FIP (psi)

Max return

perm (%

)

30 minute

API filtrate loss (m

l)Spurt loss (m

l)1

UltraCarb-2Nugget sandstone

40.12

100Single

Short coreOpen hole

NS-22

72.33.74

02

UltraCarb-2Nugget sandstone

260.13

140Two

Short coreOpen hole

NS-36

48.43.82

0

3UltraCarb-2

Texas limestone

240.28

100Single

Short coreO

pen holeLS-1

156.6

4.790.23

4UltraCarb-2

Texas limestone

180.28

100Single

Short coreO

pen holeLS-13 (Repeat)

255

4.550.2

5UltraCarb-2

Texas limestone

15 (keff oil)0.30

100Two

Short coreOpen hole

LS-122

92.84.84

0.36

BentoniteTexas lim

estone26

0.28100

SingleShort core

Open hole

LS-51

11722.4

17

UltraCarb-2Texas lim

estoneNA

0.31100

SingleShort core

Single perf. (1/4" dia. 1/2" len.)LS-9

178.9

0.160.1

8UltraCarb-2

Berea sandstone60

0.17100

SingleShort core

Open holeBS-4-2-04-I

450.4(20 psi)

4.650.2

9UltraCarb-2

Berea sandstoneNA

0.17100

SingleShort core

Single perf. (1/8" dia. 1/2" len.)BS-2-2-04-I

1096.8

0.020.01

10UltraCarb-2

Berea sandstone285

0.20100

TwoShort core

Open hole

BS-11-11-03-I7

29 (10)5.47

0.2611

BentoniteBerea sandstone

NA0.20

100Two

Short core3 Perf. (1/8"dia.1/2"len.)

BS-12-22-03-I8

55 (14)1.33

0.0612

BentoniteBerea sandstone

NA0.20

100Two

Short coreSingle perf. (1/8"dia.,1/2"len.)

BS-12-15-03-I14

72 (14)NA

NA13

UltraCarb-2Berea sandstone

NA0.20

100Two

Short coreSingle perf. (1/8"dia.,1/2"len.)

BS-12-08-03-I15

56 (15)NA

NA14


1530.15

100Single

Long coreO

pen hole BS-4-29-04-long-#3

367.8

6.390.63

15UltraCarb-2

Berea sandstone149

0.19100

SingleLong core

Open hole

BS-4-29-04-long-#42

765.46

0.5616


2070.19

100Single

Long coreO

pen holeBS-6-5-04-long-#5

271

6.370.88

17UltraCarb-2

Berea sandstone187

0.19100

SingleLong core

Single perf. (1/8" * 1")BS-6-5-04-long-#6

473

0.50NA

18UltraCarb-2

Berea sandstone190

0.19100

SingleLong core

Single perf. (1/8" * 2")BS-6-5-04-#7

374

0.87NA

19UltraCarb-2

Berea sandstone216

0.20100

SingleLong core

Single perf. (3/8" * 1")BS-6-13-04-8

3.563.1

1.15NA

20UltraCarb-2

Berea sandstone212

0.20100

SingleLong core

Single perf. (1/4" * 2")BS-6-13-04-9

<1.593

1.92NA

21UltraCarb-2

Berea sandstone207

0.20100

SingleLong core

Single perf. (1/4" * 1")BS-6-19-04-#10

464

0.89NA

22UltraCarb-2

Berea sandstone133

0.20100

SingleLong core

Single perf. (1/8" * 1")BS-1by8india-1indepth-#11

1096

0.46NA

23UltraCarb-2

Berea sandstone175

0.20100

SingleLong core


1478.9

1.06NA

24UltraCarb-2

Berea sandstone144

0.19100

SingleLong core


274.4

0.99NA

25UltraCarb-2

Berea sandstone174

0.19100

SingleLong core


187

1.72NA

25UltraCarb-2

Berea sandstone129(keff oil)

