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Singgih Suganda, B.Eng., Master Student of Bandung Institute of Technology
Mukhammad Taufan, B.Eng., Master Student of Bandung Institute of Technology*
Ir. Zuher Syihab, M.Sc., Ph.D., Bandung Institute of Technology**
Prof. Ir. Pudjo Sukarno, M.Sc., Ph.D., Bandung Institute of Technology**
Fully Coupled Geomechanics and Its Effect
to the IPR Correlation
for Gas Single Phase Reservoir
Student Paper Contest (SPC)
for Postgraduate Student
2013 APOGCE, Jakarta-Indonesia
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OUTLINE
Introduction
Objective
Background Theory
Modified Fluid Flow for Geomechanic Reservoir
Rock Geomechanic Equations
Base Case Study
Result of Sensitivity Study
Conclusions
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Effect of Reservoir Properties Changing toDry Gas Single Phase IPR
Unrealistically IPR due to
reservoir properties changing
IPR calculation
procedures must be
corrected
Future Single
Phase IPR can be
predicted
GeomechanicAspects
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1
Presenting method to calculate
single phase IPR in Dry Gas Res.by considering Geomechanic
aspects.
To know the effect of Geomechanic
aspects in Gas Single Phase IPR2
3To establish new dimensionless
correlation for Gas Single-
phase IPR with influence of
reservoir Geomechanic effects
OBJECTIVE
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Darcys Law(gravity
assumed to be
neglected)
Conservation of
Mass
Equation of State
(isothermal)
Background Theory(Modified Fluid Flow for Geomechanic Reservoir)
0).(
)(
gg
g
ut
0)]1.([)]1([
ss
s ut
pkuu sg
)(
pcg
1
pcr
1
Gas Flow
Modified
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Strain-Stress-PressureStress Equilibrium
Rock
Equations
Strain Displacement
Background Theory(Rock Geomechanic Equations)
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Stress Equilibrium
Poroelastic theory (shu, 2003) :
0
z
zx
y
yx
x
x
0
z
zy
y
y
x
xz
0
z
z
y
yz
x
xz
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Strain-Stress-Pressure
HookesLaw :
)(2 zyxxx GP
)(2 zyxyy GP
)(2 zyxzz GP
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Strain displacement
There are two basic assumptions in deformation :
Free deformation and Uniaxial deformation (Settari,
2005)
ue zzyyxx
.
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Basic Numerical
Coupled these two equations
will result fluid flow behavior
under Geomechanic effect
Modified Fluid
Flow Eq.
Rock Mechanic
Eq.
General Equation in Geomechanic Reservoir
dt
dp
dp
dcccccp
k msbsbfg
)()1(.
pfuGuG i ).()(2
Numerical Building
These equations are coupled
and combine with other
equations in developed
simulator. And being validate
with commercial simulator
Basic Numerical
Dont forget to underlined
that Porosity & Permeability
are under mean effective
stress function
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1. Construct the base case IPR.(The data is obtained from ARMA/USRMS
05-769 paper, titled: Applying fully coupledgeomechanics and fluid flow model to
petroleum wells (Hunt et. al., 2005),
2. Sensitivity study from base case is theninvestigated for all parameters.
3. Build future IPR, then modified as
dimensionless IPR and plotted in the same
graph.
4. Regression results new dimensionless
future IPR correlation for dry gas reservoir
Base Case Study
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1. PVT data is taken from SPE 16000 Fifth Comparative Solution Project:
Evaluation of Miscible Flood Simulators.
2. Simulation is run till 4000 days (11 years).
Base Case Simulation Result
Fig.Comparison in Average Reservoir Pressure Between
Conventional and Geomechanics Model.
Fig.Comparison in Producer Rate Between
Conventional and Geomechanics Model
Vid. Base Case Simulation is Running Using
Developed Simulator
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0
1000
2000
3000
4000
5000
6000
0 2 4 6 8 10 12 14 16 18 20
Pwf(psi)
Qg (MMSCFD)
IPR Base case Initial Fetkovich
IPR base case geo
IPR - Base Case Study
Conventional Res. Geomechanic Res.
Fig. Base Case IPR Comparison for Geo and Non-Geomechanic Reservoir
Fig. Comparison Of Isochronal Log-Log Plot Analysis Between Non-Geomechanics (Left Side)
And Geomechanics Reservoir (Right Side)
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IPR - Base Case Study Sensitivity
1. Sensitivity analysis is undergone to test the model for its behavior to these
changes of its variables.
2. Sensitivity analysis is conducted by varying : poisson ratio (v), modulusyoung (E), porosity (), and well radius (rw).
3. Geomechanic effect is pressure dependent variable, sensitivity in the future
reservoir condition is highly expected, and it has been performed in this
study.
4. Regression from combination of Pwf/Pres and Qg/Qmax in the same graph,
resulted new dimensionless IPR correlation for dry gas reservoir
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20
Pwf(psi)
Q (MMSCFD)
E = 5x10^5
E = 1x10^5
E = 1x10^6
Base case IPR Geo
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20
Pwf(psi)
Q (MMSCFD)
rw = 0.205
rw = 0.45
Bass case IPR geo
Fig. Modulus Young and Well Radius Sensitivity
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Future IPR Construction
-1000
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20
Pwf
Q (MMSCFD)
Initial condition
future 1 Geo
Future 1 Fetkovich
Future 3 Geo
Future 3 FetkovichFuture 4 Geo
Future 4 Fetkovich
Initial condition fetkovich
Future 2 Geo
Future 2 Fetkovich
Future 5 Geo
Future 5 Fetkovich
Future 6 Geo
Future 6 Fetkovich
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Pwf/P
res
Qg/Qmax
= 1 0.53
0.47
2
assumptions : Laminar flow, Dry gas
single phase, Pseudo-steady state
condition, No skin, Homogeneous
reservoir, and there is no fluid influx.
