Coal Bed Methane Reservoir Simulation Studiesdocshare01.docshare.tips/files/14784/147842546.pdf · methane reservoir. First, the theory and reservoir engineering aspects of coal bed

Coal Bed Methane Reservoir Simulation Studies

By

Kaveh Karimi

Supervisor

Prof. W. V. Pinczewski

A thesis submitted in partial fulfillment of the requirement

for the

Degree of Master of Engineering

School of Petroleum Engineering

The University of New South Wales

June, 2005

II

Abstract

The purpose of this study is to perform simulation studies for a specific coal bed

methane reservoir. First, the theory and reservoir engineering aspects of coal

bed methane reservoirs, such as dual porosity concept, permeability

characteristics of CBM reservoirs and mechanism of gas storage and gas

transportation in CBM reservoir have been discussed. Next, simulation results for

the CBM reservoir presented. Simulation studies were carried out by using the

CBM reservoir simulator, SIMED II. Injection/fall-off test pressure data were

interpreted based on the pressure history matching method. The interpretation

results include the determination of reservoir permeability and identification of

the reservoir altered zone. Also available production histories were used to

simulate the reservoir production behavior. Then the production model was used

to predict the reservoir future production and to carry out sensitivity analysis on

reservoir performance.

For natural pressure depletion, methane recovery was increased significantly as

reservoir permeability was increased. Well-bore fracturing creates a fractured

zone with higher permeability. This increases methane production rate during

early time of reservoir life. Reservoir matrix porosity has a significant effect on

the reservoir performance. Higher production peak rate and also higher methane

recovery was obtained for the reservoir with lower porosity values. Any increase

in the reservoir compressibility causes greater reduction in reservoir absolute

permeability as well as relative permeability to gas throughout the reservoir.

III

Therefore, methane recovery decreased as the reservoir compressibility

increased. The reservoir production behavior was strongly affected by changes in

reservoir size. The production peak rate was significantly postponed and lowered

as reservoir size was increased. The effect of reservoir initial pressure was

investigated and the results show that higher initial reservoir pressure leads to

higher production rate during early years of production. However, for the later

years of reservoir life, the production profile is almost identical for different

initial pressures. Coal desorption time constant affects the methane production

by its own scale. In this study, the range of desorption time did not exceed

longer than three days and therefore the difference in production rate was

observed only in the first few days of production.

IV

List of Contents

List of Contents ............................................................................. I

List of Figures .............................................................................VII

List of Tables ...............................................................................XI

1 Introduction ........................................................................... 1

1.1 Coal Bed Methane Production................................................. 1

1.2 Scope of Present Study ........................................................ 4

2 Theory and Reservoir Engineering Aspects of Coal Bed Reservoirs........... 5

2.1 Coal Porosity System ........................................................... 5

2.2 Permeability in coal bed methane reservoirs .............................. 6

2.3 Pressure-dependent rock properties......................................... 9

2.4 Relative Permeability in coal bed reservoir ............................... 14

2.5 Methane storage in coal ...................................................... 20

2.5.1 Methane adsorption ...................................................... 20

2.5.2 Langmuir adsorption model............................................. 22

2.6 Gas Transport in Coal ......................................................... 26

2.6.1 Gas Desorption............................................................ 27

2.6.2 Gas Diffusion in Coal ..................................................... 31

2.6.3 Gas Permeation in CBM Reservoirs .................................... 32

2.7 Gas Transport Modeling in CBM reservoirs ................................. 34

2.7.1 Gas Desorption Modeling ................................................ 35

2.7.2 Gas Diffusion modeling .................................................. 36

V

3 The Application of Simulation Studies in Coal Bed Reservoir Characterization

43

3.1 Well Testing .................................................................... 43

3.2 Injection fall-off test.......................................................... 45

3.3 SIMED II, the simulation tool ................................................. 46

3.4 Case Study ...................................................................... 46

3.5 Injection fall off (IFO) test analysis......................................... 47

3.5.1 IFO test in well D – Object 4:........................................... 48

3.5.2 IFO test in well D, object 3 ............................................. 54

3.5.3 IFO test well D, Object 8b .............................................. 60

3.5.4 IFO test in well D, object 8a ........................................... 66

3.5.5 IFO test in well D - object 7 ............................................ 71



3.5.8 IFO test in well C, object 1: ............................................ 86

3.6 Production History Match for Object 1 in Well D ......................... 91

3.6.1 Coal Seam Geological Setting .......................................... 91

3.6.2 Simulation Model of Well D ............................................. 91

3.6.3 Simulation Input Parameters ........................................... 92

3.6.4 Production History Matching Results .................................. 95

3.6.5 Comparison with characterization studies ........................... 96

3.6.6 Production Prediction of the Well D................................... 96

3.7 Production History Match for Object 2 in Well A ........................101

VI

3.7.1 Coal Seam Geological Setting .........................................101

3.7.2 Simulation Model of Well A ............................................101

3.7.3 Simulation Input Parameters ..........................................102

3.7.4 Production History Matching Results .................................104

3.7.5 Comparison with characterization studies ..........................105

3.7.6 Production Prediction of Well A ......................................105

3.8 Sensitivity Analysis ...........................................................109

3.8.1 Effect of reservoir permeability ......................................109

3.8.2 Effect of fractured zone permeability ...............................112

3.8.3 Effect of relative permeability........................................114

3.8.4 Effect of porosity........................................................118

3.8.5 Effect of formation compressibility (cf) .............................120

3.8.6 Effect of drainage area.................................................122

3.8.7 Effect of reservoir initial pressure....................................125

3.8.8 Effect of desorption time constant...................................127

3.9 Conclusions ....................................................................129

References ................................................................................132

VII

List of Figures

Figure 1.1 - Comparison of CBM and typical gas reservoir producing by pressure

depletion, CBM reservoir (Ma 2004) ............................................... 3

Figure 2.1 – Fracture System in coal (Shi and Durucan 2003)....................... 5

Figure 2.2 – Face and butt cleats in coal (Ma 2004).................................. 8

Figure 2.3a - Relative permeability in coal from laboratory testing ............. 17

Figure 2.3b – Coal relative permeability curves obtained by history matching

(Meaney and Paterson 1996)....................................................... 18

Figure 2.4 – Schematic illustration of adsorbed gas on coal surface (Ma 2004) 21

Figure 2.5 – Chemical adsorption in which there is a chemical bond between

methane and coal molecules (Ma 2004) ......................................... 22

Figure 2.6 – Adsorption isotherms (Ma 2004) ......................................... 25

Figure 2.7 – Gas movement in coal bed reservoirs (Reeves and Pekot 2001) ... 27

Figure 2.8 – Desorption includes both physical and chemical adsorbed gas

molecules (Ma 2004) ................................................................ 29

Figure 2.9 - Determination of desorption time constant by straight line method

(Mavor, Owen et al. 1990) ......................................................... 31

Figure 2.10 – Production regime in coal bed reservoirs (Pinzon and Patterson

2004) .................................................................................. 34

Figure 2.11 – Adsorption isotherms may be used to model desorption process (Ma

2004) .................................................................................. 36

VIII

Figure 2.12 – Bidisperse model scheme including micro spheres inside the macro

spheres (Shi and Durucan 2003)................................................... 40

Figure 2.13 – Spherical matrix elements in coal bed reservoirs (Kolesar and

Ertekin 1986)......................................................................... 40

Figure 3.1 - Field kr curves .............................................................. 51

Figure 3.2 - Pressure history match for IFO test on Object 4 in well D .......... 52

Figure 3.3 - Field kr curves .............................................................. 57

Figure 3.4 - IFO test pressure history match for object 3, well D ................ 59

Figure 3.5 - Reported changes in the injection rate of IFO test on well D, Object

3........................................................................................ 59

Figure 3. 6 – Faults map in coal seam number XV (Tran 2005) .................... 61

Figure 3.7 - Field relative permeability curves ...................................... 64

Figure 3.8 - Object 8b pressure profile match....................................... 65

Figure 3.9 - Field relative permeability curves ...................................... 69

Figure 3.10 - Object 8a pressure profile match...................................... 70

Figure 3.11 - Field relative permeability curves..................................... 74

Figure 3.12 - Object 7 pressure profile match ....................................... 75





Figure 3.17 - Field kr curves............................................................. 89

Figure 3.18 - History match for fall-off pressure data of object 1, well C ..... 90

IX

Figure 3.19 - Adsorption/desorption behavior of coal seam in different pressures

......................................................................................... 94

Figure 3.20 - Field kr curves............................................................. 95

Figure 3.21 - Production history match for object 1, well D ...................... 96

Figure 3.22 - Object 1 predicted production profile over 25 years............... 99

Figure 3.23 - Predicted cumulative production of object 1 in well D ............ 99

Figure 3.24 - Object 1 methane recovery after 25 years..........................100

Figure 3.25 - Coal adsorption behavior against pressure changes ...............103

Figure 3.26 - Modified field kr curves.................................................103

Figure 3.27 - Object 2, well A, production history match ........................104

Figure 3.28 - Object 2, well A, predicted production profile ....................106

Figure 3.29 - Object 2 cumulative production profile .............................107

Figure 3.30 - Methane recovery from object 2 in well A ..........................107

Figure 3.31 - The effect of kres changes on production rate ......................111

Figure 3.32 - The effect of kres on methane recovery .............................111

Figure 3.33 - Reservoir sensitivity investigation to kfrac ...........................113

Figure 3.34 - Methane recoveries associated with different kfrac ................113

Figure 3.35 - Three sets of kr curves (permeable to gas, base case and permeable

to water).............................................................................116

Figure 3.36 - The effect of different kr behavior on reservoir performance...117

Figure 3.37 - Methane recoveries obtained by using different kr curves .......117

Figure 3.38 - The effect of porosity changes on production rate ................119

Figure 3.39 - Methane recoveries sensitivity investigation to porosity changes119

X

Figure 3.40 - Production profiles with different cf values ........................121

Figure 3.41 - The effect of cf changes on methane recovery.....................122

Figure 3.42 - The effect of drainage area size on reservoir performance......124

Figure 3.43 - Methane recovery sensitivity to variations in drainage area .....124

Figure 3.44 - Reservoir performance sensitivity to Pi..............................126

Figure 3.45 - The effect of different Pi on methane recovery ...................126

Figure 3.46 - Early time production rates with different desorption time constant

........................................................................................128

XI

List of Tables

Table 3.1 - The depth of different coal seams in well D ............................. 48

Table 3.2 - Object 4 simulation input data............................................. 50

Table 3.3 - Adsorption characteristics of coal seam in well D ...................... 50

Table 3.4 - Field scale relative permeability data .................................... 50

Table 3.5 - Object 3 simulation input data............................................. 56

Table 3.6 - Adsorption characteristics of coal seam in well D ...................... 56

Table 3.7 - Field scale relative permeability data .................................... 56

Table 3.8 - Object 8b rock/fluid properties............................................ 63

Table 3.9 - Adsorption Isotherm Data ................................................... 63

Table 3.10 - Field relative permeability data.......................................... 63

Table 3.11 - Object 8a rock/fluid properties .......................................... 68

Table 3.12 - Adsorption Isotherm Data.................................................. 68


Table 3.14 - Object 7 rock/fluid properties............................................ 73








XII

Table 3.22- Field relative permeability data........................................... 83

Table 3.23 - Object 1, well C simulation input data .................................. 88

Table 3.24 - Adsorption characteristics of coal seam in well D ..................... 88

Table 3.25 - Field scale relative permeability data................................... 88

Table 3.26 - Object 1 (well D) simulation input data for production history

matching................................................................................ 93

Table 3.27 - Adsorption characteristics of coal seam in well D ..................... 93

Table 3.28 - Field scale relative permeability data................................... 94

Table 3.29 - Object 1, well D, average yearly production data..................... 98

Table 3.30 - Object 2, well A simulation input data .................................102

Table 3.31 - Coal adsorption characteristics in object 2, well A ..................102

Table 3.32 - Object 2 average yearly production data ..............................108

Table 3.33 - Summery of permeability values for coal seams in well D ..........129

1

1 Introduction

1.1 Coal Bed Methane Production

Coal bed methane is an important part of the world’s natural gas resource. The

energy industry classifies coal beds as “unconventional gas reservoirs” and

continuously looks for methods to economically develop gas production from

them (Pinzon and Patterson 2004). Coal deposits act as self-sourced natural gas

reservoirs wherein the three crucial elements of petroleum system, which are

source rock, reservoir and trap, are located together in a single geological unit.

Thus, coal deposits represent a relatively simple, low risk exploration target with

respect to locating natural gas accumulations. The major risk in most coal bed

methane developments is generally not the drilling of a dry hole; rather it is not

being able to produce commercial amount of natural gas from the reservoir

(Nelson 2000). Although up to 1400 m3 of gas may be generated per ton of coal,

only a small fraction of this amount can be produced which is typically not more

than 20 m3/ton (Stevenson 1997).

