The Third PorosityUnderstanding the role of hidden porosity

in well test interpretation

Patrick Corbett, Sebastian GeigerLindemberg Borges, Roman Camillo, Julio Gonzalez

Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh

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Geological Society Carbonate Seminar, 4-5th November, 2010(SPE 130252, June, 2010: LPS Sept 2010: AFES Oct 2010)

Definitions

• Single Porosity – Matrix only

• Classic “Double Porosity” - Fractured Reservoirs

• “Double Matrix” Porosity Reservoirs – New awareness

• “Triple Porosity” - Fractured Double Matrix Reservoirs

• Numerical (geological) well testing – emerging standard workflow

• Petroleum Geoengineering – integrated geo-petrophys-eng workflow

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Workflow

Outcrop

Wireline logs

Well Test

Parameters

GEOENGINEERING

3D model

Syntheticresponse

Corbett et al., SPE 130252, 2010

Outline

• Definition of Single and Double Matrix Porosity Reservoirs

• Well testing concepts (WT - a geological tool)

• Numerical modelling of well tests

• Double Matrix Porosity

• Fractured systems

• Fracture + Double Matrix = Triple Porosity

• The Missing Third Porosity

• Fractured Well test interpretation

• Conclusions

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c) Microport

Phi=10%, K=5mD

b) Macroport

Phi=25%, K=250mD

a) Mesoport

Phi=25%, K=50mD

Rock Types (Martin, et al 1997)

Rock Type Pore Throat Size (µm)

Mean K (mD) Swi Sro Rock Fabric

Macroport 2 - 10 250 0.15 0.2 Grainstone oolitic

Mesoport 0.5 - 2 50 0.25 0.3 Grainstone oolitic

Microport < 2 5 0.35 0.35 Grainstone oolitic

Double Matrix Geological Model

Morales, 2009

Ahr, 2008

Double Matrix Porosity

• Lorenz coefficient (Lc) is related to local heterogeneity (close to the well), and the pressure response investigates bigger volume of reservoir.

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DoublePorosity

Reservoirs

Well testing

• Simple well testing history

q

0tp t

Well producing Well shut-in

t

P

0tp t

Draw-down Build-up

t

∂ 2 P∂X2 ηx +

∂ 2 P∂Y 2 ηy +

∂ 2 P∂Z 2 ηz =

∂P∂t

η j =kj

φµCt

, j = x, y,z

• Diffusivity equation

• Hydraulic diffusivity

(From Corbett, DISC, 2009, after Zheng)

Skin

• Difference between pressure at shut-in and after 1hr (on the Horner straight line) (Bourdarot,1998)

−∆PskinP2

P1

+∆Pskin

+ve : Extra pressure drop at wellbore

-ve : Reduced pressure drop at wellbore

(From Corbett, DISC)

Pressure derivative plots (in a box)

Flow lines in an infinite linear strip

Infinite extent

Pressure contour in an infinite linear strip

Infinite extent

L

W Well

MTR Radial Flow infinite acting

Half slope linear flow

Unit slope PSS

LOG(TD) (Dimensionless)

LO

G(D

PD/D

TD

) (D

imen

sion

less

)

Flow regimes

No flow boundary with pressure depletion

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3

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3

Sst

(From Corbett, DISC, 2009, after Zheng)

Well testing Simplified

ETR MTR LTR

Log(t)

DP __ DT

ETR - near well bore phenomena, skin

MTR - radial flow, kh

LTR - Boundaries, pressure support, contacts

The rate that the pressure response moves away from the well is a function of the diffusivity (k/µφc)

Early Time Region Middle Time Region Late Time Region

(From Corbett, DISC, 2009)

Methodology: Workflow

Geological Model Flow Simulation

Drawdown Analysis

Forward problem where the model is built and then the pressure response is simulated and analyzed

Model 04c

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Methodology: Geological Model

• Very low permeability rock type (microport) was distributed as background

• Good permeability rock type (macroport) was distributed as objects (ellipse and quart ellipse)

Macroport

Microport

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Methodology: Geological Model• Porosity was set constant value for the whole model

• Permeability was distributed using Sequential Gaussian Simulation (SGS) -variogram (spherical type)

• Very low permeability was distributed in the background rock type

• High permeability was distributed in the objects

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Methodology: Flow Simulation• Model size 1000m x 1000m x 50m

• Grid size 10mx10mx1.67m ; Cells NX=100, NY=100, NZ=30 (300,000 cells)

• Refinement close to the well - cell of 1m x 1m x 1.67m

• Oil properties from North Sea Field

• Oil rate constant 500 stb/day ; BHP limit of 1000 psia (single phase flow)

