Modeling Fluid Flow Through Single Fractures Using Experimental, Stochastic and Simulation...

Post on 20-Dec-2015

216 views 3 download

Tags:

Transcript of Modeling Fluid Flow Through Single Fractures Using Experimental, Stochastic and Simulation...

Modeling Fluid Flow Through Single Fractures

Using Experimental, Stochastic and Simulation

Approaches

Dicman AlfredDicman Alfred

Masters DivisionMasters Division

TAMUTAMU

Introduction

• A NFR with extensive fractures

• Poor ultimate recoveryGlasscock Co

Reagan CoUpton Co

Midland Co

Martin Co Borden Co

Spraberry Trend AreaSpraberry Trend Area

Reserves 10B bbls

Recovery < 10 %

TAMUTAMU

Why study fracture flow?

Improve prediction of sweep in Naturally Fractured reservoirs

Improve modeling of tracer studies

ShaleShale

TAMUTAMU

Knowledge of the nature and mechanics of flow through a fracture becomes

critical.

Starts from basic understanding of core studies.

Getting the basics right!Getting the basics right!

TAMUTAMU

Fractures as parallel plates

Historical perspectiveHistorical perspective

Constant Constant widthwidth

TAMUTAMU

Fracture Model

w12

2wK f

Historical perspectiveHistorical perspective

Constant permeability fracture surface

TAMUTAMU

L

pplbq L 0

3

12

Cubic Law of Fractures

Historical perspectiveHistorical perspective

Aperture half width

Fracture length

TAMUTAMU

w

Fractures cannot be assumed as parallel plates.

Reality ?Reality ?

TAMUTAMU

Fractures cannot be assumed as parallel plates.

Reality ?Reality ?

A real fracture surface is rough and tortuous.

TAMUTAMU

Tracy (1980)

Iwai (1976)

Neuzil(1980)

Witherspoon (1980)

The flow through a fracture follows preferred paths because of the variation in fracture aperture.

Issues Issues

TAMUTAMU

Tsang&Tsang(1988)Brown (1987)

The friction associated with the rough fracture surface affects the flow

performance.

More issues More issues

TAMUTAMU

The story so far …

Effect of friction in fracture flow simulations

Aperture Width ?

Stochastic aperture simulations

Experimental support

TAMUTAMU

1. How do we obtain fracture aperture width?

2. How do we simulate flow through fractures effectively?

The objectiveThe objective

Application of water-resource research technology into petroleum engineering

TAMUTAMU

The approachThe approach

Experimental Analysis

Aperture width, qm, qf

Fracture simulation

Simulation

Aperture distribution

Stochastic Analysis

TAMUTAMU

Fracture simulation

Simulation

Aperture distribution

Stochastic Analysis

The approachThe approach

Experimental Analysis

Aperture width, Qm, Qf

TAMUTAMU

Information from experiments?

•Fracture permeability

•Fracture aperture

•Matrix and fracture flow contributions

•How these properties change with overburden stress

Motivation Motivation

TAMUTAMU

In the past …

Impermeable surface

Sand grains

Apertures measured physically

Flow experiments

TAMUTAMU

New perspective…New perspective…

500 psi 1000 psi

1500 psi

To quantify the change in aperture with overburden pressure

TAMUTAMU

km

Experimental Experimental setupsetup

CORE HOLDER Permeameter

Accumulator

Graduated Cylinder

Pump

Hydraulic jack

Matrix

L=4.98 Cm

A=4.96 Cm2

Core : BereaCore : Berea

TAMUTAMU

Experimental Experimental setupsetup

kavCORE HOLDER Permeameter

Accumulator

Graduated Cylinder

Pump

Hydraulic jack

Core : BereaCore : Berea

Matrix

L=4.98 CmA=4.96 Cm2

Fracture

km

TAMUTAMU

Permeability Changes at Permeability Changes at Variable Overburden PressureVariable Overburden Pressure

kav

km

800

1400

0

0 1000 2000

Overburden Pressure (Psia)

Per

mea

bili

ty (

md

)

400

TAMUTAMU

Using weighted averaging

ffmmav AkAkAk

Fracture aperture?Fracture aperture?

wl

wlAkAkk mavf

)(

w

l

The unknowns k f and w

(1)

TAMUTAMU

From parallel-plate assumption

291045.8 wk f (2)

Combine the two equations to derive aperture width, w

0)(1045.8 39 wlAkAklw mav

Average aperture equationAverage aperture equation

TAMUTAMU

Fracture apertureFracture aperture

Increase in overburden pressure decreases aperture width

0

0.002

0.004

0.006

0 400 800 1200 1600

Overburden Pressure (Psia)

Fra

ctu

re A

per

ture

(cm

)

5 cc/min

10 cc/min

15 cc/min

20 cc/min

5 cc/min5 cc/min10 cc/min10 cc/min15 cc/min15 cc/min20 cc/min20 cc/min

TAMUTAMU

Matrix flow rateMatrix flow rate

0.00

5.00

15.00

25.00

0 400 800 1200 1600

Overburden Pressure (Psia)

Mat

rix

Flo

w R

ate

(cc/

min

)

5 cc/min

10 cc/min

15 cc/min

20 cc/minL

pAkq mm

TAMUTAMU

Fracture flow rateFracture flow rate

0.00

2.00

4.00

8.00

12.00

16.00

0 400 800 1200 1600Overburden Pressure (Psia)

Fra

ctu

re F

low

Rat

e (c

c/m

in)

5 cc/min

10 cc/min

15 cc/min

20 cc/min

L

plwq f 12

1086.93

9

Km = 200 mdKf = 10-50 darcy

TAMUTAMU

Experimental Analysis

Aperture width, Qm, Qf

Fracture simulation

Simulation

Aperture distribution

Stochastic Analysis

The approachThe approach

TAMUTAMU

o Is it possible to create an entire aperture distribution from a single value of mean aperture?

o From experimental analysis

waperture

MotivationMotivation

TAMUTAMU

2ln

2

1exp

2

1)(

x

xxf

Log-Normal Mean

Log-Normal Deviation

Variable( Aperture )

Aperture distributionAperture distribution

Apertures distributed log-normally

TAMUTAMU

Generation of aperturesGeneration of apertures

Through a mean and a variance

TAMUTAMU

Application?Application?