0.20100

TwoShort core

Open hole

BS-174

72.34.6

0.5726

2+12+20Berea sandstone

144(keff oil)0.20

500Two

Short coreOpen hole

BS-192

713.2

1.1627

2+12+20Berea sandstone

138(keff oil)0.20

500Two

Short coreOpen hole

BS-20 (Back pr = 500 psi)2

583.72

0.8128


146(keff oil)0.20

100Two

Short coreOpen hole

BS-214

853.41

0.13

29UltraCarb-20

Boise sandstone885

0.28100

SingleShort core

Open hole

Bo-13

204.16

0.4730

BentoniteBoise sandstone

9820.28

100Single

Short coreO

pen holeBo-2

125

31.10.68

31UltraCarb-20

Boise sandstoneNA

0.29100

SingleShort core

Single perf. (1/8"dia.,1/2"len.)Bo-4

238

0.120.015

32UltraCarb-20

Boise sandstoneNA

0.28500

SingleShort core

Single perf. (1/8"dia.,1/2"len.)Bo-6

521

0.10.018

33UltraCarb-20

Boise sandstone600(keff oil)

0.28100

TwoShort core

Open hole

Bo-72

953.23

0.65

34UltraCarb-2

Aloxide960

0.44100

SingleShort core

Open hole

AL-18

5 (50)14.9

3.6235

UltraCarb-20Aloxide

13130.44

100Single

Short coreOpen hole

AL-24

7.6 (50)8.04

1.0436

UltraCarb-20Aloxide

965 (keff oil)0.42

100Two

Short coreO

pen holeAL-3

326.5 (50)

5.61.1

377

Appendix-H: Detailed information of all the fluid filtration experiments with constant rate flowback condition

378

Test No.

Mud UsedRock Type

Av. Brine Perm (md)

Av. oil Perm (md)

Av. Porosity

Over balance

(psi)

Temp ( oF)

PhaseCore type*


Type

Core Sample Name

Flow back rate

(ml/min)

Peak pressure

(psi)

FIP (psi)

Return perm (%)

API filtrate (ml)

1UltraCarb-2

Berea sandstone60

N/A0.17

100150

TwoShort core

Open holeBS-4-16-03-II

111.9

8.95N/A

6.152


247217

0.19100

150Two

Short coreOpen hole

BS-8-27-03-III5

18.2713.93

266

3UltraCarb-2 (no starch)

Berea sandstone60

N/A0.20

100150

TwoShort core


113.3

10.7814

25.34

UltraCarb-2 (no xanthan)Berea sandstone

60N/A

0.19100

150Two

Short coreOpen hole

BS-4-21-03-III1

6.23.57

13.117.2

5UltraCarb-2 (no starch and xanthan)

Berea sandstone186

1290.20

10075

TwoShort core

Open holeBS-6-8-03-IV

12.1

0.329

3216

UltraCarb-2 (no starch and xanthan)Berea sandstone

13087

0.20100

75Two

Short coreOpen hole

BS-6-8-03-V1

2.50

22304

7UltraCarb-12

Berea sandstone190

1340.19

10075

TwoShort core

Open holeBS-6-8-03-VI

39.52

7.3333.9

3.628

UltraCarb-12 (no starch)Berea sandstone

12892

0.17100

75Two

Short coreOpen hole

BS-6-8-03-IX5

2920

2948.9

9UltraCarb-12 (no xanthan)

Berea sandstone252

1620.19

10075

TwoShort core

Open holeBS-6-8-03-VIII

57.47

4.0747

23.710


8570.5

0.20100

75Two

Short coreOpen hole

BS-6-8-03-VII5

12.536.53

70435.7

11UltraCarb-12 + RevDust

Berea sandstone233

2140.21

10075

TwoShort core


513.47

10.236

3.98

12UltraCarb-20

Berea sandstone247

1990.20

10075

TwoShort core


513.44

9.9733.4

4.513

UltraCarb-20 (no starch)Berea sandstone

535287

0.19100

75Two

Short coreOpen hole

BS-8-11-03-XI5

7.014.71

41.225.13

14UltraCarb-20 (no xanthan)