In conventional gas reservoirs, gas is stored as free gas in the pore spaces of the

reservoir rock. While in coal bed reservoirs the gas may be stored as a free gas in

the secondary porosity system, natural fracture network, it is also stored at

almost liquid densities on the internal surfaces of coal matrix by physical

adsorption.

2

The adsorbed gas is generated as a by product during coalification process. It

usually accounts for as much as 99 percent of the gas-in-place in coal bed

reservoir (Roadifer, Moore et al. 2003).

To produce gas from a coal bed reservoir, gas must be desorbed from the coal.

This is achieved by depressurizing the coal seam. Since most coal bed reservoirs

are 100 percent water saturated in the natural fracture network, it is necessary

to produce this water to depressurize the coal and create the necessary pressure

gradient for the gas desorption process. As gas desorbs from the coal, changes in

gas/water saturation in fractures result in fluid mobility changes in the fracture

network. This leads to a unique feature observed during coal bed methane

production, an initial negative gas decline rate. The gas production rate initially

increases to a peak production rate, as the seam dewaters and the relative

permeability to gas increases. This is followed by a normal decline in production

rate as reservoir pressure decreases with continued production (Roadifer, Moore

et al. 2003; Pinzon and Patterson 2004).

Figures 1.1 shows a comparison between the production characteristics of a coal

bed reservoir and a conventional gas reservoir producing by pressure depletion

(Ma 2004; Pinzon and Patterson 2004).

As shown in Figure 1.1, at 50 percent reservoir pressure depletion only 17

percent of original gas-in-place is produced from the coal bed, while at the same

pressure depletion 44 percent of the original gas-in-place is produced in the case

of a conventional gas reservoir.

3

Figure 1.1 - Comparison of CBM and typical gas reservoir producing by pressure

depletion, CBM reservoir (Ma 2004)

Figure 1.1 also shows that to recover 50 percent of original gas-in-place,

reservoir pressure must be depleted up to 56 percent for the case of a

conventional gas reservoir, while in a coal bed reservoir, 78 percent pressure

depletion is needed to produce the same amount of gas from the well. This

indicates that to recover a substantial fraction of the original gas in place in coal

bed reservoirs, a low bottom-hole pressure is required for the producing wells.

0

20

40

60

80

100

0 500 1000 1500 2000 2500Reservoir Pressure (psi)

% G

as in

Pla

ce

Reservoir Pressure Depleted by 50%

17% of Gas Produced

CBM Reservoir

Conventional Gas Reservoir

44% of Gas Produced

4

1.2 Scope of Present Study

The purpose of this study was to perform reservoir simulation studies for a

specific case study. As a simulation tool, SIMED II, an implicit, three-dimensional,

dual porosity, multi-component, finite difference reservoir simulator

incorporating gas adsorption models was used.

Chapter 2 reviews the theory and reservoir engineering aspects of coal bed

methane reservoirs, such as the dual porosity concept, permeability

characteristics of CBM reservoirs, adsorption mechanism of gas storage, multi

mechanism gas transport and CBM well production behavior.

Chapter 3 presents simulation results for the case study, including the

interpretation of injection/fall-off tests through simulation and pressure history

matching. The recorded well pressures are matched by the simulator and the

model parameters are considered to be indicative of actual reservoir

characteristics. This method produces formation properties on reservoir scale.

Properties at this scale can be used to predict future reservoir production rates.

Sensitivity analysis was performed on reservoir parameters such as reservoir

absolute and relative permeability, porosity, compressibility, initial pressure,

desorption time and well drainage area. This analysis shows potential impact on

predicted reservoir performance, when uncertainties in reservoir parameters are

inherent.

5

2 Theory and Reservoir Engineering Aspects of Coal

Bed Reservoirs

2.1 Coal Porosity System

Coal seams are characterized by two distinctive porosity systems: a well-defined

and almost uniformly distributed network of natural fractures (cleats), and a coal

matrix containing a highly heterogeneous porous structure between the cleats

(Shi and Durucan 2003). (Figure 2 – 1)

Figure 2.1 – Fracture System in coal (Shi and Durucan 2003)

6

Cleats account for less than 2 percent of the seam bulk volume. Therefore,

storage of free gas in the pore spaces of coal cleats represents a minor part of

the total gas-in-place. However, the cleat porosity system is very important in

coal bed reservoirs because nearly all the reservoir permeability comes from

presence of cleats network in the coal seams.

The coal matrix contains very fine pore spaces. These pores are referred to as

micro pores. It has been reported that coal micro pores can be as small as a few

nanometers in diameter (Shi and Durucan 2003). Micro pores do not contribute

significantly to permeability, but they are excellent sites for gas storage in

adsorbed form. Because of coal micro pores, it is estimated that a gram of coal

may contain up to 200 square meters of internal surface for methane adsorption

(Reeves and Pekot 2001; Shi and Durucan 2003).

Micro pores are commonly referred to as the coal primary porosity system

whereas cleats are referred to as coal secondary porosity system caused by

geological processes such as structural deformation, differential compaction and

volume contraction. The following section provides more detailed description of

secondary porosity generation in coal seams (Nelson 2000).

2.2 Permeability in coal bed methane reservoirs

Naturally occurring micro fractures, for instance cleats, provide the permeability

essential for bulk fluid flow in coal bed reservoirs. The bulk fluid flow is

controlled by the fractures physical properties, specifically their orientation,

spacing, compressibility and effective porosity. If the fractures are

7

interconnected and continuously distributed throughout the reservoir, the

effective permeability is high (Nelson 2000).

Natural fractures in rocks have various origins and are formed when the applied

stress exceeds the yield stress of the bulk rock matrix material. The applied

stress may be the result of either a physical or chemical process and it may

originate either externally or internally to the rock body. Natural fracture

formation in coal bed reservoir results from stresses generated by such varied

geological processes as structural deformation, differential compaction and

volume contraction (Nelson 2000).

Five types of natural fractures are distinguishable in coal bed reservoirs. The two

commonly observed types of natural fractures are face and butt cleats. Face and

butt cleats are orthogonal sets of fractures oriented perpendicular to the

bedding plane. The face cleats are long, linear micro fractures continuously

distributed throughout the seam whereas the butt cleats are short and terminate

against face cleats. This is interpreted as indicating that butt cleats were formed

later in geological time. Hence, the face and butt cleats are referred to as

primary and secondary cleats, respectively.

Coal cleats are extension (opening-mode) fractures that form as a result of the

stress generated by the volume contraction or shrinkage of coal matrix as a

result of desiccation during thermal maturation (Nelson 2000).

Three other fracture system that may be observed in coal beds, referred to as

tertiary cleats, joints and faults. Tertiary cleats are micro fractures whose

orientations are different than those of either the face and butt cleats. The

8

tertiary cleats terminate against either face or butt cleats. This indicates that

they were formed later in geologic time.

Joints and faults are larger-scale fractures that typically cut across the coal bed

and the other formations (Nelson 2000).

Figure 2 – 2 shows a set of fractures in a coal seam.

Face CleatsFace Cleats

Butt CleatsButt Cleats

Figure 2.2 – Face and butt cleats in coal (Ma 2004)

9

2.3 Pressure-dependent rock properties

During primary methane production, two distinct phenomena are associated with

reservoir pressure depletion, which have an opposing effect on coal

permeability. The first is an increase in the effective stress during production

(Shi and Durucan 2003). The effective stress is equal to the in-situ overburden

stress minus the reservoir pore pressure. As reservoir pore pressure decreases

due to water and gas production, the effective stress applied to the coal seam

increases while the overburden stress remains constant. This causes a reduction

in permeability under uniaxial strain.

The opening and closing of cleats is particularly sensitive to effective horizontal

stresses, because the cleat system is oriented normal to the bedding plane. As a

result, the cleat system permeability is primarily controlled by changes in

effective horizontal stresses.

The second phenomenon is methane desorption from the coal matrix (Shi and

Durucan 2003). When reservoir pore pressure falls below the desorption pressure,

methane begins to desorb from the coal matrix, resulting in coal matrix

shrinkage. As the coal matrix shrinks, the effective horizontal stresses are

partially relaxed. This results in a reduction in the reservoir effective horizontal

stresses causing cleat reopening and an overall increase in permeability.

The purpose of this section is to present a theoretical formulation for

permeability and porosity dependence on pressure which includes both stress and

matrix shrinkage effect in a single equation. The equation is derived under

uniaxial condition (Palmer and Mansoori 1996).

10

The derivation starts from the following equation of linear elasticity for strain

changes in porous rock:

( ) gpr εφφεε −+= 1

where

rε is rock volume strain, pε is pore volume strain, gε is grain volume strain and

φ is porosity value of the rock (coal).

Since the rock body consists of grain particles as well as pore spaces among the

grains, the total rock strain includes two strain components: the strain in pore

volume, pφε (reduction in pore spaces between the grains) and also strain in

grains volume, ( ) gεφ−1 .

The pore volume strain may be written as:

( ) grp εφεφε −−= 1

The incremental form of the equation is

( ) grp ddd εφεεφ −+= 1

or

gr

p ddd εφφ

φε

ε ⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

1 (2 – 1)

where

pdε is incremental pore volume strain

rdε is incremental rock volume strain

gdε is incremental grain volume strain

φ is coal porosity

11

The incremental pore volume strain pdε is a result of a simple volumetric

balance. The incremental rock strain causes incremental strain in pore volume

and therefore a reduction in the pore volume, whereas incremental grain volume

strain increases the pore volume.

In this equation, it is assumed that changes in porosity are small (linear

elasticity). The change in pore volume strain pdε leads to a change in porosity as

follows: (Palmer and Mansoori 1996)

( ) ( ) ( ) dTMKdPc

MKdPdSfc

Md gg αφφφφ ⎥⎦

⎤⎢⎣⎡ −−−⎥⎦

⎤⎢⎣⎡ −−+−⎥⎦

⎤⎢⎣⎡ −−=− 11)(11

(2 – 2)

Where

gc : Grain compressibility

α : Grain thermal expansibility

f : A fraction 0→ 1

dS : Changes in overburden stress

dP : Changes in pore pressure

dT : Changes in temperature

M (constrained axial modulus) and K (buck modulus) are related to Young’s

modulus, E and Poisson’s ratio, ν , via isotropic elasticity theory.

12

( )( )ννν

2111

−+−

=EM

(2 – 3)

⎟⎠⎞

⎜⎝⎛−+

=νν

11

31

MK

(2 – 4)

For porosity, φ <<1, as is the case in coal beds for constant overburden stress

( 0=dS ), we have:

dTMKdPcf

MKdP

Md g αφ ⎥⎦

⎤⎢⎣⎡ −−⎥⎦

⎤⎢⎣⎡ −++−=− 111

(2 – 5)

The term dTα is a temperature expansion/constriction term (if the temperature

drops, the matrix fabric shrinks and the cleat width increases).

This is directly analogous to matrix shrinkage where cleat width increase as gas

desorbs during pressure drawdown (Palmer and Mansoori 1996).

On the other hand, according to laboratory evidence the lab measured matrix

shrinkage strains may be fitted to a Langmuir type curves with ease and accuracy

(Harpalani and Schraufnagel 1990; Palmer and Mansoori 1996). Therefore:

dPPP

PdPddT l

⎟⎟⎠

⎞⎜⎜⎝

⎛+

≡ε

εα (2 – 6)

lε and εP are parameter of Langmuir curve match to volumetric strain change

due to matrix shrinkage.

dPPP

PdPd

MKdPcf

MK

MdPd l

g ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎥⎦

⎤⎢⎣⎡ −−⎥⎦

⎤⎢⎣⎡ −++−=−

ε

εφ 11 (2 – 7)

The module M and K are independent of pressure. This leads to:

13

dPPP

PdPd

MKdPcd lm ⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎥⎦

⎤⎢⎣⎡ −+=

ε

εφ 1 (2 – 8)

Where

gm cfMK

Mc ⎥⎦

⎤⎢⎣⎡ −+−= 11

(2 – 9)

By integrating and dividing to 0φ we have:

( ) ⎥⎦

⎤⎢⎣

⎡+

−+

⎟⎠⎞

⎜⎝⎛ −+−=−

0

000 1

PPP

PPP

MKPPc lm

εε

εφφ (2 – 10)

P : Reservoir pressure

0P : Initial reservoir pressure

( ) ⎥⎦

⎤⎢⎣

⎡−

−−

⎟⎠⎞

⎜⎝⎛ −+−+=

0

0

00

00

11PP

PPP

PMKPP

c lm

εεφε

φφφ

(2 – 11)

Assuming permeability varies with porosity as follows: (Palmer and Mansoori

1996)

3

00⎟⎟⎠

⎞⎜⎜⎝

⎛=

φφ

kk

(2 – 12)

now the permeability and porosity changes can be expressed as functions of

elastic modules, initial porosity, shrinkage characteristics and reservoir pressure

drawdown.

