Overburden Pressure Affects Fracture Aperture and

Permeability in a Stress-Sensitive Reservoir

Vivek Muralidharan

MatrixPorosity Permeability

FracturePermeability

Problems

• Fracture behavior is complex.

• Overburden Pressure affects fracture parameters.

What has been done

• Observed the change in permeability with overburden pressure (Fatt and Davis, 1952; Jones,1975 and Cook et al, 2001).

• Measured fracture aperture physically (Jones et al, 1968; Gentier,1986; Arun et al,1997).

• Studied the effect of overburden pressure using unfractured cores (Holt,1990; Keaney et al,1998).

What has not been done

• Determination of fracture aperture during fluid flow.

• Determination of matrix and fracture flow contributions.

Approach

• Perform laboratory experiments with different overburden pressure.

• Develop an equation to determine the fracture aperture and flow contributions.

• Perform simulation modeling based on experimental results.

Approach

• Perform laboratory experiments with different overburden pressure.

• Develop an equation to determine the fracture aperture and flow contributions.

• Perform simulation modeling based on experimental results.

Laboratory Experiments

• How do we analyze the experimental results ?• What information can be deduced from

experimental results?• Fracture Aperture• Fracture permeability• Matrix and fracture flow contributions• How these properties change with

overburden stress

CORE HOLDER PERMEAMETER

HYDRAULIC JACK

Matrix4.98 Cm

A=4.96 Cm2

Fracture

Graduated Cylinder

Accumulator 1 Accumulator 2

PUMP 1 PUMP 1

Graduated Cylinder

BLACK

RED

CORE HOLDER PERMEAMETER

HYDRAULIC JACK

Matrix4.98 Cm

A=4.96 Cm2

Fracture

Graduated Cylinder

Accumulator 1 Accumulator 2

PUMP 1PUMP 1 PUMP 1PUMP 1

Graduated Cylinder

BLACK

RED

Experimental Apparatus

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Overburden Pressure (Psia)

Per

mea

bili

ty (

md

)

Unfractured Core Fractured Core Expon. (Fractured Core) Expon. (Unfractured Core)

Permeability changes at variable overburden pressure

km

kav

Approach

• Perform laboratory experiments with different overburden pressure.

• Develop an equation to determine the fracture aperture and flow contributions.

• Perform simulation modeling based on experimental results.

Experimental Data Analysis

291045.8 wk f

wl

wlAkAkk mavf

)(

0)(1045.8 39 wlAkAklw mav

L

pAkq mm

L

plwq f 12

1086.93

9

Parallel plate assumption:

Fracture Permeability :

Combining above equations to determine w:

Contribution of flow from matrix and fracture systems:

w Al

L

Fracture Aperture

0)(1045.8 39 wlAkAklw mav

0

0.001

0.002

0.003

0.004

0.005

0.006

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure ( Psia )

Fra

ctu

re A

per

ture

(cm

)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

500 psia 1000 psia 1500 psia

w w w

5 cc/min

20 cc/min

5 cc/min 10 cc/min 15 cc/min 20 cc/min

w w w

5 cc/min

20 cc/min

0

0.001

0.002

0.003

0.004

0.005

0.006

0 200 400 600 800 1000 1200 1400 1600

)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

w w w

5 cc/min

20 cc/min

)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

w w w

5 cc/min

20 cc/min

5 cc/min 10 cc/min 15 cc/min 20 cc/min

w w w

5 cc/min

20 cc/min

Fracture Permeability

291045.8 wk f wl

wlAkAkk mavf

)( OR

0.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

0.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

0.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

Fracture Permeability

291045.8 wk f wl

wlAkAkk mavf

)( OR

0.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

0.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

0.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

Overburden Pressure (Psia)

Fra

ctu

re P

erm

eab

ility

(m

d)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

: Hysteresis

5 cc/min

20 cc/min

W1

W2

W2 < W1

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure ( Psia )

Fra

ctu

re F

low

Rat

e (c

c/m

in)