2
max
47.053.01
P
P
P
P
Q
Q wfwfg
Fig . Future IPR Result
Fig. Dimensionless IPR from Initial Base Case DataIn Every Future Condition
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Base Case Dimensionless Future IPR
Prod Time
(year)Gp (MMSCF)
QmaxF
(MMSCFD)
PresF
(psi)
PresF/
PresP
QmaxF/
QmaxP
1 1884.3690 14.9029 4577 0.9535 0.8159
2 9693.1070 10.4623 3913 0.8152 0.5728
3 9693.1070 8.3350 3470 0.7229 0.4563
4 12452.2000 6.4304 3143 0.6548 0.3520
5 14519.2600 5.3513 2893 0.6027 0.2930
6 16251.8300 4.5214 2691 0.5606 0.2475
7 17723.9900 3.8995 2526 0.5263 0.2135
8 18894.8700 3.7361 2387 0.4973 0.2045
9 20022.2900 3.3347 2267 0.4723 0.1826
10 21010.2600 2.8939 2163 0.4506 0.1584
11 21886.9600 2.5823 2072 0.4317 0.141412 22737.1400 2.1222 1991 0.4148 0.1162
13 23378.6200 2.0948 1919 0.3998 0.1147
14 24079.1900 1.7506 1854 0.3863 0.0958
Prod Time
(year)Gp (MMSCF)
QmaxF
(MMSCFD)
PresF
(psi)
PresF/
PresP
QmaxF/
QmaxP
1 1873.96518 14.68934 4562 0.9504 0.9618
2 6394.98138 10.17555 3864 0.8050 0.6663
3 9552.55706 7.88285 3417 0.7119 0.5161
4 12173.47170 6.22692 3095 0.6448 0.4077
5 14167.89910 5.17778 2851 0.5940 0.3390
6 15852.68840 4.39993 2654 0.5529 0.2881
7 17279.20130 3.78759 2494 0.5196 0.2480
8 18513.90360 3.30370 2359 0.4915 0.2163
9 19509.78460 3.19868 2244 0.4675 0.2094
10 20554.82160 2.59331 2143 0.4465 0.1698
11 21403.39200 2.30826 2055 0.4281 0.151112 22165.94640 2.08236 1977 0.4119 0.1363
13 22851.54710 1.87303 1907 0.3973 0.1226
14 23484.47950 1.72980 1844 0.3842 0.1133
0
0.2
0.4
0.6
0.8
1
1.2
0.2 0.4 0.6 0.8 1
QmaxF/Qmax
P
PresF/PresP
Base Data Geomechanic Effects
Base Data Non-Geomechanic Effects
Fig . Comparison Dimensionless Future IPR Relationship for Base Case Data
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- Each point in graph above represents the IPR curves at future reservoirconditions.
- Regression results new-correlation to predict future IPR for Gas single phase
reservoir by considering geomechanics factor.
-
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
QmaxF/QmaxP
PresF/PresP
Base case data
rw = 0.205
rw = 0.45
porosity 0.1
porosity 0.3
Poisson ratio 0.15
Poisson ratio 0.35
Mod Young = 1x10^5
Mod Young = 1x10^6
Dimension x 1.5
Dimension x 0.5
kh = 0.5h=x2.0
h=x0.5
kh = 2.0
kh = 0.1
kh = 10
= 0.833(
)2 + 0.145(
) 0.084
Result of Sensitivity Study
084.0145.0833.0
2
Prmax
max
presentres
futureres
presentres
futureres
esentg
Futureg
P
P
P
P
Q
Q
Fig. Dry Gas Future IPR Under Geomechanics Effect
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Non-Geomechanic Reservoir Comparison
R = 0.996
0
0.2
0.4
0.6
0.8
1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
QmaxF/QmaxP
PresF/PresP
Geomechanics Reservir
Non-Geomenchanics Reservoir
Poly. (Geomechanics Reservir)
= 0.833(
)
2
+ 0.145(
) 0.084
At the beginning of production process, the ratio from AOF in geomechanic
reservoir has a lower value at the same value of ratio pressure reservoir
Fig. Comparison Sensitivity Result of Dimensionless Future IPR
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Applying Dimensionless IPR Correlation
Combining both equations, we will can easily predict the IPR curve in every condition of
reservoir. Example, if we have geomechanic reservoir with data:
- Pr = 3900 psi. Pwf = 1000 psi; Qg = 12.1 MMSCFD;
- By varying of bottomhole pressure will result:
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 5 10 15 20
Pwf(psi)
Qg (MMSCFD)
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 5 10 15 20
Pwf(psi)
Qg (MMSCFD)
Intial Condition
Future 1
Future 2
Fig. Initial & IPR Prediction Using Proposed IPR Dimensionless Correlation
2
max
47.053.01
P
P
P
P
Q
Q wfwfg084.0145.0833.0
2
Prmax
max
presentres
futureres
presentres
futureres
esentg
Futureg
P
P
P
P
Q
Q
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Geomechanics aspects affect deliverability of gas reservoir, hence
IPR need to be corrected to accommodate the impact ofgeomechanics.
Effect of geomechanic aspects to gas single-phase IPR will makethe AOF increase and ascend the IPR curve.
The geomechanic aspects made reservoir pressure and production
rate of gas reservoir higher than the conventional reservoir.
New dimensionless future IPR correlation for single phase gas
reservoir under influence of geomechanic aspects has beengenerated and the trend is polynomial second order.
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