Palmer and Mansoori (Palmer and Mansoori 1996) suggested the following

equation (Equation 2 -13) for the pressure at which permeability will rebound:

( ) εεε PEPP lc −= 5.048.0 (2 – 13)

where cP is the rebound pressure

14

This rebound pressure as presented is independent of reservoir initial pressure,

0P .

At early production time when matrix shrinkage can be neglected and if grain

compressibility is also very small, then porosity and permeability function may be

written as:

MPP

0

0

0

1φφ

φ −+= (2 – 14)

3

0

0

0

1 ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+=

MPP

kk

φ (2 – 15)

2.4 Relative Permeability in coal bed reservoir

Relative permeability is a primary parameter in determining coal bed reservoir

production characteristics. Gas and water flow in cleats are mainly controlled by

relative permeability. Therefore, an appropriate estimation of relative

permeability characteristics of the coal seam is needed to understand the

reservoir performance properly.

Relative permeability data can be obtained by the following methods:

Laboratory based relative permeability investigation: there are two standards

methods for gas/water relative permeability measurements, unsteady state and

steady state methods.

In the unsteady state technique the core is saturated with brine which is

subsequently displaced by gas injection. The production volumes of both

fluids and the differential pressure or total flow rates are monitored and

15

recorded as a function of time. A mathematical model, such as that of

Jonhson, Bossler and Naumann (Johnson, Bossler et al. 1959) is used to

derive a set of relative permeability characteristics from the production

data. The derived relative permeability values are determined as a

function of the mobile water saturation at the end-face.

The unsteady state technique is limited by the simplifying assumptions of

the mathematical models which include the assumption that the core

samples should be isotropic and homogeneous (Ohen, Amaefule et al.

1991).

The most attractive feature of the unsteady state technique is the

reduced testing time as compared to the steady state.

Figure 2.3a shows some coal relative permeability curves obtained in the

lab using unsteady state methods (Meaney and Paterson 1996).

The steady state technique is preferred for heterogeneous sandstone and

carbonate samples as well as coal. In the steady state process, fluids are

injected simultaneously at fixed flowing ratios. Saturation distributions

are monitored until equilibrium is established. This is evidenced by the

constancy in differential pressure. Once equilibrium is achieved, fluid

saturations are directly measured by one of the following independent

techniques: gravimetric or volumetric material balance, X-ray or gamma

scanning or CT scanning. The relative permeability values are determined

by the application of Darcy’s law.

16

Steady state data typically cover a broader range of saturation than

unsteady state data.

The main disadvantage of the steady state process is the time required

to achieve the saturation equilibrium, which can be substantial,

especially for low permeability samples (Ohen, Amaefule et al. 1991).

Well transient pressure testing: Transient pressure testing is used to calculate

the in-situ relative permeability characteristics. The period over which typical

test in coal seams are performed is on the order of hours. During such a short

time, fluid saturation and capillary pressure remains fairly constant. Therefore,

effective gas and water permeability can be determined at a particular fluid

saturation. A similar test after some time, on the order of month, when gas and

water ratio has changed, will provide gas and water permeability at a different

fluid saturation. By performing more similar tests, field-representative relative

permeability curves can be generated (Ahmed, Johnston et al. 1991).

Simulation based relative permeability curves: Another source of relative

permeability data is from history matching fluid production rates and bottom-

hole pressure data with a reservoir simulator. The initial predictions are based on

an assumed or measured relative permeability curves. The curves are varied until

a match between observed and computed production and pressure is obtained.

This method is often limited by the assumption that all the other reservoir

parameters, including the absolute permeability values, porosity, drainage area

and well skin factor, are known and sufficiently accurate (Conway, Mavor et al.

17

1994). Some coal relative permeability curves derived from field history

matching are shown in Figure 2.3b.

Figure 2.3a - Relative permeability in coal from laboratory testing

18

Figure 2.3b – Coal relative permeability curves obtained by history matching (Meaney

and Paterson 1996)

According to the published literature (Meaney and Paterson 1996), substantial

differences exist between relative permeability curves measured in the

laboratory and field relative permeability curves obtained by history matching

reservoir performance. Filed relative permeability curves are generally

characterized by high values of residual water saturation, which often are in

excess of 80%.

The extremely heterogeneous nature of coal is known to be primarily responsible

for the difference between lab and field relative permeability curves (Meaney

and Paterson 1996). Obviously, laboratory measured relative permeability curves

which are obtained from small core plugs can not be representative of reservoir

heterogeneity spanning several length scales.

19

There are other reasons for such differences which originate from the nature of

fluid flow in coal bed reservoirs.

As mentioned before, it is generally assumed that cleats are initially saturated

with water and as the reservoir pressure is reduced, gases desorb from the coal

surface, diffuse through the matrix and flow to the well bore via the fracture

system (cleats) (Roadifer, Moore et al. 2003). The adsorbed gas displaces water

from the fractures. This leads to viscous fingering in the fracture system. Viscous

fingering occurs during fluid flow in a porous medium where a less viscous fluid

like gas displaces a more viscous fluid like water. In this case, the displacement

front forms as an uneven fingered front with the viscous fingers propagating

rapidly and causing early breakthrough and poor displacement efficiency.

Viscous fingering is associated with large-scale by-passing of water and this is the

likely explanation for the high residual water saturation associated with coal bed

gas production.

Finally, gravity forces can also affect coal bed reservoir relative permeability

behavior. For instance, if gas displaces water vertically downwards the density

differences can make the fluids partitioned and delay breakthrough of methane.

On the other hand, in horizontal flow gravity override can have a similar effect

to viscous fingering resulting in early gas breakthrough (Meaney and Paterson

1996).

20

2.5 Methane storage in coal

Methane is mainly stored in coal as adsorbed gas on the surfaces of micro

fractures in the coal matrix (Figure 2.4). The adsorbed methane in coal bed

reservoirs accounts for more than 90 % of total gas-in-place. Methane can be also

present in the form of free gas in natural fracture system and it has been

reported that in high volatile sub-bituminous coals free gas can comprises up to

70 % of the total storage capacity (Roadifer, Moore et al. 2003; Shi and Durucan

2003).

2.5.1 Methane adsorption

The adsorption process occurs between the gaseous methane phase and the coal

as the solid phase in two types of physical and chemical adsorption. However, it

is believed that the physical adsorption is the prevailing mechanism in coals. In

physical adsorption methane is adsorbed as a result of intermolecular forces,

van der Waals forces, between methane molecules and the coal molecules while

chemical adsorption involves sharing or transfer of an electron (Figure 2.5) (Ma

2004).

Physical adsorption characteristics are described as follows: (Ma 2004)

• Physical adsorption is nearly instantaneous and equilibrium in quickly

established.

• It is usually reversible due to low energy requirements (activation energy

is usually very low)

• The degree of physical adsorption decreases with increasing temperature.

21

• It is not limited to a monolayer but a series of layers may pile up.

Figure 2.4 – Schematic illustration of adsorbed gas on coal surface (Ma 2004)

22

Figure 2.5 – Chemical adsorption in which there is a chemical bond between

methane and coal molecules (Ma 2004)

2.5.2 Langmuir adsorption model

The adsorption model in coal bed methane reservoir engineering is a parametric

curve which relates the coal adsorption capasity to pressure at the coal seams

temperature (Figure 2.6). One of most commonly used models is Langmuir model

which is based on the following assumptions: (Stevenson 1997)

• Gas-gas interactions in the adsorbed phase are negligible.

• Adsorbed molecules occupy only one adsorption site at ant one time.

• Adsorption molecules form only a monolayer.

• All the surfaces have the same energy for adsorption.

• Surface forces do not overlap or interfere.

23

The adsorption rate is assumed to be proportional to the number of free

adsorption sites and to the rate of connection between free gas molecules and

the surface. The latter is directly proportional to the bulk pressure. The overall

rate of adsorption is given bellow: (Stevenson 1997)

Rate of adsorption = ⎟⎟⎠

⎞⎜⎜⎝

⎛−

m

aa n

nPc 1 (2 – 16)

Where P is the pressure, an is the number of occupied adsorption sites (per unit

weight of adsorbent), mn is the total number of adsorption sites and ac is the

proportionality constant for adsorption.

Desorption occurs when the molecular vibration in the normal direction to the

surface is sufficient to overcome the adsorption potential i.e. when molecule

vibration increases due to the thermal energy, the probability for the molecules

to move away from the surface increases. The probability of this occurring within

any given time period is predicted by a statistical time constant that depends on

temperature and the characteristic adsorption energy of the site.

The overall rate of desorption is assumed to be proportional to the probability of

normal vibration and to the number of occupied sites: (Stevenson 1997)

Rate of desorption = m

aTkd n

nec B

⎟⎟⎠

⎞⎜⎜⎝

⎛−

ε

(2 – 17)

Where T is the absolute temperature, ε is the characteristic adsorption energy

of the site or activation energy (an increase in ε decreases the rate of

24

desorption), Bk is the Boltzmann constant described bellow and dc is the

statistical time constant of desorption.

oKJ

NRk

AB

231038066.1 −×== (2 – 18)

where

R is Universal gas constant = 8.3145 omolK

J and

AN is Avogadro’s number = 23100221.6 ×

Equating the rates of adsorption and desorption at a given pressure, P gives:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

m

aa n

nPc 1 =

m

aTkd n

nec B

⎟⎟⎠

⎞⎜⎜⎝

⎛−

ε

(2 – 19)

Defining ),( Tb ε and 0b as

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

== TkTk

d

a BB ebecc

Tbεε

ε 0, (2 – 20)

allows above equation to be written in the more recognized form of the Langmuir

equation: (Stevenson 1997)

25

bPbP

nn

m

a

+=

1 (2 – 21)

Adsorption Isotherm Curve

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000

Pressure

Ads

orpt

ion

(sc

f/to

n)

An adsorption Isotherm curve defines the holding capacity of gas as a function of pressure.

Figure 2.6 – Adsorption isotherms (Ma 2004)

The proportion of occupied adsorption sites to the total number of adsorption

site may be substituted by the proportion of adsorbed gas volume at a given

pressure to the adsorbent total adsorption capacity:

L

ads

ads

ads

m

a

VV

VV

nn

MAX

== (2 – 22)

also if we define a new parameter as:

26

bPL

1= (2 – 23)

The parameters, LV and LP are called Langmuir parameters and the form of

Langmuir equation is:

LLads PP

PVV+

= (2 – 24)

Where

LV is The Langmuir volume or the maximum amount of gas that can be adsorbed

on coal surface as monolayer at a given temperature.

LP is The Langmuir pressure or the pressure at which the volume of adsorbed gas

is half of LV (MAXadsV )

2.6 Gas Transport in Coal

Gas movement through coal takes place in three stages: (i) gas desorbs off the

internal coal surfaces (ii) gas diffusion (mainly Knudsen diffusion) through the

micro pore structure towards the larger pores in response to a concentration

gradient by Fick’s law and finally (iii) freed gas flow (Darcy flow) in sufficiently

large pores and cleats out of the coal matrix in response to pressure gradients

(Crosdale, Beamish et al. 1998) (Figure 2.7).

27

Figure 2.7 – Gas movement in coal bed reservoirs (Reeves and Pekot 2001)

2.6.1 Gas Desorption

Desorption process along with diffusion refers to: the detachment of gas

molecules from the coal micro pore surfaces (Figure 2.8), migration of this

desorbed gas though the coal matrix to the cleat as a result of concentration

gradients in the matrix and flow to well through the cleat system. The diffuson

of gas through the coal matrix is described mathematically by Fick’s first law:

(Sawyer, Paul et al. 1990)

28

( )( )pCCV

q mdes −=

τ (2 – 25)

where C , is the average matrix gas concentration, mV is the bulk volume of a

matrix block and τ is the desorption time constant defined by

στ

D1

= (2 – 26)

where D is the diffusion coefficient of gas in the coal matrix and σ is a shape

factor discussed by Warren and Root (Warren and Root 1963).

To understand the physical meaning of desorption time, Fick’s equation can be

rewritten in derivative form as

( )ECCdtdC

−−=τ1

(2 – 27)

where EC is the gas concentration at the boundary between the matrix and cleat

system.

The solution to Equation (2 – 27) with initial and boundary conditions as

iCC = at 0=t

ECC = for 0≥t at the boundary

is

( ) ( )⎟⎠⎞

⎜⎝⎛ −

−+= τt

EiE eCCCtC (2 – 28)

at the time τ=t Equation (2 - 28) may be rearranged as

29

( )63.011 =−=

−−

eCCCC

Ei

i τ (2 – 29)

and because concentration is proportional to mass, then according to equation (2

– 29), the desorption time may be defined as the time at which approximately

63% of the gas contained between iC in the matrix and EC at the boundary has

diffused to the boundary.