Km

= 200 md

Kf= 10,000 -50,000 md

5 cc/min

20 cc/min

5 cc/min 10 cc/min 15 cc/min 20 cc/min

Km

= 200 md

Kf= 10,000 -50,000 md

5 cc/min

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 200 400 600 800 1000 1200 1400 1600

m= md

f= - md

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 200 400 600 800 1000 1200 1400 1600

m= md

f= - md

5 cc/min 10 cc/min 15 cc/min 20 cc/min

m= md

f= - md

Fracture Flow Rate

L

plwq f 12

1086.93

9

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure ( Psia )

Fra

ctu

re F

low

Rat

e (c

c/m

in)

Km

= 200 md

Kf= 10,000 -50,000 md

5 cc/min

20 cc/min

5 cc/min 10 cc/min 15 cc/min 20 cc/min

Km

= 200 md

Kf= 10,000 -50,000 md

5 cc/min

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 200 400 600 800 1000 1200 1400 1600

m= md

f= - md

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 200 400 600 800 1000 1200 1400 1600

m= md

f= - md

5 cc/min 10 cc/min 15 cc/min 20 cc/min

m= md

f= - md

Fracture Flow Rate

L

plwq f 12

1086.93

9

0.00

5.00

10.00

15.00

20.00

25.00

0 200 400 600 800 1000 1200 1400 1600Overburden Pressure ( Psia )

Ma

trix

Flo

w R

ate

(c

c/m

in)

5 cc/min 10 cc/min 15 cc/min 20 cc/min

5 cc/min

20 cc/min

5 cc/min 10 cc/min 15 cc/min 20 cc/min

0)

5 cc/min 10 cc/min 15 cc/min 20 cc/min5 cc/min 10 cc/min 15 cc/min 20 cc/min5 cc/min 10 cc/min 15 cc/min 20 cc/min

Matrix Flow Rate

L

pAkq mm

Approach

• Perform laboratory experiments with different overburden pressure.

• Develop an equation to determine the fracture aperture and flow contributions.

• Perform simulation modeling based on experimental results.

Modeling Laboratory Experiment

• Is single fracture aperture sufficient for modeling the flow through the fracture?

• Model for future reservoirs

Simulation Parameters

Single phase black oil simulation Laboratory dimensions (4.9875” x 2.51”) 31x1x31 layers Matrix porosity = 16.764% Matrix permeability = 296 md Fracture properties is introduced in 16th

layer Fracture porosity = 0.56% Mean fracture aperture = 56.4 micro meter

Example of flow through single fracture aperture

Injection Rate

Fracture Flow

Matrix Flow

Outlet Pressure

Inlet Pressure

Simulation Result for 500 psi and 5cc/min Flow

Match between Laboratory data and Simulation Results for 500 psi and 5cc/min flow

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Flo

w R

ate

(c

c/m

in)

qf(Obs. Data) qf(Sim. Result) qm(Obs. Data) qm(Sim. Result)

Observed

SimulatedFracture

Matrix

Match between Laboratory data and Simulation Results for 5 cc/min

0

1

2

3

4

5

6

7

0 200 400 600 800 1000 1200 1400 1600

Overburden Pressure (Psia)

Pre

ss

ure

Dro

p (

Ps

ia)

dP(Obs. Data) dp(Sim. Result)

Observed

Simulated

Actual Fracture Face

• Single fracture aperture cannot be used in modeling the experimental data.

• The fracture aperture must be distributed.

Lesson Learned !

Log-normal Distribution of Fracture Aperture

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 50 100 150 200 250 300 350

x(microM)

f(x)

Variogram Modeling to Generate Fracture Aperture Distribution

Core Surface Generated after Krigging

Example of flow through different fracture spatial heterogenity

1. Effect of stresses are most pronounced in fractured reservoirs.

2. The fracture aperture equation has been developed and thus, the matrix and fracture flow contributions can be estimated.

3. The spatial heterogeneity in the fracture aperture must be included in the modeling of fracture system.

Conclusions

Acknowledgement

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

• Dr. Erwin Putra, Texas A&M University

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