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Simulation Study of The Effect of Well Spacing, Permeability Anisotropy, and Palmer and Mansoori Model on
Coalbed Methane Production
Ismail Zulkarnain
Harold Vance Department of Petroleum Engineering.
Texas A&M University
25th July, 2005
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Outline 2
• Objectives
• US coalbed Methane Resource
• CBM and Conventional Natural Gas Reservoirs
• Reservoir Characteristics of Coals
• Adsorption and Desorption Phenomena
• Dual Porosity Model
• Simulation Data
• Well Spacing Effect
• Permeability Anisotropy
• Palmer and Mansoori Theory
• Conclusions
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Objectives
Study the effect of interference between wells on the
reservoir performance coalbed methane production. It
also is known as well spacing effect on coalbed
methane production.
Study the effect of well configuration on an
anisotropic coal bed methane reservoir.
Study the effects of Palmer and Mansoori Theory (Matrix Shrinkage Effect and Cleats Compression Effect) on the reservoir performance of coal bed methane (CBM).
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CBM in the United States
• Early CBM wells were drilled to release gas as a safety measure prior to coal mining operations.
• Increase in natural gas prices in he 1970’s encouraged intensive research efforts and federal tax credits catalyzed CBM exploration and development to produce CBM for profit.
From Kentucky Geological Survey
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“ Coalbed methane activity is increasing in the U.S., the world leader in reserves and production, due to recent high gas prices and dwindling conventional gas supplies” Walter B. Ayers
US Coalbed Methane Resource 5
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Proved Reserves18,743 bcf
US Production (2003)1600 bcf
8% of US dry gas production
US Coalbed Methane Resource 5
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Sandstones and Coal Reservoirs
Surface Area of Coals are in the range of; 2,150 – 3,250 ft2/g (SOURCE: Marsh (3), 1965)
295ft x 147 ft
Surface Area Can
EQUAL
Micro-particle of Coal
A block of Coal
• Large Internal Surface Area of Coal
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If average surface area of coal is 2700 ft2/g,
16 gram of coal has surface area equal to a football field area.
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CBM and Conventional Natural Gas
Typical Conventional Natural Gas
CBM
Depth 150 to 3000m 150 to 1500m
Water
Rates may increase during production
Rates typically decreases during production life
Well Spacing Normally, 1 well per square mile but density may be increased
2 to 8 wells per square mile
Gas Storage
Stored in macropores
or fractures
Stored as adsorbed gas on the coal matrix
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Reservoir Characteristics of Coal
• Matrix (micro pores)
• Fracture/Cleats (macro pores) Face Cleats (continuous throughout the reservoir) Butt Cleats (discontinuous, terminated at an intersection)
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Coalbed Recovery Mechanism q g,
q w
3 Stages in Primary Recovery;• Dewatering: to reduce cleat pressure• Stable Prod. Stage: Methane desorbing from matrix and flowing to the cleat• Decline Stage: Methane and water flow to the well bore
• All the flow is in fractures• Fractures are 100% saturated with water
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Schematic of Coalbed Methane Well11
PUMP
GAS
COAL
WATER
CEMENTOVERBURDEN
Water
(Sand, shale, and thinner coal beds)
PUMP MAY BE SET IN COAL RATHER THAN IN RAT HOLE
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Adsorption Phenomena
• Physical adsorption between methane and the coal solid molecules
involves intermolecular forces (Van der Waals forces)
• Adsorption is instantaneous
• Equilibrium adsorption model
Gas adsorption/desorption is pressure dependent LANGMUIR ISOTHERM
Adsorption
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Langmuir Equation
Relationship used to represent the sorption mechanism in coal bed methane reservoir is given as:
Lpp
pVpV L
)( (Seidle et al, 1990)
Where;
V(p) = gas content (scf/ft3)
VL = Langmuir volume (scf/ft3)
(Saturated monolayer volume)
p = gas pressure (psi)
pL = Langmuir pressure
(Pressure at half of the Langmuir volume) www.hycal.com (2004 CIPC Session 31)
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Langmuir Adsorption18
Matrix may be “undersaturated” if gas is not available at initial conditionsDesorption pressure is less than initial pressure (pd < pi)Desorption pressure determines the adsorbed gas content Desorption pressure is analogous to bubble point pressure for oil
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Langmuir Sorption Isotherm“Single layer sorption theory” Developed in 1916 by Irving Langmuir
• Isotherm is used to
predict the release of
gas from the reservoir
as pressure is reduced.