Figure 2.8 – Desorption includes both physical and chemical adsorbed gas molecules

(Ma 2004)

The definition of desorption time is the basic concept for its measurement in the

laboratory. The method is to plot a graph of desorbed gas volume against elapsed

time. The desorption time can be obtained by reading the time corresponding to

30

the desorbed gas volume equal to 63% of total gas content. This method may be

used in any circumstance, regardless of coal metrix geometry (Xingjin 2003).

Another method was introduced by Mavor and Pratt (Mavor, Pratt et al. 1994)

based on a simplification to the solution of partial diffusion equation (Xingjin

2003):

lt QtrDCQtQ −= 2)(

Where )(tQ represents the desorbed gas volume at time t , C is unit conversion

factor, D the diffusion coefficient of gas in coal matrix, r is the sample

characteristic diffusion distance and for the geometry of a cylindrical core

sample, it is equal to the radius of cylinder. lQ is the lost gas volume.

Mavor and Pratt (Mavor, Pratt et al. 1994) suggest that if the desorbed gas

volume, )(tQ , is plotted against the root of time, t , the slope of straight line

fitted to the early time data may be used to determine 2rD

:

2rDCQm t=

2

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

tCQm

rD

Since

⎟⎠⎞

⎜⎝⎛=

Dστ 1

and 2

8r

=σ for cylindrical core sample then:

22

81

81

⎟⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

mCQ

Dr tτ

31

and desorption time constant can be calculated. Figure 2.9 shows an example of

desorbed gas volume plotted against t as well as an straight line fitted to early

time data (Mavor, Owen et al. 1990)

Figure 2.9 - Determination of desorption time constant by straight line method

(Mavor, Owen et al. 1990)

2.6.2 Gas Diffusion in Coal

Three mechanisms have been identified for diffusion of an adsorbing gas in the

matrix larger pores (macro pores). They are molecular diffusion (molecule-

molecule collisions dominate), Knudsen diffusion (molecule-wall collision

dominate) and surface diffusion (transport through physically adsorbed layer).

The effective macro pores diffusivity is thus a complex quantity which often

includes contribution of more than one mechanism among which molecular

diffusion prevails when the pore diameter is greater than ten times the mean

free path; Knudsen diffusion may be assumed when the mean free path is greater

32

than ten times the pore diameter. In the intermediate regime both wall collision

and inter molecular collision contribute to the diffusion resistance and the

effective diffusivity depends on both the Knudsen and molecular diffusivities.

Due to dependence of gas molecule mean free path on pressure, there will be a

transition from Knudsen flow at low pressures to molecular diffusion at high

pressures. It has been estimated that the mean free path of the methane

molecule at standard conditions (room temperature and atmospheric pressure

0.1 MPa) is about 50 nm. In deep coal seems, the reservoir pressure will be much

higher (> 5MPa) and thus the mean free path would be much lower than 50 nm.

This implies that molecular and transition (surface) diffusion, rather than

Knudsen diffusion, would control the diffusion process in the macro pores of

deep coal seams. In micro pores (<2nm) because of extremely small pore sizes,

gas diffusion is controlled by a distinctively different mechanism. In fine micro

pores (<1nm), the diffusing molecules never escape the potential site instead

their transport occurs by jumps between adsorption sites. Therefore, the process

is considered to be more similar to surface diffusion, however the domain

through which diffusing molecules migrate is not a two dimensional surface but

rather a three dimensional space (Shi and Durucan 2003).

2.6.3 Gas Permeation in CBM Reservoirs

Coal bed wells exhibit three distinct stages in methane production (Pinzon and

Patterson 2004). The first stage, Phase I, is characterized by a constant water

production rate and declining flowing bottom-hole pressure. Phase II is

33

characterized by “negative decline” in the gas production rate as well as a

significant decline in the water production rate and finally Phase III which begins

when well has reached its peak in gas rate and gas production is characterized by

a more typical positive decline trend (Figure 2.10) (Pinzon and Patterson 2004).

Since cleat system are fully water saturated at initial conditions. Water must be

displaced from the cleats before gas can effectively flow to the well. This

process is called “dewatering”. Dewatering occurs mainly during phase I and

continues in Phase II. As water is displaced from the cleat system, reservoir

pressure decreases. When the reservoir pressure falls down to gas desorption

pressure, the gas desorbs from the coal and flows through the cleats. This

increases the gas saturation in the cleats. Therefore the cleats relative

permeability to gas increases. This is known as the primary explanation for the

increasing gas production rate during phase I and II.

The well is considered to be dewatered at the beginning of phase III (water

production is low and/or negligible and gas and water saturation remains with

very little changes) and pseudo-steady state flow exists for the rest of reservoir

life (Pinzon and Patterson 2004).

34

Figure 2.10 – Production regime in coal bed reservoirs (Pinzon and Patterson 2004)

2.7 Gas Transport Modeling in CBM reservoirs

Coal bed reservoir gas transport has been described by three types of

mathematical models. They are empirical models, equilibrium adsorption models

and non- equilibrium adsorption models (Guo, Du et al. 2003).

Empirical models are mainly used to predict methane release according to simple

mathematical descriptions for the physical phenomena of gas transport.

Gas transport in the coal micro pores in generally modeled with equilibrium and

non-equilibrium adsorption formulations. Gas adsorption/desorption in

equilibrium adsorption models is assumed to be strictly pressure dependent while

gas adsorption/desorption in non-equilibrium models is assumed to be a function

35

of pressure and time. Non-equilibrium adsorption models are further classified as

unsteady state and quasi-steady state models.

In a quasi-steady state model the desorption rate is proportional to the

difference between the gas concentration at the external matrix surface and the

average concentration contained within the matrix, whereas in unsteady state

adsorption models, desorption rate is related to the concentration gradient at

the external surface of the coal matrix (Kolesar and Ertekin 1986; Guo, Du et al.

2003).

2.7.1 Gas Desorption Modeling

Desorption is modeled using desorption isotherms. Laboratory measurements

show that there is no significant hysteresis in desorption isotherm campaing to

adsorption isotherm (Clarkson and Bustin 1999; Ma 2004). Therefore Langmuir’s

equation may be used to model desorption process as pressure changes in the

system (Figure 2.11).

36

Adsorption Isotherm Curve

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000

The desorption of the methane gas generally follow down the adsorption isotherm curve.

Pressure

Ads

orpt

ion

(sc

f/to

n)

Figure 2.11 – Adsorption isotherms may be used to model desorption process (Ma

2004)

2.7.2 Gas Diffusion modeling

The pore structure of coal is highly heterogeneous, with the pore size varying

from a few Angstroms to frequently over a micrometer in size. According to

International Union of Pure and Applied Chemistry (IUPAC) classification pores

may be divided into macro pores (>50 nm), transient or mesopores (between 2

and 50nm) and micro pores (<2 nm). It has been reported that coals mainly

exhibit a bidisperse structure, with significant fractions of the pores in size

greater than 30 nm and less than 1.2 nm (Shi and Durucan 2003).

In the bidisperse model, the sorption behavior is modeled by a macro sphere

comprised of micro spheres (Figure 2.12 and 2.13). Two phases of gas movement

37

are described: firstly by movement of the gas to the outside of the micro sphere

and secondly by gas movement in the spaces between the micro spheres until the

gas reaches the outside of the macro sphere. These two phases simulate

desorption and diffusion of gas in coal bed matrix blocks (stage (ii) and (iii) in

section 2.6) (Crosdale, Beamish et al. 1998; Shi and Durucan 2003).

The mathematical approach is a combination of bidisperse mass balance

equations and following quasi-steady state equation describing gas diffusion in

coal matrix: (Shi and Durucan 2003)

( )[ ]pUUdtdU

E−−=τ1

(2 - 30)

The equilibrium gas concentration EU is related to the cleat gas pressure by

Langmuir isotherm: (Shi and Durucan 2003)

( )bpbpUpU L

E +=

1 (2 - 32)

The mass transfer rate between the matrix blocks and cleats is given by

dtdUsqdes −= (2 - 33)

where s is a scaling factor.

Rearranging Equation (2 – 30) in order to separate the differential variables,

gives: (Shi and Durucan 2003)

( ) dtpUU

dU

E τ1

−=−

(2 - 34)

Integrating over a time step t∆ leads to

38

⎟⎠⎞

⎜⎝⎛ ∆−

+

++

=−

− τt

nE

n

nE

n

eUU

UU

21

21

1

(2 – 35)

by rearranging,

2)1(

11

+⎟⎠⎞

⎜⎝⎛ ∆−⎟

⎠⎞

⎜⎝⎛ ∆−

+ +−+=

nE

nE

tn

tn UUeUeU ττ (2 – 36)

where subscript n represents time step.

The average desorption rate over time step t∆ is given by:

tUUsq

nnn

des ∆−

−=+

+1

21

(2 – 37)

or in terms of the equilibrium gas concentration in Equation (2 – 36):

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

∆−=

+⎟⎠⎞

⎜⎝⎛ ∆−

+ nn

En

Et

ndes U

UUe

tsq

21

1

21

τ (2 – 38) In

the bidisperse model, molar concentrations of free gas in the cleats and macro

pores and the adsorbed phase in the micro pores are used as the dependent

variables. The mass balance equations may be expressed in terms of the volume

averaged variables over an entire porous particle. The resulting equations are,

(Shi and Durucan 2003)

For the micro pores:

( ) ( ) ( )[ ]RVCVrD

tRV

pEc

m −=∂

∂2

15 (2 – 39)

where

V is the volume of adsorbed gas per unit of coal matrix block in bidisperse

model, EV is the volume of adsorbed gas in equilibrium with free gas phase, V is

39

the volume-average of V over an entire micro porous particle, cr is the radius of

micro porous particles in the matrix, pC is the gas concentration in the macro

pores between the micro porous particles, mD is the micro pores diffusion

coefficient.

and

( ) 015

2 =−−+ p

p

ppp CC

R

DdtVd

dtCdφ (2 – 40)

for the macro pores.

where

V is the volume-average of V over an entire matrix block, pR is the radius of

matrix block, C is the gas concentration in the cleat, pC is the volume-average

of pC over an entire matrix block, pφ is the macro pores porosity and pD is the

macro pores diffusion coefficient.

40

Figure 2.12 – Bidisperse model scheme including micro spheres inside the macro

spheres (Shi and Durucan 2003)

Figure 2.13 – Spherical matrix elements in coal bed reservoirs (Kolesar and Ertekin

1986)

41

Using the equation of state for a real gas, the equilibrium gas concentration is

related to the macro pore gas concentration by Langmuir equation (Shi and

Durucan 2003)

( )TRzbCTRzbCV

CVgpp

gppLpE +=

1 (2 – 41)

where gR is the universal gas constant, T is coal bed reservoir temperature and

pz is the compressibility factor for free gas in the macro pores.

Similar to the unipore quasi-steady state adsorption model the following diffusion

time constant can be defined for the macro pores and micro pores respectively:

p

pp D

R15

2

=τ (2 – 42)

m

cm D

r15

2

=τ (2 – 43)

The micro pore mass balance Equation (2 – 39) may be further integrated over a

matrix block to yield:

[ ]VVdtVd

E

m

−=τ1

(2 – 44)

where

( ) dRRCVR

V pR

R pEp

E2

03

3∫ =

= (2 – 45)

If the incremental changes in the concentration profile within the particle over a

time step, t∆ , is sufficiently small then

( ) 1<<− ppgp CCTRbz , pRR ≤≤0

42

pgppgp CTRbzTCRbz +≈+ 11 , pRR ≤≤0 (2 – 46)

( )∫ ==

+≈ pR

RpE

gpp

gppL

p

E CVdRRTRzCb

TRzbCV

RV

0

23 1

3 (2 – 47)

Therefore, for a sufficiently small time step t∆ , Equation (2 – 44) may be

approximated by

( )[ ]VCVdtdV

pEm

−≈τ1

(2 – 48)

Given the similarity between Equations (2 – 30) and (2 – 48) the micro pore mass

balance equation may be integrated over a time step ( nn ttt −=∆ +1 ) to yield

( ) ( )2

)1(11 p

nEp

nE

tn

tn CVCVeVeV mm

+⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−⎟⎟

⎠

⎞⎜⎜⎝

⎛ ∆−+ +

−+= ττ (2 – 49)

The macro pore mass balance equation is discretised using the standard finite

difference method:

( ) 01 11

11

=−−∆−

+∆− ++

++

np

n

p

nnnp

np

p CCtVV

tCC

τφ (2 – 50)

Since

( )1121 1 +++ −= n

pn

p

ndes CCq

τ (2 – 51)

The average mass transfer rate (per unit volume of coal bed reservoir) between

the cleats and macro pores over time step t∆ is given by: (Shi and Durucan 2003)

tVV

tCCq

nnnp

np

pn

des ∆−

+∆−

=+

++

11

21

φ (2 – 52)

where 1+n

V can be obtained from Equation (2 – 49).

