Vivek Muralidharan Simulation and imaging experiments of fluid flow through a fracture surface: a new perspective

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Vivek Vivek MuralidharanMuralidharan

Simulation and imaging Simulation and imaging experiments of fluid flow through a experiments of fluid flow through a

fracture surface: a new fracture surface: a new perspectiveperspective

Log Log AnalysisAnalysis

Fracture Fracture CharacterizationCharacterization

Aperture distribution

Fracture Fracture ModelModel

ww

Fractured Reservoirs

Poor recovery

Laboratory Laboratory ExperimentsExperiments

SimulationSimulation

Workstation 3D CT Image3D CT Image

Digital DetectorX-Ray Source

Object

X-Ray Tomography

X-ray CT scanner

Presentation Outline

• Historical Perspective Historical Perspective

• Objectives and ApproachObjectives and Approach

• ApplicationsApplications

• ConclusionsConclusions

Fracture Model

Historical perspective Historical perspective

w

Constant fracture aperture

Historical perspective Historical perspective

Cubic Law

L

pplbq L

03

12

Aperture Size

Parallel Plate Assumption Parallel Plate Assumption

w

Single Fracture Aperture

Fracture Aperture Fracture Aperture

Fracture roughness

Better History Match

Realistic simulation model

Fracture Aperture Fracture Aperture DistributionDistribution

Fracture aperture

distribution

Pyrak-Nolte et al., (1987)

Tsang et al., 1987

Gale, 1987Keller, (1996)

Lognormal distribution for natural fractures

2ln

2

1exp

2

1)(

x

xxf

Log-Normal Mean

Log-Normal Deviation

Variable( Aperture )

Apertures distributed log-normally

Lognormal Function Lognormal Function

Generation of aperturesGeneration of apertures

Smooth fracture surfaceSmooth fracture surface

Aperture Distribution Aperture Distribution

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0 200 400 600 800 1000 1200

Fracture aperture, microns

Rel

ativ

e fr

equ

ency

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0 200 400 600 800 1000 1200


Rel

ativ

e F

req

uen

cy


Slightly rough fracture surfaceSlightly rough fracture surface

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0 200 400 600 800 1000 1200


Rel

ativ

e F

req

uen

cy

Highly rough surface fractureHighly rough surface fracture


Larger Aperture Size

Problems Problems

• Aperture distribution is proved for fractures without experiencing any stress.

• Aperture distribution has not yet been investigated under different stress condition.

• Single fracture aperture does not represent the actual flow through fracture


• Historical PerspectiveHistorical Perspective




Objectives Objectives

X-ray CT scanner

Stress

Aperture distribution?

Aperture distribution has not yet been investigated

under different stress condition.

Problem:


X-ray CT scanner

Gravity drainage experiment

Single fracture aperture does not represent the actual flow through fracture

Problem:

Aperture distribution under Aperture distribution under stress using X-ray CT scanner stress using X-ray CT scanner

Workstation 3D CT Image3D CT Image

Digital DetectorX-Ray Source

Object

X-Ray Tomography

Experiments in X-ray CT scanner

ApproachApproach

Scan

Scans at multiple locations

Calibration

Aperture Distribution

X-ray CT Scanner

CT scanner analyzes density differences between objects

Matrix and fracture identification

Density of rock

Density of fluid in fracture

1000

1200

1400

1600

0 20 40 60 80

Pixel number

CT

nu

mb

er

X-ray CT Scans

Matrix

Fracture

CT numbers are different from actual aperture size Calibration Technique to

correlate CT to obtain fracture aperture size

No direct measurement of fracture aperture

Scanned the core between

feeler gauges

Calibration Procedure

Smooth surface

Feeler gauge of known size


Fracture

Matrix

Min rock CT


Integrated CT area

0

1000

2000

3000

4000

5000

6000

7000

8000

0 100 200 300 400 500 600 700 800 900

Fracture aperture (microns)

Inte

gra

ted

CT

sig

nal

Calibration Curve

7.4607616.8 xCTarea

Feeler gauge size

Calibration curve

Integrated CT area

Scans of fractured core of unknown

apertures

Fracture aperture

0

1000

2000

3000

4000

5000

6000

7000

8000

0 100 200 300 400 500 600 700 800 900

Fracture aperture (microns)