• Isotherm is based on the theory that simply states that the rate of molecules arriving and adsorbing on the solid surface should equal the rate of molecules leaving the surface
0
200
400
600
800
1000
1200
0 500 1000 1500 2000 2500 3000
Gas
Conce
ntr
ati
on, sc
f/to
n
Pressure, psi
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0
200
400
600
800
1000
1200
0 500 1000 1500 2000 2500 3000
Theoretical Isotherm;Pi=Pd ; pd=pm
Undersaturated Isotherm; Pi>Pd ; pd=pm
Pd
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Dual Porosity Model (Coalbed modeling)
Warren and Root (paper SPE 426)
Fracture Cell, “f”
Matrix Cell, “m”
Actual Reservoir Model Reservoir
Matrix FractureMatrixFracture
• Analogous to Warren and Root Model• Modeling two interconnected systems
Coal matrix and Permeable rock fractures
Warren & Root Coal Bed Methane
Initial Gas Storage
Free gas in pores OR Fractures(Cleats)
Adsorbed to coal ORFree gas in fractures
Matrix / fractureflow
)( fm ppCq
“Pseudo Steady State Model” )(1
fpCCq
Darcy’s Law Fick’s Law (Diffusion)
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Diffusive Flow of Gas in CBM Reservoirs
dL
dcDAq '
Fick’s law of diffusion is given as:
Diffusion of gas out of the coal matrix can be expressed by a
simple diffusion equation:
Driving force for this mode of transport is a concentration
gradient between the matrix and the cleat.
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)]([ fs pCCDFt
C
)]([1
fpCCt
C
days
FD s
,*
1Average gas
concentrationin the matrix
Concentrationin the outer surface of the coal
Lf
fL PP
PVPV
)(
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Simulation Details
• Construct a dual porosity simulation model using CMG toConstruct a dual porosity simulation model using CMG to
simulate the process of primary production from a single simulate the process of primary production from a single
coal seam.coal seam.
• Model consists ofModel consists of
- 21 * 21 * 1 grid system21 * 21 * 1 grid system
- 1 producing well1 producing well
Producer
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Relative Permeability Curves
0
0. 2
0. 4
0. 6
0. 8
1
0 0. 2 0. 4 0. 6 0. 8 1
Gas Saturati on, Sg, Fracti on
Relative Permeability, krw
(fraction)
0
0. 2
0. 4
0. 6
0. 8
1
Relative Permeability, krg
(fraction)
krw; matr i x
krg; f racture
krw; f racture
krg; matr i x
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Well Spacing EffectComparison of an 80 acre
well and a 40 acre well
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Simulation scenarios28
y = 1866.76 ft
x = 1866.76 ft
80 acre-Isotropic Reservoir
A
y = 1320 ft
x = 1320 ft
40 acre-Isotropic Reservoir
B
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Comparison of 80 acre spacing, 40 acre spacing, 20 acre spacing,
and 5 acre spacing on an 80 acre reservoir
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Reservoir model
y = 1866.76 ft
x = 1866.76 ft
Isotropic-Square Reservoir System
80 acre
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Simulation scenarios33
80 acre reservoir with 80 acre
spacing
80 acre reservoir with 40 acre
spacing
80 acre reservoir with 5 acre spacing
80 acre reservoir with 20 acre
spacing
A B
C D
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Problem Statement
Coalbed methane is a naturally fractured reservoir.
Coalbed methane reservoir is consisted of the face
cleats (continuous fractures) and the butt cleats
(discontinuous fractures).
The existence of the face cleats and the butt cleats
causes the permeability anisotropy in coalbed methane
reservoirs.
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Problem Statement
y
x
Anisotropic - Reservoir System
Permeability in x-direction is higher than permeability in y-direction
Butt Cleats
Face Cleats
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Reservoir model
y = 1866.76 ft
x = 1866.76 ft
Anisotropic-Square Reservoir System
(kX=1 md and kY=0.01 md)
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Effect of well configuration on anisotropic reservoir
Scenario A The reservoir is 80 acre area. The reservoir has 4 wells. Each of the well has the same drainage area, 20 acre. Each of the well is located in the center of square reservoir area.
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Effect of well configuration on anisotropic reservoir
Scenario B The reservoir is 80 acre area. The reservoir has 4 wells. Each of the well has the same drainage area, 20 acre. Each of the well is located in the center of rectangular reservoir area. Placement of wells is aligned to the direction of lower permeability direction.
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Effect of well configuration on anisotropic reservoir
Scenario C The reservoir is 80 acre area. The reservoir has 4 wells. Each of the well has the same drainage area, 20 acre. Each of the well is located in the center of rectangular reservoir area. Placement of wells is aligned to the direction of higher permeability direction.
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Palmer and Mansoori theory models low pressure k rebound in coals:
At higher pressures, k decreases with pressure due to compaction (cleats compression)At lower pressures, k increases with pressure due to matrix shrinkage during gas desorption.