43

3 The Application of Simulation Studies in Coal Bed

Reservoir Characterization

3.1 Well Testing

The interpretation of well pressure test data is a key element in formation

evaluation and reservoir characterization. The main advantage of well pressure

testing is that the well test provides information on the scale of the test radius

of investigation as compared to core data which provides information on the

centimeter scale and well logs which provide data on the tens of centimeter

scale. The main disadvantage, however, is that the pressure changes in a

reservoir are diffusive in nature and therefore relatively insensitive to the finer

details of reservoir heterogeneity. There is a limit to the scale of heterogeneity

or detail in reservoir description which can be resolved with well pressure testing

and most well tests provide estimates of bulk or average reservoir properties.

The injection fall-off tests conducted here consist of the following steps:

1. A pressure change is created in the reservoir by injecting a fluid into the

formation followed by a shut-in period to depressurize the well called

pressure fall-off period.

2. The pressure response at the well is monitored as a function of time by a

sensitive pressure gauge suspended on a wire line close to the

perforations.

44

3. A reservoir simulator is used to analyze and interpret the measured

pressure response. We use the SIMED simulator. Details of the simulator

model are the same as those given in the previous chapter.

The interpretation refers to an attempt to match the well actual response with

the one predicted by the reservoir model. The predicted pressure response is

produced with best estimates of reservoir parameters obtained on the basis of

available laboratory data and field observations. When the model output

matches the well actual test response, the model input parameters are

considered to be representative of the reservoir characteristics.

The following reservoir parameters are usually determined by the matching

process:

• Well deliverability or permeability-thickness product, kh and well

bore skin factor, s or formation damage.

• Initial reservoir pressure, iP and average reservoir pressure, P for

production wells.

• Identification of reservoir limits or boundaries, DA .

A serious difficulty with the history matching process is non-uniqueness. The

model may produce a response which is very close to the actual response even

though the model parameters are very different from the actual reservoir. In the

other words, there may be more than one set of model parameters which

produce a satisfactory match to the test data.

45

The problem of non-uniqueness may be reduced by careful design and

implementation of the well test and by firmly anchoring the reservoir model to

geological description and core and log data.

3.2 Injection fall-off test

A well which is static, stable and shut-in is subjected to the injection of a fluid,

which is in this case water, at a constant rate for a specific period of time, and

then the well is shut-in and the pressure decline due to fluid discharge into the

reservoir is monitored.

The best time to test coal seams is prior to production when the reservoir is 100

percent water saturated. Interpretation of tests run on coal wells after pressure

drawdown, when two phase flow conditions are established in the reservoir is

difficult. The injection fall off test determines the coal seam properties that are

important to both reservoir characterization and methane production. The

estimated parameters are formation flow capacity of the seam (kh), reservoir

pressure and well bore skin factor.

From a practical viewpoint, the injection phase of the test can be performed at

either constant injection rate or constant injection pressure. Common practice is

to maintain a constant injection rate. The radius of investigation for the test

must be greater than the extent of formation damage caused by the drilling and

completion fluids and near well bore gas desorption. The maximum test pressure

is usually 60 percent of the fracture gradient to prevent fracturing the

46

formation. (Hopkins C.W. et al. (1998), Badri M. et al. (1996) and Zuber M.D. et

al. (1990))

3.3 SIMED II, the simulation tool

SIMED II is a coal seam reservoir simulator that models the gas and water flow in

coal seams. SIMED II is a two phase (gas and water), three dimensional, multi

component (more than one gas), single or dual porosity simulator.

To model coal bed methane reservoir behavior, a number of parameters

describing the reservoir must be measured or estimated. These include gas

content, permeability, porosity, seam thickness, Langmuir isotherm data,

desorption time constant, relative permeability and reservoir pressure. The

characteristics of these parameters were discussed in the previous chapter.

3.4 Case Study

The pressure fall-off tests conducted in this study are for the wells in a coal bed

methane field. The coal formation consists of several coal seams.

The coal seams are labeled in Latin numbers from coal seam number (I), the

deepest, to coal seam number (XVIII), the shallowest. The depth of coal seams

varies from about 1100 meters to nearly 500 meters.

Four production wells were drilled in the first stage of this project, well A, B, C

and D. The first producing well, well D, started methane production in August

2000. Well B was put on production in November 2000. Well A commenced

production in January 2001.

47

Before production started, several injection fall-off tests were conducted in

wells B, C and D to investigate reservoir characteristics.

Production data were available for a coal seam in well D and well A. The

following chapter describes the history matching process for the injection fall-off

tests and the production data for these wells.

3.5 Injection fall off (IFO) test analysis

The injection fall-off tests were for well B, C and D. Since the wells intersect

coal seams in different depths, several intervals were used for testing. In some

cases more than one interval was used to run the test on an individual seam. The

coal seam or part of a coal seam on which an IFO test was run is called an

object. For example, the first IFO test in well D was done on coal seam number

(V), but because it was the first interval tested in this well, the interval was

called: interval number 1 and the corresponding part of the seam was called

object number 1 in well D.

The following table shows the coal seam intersections with well D as well as all

the intervals (objects) tested in this well.

48

Table 3.1 - The depth of different coal seams in well D

Seam No. Object No. Perforation Interval (m)

V+VI I 1156 – 1159 1147 – 1150 1141 – 1144

VIII II

1050.5 – 1053.5 1056.5 – 1060.5 1065.5 – 1067.5

1079 – 1081 IX III 982 – 984 X IV 852 – 855

XIVa VII 663 – 666 XV VIIIa 614 – 617 XV VIIIb 602 – 605.5 XVII IX 316 – 319

3.5.1 IFO test in well D – Object 4:

3.5.1.1 Coal Seam Geological Setting

This IFO test was conducted on coal seam number X. The object number is 4 in

well D. Coal seam corresponding depth and thickness are 2778 and 26.2 feet,

respectively. Since no information was available regarding the existence of any

major heterogeneity in this seam, the reservoir was considered to be

homogeneous.

3.5.1.2 Test Description

The coal seam was subjected to water injection for 12:40 hours (12 hours and 40

minutes). The average injection rate was 56.4 liter/hour (or 8.5 BBL/day), then

the well was shut for 29:45 hours to let the pressure fall-off establish. The

49

bottom-hole pressure was monitored and the reported pressures are corrected

for depth to mid-point of the perforations.

3.5.1.3 Simulation Model of the Test

The simulation was set up with a 33 by 33 blocks in x-y directions (Cartesian

system) by one block in z direction. The block size varied from 1.75 feet for the

area around the well bore to 22 feet for the furthest grid blocks from the well.

The well was placed in the center grid.

The porous medium was considered as a dual porosity medium in the simulation

model to incorporate the impact of this mechanism in CBM reservoirs

performance as discussed in the previous chapter.

Reservoir permeability was defined as a function of reservoir pressure and

formation compressibility due to the effect of compaction phenomena on

reservoir performance.

3.5.1.4 Simulation Input Parameters

The input data are also shown in Tables 3.2 to 3.4 as well as Figure 3.1. These

data were presented in the field reports provided by field authorities.

50

Table 3.2 - Object 4 simulation input data

Reservoir Properties Descriptions Reservoir fluid components Water & Methane Initial water saturation 100% Water viscosity 0.446 cp Water formation volume factor 1.019 Water compressibility 2.93e-9 Reservoir Temperature 50 ºC Porosity system Dual Porosity

Permeability/porosity model Compressibility/reservoir pressure based analytical model

Compaction reversibility Reversible compaction Reservoir porosity 6.2%

Formation compressibility Fractured zone: 5.0e-5 Intact zone: 5.0e-5

Table 3.3 - Adsorption characteristics of coal seam in well D

Model Specifications Descriptions Adsorption Model Extended Langmuir Model Coal Density 89.27 lb/ft3 Langmuir Pressure 455.4 psia Langmuir Adsorption Volume 554.1 SCF/UST Desorption Time 2.9 days Reservoir Desorption Pressure 1130 psia

Table 3.4 - Field scale relative permeability data

Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

51

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Water Saturation (%)

Rel

ativ

e Pe

rmea

bilit

y

krg

krw

Figure 3.1 - Field kr curves

3.5.1.5 Test interpretation results

The unknown reservoir parameters are initial reservoir pressure, reservoir

permeability and well bore skin factor.

Simulation studies for this test indicate to the existence of a fractured zone

around the well bore. The fractured zone connects the well-bore to the reservoir

by its higher permeability so that pressure gradient in the well bore can be felt

more efficiently by the reservoir.

According to pressure history matching method, reservoir parameters are

determined in the way that the pressure history (pressure data) can be

reproduced by the simulator (SIMED II). A good match between measured

pressure data and simulation is obtained with the following parameters:

52

Seam permeability: 0.12 md

Fractured zone permeability: 0.70 md

Extent of fractured zone: 12 feet

Initial pressure was set to 1130 psia.

The radius of investigation for the test was determined by trial and error method

using successive simulations to determine the maximum distance from the well-

bore affected by the pressure treatment transient. This was approximately 230

feet. Since the radius of the altered zone was 12 feet, the value of permeability

for the unaltered zone is considered to be representative of the permeability

which may be expected in the drainage area for the well.

Figure 3.2 shows the recorded pressure as well as the simulated match.

700

800

900

1000

1100

1200

1300

1400

1500

1600

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Figure 3.2 - Pressure history match for IFO test on Object 4 in well D

53

Since the coal seam is fractured through well bore stimulation, a negative skin

factor is expected. The skin factor can be calculated from the fractured zone

characteristics by using the following equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=

w

frac

farc

res

rr

kk

s ln1

(3 - 1)

where

s is well bore skin factor, resk is reservoir permeability, frack and fracr are the

fractured zone permeability and radius respectively and wr is the well bore

radius which is 0.328 feet in this case. The well bore skin factor is -2.9 which is

consistent with a stimulated well.

3.5.1.6 Comparison with characterization studies

The reservoir permeability value estimated by the simulation studies is 0.12 md.

This value is within the range of permeabilities determined by log interpretation.

The log interpretation method shows that the seam permeability value varies

between zero and 0.25 md (Wang June 2005).

Also, pre-fracturing well tests indicate an initial reservoir pressure of 1187 psia

for this seam. The initial reservoir pressure used in the test simulation, however,

was set to 1130 psia to obtain a good match.

54

3.5.2 IFO test in well D, object 3


This test was done in well D, seam number (IX), object 3. The coal seam is

located at the depth of 3218 feet and its net thickness is 11.5 feet. However, the

coal seam was perforated at the depth of 3321-3228 feet. Since no information

was available regarding the existence of any major heterogeneity in this seam,

the reservoir was considered to be homogeneous.


Water injection was carried out for 19:25 hours at the average rate of 140.4

lit/hr (21.2 bbl/day). The well afterward was shut for 32:55 hours. The bottom-

hole pressure was monitored and the reported pressures were corrected for

depth to mid-point of the perforations.

3.5.2.3 Simulation Model of the test





The porous medium was considered as a dual porosity medium and reservoir

permeability was defined as a function of reservoir pressure and formation

compressibility.

55


The tables 3.5 to 3.7 as well as Figure 3.3 represent the simulation input data for

this test.

56

Table 3.5 - Object 3 simulation input data








Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

57

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw


3.5.2.5 Test Interpretation Results

The best match between measured pressure data and simulation is obtained with

the following parameters:





Figure 3.4 shows that the match for the fall-off period is very good but that for

the injection period was not so well matched. It was not possible to

simultaneously match both the injection and fall-off periods.

58

According to provided operational details for this particular test (IFO test field

report for Well D – Object 3), the test was not conducted at a constant injection

rate. The simulation was carried out with a constant (average) injection rate.

The increasing actual rate is consistent with an overestimation of injection

pressures early in the flow period. However, simulation with a variable rate

failed to produce a significantly better match.







In the same way, well bore skin factor was calculated from Equation 3.1, the

well bore skin factor was -4.0.

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=

w

frac

farc

res

rr

kk

s ln1

(3 - 1)

where

s is well bore skin factor, resk is reservoir permeability, frack and fracr are the

fractured zone permeability and radius respectively and wr is the well bore

radius which is 0.328 feet in this case.

59

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Recorded Trace

Simulated Trace

Figure 3.4 - IFO test pressure history match for object 3, well D

0

1

2

3

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (day)

Injection Rate (lit/min)

Figure 3.5 - Reported changes in the injection rate of IFO test on well D, Object 3

60

3.5.2.6 Results Comparison with the Characterization Studies

No reservoir characterization study was conducted for this particular seam (seam

number IX). However, the seam permeability, 0.55 md, is of similar order to that

determined for the previous test (0.12 md for object 4 in well D).