Berea sandstone291

1660.19

10075

TwoShort core

Open holeBS-8-11-03-XII

57.59

4.3653.1

27.715


142128

0.20100

75Two

Short coreOpen hole

BS-8-11-03-X5

9.395

44.8515

16UltraCarb-20 + RevDust

Berea sandstone272

1840.21

10075

TwoShort core


515

11.5339

4.44

17Brine

Berea sandstone223

1880.19

10075

TwoShort core


55.71

2.5152

95118

Brine + pH BufferBerea sandstone

231176

0.19100

75Two

Short coreOpen hole

BS-8-11-03-XIII5

4.952.35

72

19UltraCarb-20

Boise sandstone1121

0.29100

75Single

Short coreOpen hole

Bo-35

3.762.8

9.834.52

379

Nomenclature

A : cross-section area of the core

As : Happel’s geometric parameter

ap : radius of the injected particle

c : concentration of suspended fluid

dp : pore throat diameter

dg : grain diameter

DBM : Brownian diffusion coefficient

dp : diameter of the injected particle

fv : pore volume distribution function

f (r) : probability distribution function for radii of pore-segments and

capillary tubes

g : pore-segment conductance

g m : effective mean conductance during flowback

g mo : effective mean conductance for single phase flow when all the

pore-segments are allowing flow and are accessible

G’ : elastic modulus

G” : viscous modulus

G (g) : single-phase conductivity distribution function

G d, f (g) : conductivity distribution function for the displacing fluid

G d, f (g) : allowable conductivity distribution function displacing fluid

h : cake thickness

H : Hamakar constant for the particle medium system (~ 1*10-13 erg)

k : permeability

Kdp : reduced porosity fraction

Kds : increased surface area fraction

Kdt : increased tortuosity fraction

l : length of pore-throats in a network and length of bundle of

capillary tubes

380

L : core length

NLO : London group

NR : Relative size group

NG : Gravity group

NPE : Peclet number

P : pressure

q : flow rate

Q : filtrate loss

Qsp : spurt loss

r : radius of pore-throats and capillary tubes

R : radius of the largest capillary tube

rw : radius of the well

u : darcy velocity

V (r) : probability distribution function for volume occupied by pore-

segments and capillary tubes

X f : fraction of pores allowed to flow and can have displacement of

the Bingham fluid by the displacing fluid

X d, f : fraction of pores accessible to flow and have displacement of the

Bingham fluid by the displacing fluid

X c : Percolation threshold for a Bethe tree, i.e. the maximum

inaccessible fraction of pores

Xd : depth of solids invasion, inch

Z : average coordination number of the three dimensional network

that approximates pore space topology

Z b : local coordination number of Bethe tree

Greek Symbols

∆P : pressure difference across pore-segments and capillary tubes

381

τ : yield stress

γ : strain

µ : viscosity

δ (g) : Dirac delta function

φ : porosity

σ : specific deposit (volume of deposited particles per unit bulk

volume)

λ : filtration coefficient

η : collection efficiency

ρp : injected particle density

ρf : fluid density

γu : velocity dependence parameter for filtration coefficient

ν : superficial flow velocity

φcrit : critical porosity

382

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389

Vita

Ajay Suri was born in Delhi, India, on June 8 1975, as the son of Avinash

Chander Suri and Sita Rani. He received the degree of Bachelor of Technology in

petroleum engineering from the Indian School of Mines in 1998. In December 2000, he

graduated from the University of Texas at Austin with a MS in petroleum engineering.

He worked at Vignette Corporation from 2000 to 2001. In August 2002, he joined the

University of Texas at Austin to pursue a doctoral degree in petroleum engineering.

Permanent Address: A-41 Panchvati,

Near Azadpur,

Delhi, India - 110033

This dissertation was typed by Ajay Suri.

Copyright by Ajay Suri 2005

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Transcript of Copyright by Ajay Suri 2005