52Palmer and Mansoori model
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Overburden pressure
coal matrixfracture
(a) Before cleats compression
(b) After cleats compression
Cleats compression
k
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Matrix shrinkage
Width of cleats after shrinkage
Coal matrix after shrinkage
Width of cleats before shrinkage
Coal matrix before shrinkage
Fractures/cleats
Coal matrix Coal matrix Coal matrix
k
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Palmer and Mansoori model
Cleats Compression Matrix Shrinkage
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Palmer and Mansoori model
It has an implication on the gas production:
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Sensitivity Analysis on Palmer and Mansoori Model Parameters
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Sensitivity Cases
• Young’s Modulus, psia
500,000 psia, 750,000 psia, 1,000,000 psia, 1,500,000 psia, 2,000,000
psia, 3,000,000 psia, 4,000,000 psia, and 5,000,000 psia,
• Poisson’s Ratio, fraction
0.1, 0.2, 0.3, 0.4, 0.5,
• Strain Maximum, dimensionless
0.001, 0.005, 0.01, 0.02, 0.05, 0.1
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Young’s modulus, E
stressverticalpsizz ),(
?
?
,
rock
steel
zz
zz
zz
E
E
E
z
zstrainvertical
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Poisson Ratio, ν
stressverticalpsizz ),(
ibleincompressrubber
steel
cork
zz
xx
5.0
3.0
0
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Bulk modulus, K
stressverticalpsixx ),(
?
?
,
rock
steel
zz
zz
zz
E
E
E
z
zstrainvertical
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Young’s modulus, E
stressverticalpsixx ),(
?
?
,
rock
steel
zz
zz
zz
E
E
E
z
zstrainvertical
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Young’s modulus, E
)( psi
)(/1
/
ilitycompressibcK
VVK
V
Vstrainbulk
)( psi
)( psi
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Young’s Modulus
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Poisson’s Ratio64
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Poisson’s Ratio 65
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Poisson’s Ratio
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Strain Maximum 67
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Strain Maximum 68
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Strain Maximum
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Conclusions
Well Spacing
1. Interference between wells creates beneficial effect on coalbed methane production. The more interference is created, the higher the production is.
2. Interference between wells accelerates the dewatering stage.3. The closer well spacing, the higher and earlier peak gas rates. Closer well
spacing results in higher cumulative gas production.
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Permeability Anisotropy
1. The existence of face cleats and butt cleats creates permeability anisotropy in coalbed methane reservoir.
2. Placement of wells should be considered based on the existence of permeability anisotropy.
3. Wells aligned or placed along the lower permeability direction results the higher gas production and cumulative gas production.
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Conclusions
Palmer and Mansoori Theory
1. We observe that Palmer and Mansoori model should be considered and included in the modeling and simulation of coalbed methane performance.
2. The higher the Young’s Modulus is the higher the gas rate and cumulative gas production is.
3. The higher the Poisson’s Ratio is the lower the gas rate and cumulative gas
production is.
4. The higher the strain maximum is the higher the gas rate and cumulative gas production is.
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Nusantara Archipelago, Indonesia-Southeast Asia
Thank You
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Simulation Study of The Effect of Well Spacing, Permeability Anisotropy, and Palmer and Mansoori Model on
Coalbed Methane Production
Ismail Zulkarnain
Harold Vance Department of Petroleum Engineering.
Texas A&M University
25th July, 2005
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• CMG shows that mass transfer rate from matrix cell “m” bounded by a set of fracture associated with a fracture cell “f” can be expressed as :
Diffusive Flow of Gas
Where;Vol = Bulk Volume
Shape = Shape factor (matrix-fracture interface area per unit volume)
Diffus(k)= Diffusion value (COAL-DIF-COMP)
SgA-mod = gas saturation in the matrix (default = 1)
C(k,gas,m) = Concentration of component ‘k’ in gas phase of matrix cell “m”
C(k,gas,f) = Concentration of component ‘k’ in gas phase of fracture cell “f”
Lg
gLgm PP
PVPC
)(
dayskDiffusShape
TIMEDIFCOAL ,)(*
1
)),,(),,((**)(** mod fgaskCmgaskCSkDiffusShapeVolRate AgBlock
2)/1*4 gFracSpacinShape
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RF Gas (fraction) per well basis
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RF Water (fraction) per well basis
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Tabulated Result
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Young’s modulus
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Young’s modulus
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Poisson’s ratio
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Poisson’s ratio
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Strain maximum
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Strain maximum
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Reservoir Model
30 ft
1866.76 ft
1866.76 ft
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Transformation (Wattenbarger and Arrevallo)
Simulation:
y = 1866.76 ft
x = 1866.76 ft
Anisotropic-Square Reservoir System
(kX=1 md and kY=0.01 md)
a
Isotropic-Rectangular Reservoir System
(k = 0.1)
x = 590.32 ft
y = 5903.2 ft
b
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Dual Porosity (Warren and Root)
(a) (b)
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Diffusion and Flow of Methane
(a)
(b)
(c)
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Scenario A
y-direction/low permeability
x-direction/high permeability
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Scenario B
y-direction/low permeability
x-direction/high permeability
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Scenario C
y-direction/low permeability
x-direction/high permeability