3.5.3 IFO test well D, Object 8b


This IFO test was conducted on coal seam number XV. The object number is

called 8b in well D. The coal seam depth is 1973 feet and its thickness is 13 feet.

Reservoir characterization studies have identified a number of faults in this seam

(Tran 2005). They are shown in Figure 3.6. The nearest fault to well D is located

approximately 400 feet far from the well.

Since these faults are located sufficiently far from the well-bore (well D)

comparing to the test radius of investigation, the seam may also be considered to

be homogeneous for this test.

61

2620117

2620317

2620517

2620717

2620917

2621117

433221 433321 433421 433521 433621 433721 433821 433921 434021 434121

Well A

Well D

Well B

Well C

Figure 3. 6 – Faults map in coal seam number XV (Tran 2005)


The coal seam was subjected to water injection for 15:30 hours. The average

injection rate was 44.9 liter/hour (or 5.9 BBL/day), the well was then shut for

32:30 hours to let the pressure fall-off establish. The bottom-hole pressure was

monitored and the reported pressures were corrected for depth to mid-point of

the perforations.



system) by one block in z direction. The size of grid blocks was 8.0 feet for all

the blocks in the grid system. The well was placed in the center grid block.

62



compressibility due to the effect of compaction phenomena on reservoir

production.


The tables 3.8 to 3.10 as well as Figure 3.7 represent the simulation input data

for this test.

63

Table 3.8 - Object 8b rock/fluid properties



Compaction reversibility Reversible compaction Reservoir porosity 5.7% Reservoir initial pressure 824 psia


Table 3.9 - Adsorption Isotherm Data


Table 3.10 - Field relative permeability data

Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

64

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw

Figure 3.7 - Field relative permeability curves



single permeability of 0.285 md and a reservoir radius of 50 feet.





There is no record of any operational problem during the test or detailed

injection rate data and therefore it is not possible to be conclusive as to the

reason for the poor match during the injection period. However, it is considered

65

to be a consequence of possibly more tortuous (initially non radial) injection flow

paths in the near borehole region as a result of formation damage.

Since the test investigated a distance of only 50 feet from the well-bore, it is not

possible to conclude that the permeability of 0.285 md is indicative of the

formation or an altered zone about the well-bore. However, comparing with the

permeability values of the other test in this series, the value of the permeability

is consistent with the permeability for a fractured zone.

0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Recorded Trace

Simulated Trace

Figure 3.8 - Object 8b pressure profile match


The well testing interpretation results are independent to the characterization

studies in this case, because the injection/fall-off test results represent only a

66

single permeability value and it is not possible to be conclusive whether the

permeability is the formation permeability or any altered zone permeability.

Also, pre-fracturing well tests indicate an initial reservoir pressure of 845 psia for

this seam. The initial reservoir pressure used in the test simulation, however,


3.5.4 IFO test in well D, object 8a


The injection/fall-off test was conducted on coal seam number XV in well D. The

coal seam depth is 2011 feet and the net thickness measured 15 feet at the

well/seam intersection. According to characterization studies some major faults

were recognized in this seam as they were shown in Figure 3.6. The nearest fault

to well D is located approximately 400 feet far from the well.

Since these faults are located sufficiently far from the well (well D) comparing to

the test radius of investigation, the seam may also be considered to be

homogeneous.


Water was injected for 19:08 hours at the average rate of 45.7 litter/hour (6.9

bbl/day). The well bore was shut for 49:45 hours and bottom-hole pressure was

recorded and corrected for depth to mid-point of the perforations.

67



system) by one block in z direction. The size of grid blocks was 7.5 feet for all of

the blocks in the grid system. The well was placed in the center grid.




production.

3.5.4.4 Simulation Input Data


for this test.

68

Table 3.11 - Object 8a rock/fluid properties



Compaction reversibility Reversible compaction Reservoir porosity 5.7% Reservoir initial pressure 845 psia Formation compressibility

Fractured zone: 5.0e-5 Intact zone: 5.0e-5




Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

69

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw




single permeability of 0.65 md and reservoir radius of 75 feet.





There is no record of any operational problem during the test or detailed rate

data and it is not possible to be conclusive as to the reason for the poor match

during the injection period.

70

Since the test investigated a distance of only 75 feet from the well-bore, it is not

possible to conclude that the permeability of 0.65 md is indicative of the




400

500

600

700

800

900

1000

1100

1200

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Simulated Trace

Recorded Trace

Figure 3.10 - Object 8a pressure profile match






71


this seam. The initial reservoir pressure used in the test simulation, however,


3.5.5 IFO test in well D - object 7


This IFO test was conducted on coal seam number XIVa. The object number is 7

in well D. Coal seam corresponding depth and thickness is 2165 and 26.2 feet,

respectively. Since no information was available regarding the existence of any


homogeneous.



injection rate was 48.6 liter/hour (or 7.3 BBL/day), then well was shut-in for

`47:10 hours to let the pressure fall-off establish. The bottom-hole pressure was


the perforations.



system) by one block in z direction. The size of grid blocks was set to 16 feet

throughout the grid system. The well was placed in the center grid block.

72




production.



for this test.

73

Table 3.14 - Object 7 rock/fluid properties








Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

74

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw





Single permeability of 0.55 md and reservoir radius of 155 feet








75

Since the test investigated a distance of only 155 feet from the well-bore, it is

not possible to conclude that the permeability of 0.55 md is indicative of the




600

700

800

900

1000

1100

1200

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Recorded Trace

Simulated Trace

Figure 3.12 - Object 7 pressure profile match






76


this seam. The same value of initial reservoir pressure was used in the test

simulation.



The injection/fall-off test was conducted on coal seam number VIII in well D. The

coal seam depth is 3485 feet and the net thickness measured 34 feet at the

well/seam intersection. Since no information was available regarding the

existence of any major heterogeneity in this seam, therefore the reservoir was

considered to be homogeneous.

3.5.6.2 Test description











77


production.

3.5.6.4 Simulation Input Data


for this test.

78









Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

79

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw



A good match between measured pressure data and simulation is obtained with










80



Well bore skin factor was calculated -3.0 using Equation (3 – 1). The skin factor

has a negative value which is because of the existence of fractured zone around

the well-bore.

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Recorded Trace

Simulated Trace



The reservoir permeability value estimated by the simulation studies is 0.06 md.

This value is within the range of permeabilities determined by the log

interpretation. The log interpretation method shows that the seam permeability

value varies between zero and 0.2 md (Wang June 2005).

81






This IFO test was conducted on coal seam number (V+VI). The object number is 1

in well D. The coal seam corresponding depth and thickness are 3742 and 30.0

feet, respectively. Since no information was available regarding to the existence

of any major heterogeneity in this seam, the reservoir was considered to be

homogeneous.



injection rate was 148 liter/hour (or 22.3 BBL/day), then well was shut for 24:52

hours to let the pressure fall-off establish. The bottom-hole pressure was


the perforations.




area around the well bore to 8.0 feet for the furthest grid blocks from the well.


82




production.



for this test.

83








Table 3.22- Field relative permeability data

Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

84

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw












85










Well bore skin factor was calculated -3.4 in this case. The results were based on

history matching of fall-off pressure data. Figure 3.16 shows the simulated

pressure profile as well as the recorded one.

1200

1400

1600

1800

2000

2200

2400

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Simulated Trace

Recorded Trace


86


The reservoir permeability value estimated by simulation studies is 0.08 md. This

indicates to a greater reservoir permeability value comparing to the log

interpretation results. Log interpretation method shows that the seam

permeability value varies between zero and 0.022 md (Wang June 2005).




3.5.8 IFO test in well C, object 1:


The injection/fall-off test was conducted on coal seam number (V+VI) in well C.

The coal seam depth is 3343 feet and the net thickness measured 29.5 feet at

the well/seam intersection. Since no information was available regarding the

existence of any major heterogeneity in this seam, the reservoir was considered

to be homogeneous.





87




area around the well bore to 5.0 feet for the furthest grid blocks from the well

bore. The well was placed in the center grid.

The porous medium was considered as a dual porosity medium and the


compressibility.


The input data are also shown in tables 3.23 to 3.25 as well as Figure 3.17.

88

Table 3.23 - Object 1, well C simulation input data








Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

89

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw









The skin factor was calculated -3.5.




90










Figure 3.3 shows the recorded pressure as well as the simulated match.

600

800

1000

1200

1400

1600

1800

2000

2200

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Time (days)

Bot

tom

-hol

e pr

essu

re (p

sia)

Recorded Trace

Simulated Trace

Figure 3.18 - History match for fall-off pressure data of object 1, well C

91


The reservoir permeability value estimated by simulation studies is 0.045 md.

This indicates to a greater reservoir permeability value comparing to the log

interpretation results. Log interpretation method shows that the seam

permeability value varies between zero and 0.015 md (Wang June 2005).


for this seam. The initial reservoir pressure used in the test simulation was also

set to 1395 psia.

3.6 Production History Match for Object 1 in Well D

3.6.1 Coal Seam Geological Setting

Coal seam number (V+VI) refers to a single coal seam in well D. Coal seam

number V+VI was put on production individually while the other coal seams in the

well were presumably packed. The coal seam depth is 3742 feet and its thickness

is 79 feet. Since no information was available regarding the existence of any


homogeneous.

3.6.2 Simulation Model of Well D

Production history is available over nearly three months for this seam. Based on

the production history, a three dimensional simulation was performed to obtain a

match for the history and predict the gas production and recovery for the rest of

reservoir life.

92





Also, to obtain more realistic simulation response, a dynamic permeability model

was used for the reservoir. In this model, permeability changes were defined as a

function of reservoir pressure. Reservoir permeability was related to the

reservoir pressure by coal seam compressibility factor. This leads to take into

account the early time formation compaction which occurs due to pressure

depletion and reduces permeability. However, permeability may increase later

on because of coal shrinkage phenomena (reversible compaction).

3.6.3 Simulation Input Parameters

According to corresponding IFO test results the reservoir pressure was set at 1700

psia for this depth. The well was producing at bottom-hole pressure of 50.0 psia

throughout the history time and the same value was used for the well

performance in the rest of reservoir life.

Tables 3.26 to 3.28 as well as Figures 3.19 and 3.20 represent the reservoir

properties used in the simulation:

93

Table 3.26 - Object 1 (well D) simulation input data for production history matching



Compaction reversibility Reversible compaction Reservoir porosity 5.5% Reservoir initial pressure 1700.0 psia




94

0

100

200

300

400

500

600

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Pressure (psia)

Adsorbed Gas Volume (SCF/UST)

Reservoir gas content at in-situ conditions

Reservoir initial pressure

Figure 3.19 - Adsorption/desorption behavior of coal seam in different pressures


Sw krw krg pcgw 0.00 0.00 1.00 0.0 0.44 0.00 1.00 0.0 0.50 0.05 1.00 0.0 0.57 0.10 1.00 0.0 0.62 0.145 0.85 0.0 0.80 0.36 0.36 0.0 0.88 0.53 0.13 0.0 0.91 0.61 0.05 0.0 0.94 0.74 0.02 0.0 0.97 0.86 0.00 0.0 1.00 1.00 0.00 0.0

95

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw


3.6.4 Production History Matching Results

A good match between recorded production data and simulation is obtained with





A drainage area of 10 acre provided a good match for the production history

along with the above parameters.

The well bore skin factor was calculated -3.0 from Equation (3 - 1).

Figure 3.21 shows the actual production profile as well as simulated one.

96

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

23 33 43 53 63 73 83 93 103

Time (Days)

Gas

pro

duct

ion

(m3 /d

ay)

Recorded Production Rates

Simulated Production Rates

Figure 3.21 - Production history match for object 1, well D

3.6.5 Comparison with characterization studies

The reservoir permeability value estimated by production history matching is

0.14 md. This indicates to a greater reservoir permeability value comparing to

the injection/fall-off test and log interpretation results. The seam permeability

was obtained 0.08 md from injection/fall-off test simulation. Also, log

interpretation method shows that the seam permeability value varies between

zero and 0.022 md (Wang June 2005).

3.6.6 Production Prediction of the Well D

The production rates were predicted over next 25 years of reservoir life. This

prediction was based on the reservoir model obtained during the production

97

history matching. Because the model satisfied and fit the production history, it is

accepted as a reservoir model which can represent properly reservoir conditions

in future too. Figure 3.22 and 3.23 present production rate forecast and

cumulative production estimation in 25 years of reservoir life.

A peak was forecasted by simulation to occur at the end of year three and

continue during year four. The peak rate is nearly as high as 90 MSCF/D in year

four entirely.

