2012-simulating effects of adsorption, diffusion, and convection in tight formations

7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations

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UNIVERSITY OF OKLAHOMA

GRADUATE COLLEGE

SIMULATING EFFECTS OF ADSORPTION, DIFFUSION, AND CONVECTION IN TIGHT

FORMATIONS

A THESIS

SUBMITTED TO THE GRADUATE FACULTY

in partial fulfillment of the requirements for the

Degree of

MASTER OF SCIENCE IN NATURAL GAS ENGINEERING AND MANAGEMENT

By

JIAZUN LI

Norman, Oklahoma

2012


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SIMULATING EFFECTS OF ADSORPTION, DIFFUSION, AND CONVECTION IN TIGHT

FORMATIONS

A THESIS APPROVED FOR THE

MEWBOURNE SCHOOL OF PETROLEUM AND GEOLOGICAL ENGINEERING

BY

______________________________Dr. Maysam Pournik, Chair

______________________________

Dr. Ahmad Jamili

______________________________

Dr. Deepak Devegowda


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Copyright by JIAZUN LI 2012

All Rights Reserved.


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To Mom, Dad, Grandma, and Grandpa

I love you so much!


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iv

Acknowledgements

I wish to express my sincere appreciation and thanks to my advisors Dr. Pournik and

Dr. Jamili for their infinite support and guidance throughout my thesis studies. I will

always remember their help and encouragement in my most difficult time. I also want to

thank my committee member Dr. Devegowda for his interest in my work and attention

on my project. Their religious attitude to science will impact my whole life.

I would like to thank Dr. Sharma for offering me the opportunity to study in our

department. I can feel his warm care in all my study life in OU. I would like to thank

Dr. Vaughn and Lori Stevens for their help in my difficult time.

I would like to extend my thanks to all professors teach me courses: Dr. Callard, Dr.

Samuel, Dr. Civan, Dr. Akkutlu, and Dr. Ahmed. The knowledge I learned in their

classes are solid academic foundation for my future study and work. Special thanks to

Srinivasan for giving me advice when I started using ECLIPSE* to study my thesis

project.

Last but most importantly, I would like to thank my family and friends. The infinite

love, support, and trust my parents gave me are always the strongest encouragement for

me to study abroad. And my dear friends, Yue, C.Chen, Yuqi, Yuntao, Yijia, Xinya,

Ronald, Eric, Darren, Ali, Jide, Busayo, Mitchell, Kiersten, Hannah, Panyu, Z.Jian,

Wanwei, Shuoshi, Jiangang, Liqiang, Luding, thank you all for accompanying and

helping me since I came to OU. I will never forget the happy time we spent together.


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Table of Contents

Acknowledgements .......................................................................................................... iv

Table of Contents .............................................................................................................. v

List of Tables .................................................................................................................... vii

List of Figures .................................................................................................................... ix

Abstract .......................................................................................................................... xvi

Chapter 1: Introduction .................................................................................................... 1

1.1 Properties of shale formations ............................................................................. 2

1.2 Adsorption in shale formations ............................................................................ 5

1.3 Gas flow mechanisms in shale formations ........................................................... 7

1.3.1 Flow in micropores ...................................................................................... 7

1.3.2 Flow in nanopores ....................................................................................... 8

Chapter 2: Modeling of Gas Transport in Conventional Gas Reservoirs and Tight Gas

Reservoirs/Shales ............................................................................................... 16

2.1 Objective ............................................................................................................. 16

2.2 Model specification ............................................................................................ 17

Chapter 3: Results and Discussion .................................................................................. 24

3.1 Grid size .............................................................................................................. 24

3.2 Adsorption .......................................................................................................... 37

3.3 Molecular diffusion............................................................................................. 50

3.4 Adsorption and diffusion .................................................................................... 64

Chapter 4: Conclusions and Suggestions ........................................................................ 72


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4.1 Conclusions ......................................................................................................... 72

4.2 Suggestions for future work ............................................................................... 73

Nomenclature ................................................................................................................. 74

References ...................................................................................................................... 77

Appendix A: Estimation of Diffusion Coefficients .......................................................... 81

Appendix B: Relationship between Two Diffusion Coefficients ..................................... 85

B.1 Concentration gradient driving diffusion model ................................................ 85

B.2 Chemical potential gradient driving diffusion model......................................... 85