• Oil density of 42 API (50.9 lb/ft3 or 0.815 g/cc) ; µ = 0.82 cP, Bo = 1.21 rb/stb, Pb = 980 psia, Pi = 2436 psia @ 1585m (5200 ft) 14

Methodology: Flow Simulation

Cross section showing k distribution(Model 04c5)

Cross section showing the pressure behaviour during the drawdown

Delta P = 137 psia

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Methodology: Well Testing Analysis

• Transient pressure analysis performed in the drawdown test period

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Results and Discussion• Validation of the workflow: transient pressure response is

consistent with the geometric average in the case of model 04c and arithmetic average for model 05c

Model 04c Whole model 04cKar (mD) 31Kgeo (mD) 3

Well locationKar (mD) 28Kgeo (mD) 8

Model 05c Whole model 05cKar (mD) 59Kgeo (mD) 5.6

Well locationKar (mD) 76Kgeo (mD) 10

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“Geoskin”

Results and Discussion

Model 04c Model 04c7 Model 04c2

Krange= 10 to 400 mD Krange= 10 to 4,000 mDKrange= 1 to 40 mD

• Different permeability ranges distributed in models with the same vuggy patch arrangement present similar pressure response. Same distribution of in all 3 layers.

18Systematic double porosity, vuggy carbonate geotype curves

Results and Discussion

Model 04c5 Model 04c8

Krange= 1 to 40 mDKrange= 1 to 4,000 mD

• Different permeability ranges distributed in models with the same vuggy patch arrangement present similar pressure response, in these cases different distributions per layer.

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Results and Discussion• Different models with good connectivity between vuggy

patches present similar pressure response even with different vuggy patch distributions

Model 06cModel 05c Model 08c

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The obtained results validate the numerical well test workflowapplied in this study.

The model dimensions and grid size used in this study were suitableto generate simulated pressure data to be analyzed.

Visualise tortuous flow path to the well

Dual permeability (Dual porosity) flow model was interpreted for allmodels.

No Fractures in the model but we get a faulted/fracced response

Object modeling good representation of a vuggy carbonate.

Methodology to generate Carbonate Geotype curves

Double Matrix Carbonate Conclusions

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Fractured ReservoirsStorativity Ratio (ω) and Interporosity flow coefficient (λ)

“ω defines the contribution of the fissure system to the total

storativity”

Bourdet, D. (2002). Well Test Analysis: The Use of Advanced Interpretation Models

mtft

ft

VcVcVc

)()()(φφ

φω

+=

kkr m

w2αλ =

“λ defines the ability of the matrix blocks to produce into the fissure

system”

NE-FracSet

E-FracSet

K (md)

ω S Lambda

E-Frac Set186 0.51 -4.5 1.1e-06

NE- Frac Set 143 0.50 -5 6.72e-07

Fractured Reservoirs

East Set North-East Set

3 hrs122 hrs

1500 hrs

WELL

Outcrop-derived Fracture Model

E-Frac Set

NE-FracSet

Matrix Permeability – Vuggy zones

High Permeable Matrix

Low Permeable Matrix

K (md) ω S Lambda

E-Frac Set210 0.33 -4.6 1e-06

NE- Frac Set 183 0.42 -4.9 3.96e-07

East Set North-East Set

3 hrs122 hrs

1500 hrs

Numerical Well Test Modelling

Numerical solution provides ability to model fractures and matrix

Analyse tortuous flow along different fracture sets

Investigate effects of different oil viscosities

See typical fracture double porosity response – but not tripleporosity response

Difficult to relate WT parameters back to the model and thereservoir description

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Fracture Well Test Analysis

K x h = 600mDftWhere h = 60ft

Which K = 10mD???

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Fractured Reservoir Well Testing

CorePetrophysicalOutcrop

Triple porosity

Restricted interporosity flow condition

Pseudo-steady state dual

porosity model

>>>>>>>> How do we recover separate matrix and fracture descriptions?

Reservoir Matrix in Carbonate Reservoirs prone to doublematrix porosity (WT) behaviour

Add fractures and carbonate reservoirs tend to triple-porosity system: matrix (micro), vuggy (macro) andfractures with high tortuosity

Well testing response doesn’t show triple porosity

Well Testing response is “effective” double porosity

How do we extract the double matrix and fracturecharacteristic parameters?

Role of numerical well test modelling in carbonates crucialto well test interpretation and reservoir characterisation.

Limitations in the models and/or in the responses?

Conclusion

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ACKNOWLEDGEMENTS

Providers of the various software packages used in this study

• Schlumberger – Petrel and Eclipse• CSMP• Weatherford – PanSystem

ICCR Sponsors

• BG and Petrobras