The production declines rapidly after year 4 and decreases during the rest of

reservoir life. However, decline rate is more gradual in later years. The

predicted production rate in year 25 is 15 MSCF/D or 425 cubic meters per day.

Average yearly production data are provided in Table 3.29.

98

Table 3.29 - Object 1, well D, average yearly production data

Years Cumulative Production (MMSCF)

Yearly Production (MMSCF)

Average Production Rate

(MSCF/D) 1 12.5 12.5 34.3 2 27.8 15.3 41.9 3 54.6 26.8 73.4 4 87.4 32.8 89.8 5 118.0 30.6 84.0 6 145.1 27.1 74.2 7 168.6 23.5 64.5 8 189.2 20.5 56.3 9 207.6 18.4 50.5 10 223.9 16.3 44.6 11 239.1 15.2 41.8 12 252.5 13.4 36.6 13 264.6 12.1 33.1 14 276.2 11.6 31.9 15 286.7 10.5 28.8 16 295.9 9.2 25.2 17 304.9 8.9 24.5 18 313.5 8.6 23.7 19 321.7 8.2 22.5 20 329.0 7.3 19.9 21 335.9 6.8 18.8 22 342.3 6.5 17.7 23 348.5 6.1 16.8 24 354.3 5.8 15.9 25 359.8 5.5 15.1

99

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

Figure 3.22 - Object 1 predicted production profile over 25 years

1.00E+02

1.00E+03

1.00E+04

1.00E+05

1.00E+06

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas Cumulative Production (MSCF)

Figure 3.23 - Predicted cumulative production of object 1 in well D

100

The cumulative gas production at the end of the history was 3.8 MMSCF or 107287

cubic meters. This amount was about 360 MMSCF at the end of year 25.

The original gas in place was calculated by the simulator as 655 MMSCF with 10

acres reservoir limits. By the end of production history, just 0.58 percent of this

volume was produced, while the methane recovery was estimated to be nearly

55 percent of original gas in place after 25 years. Figure 3.24 shows predicted

methane recovery during 25 years.

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Years

Methane Recovery (%)

Figure 3.24 - Object 1 methane recovery after 25 years

101

3.7 Production History Match for Object 2 in Well A

3.7.1 Coal Seam Geological Setting

The coal seam number XV was put to production through the interval (object) 2

in well A. Presumably the other coal seams were packed during the production

from this seam. The interval (object) depth is 1610 feet and the seam thickness

is 56 feet. Since no information was available regarding the existence of any


homogeneous.

3.7.2 Simulation Model of Well A

Seam number (XV) was put to production in January 2001. The well initially

produced at the rate of 200-300 m3/Day. The production peak occurred in August

2001 and the peak rate was 4800 m3/day. The production thereafter declined

significantly to 1000 m3/day by January 2002 and continuously reduced to 500

m3/day in August 2003.

The historical data are available for two years of production upon which the

simulation studies were done. Production history match was obtained and based

on the obtained model, reservoir production was forecasted and gas recovery

was calculated over a 25 years time period.

Alike previous case, the simulation model consists of 39 by 39 blocks in x-y

directions and one block in z direction. The blocks size was chosen smaller for

the area around the well bore, 15 feet, and considered larger in corner areas, 41

feet. The grid system sizing gives a total area of 40 acres.

102

The porous medium was considered as a dual porosity medium. Also, similar to

previous cases reservoir permeability was defined as a function of reservoir

pressure and formation compressibility due to the effect of compaction/

shrinkage phenomena on reservoir production.

3.7.3 Simulation Input Parameters

Tables 3.30 and 3.31 and Figures 3.25 and 3.26 show all the simulation input data

as reservoir parameters:

Table 3.30 - Object 2, well A simulation input data



Compaction reversibility Reversible compaction Reservoir porosity 5.5% Reservoir initial pressure 1700.0 psia


Table 3.31 - Coal adsorption characteristics in object 2, well A


103

0

100

200

300

400

500

600

700

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Pressure (psia)

Adsorbed Gas Volume (SCF/UST)

Reservoir gas content at in-situ conditions

Reservoir initial pressure

Figure 3.25 - Coal adsorption behavior against pressure changes

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Rel

ativ

e Pe

rmea

bilit

y

krg

krw

Figure 3.26 - Modified field kr curves

104

To obtain a good match for the production history, the provided relative

permeability curves were modified to the one presented in Figure 3.26.

3.7.4 Production History Matching Results

A good match between recorded production data and simulation is obtained with





The calculated well skin factor was -5.5.

The Figure 3.27 represents the production history match for this well:

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

150 240 330 420 510 600 690 780 870 960 1050

Time (Days)

Gas production (m3/day)

Recorded Production Rates

Simulated Production Rates

Figure 3.27 - Object 2, well A, production history match

105

The well stimulation process has improved effectively the reservoir permeability

in the area around the well bore to 1 md which represents a great difference

comparing to the reservoir permeability in the intact areas.

3.7.5 Comparison with characterization studies

The reservoir permeability value estimated by production history matching

method is 0.008 md. The log interpretation results indicate to similar

permeability values for seams XV2 and XV3. The average permeability values of

these seams are 0.0059 and 0.0093 md respectively. However, the average

reservoir permeability was evaluated 0.19 md in seam XV1 (Wang June 2005).

3.7.6 Production Prediction of Well A

Because of reservoir tightness, the production rates declined rapidly after almost

one year of reservoir life from a high peak rate to low rates for the rest of

reservoir life. Figure 3.28 shows well production forecast for next 25 years.

106

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (years)

Gas Production Rates (MSCF/D)

Figure 3.28 - Object 2, well A, predicted production profile

Also, reservoir low permeability has strongly affected the reservoir methane

recovery from this well as methane recovery factor is less than 5 percent of

original gas-in-place after 25 years of production which is a very low percentage

for gas recovery even from a CBM reservoir.

These results show that how important is the reservoir permeability role in gas

production and recovery and also this fact that induced fractures can greatly

enhance gas production and therefore the final recovery.

Figure 3.29 and 3.30 represent the cumulative gas production and gas recovery

predicted by the simulation model over next 25 years in reservoir life.

107

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (years)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SCF)

Figure 3.29 - Object 2 cumulative production profile

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (years)

Gas Recovery (%)

Figure 3.30 - Methane recovery from object 2 in well A

108

According to simulation results by having 40 acres as reservoir drainage area, the

original gas in place is 1966 MMSCF (almost 2 BCF) from which only 97 MMSCF will

be produced over 25 years.

Predicted average yearly production rates are presented in Table 3.32.

Table 3.32 - Object 2 average yearly production data

Years Cumulative Production (MMSCF)

Yearly Production (MMSCF)

Average Production Rate

(MSCF/D) 1 14.6 14.6 40.0 2 25.0 10.4 28.5 3 31.2 6.2 17.1 4 36.1 4.9 13.3 5 40.1 4.1 11.1 6 43.8 3.6 9.9 7 47.1 3.3 9.1 8 50.2 3.1 8.5 9 53.1 2.9 8.1 10 55.9 2.7 7.5 11 58.5 2.6 7.1 12 61.0 2.5 6.8 13 63.5 2.5 6.8 14 65.9 2.4 6.7 15 68.2 2.3 6.2 16 70.4 2.2 6.0 17 72.5 2.2 5.9 18 74.7 2.1 5.9 19 76.8 2.1 5.8 20 78.9 2.1 5.7 21 80.9 2.0 5.4 22 82.8 1.9 5.3 23 84.7 1.9 5.2 24 86.6 1.9 5.2 25 88.5 1.9 5.2

109

3.8 Sensitivity Analysis

The sensitivity of production profile to variations in reservoir properties was

investigated for case study 1. These properties include reservoir and fractured

zone permeability, relative permeability, porosity, formation compressibility,

reservoir limit or drainage area, reservoir initial pressure and finally desorption

time constant.

The range of the reservoir parameters investigated is similar to the range

reported in previous studies (Roadifer, Farnan et al. 2003; Roadifer, Moore et al.

2003; Aminian, Ameri et al. 2004).

The obtained results in long term production profile from the single well

development are qualitatively similar to that reported in previous studies

concerned with pressure depletion (Remner, Ertekin et al. 1986; Stevenson 1997;

Derickson, Horne et al. 1998; Roadifer, Moore et al. 2003).

3.8.1 Effect of reservoir permeability

The effect of initial reservoir permeability on reservoir performance was

examined by performing simulations for three levels of permeability k1 = 0.07 md

(low permeability), k2 = 0.14 md (base case) and k3 = 0.28 md (high

permeability). The selected range of permeability represents the range of seam

permeability values obtained from injection/fall-off test results. The other

reservoir properties were held constant at the base case values.

110

Methane recoveries after 25 years are 64% (high permeability), 55% (base case

permeability), and 42% (low permeability). The higher recoveries are associated

with higher production rates of methane. For natural pressure depletion, the

reservoir production is primarily controlled by the total kh-product for the coal

bed.

The peak production rates are 150 MSCF/D, 91 MSCF/D and 82 MSCF/D for the k1

= 0.28 md, 0.14 md and 0.07 md cases, respectively (Figure 3.32).

For 0.28 md case, the production rate decreases rapidly after the peak is

reached. The decline in production rate is considerably slower for the 0.14 md

case. For the 0.07 md case, the peak in production is not reached until 6 years

after the start of production and the subsequent decline in production is gradual

(Figure 3.31).

After nearly 15 years of production, methane production rate for 0.07 md case is

predicted to be slightly greater than that for the higher permeability cases. This

is simply because the reservoir is depleted of methane at this time for the higher

permeability cases.

111

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

kres = 0.28 md

kres = 0.07 md

kres = 0.14 md

Figure 3.31 - The effect of kres changes on production rate

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Years

Met

hane

Rec

over

y (%

)

kres = 0.07 md

kres = 0.14 md

kres = 0.28 md

Figure 3.32 - The effect of kres on methane recovery

112

3.8.2 Effect of fractured zone permeability

The effect of fractured zone permeability on reservoir performance was

examined by selecting three levels of kfrac = 0.5 md (low permeability), kfrac = 1.5

md (base case) and kfrac = 3.0 md (high permeability). The selected range of

permeability represents the range of fractured (altered) zone permeability

values obtained from injection/fall-off test results.

Figure 3.33 shows the production profile after 25 years for these three cases.

Changes in kfrac have similar effect as that for reservoir permeability itself.

However, the difference in kfrac makes slight changes in the production rate.

Production peak was 110 MSCF/D for the case of kfrac = 3.0 md, 104 MSCF/D and

84 MSCF/D for kfrac = 1.5 md and 0.5 md, respectively.

The higher production rates for the case of greater kfrac is simply because the

more permeable fractured zone provides a better connectivity between the

producing well and the coal seam. Gas desorption occurs faster in a highly

fractured zone and desorbed gas flows more efficiently to the producing well

through such a zone.

In long term production the desorbed gas is provided from a much larger area

comparing to extend of a fractured zone. Therefore, long term production profile

is not very sensitive to changes in fractured zone permeability as it is nearly

identical after 8 years of production for all cases.

Methane recoveries were 60%, 58% and 53% where fractured zone permeability

was 3.0, 1.5 and 0.5 md, respectively. The difference only comes from the first

years greater production rates for the case of higher permeability (Figure 3.34).

113

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

kfrac = 1.5 md

kfrac = 3.0 md

kfrac = 0.5 md

Figure 3.33 - Reservoir sensitivity investigation to kfrac

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Years

Met

hane

Rec

over

y (%

) kfrac = 3.0 md

kfrac = 0.5 mdkfrac = 1.5 md

Figure 3.34 - Methane recoveries associated with different kfrac

114

3.8.3 Effect of relative permeability

Three sets of relative permeability curves were used in this study, which are

shown in figure 3.35.

The important differences between the data sets include the mobile water

saturation and the gas phase relative permeability levels. The mobile water

saturation for rock curves is 56% while for the pseudo-curves are 15% and 80%.

The first pseudo kr curves with 15% mobile water saturation represents highly

permeable to gas whereas the second pseudo-curves with 85% mobile water

saturation implies to a mainly water permeable reservoir which has lower gas

relative permeability level. In this way, the reservoir sensitivity to the coal seam

gas/water relative permeability behavior is investigated. This method was used

in the previous sensitivity studies (references).