Smooth fracture surfaceSmooth fracture surface

TAMUTAMU

Slightly rough fracture surfaceSlightly rough fracture surface

Application?Application?

TAMUTAMU

Application?Application?

Highly rough surface fractureHighly rough surface fracture

Larger Aperture Size

TAMUTAMU

Creation of the aperture map

Variogram

Stochastic analysisStochastic analysis

Lag distance

Co-

var

ianc

eKriging

TAMUTAMU

Aperture distribution mapAperture distribution map

Outcome of Kriging

0.087

0.567

1.047

1.527

2.007

2.487

2.967

3.447

3.927

4.407

4.887 2.329

2.009

1.689

1.369

1.049

0.729

0.409

0.089

2021.523

24.526

27.5

29

30.5

32

33.5

35

3D 2D

TAMUTAMU

Comparison

Not the real picture but effective

Good enough?Good enough?

TAMUTAMU

Experimental Analysis

Aperture width, Qm, Qf

Aperture distribution

Stochastic Analysis

The approachThe approach

Fracture simulation

Simulation

TAMUTAMU

Motivation Motivation

Tackle the issue of surface roughness

Match the experimental results, namely flow and pressure drop across the core

TAMUTAMU

Surface roughnessSurface roughness

2be

Louis (1974) defined a friction factor, f based on the relative roughness ,

D

e

D is the hydraulic diameter = 2 × 2b

TAMUTAMU

Surface roughnessSurface roughness

2be

He proposed that when

D

e > 0.033 f =

5.1

88.11D

e

TAMUTAMU

Surface roughnessSurface roughness

2be

Modified cubic law

L

ppl

f

bq L 0

3

12

TAMUTAMU

Permeability modification of the fracture surface

Without friction With friction

Effect of friction?Effect of friction?

400 darcy400 darcy 350 darcy350 darcy

TAMUTAMU

Simulator used : CMG Single phase black oil simulation Laboratory dimensions (4.9875” x

2.51”) Refined model : 31x15x15 layers Fracture properties is introduced in 8th

layer Matrix porosity = 0.168 Matrix permeability = 296 md

Simulation ParametersExample of flow through single fracture

SimulationSimulation

TAMUTAMU

Flow on a smooth fracture surfaceFlow on a smooth fracture surface

TAMUTAMU

Flow on the distributed fracture surfacefollows preferred flow paths

TAMUTAMU

Results Results

Observed

0

1

2

3

4

5

6

7

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure, psia

Pre

ssu

re D

rop

, ps

iaParallel Plate Theory

Simulated

TAMUTAMU

0.00

1.00

2.00

3.00

4.00

5.00

0 400 800 1200 1600

Overburden Pressure (Psia)

Flo

w R

ate

(c

c/m

in)

fracture

matrix

Flow match Flow match

Parallel Plate Theory

TAMUTAMU

The new approach The new approach

0

1

2

3

4

5

0 500 1000 1500 2000

Overburden Pressure, psia

Pre

ssu

re D

rop

, ps

ia

Observed

Simulated

TAMUTAMU

Flow match

0

1

2

3

4

5

0 500 1000 1500 2000

Overburden Pressure, psia

Flo

w R

ate

, cc

/min

fracture

matrix

The new approach The new approach

TAMUTAMU

Limitation? Limitation?

No roughness ortortuosity effect

0

1

2

3

4

5

6

0 20 40 60 80 100 120

Aperture width, microns

Flo

w r

ate

, c

c/m

in

Smooth fracture

Rough fracture

TAMUTAMU

Applications Applications

Gravity Drainage Experiment

TAMUTAMU

X-Ray

DetectorX-Ray Source

Brine

X-ray ct scan

TAMUTAMU

Parallel-Plate Theory

Applications Applications

Gravity-Drainage Experiment

TAMUTAMUGravity-Drainage Experiment

Our Approach

Applications Applications

TAMUTAMU

The new approach The new approach Gravity-Drainage Experiment

Simulation X ray CT Scan

TAMUTAMU

ConclusionsConclusions

How do we obtain fracture-aperture width ?

Obtain value for average aperture width through effective design of experiments

0

0.002

0.004

0.006

0 400 800 1200 1600

Overburden Pressure (Psia)

Fra

ctu

re A

per

ture

(cm

)

TAMUTAMU

Distribute fracture apertures

Consider effect of friction caused by rough fracture surfaces

How do we simulate flow through fractures more effectively ?

ConclusionsConclusions

TAMUTAMU

Tail of frequency distribution impacts flow performance

Tortuosity dominates fracture flow at high overburden pressures

What other factors affect flow through fractures?

ConclusionsConclusions

TAMUTAMU

Improve prediction of sweep in naturally fractured reservoirs

Improve modeling of tracer studies

Why study rugosity in fractures?

ConclusionsConclusions