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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.