Figure 3.36 shows simulated methane production rates for the single well

development with the base case data (rock curve) and pseudo-curves. There is a

considerable difference between the results. Use of water permeable curves

results in lower methane production rates comparing to the other case with less

mobile water saturations. By using pseudo-curve mainly permeable to gas (with

higher immobile water saturation), methane production rate significant

increased in first years to a peak rate of 134 MSCF/D in year 2. While using

pseudo relative permeability curves with lower immobile water saturation lead

to lower methane production rate during first years as the peak rate was 60

MSCF/D. These results are explained by the fact that the reservoir permeability

to gas increases much faster when the pseudo-curve with higher immobile water

115

saturation is used in the model. Therefore, the reservoir absolute permeability is

totally assigned to gas flow in a shorter time. This improves the gas flow

efficiency in the reservoir and causes higher gas production rate. However, the

gas production is predicted to be less for the cases with higher level of gas

relative permeability during the last years of reservoir life. It is because of

methane depletion during first years of production for the cases with improved

relative gas permeability curves.

Figure 3.37 shows that different kr curves also have significant effects on

methane recovery. Methane recoveries are 48%, 55% and 63% for water-

permeable, base case and gas-permeable cases. The difference between the

final gas recovery values comes from the higher production rate in first years of

reservoir life for gas-permeable cases.

116

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Rel

ativ

e Pe

rmea

bilit

y

krg

krw

Figure 3.35 - Three sets of kr curves (permeable to gas, base case and permeable to

water)

117

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

Permeable to water

Permeable to gas

Original curves

Figure 3.36 - The effect of different kr behavior on reservoir performance

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Years

Met

hane

Rec

over

y (%

)

Permeable to gas

Original curves

Permeable to water

Figure 3.37 - Methane recoveries obtained by using different kr curves

118

3.8.4 Effect of porosity

The effect of initial matrix porosity on reservoir performance was examined at

three levels of porosity: � = 0.025 (low porosity), � = 0.055 (base value) and � =

0.085 (high porosity). This range covers the range of porosity values presented in

field lab measurements (Field report, October 2003). Figure 3.38 shows

simulated gas production rates for the case of a single well on a 10 acre drainage

area.

It was observed that matrix porosity has some effect on reservoir performance.

The peak production rate is reduced from 148 MSCF/D to 66 MSCF/D and delayed

approximately 3.5 years when the porosity was increased from 2.5% to 8.5%.

Methane recovery after 25 years, in the other hand, was increased from 50% for

the case of 8.5% to 55% and 61% for the cases of 5.5% (base case) and 2.5%,

respectively (Figure 3.39).

Matrix porosity used in the simulator is the ratio of pore volume to the overall

bulk volume of the coal. Reduction in reservoir porosity, in fact, decreases the

pore volume in the coal seam and therefore the coal-in-place volume is

increased. This increases the coal matrix proportion to pore volume in the seam

and provides a larger adsorption site for methane.

The corresponding gas-in-place values for � = 2.5%, 5.5% and 8.5% are 676

MMSCF, 655 MMSCF and 634 MMSCF, respectively, which verify greater gas-in-

place for the cases of lower porosity.

119

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

Φ = 2.5 %

Φ = 8.5 %

Φ = 5.5 %

Figure 3.38 - The effect of matrix porosity changes on production rate

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Years

Met

hane

Rec

over

y(%

) Φ = 2.5 %Φ = 5.5 %

Φ = 8.5 %

Figure 3.39 - Methane recoveries sensitivity investigation to matrix porosity changes

120

3.8.5 Effect of formation compressibility (cf)

The effect of formation compressibility on reservoir performance was assessed

again at three levels of compressibility: cf = 2.0 × 10-5 psi-1 (less compressible), cf

= 3.5 × 10-5 psi-1 (medium compressibility) and cf = 5.0 × 10-5 psi-1 (more

compressible). The selected range of formation compressibility represents the

range of cf values obtained from injection/fall-off test results.

The porosity and permeability changes due to compaction are assumed to be

fully reversible for all simulation performances.

The greater values of cf lead to reduction in methane recovery, because as

formation compressibility increases, the reservoir effective permeability to gas

decreases. The reasons for effective gas permeability decrease are: first,

reduction in the reservoir absolute permeability value. The higher coal

compressibility, the greater permeability decrease is per unit of pressure

reduction. Second reason is when the compressibility is high, the reduction in

water saturation due to seam dewatering is compensated by pore volume

decrease. This reduces relative permeability to gas in the seam and prevents the

gas to flow effectively while water saturation remains high.

For example in this study, for the case of cf = 5.0 × 10-5 psi-1 (the highest

formation compressibility) minimum effective permeability to gas was calculated

0.1313 md while in the case of the lowest formation compressibility (2.0 × 10-5

psi-1) the value was calculated 0.1371 md. The absolute value of permeability

was initially 0.14 md.

121

Figure 3.41 shows the effect of compressibility on the performance of the single

well development. Increasing the value of cf from 2.0 × 10-5 psi-1 to 5.0 × 10-5 psi-

1 results in a decrease in methane recovery at 25 years from 55% to 53%. The long

term methane production does not appear to be sensitive to changes in cf with all

these simulations predicting similar production rate after year 8 for the rest of

reservoir life. The difference in the early time performance, however, results in

higher final recoveries at 25 years for the lower cf cases (Figure 3.40).

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

cf = 2.0e-5 psi-1

cf = 5.0e-5 psi-1

cf = 3.5e-5 psi-1

Figure 3.40 - Production profiles with different cf values

122

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Years

Met

hane

Rec

over

y (%

)

cf = 2.0e-6 psi-1

cf = 3.5e-5 psi-1

cf = 5.0e-5 psi-1

Figure 3.41 - The effect of cf changes on methane recovery

3.8.6 Effect of drainage area

The effect of variation in drainage area size on reservoir performance was

examined by performing simulations for 10, 20, 40 and 80 acre spacing in single

well development. Figure 3.42 shows production rates for 40 years of reservoir

life. Changes in drainage area have significant effects on reservoir performance

as by increasing the reservoir size, the peak production rate decreased from 91

MSCF/D for the case of 10 acre to 65 MSCD/D for the case of 80 acre. Also the

peak was considerably delayed over reservoir life, for instance, in the case of 40

acre spacing the peak was predicted to occur nearly in year 17 and for the case

of 20 acre spacing the peak is in year 8, while for the base case the peak rate is

expected in year 4. For the case of 80 acre spacing no strong peak was observed,

123

while production reaches to its highest level after year 35 and continue

constantly till year 40. This is related to the rate of gas desorption throughout

the seam. In reservoir pressure depletion mechanism, the reservoir fluids are

produced due to pressure gradient between the well-bore and the reservoir.

When reservoir size is larger, the pressure gradient is distributed to a larger

area. In this case, the pressure drawdown from the initial pressure occurs more

slowly and therefore time-to-peak is delayed.

Production decline rate reduces significantly as drainage area increases. It is

because the production decline due to gas depletion in the area near to the well-

bore is offset by desorbed gas coming from the further areas in the reservoir. As

a result, the general production decline rate is more gradual for larger drainage

areas so that no decline in production was observed for the case of 80 acre

during 40 years of production.

Methane recovery is very sensitive to the size of drainage area too. While

methane recovery at 40 years is 64% with 10 acre spacing, that is only 11% with

80 acre drainage area (Figure 3.43). This is mainly because the amount of

original gas-in-place increases with the same proportion of that reservoir size

does. Despite such an increase in OGIP, no change happens in reservoir

production mechanism and hence in the amount of methane production when

only the reservoir size is expanded. Therefore, methane production is smaller

fraction of the initial gas-in-place at any specific time for larger drainage areas.

The corresponding OGIP calculated for 10, 20, 40, 80 acre spacing are 655

MMSCF, 1250 MMSCF, 2500 MMSCF and 5000 MMSCF, respectively.

124

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

AD = 40 acres

AD = 10 acres

AD = 20 acres

AD = 80 acres

Figure 3.42 - The effect of drainage area size on reservoir performance

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40

Years

Met

hane

Rec

over

y (%

)

AD = 10 acres

AD = 20 acres

AD = 40 acres

AD = 80 acres

Figure 3.43 - Methane recovery sensitivity to variations in drainage area

125

3.8.7 Effect of reservoir initial pressure

The effect of reservoir initial pressure on reservoir performance was examined

by performing simulations using the base value Pi = 1700 psia, Pi = 1900 psia and

1500 psia. Production rates were predicted greater for the case of Pi = 1900 psia

with the peak rate of 100 MSCF/D. the peak rate were 90 MSCF/D and 80 MSCF/D

for cases of 1700 and 1500 psia, respectively. When all the other reservoir

parameters are kept constant, the higher initial reservoir pressure creates a

greater pressure gradient between the well-bore and the reservoir. This leads to

a greater desorption capacity. Since the well bottom-hole pressure is assumed

the same for all the case, the amount of gas desorbed is associated with a

greater pressure range on the coal desorption isotherm curves.

The long term production was observed not sensitive to changes in reservoir

initial pressure (Figure 3.44). During later years, since a main part of gas has

been desorbed from the coal and pressure has fallen down to lower values, the

effect of higher initial pressure fades out in the reservoir performance.

Methane recovery increased by increase of initial pressure. The difference

however in slight and caused by higher production rates during early years of

reservoir life (Figure 3.45).

126

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time (Years)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

Pi = 1500 psia

Pi = 1900 psia

Pi = 1700 psia

Figure 3.44 - Reservoir performance sensitivity to Pi

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Years

Met

hane

Rec

over

y (%

)

Pi = 1900 psia

Pi = 1700 psia

Pi = 1500 psia

Figure 3.45 - The effect of different Pi on methane recovery

127

3.8.8 Effect of desorption time constant

The effect of desorption time constant on reservoir performance was assessed at

three levels of 1 day (shorter time, faster desorption), 2 days (base case) and 3

(longer time, slower desorption). The selected range of desorption time

represents the minimum and maximum values of desorption time provided in

field reports as well as the modified value used in production history matching.

No significant changes were observed for reservoir performance as long term

production profile and methane recovery are identical where different

desorption time constant were used. However, there is a considerable change in

production rate during very first days of production. Figure 3.46 show greater

production rate during first 10 days of production when desorption time is

shorter. Although, the three production profiles come together almost after 10

days and the primary difference disappears for the rest of reservoir life.

When desorption time constant is smaller, the diffusion process occurs faster and

therefore the gas transport between coal matrix surfaces and cleats takes place

in a shorter time. This causes an earlier peak in production and a higher peak

rate. However, for the case of long term production, the reservoir performance

is mainly affected by Darcy flow regime (gas transportation in the cleat system)

and Darcy parameters, for example cleats permeability, control the reservoir

performance.

128

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Time (days)

Gas

Pro

duct

ion

Rat

e (M

SCF/

D)

Tdes = 3 days

Tdes = 1 day

Tdes = 2 days

Figure 3.46 - Early time production rates with different desorption time constant

129

3.9 Conclusions

1. The injection/fall-off tests conducted on well D and C were simulated to

obtain the permeability of coal seams in these wells. The following table

represents the summery of permeability values for different coal seams

tested in well D and C:

Table 3.33 - Summery of permeability values for coal seams in well D

Seam Number Object No. Seam Permeability (md) XV 8b 0.285 XV 8a 0.65 XIVa 7 0.55 X 4 0.12 IX 3 0.55 VIII 2 0.06 V+VI 1 0.08

2. The sensitivity of reservoir production to various reservoir parameters was

studied. The results are presented in following sections:

a. For natural pressure depletion, the reservoir production is primarily

controlled by the total kh-product for the coal bed. Methane

recovery was increased significantly as reservoir permeability was

increased.

b. Methane production rate increases during early time of production

when a fractured zone with higher permeability is created in the

reservoir. The fractured zone provides a more efficient connectivity

between the well bore and the reservoir. However, the reservoir

production is insensitive to fractured zone characteristics during

later years of production.

130

c. Reservoir gas production is increased when the coal seam relative

permeability curves present higher immobile water saturation

values. The reason is the reservoir absolute permeability is totally

assigned to gas flow for the water saturation values less than

immobile water saturation, therefore the reservoir gas relative

permeability increases faster and reaches to 100 percent in a

shorter time.

d. Reservoir matrix porosity has some effect on reservoir performance.

A higher production peak rate was obtained with lower porosity

values. The final methane recovery was also higher when the

reservoir porosity was lower.

e. Any increase in the reservoir compressibility causes greater

reduction in reservoir absolute permeability as well as relative

permeability to gas throughout the reservoir. Therefore, methane

recovery decreased as the reservoir compressibility increased.

f. The reservoir production behavior was strongly affected by changes

in reservoir size. The production peak rate was significantly

postponed and lowered as reservoir size was increased. Also the

final recovery predicted till year 40 was less for the case of larger

reservoir size.

g. The effect of reservoir initial pressure was investigated and the

results show that higher initial reservoir pressure leads to higher

rate during early years of production. However, for the later years

131

of reservoir life, the production profile is almost identical for

different initial pressures.

h. Coal desorption time constant affects the methane production in its

own scale. For instance, in this case the range of desorption time

did not exceed longer than 3 days and therefore the difference in

production rate was observed only in first days of production (first 5

days).

132

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