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 %

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Why study fracture flow?

Improve prediction of sweep in Naturally Fractured reservoirs

Improve modeling of tracer studies

ShaleShale

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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!

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Fractures as parallel plates

Historical perspectiveHistorical perspective

Constant Constant widthwidth

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Fracture Model

w12

2wK f


Constant permeability fracture surface

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L

pplbq L 0

3

12

Cubic Law of Fractures


Aperture half width

Fracture length

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w

Fractures cannot be assumed as parallel plates.

Reality ?Reality ?

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Fractures cannot be assumed as parallel plates.

Reality ?Reality ?

A real fracture surface is rough and tortuous.

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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

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Tsang&Tsang(1988)Brown (1987)

The friction associated with the rough fracture surface affects the flow

performance.

More issues More issues

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The story so far …

Effect of friction in fracture flow simulations

Aperture Width ?

Stochastic aperture simulations

Experimental support

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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

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The approachThe approach

Experimental Analysis

Aperture width, qm, qf

Fracture simulation

Simulation

Aperture distribution

Stochastic Analysis

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Fracture simulation

Simulation


Stochastic Analysis



Aperture width, Qm, Qf

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Information from experiments?

•Fracture permeability

•Fracture aperture

•Matrix and fracture flow contributions

•How these properties change with overburden stress

Motivation Motivation

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In the past …

Impermeable surface

Sand grains

Apertures measured physically

Flow experiments

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New perspective…New perspective…

500 psi 1000 psi

1500 psi

To quantify the change in aperture with overburden pressure

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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

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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

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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

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Using weighted averaging

ffmmav AkAkAk

Fracture aperture?Fracture aperture?

wl

wlAkAkk mavf

)(

w

l

The unknowns k f and w

(1)

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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

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Fracture apertureFracture aperture

Increase in overburden pressure decreases aperture width

0

0.002

0.004

0.006

0 400 800 1200 1600


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

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Matrix flow rateMatrix flow rate

0.00

5.00

15.00

25.00

0 400 800 1200 1600


Mat

rix

Flo

w R

ate

(cc/

min

)

5 cc/min

10 cc/min

15 cc/min

20 cc/minL

pAkq mm

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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

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Fracture simulation

Simulation


Stochastic Analysis


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

o From experimental analysis

waperture

MotivationMotivation

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2ln

2

1exp

2

1)(

x

xxf

Log-Normal Mean

Log-Normal Deviation

Variable( Aperture )

Aperture distributionAperture distribution

Apertures distributed log-normally

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Generation of aperturesGeneration of apertures

Through a mean and a variance

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Application?Application?

Smooth fracture surfaceSmooth fracture surface

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Slightly rough fracture surfaceSlightly rough fracture surface


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Highly rough surface fractureHighly rough surface fracture

Larger Aperture Size

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Creation of the aperture map

Variogram

Stochastic analysisStochastic analysis

Lag distance

Co-

var

ianc

eKriging

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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

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Comparison

Not the real picture but effective

Good enough?Good enough?

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Stochastic Analysis


Fracture simulation

Simulation

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Motivation Motivation

Tackle the issue of surface roughness

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

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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

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2be

He proposed that when

D

e > 0.033 f =

5.1

88.11D

e

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2be

Modified cubic law

L

ppl

f

bq L 0

3

12

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Permeability modification of the fracture surface

Without friction With friction

Effect of friction?Effect of friction?

400 darcy400 darcy 350 darcy350 darcy

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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

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Flow on a smooth fracture surfaceFlow on a smooth fracture surface

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Flow on the distributed fracture surfacefollows preferred flow paths

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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

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0.00

1.00

2.00

3.00

4.00

5.00

0 400 800 1200 1600


Flo

w R

ate

(c

c/m

in)

fracture

matrix

Flow match Flow match

Parallel Plate Theory

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The new approach The new approach

0

1

2

3

4

5

0 500 1000 1500 2000


Pre

ssu

re D

rop

, ps

ia

Observed

Simulated

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Flow match

0

1

2

3

4

5

0 500 1000 1500 2000


Flo

w R

ate

, cc

/min

fracture

matrix

The new approach The new approach

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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

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Applications Applications

Gravity Drainage Experiment

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X-Ray

DetectorX-Ray Source

Brine

X-ray ct scan

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Parallel-Plate Theory


Gravity-Drainage Experiment

TAMUTAMUGravity-Drainage Experiment

Our Approach


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The new approach The new approach Gravity-Drainage Experiment

Simulation X ray CT Scan

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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


Fra

ctu

re A

per

ture

(cm

)

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Distribute fracture apertures

Consider effect of friction caused by rough fracture surfaces

How do we simulate flow through fractures more effectively ?


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Tail of frequency distribution impacts flow performance

Tortuosity dominates fracture flow at high overburden pressures

What other factors affect flow through fractures?


TAMUTAMU

Improve prediction of sweep in naturally fractured reservoirs

Improve modeling of tracer studies

Why study rugosity in fractures?


modeling fluid flow through single fractures using experimental, stochastic and simulation...

Documents

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tamu fractures

fracture aperture width

berea slide

tamu introduction

tamu knowledge

tamu information

tamu tracy