Inte

gra

ted

CT

sig

nal

Calibration Curve

7.4607616.8 xCTarea

Determination of fracture aperture

7616.8

7.460 areaCTx

Aperture Distribution

Scans taken along the length of the core

Animation

Apertures along the length of the core

No stress 500 psi 1000 psi 1500 psi

Apertures

90 sections70 locations

Around 6000 sectionsFour different stress conditions

24000 aperturesApertures are calculated from

calibration curve

Aperture Distribution without stress

Lognormal distributionMean = 370.527

σ = 211.772

Aperture Distribution with stress

Mean = 370.527, σ = 211.772

Mean = 197.997, σ = 172.573


Mean = 370.527, σ = 211.772

Mean = 197.997, σ = 172.573

Mean = 157.418, σ = 162.395


Mean = 370.527, σ = 211.772

Mean = 197.997, σ = 172.573

Mean = 157.418, σ = 162.395

Mean = 138.656, σ = 150.33


Aperture distribution follows Lognormal distribution at all

conditions

Highly rough surface fractureHighly rough surface fracture

Larger Aperture Size

Fracture apertures have to be distributed

Lognormal Distribution Lognormal Distribution






Experimental ProcedureUnfractured Core

pPressure Drop

Km qinj/ p

Matrix Permeability

qinj

Injection rate

5 cc/min

500,1000,1500

matrix

fracture

l

Experimental ProcedureExperimental ProcedureFractured CoreFractured Core

pavg

Average Pressure

Drop

Kavg qinj/ pavg

Average Permeability

qinj

Injection rate

5 cc/min

Analytical Equations


AKwdAKwdk avgmf )(

AKAKAk avgmmff

mfinj qqq

fqinjq mq

Fracture Permeability

Area of fracture

Matrix Permeability

Area of matrix

Average Permeability

Total area of core


wd

wdAkAkk mavgf

)(

0)(1045.8 39 wdAkAkdw mavg

Combining above equations to determine w

w Ad

matrix fractureFracture Permeability

291045.8 wk f

Cubic Law

0)(1045.8 39 wlAkAklw mav

Fracture Aperture

Fracture Permeability

291045.8 wk f

Fracture Flowrate

L

pdwq avgf 121086.9

13

9

500 Psi

1000 Psi

1500 Psi

Flow through fracture and matrix

Flow through fracture

Flow through fracture and matrix


Flow through matrix

Modeling Laboratory Experiment

Simulation model using aperture distribution

Simulation Model

Model Description

• 10x10x15 grids

• Fracture in 8th block in K dirn

ij

k

Injector

Water Injection

Water Injection

Producer - matrix

Matrix Production

rate

Producer - fracture

Fracture Production

rate

Water prod

Aperture distribution in fracture region

Aperture distribution

maps

Lognormal

Mean eff aperturevariance

500 psi 1000 psi

1500 psi

Example flow on the distributed fracture surface

Flow Through Matrix and Fracture


Flow through matrix

Pressure drop


X-ray CT scanner


ApproachApproach

Gravity Drainage Experiment

X-Ray

DetectorX-Ray Source

Brine

X-ray CT scan

Fluid flow pattern

0 min

12 min

Parallel Plate

Experiment

Simulation

Flow on a smooth Flow on a smooth fracture surfacefracture surface

Lognormal distribution

Fluid flow using aperture distribution

Fluid flow using aperture distribution

Saturation

Experiment

Simulation




• ApplicationApplication


Fluid flow experiments under stress

Recap

Recap


Conclusions

•Fracture Aperture Lognormal distribution

•Parallel plate assumption valid

•Distributed apertures Realistic flow behavior

Better History Match

Acknowledgement

• Dr. D. S. Schechter, Texas A&M University

• Dr. Erwin Putra, Texas A&M University

• Mr. Dicman Alfred, Schlumberger

• Department of Energy (D.O.E) for sponsoring the project.

Thank You

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Vivek Muralidharan Simulation and imaging experiments of fluid flow through a fracture surface: a new perspective