Appendix C: Estimation of Knudsen Number and Apparent Permeability .................... 87


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List of Tables

Table 1-1: The distribution of worldwide unconventional gas resources. (Holdith, 2006)

.......................................................................................................................................... 2

Table 2-1: Model parameters in this study. .................................................................... 22

Table 2-2: Critical properties of methane for running the one component compositional

model. ............................................................................................................................. 22

Table 2-3: Specifications of simulation cases in this study. ........................................... 23

Table 3-1: Grid size effects on conventional gas reservoirs and shale formations. ....... 27

Table 3-2: Langmuir isotherm data of methane in shale formations from literature

review. ............................................................................................................................ 40

Table 3-3: Adsorption/desorption effects on conventional gas reservoirs and shale

formations....................................................................................................................... 41

Table 3-4: Methane self-diffusion coefficients from literature review and empirical

model calculations. ......................................................................................................... 54

Table 3-5: Molecular diffusion driven by concentration gradient effects on conventional

gas reservoirs and shale formations................................................................................ 55

Table 3-6: Molecular diffusion driven by chemical potential gradient effects on

conventional gas reservoirs and shale formations. ......................................................... 56

Table 3-7: Effects of different mechanisms on conventional reservoirs and shale

formations....................................................................................................................... 66

Table A-1: Parameters for estimating binary gas diffusion coefficients by empirical

models..8 2


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Table A-2: Models of estimating self-diffusion coefficients..84

Table A-3: Diffusion coefficients of methane self-diffusion system estimated by

empirical models.........................84

Table C-1: Knudsen number estimation in this study. ...89

Table C-2: Apparent permeability estimation in this study. ...89


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List of Figures

Figure 1-1 Pore distribution in conventional gas reservoirs and shale formations.

(Javadpour et al., 2007) .................................................................................................... 3

Figure 1-2: Frequency versus permeability of 152 shale gas samples from nine

reservoirs. (a) permeability distribution, (b) cumulative frequency distribution.

(Javadpour et al., 2007) .................................................................................................... 4

Figure 1-3: A typical Langmuir isotherm curve. (Das et al., 2012) ................................. 6

Figure 1-4: Gas molecules movements in shale formations. (Javadpour, 2009).............. 8

Figure 2-1: Simulation and experimental results showing the impact of pore pressure on

the interactions between gas molecules and pore wall. (Fathi et al., 2012) ................... 20

Figure 2-2: Dimensions and grid blocks for reservoir models; using grid blocks of

(11x11x1) and (110x110x10); (X, Y, Z) orders. ............................................................ 20

Figure 2-3: The relative permeability curve (top) and capillary pressure curve (bottom)

used in this study. ........................................................................................................... 21

Figure 3-1: gas production rate in different models ....................................................... 28

Figure 3-2: Pressure gradient in different grid size models. .......................................... 28

Figure 3-3: Impact of grid size on gas production rate with time (100 days) for

conventional gas reservoirs. ........................................................................................... 29

Figure 3-4: Semi-log plot shows the impact of grid size on cumulative gas production

with time (1000 days) for conventional gas reservoirs. ................................................. 29

Figure 3-5: Impact of grid size on reservoir pressure with time (100 days) for

conventional gas reservoirs. ........................................................................................... 30


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Figure 3-6: Impact of grid size on gas-in-place with time (100 days) for conventional

gas reservoirs. ................................................................................................................. 30

Figure 3-7: Impact of grid size on gas production rate with time (50 years) for shale

formations....................................................................................................................... 31


with time (50 years) for shale formations....................................................................... 31

Figure 3-9: Impact of grid size on reservoir pressure with time (50 years) for shale

formations....................................................................................................................... 32

Figure 3-10: Impact of grid size on gas-in-place with time (50 years) for shale

formations....................................................................................................................... 32

Figure 3-11: Impact of grid size on gas production rate in the first year for shale

formations with fractures................................................................................................ 33

Figure 3-12: Impact of grid size on gas production rate with time (50 years) for shale



with time (50 years) for shale formations....................................................................... 34



Figure 3-15: Impact of grid size on gas in place with time (50 years) for shale


Figure 3-16: Pressure drop in conventional reservoirs for 100 days.............................. 35

Figure 3-17: Pressure drop in shale formations for 50 years.......................................... 36

Figure 3-18: Pressure drop in shale formations with fractures for 50 years................... 36


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Figure 3-19: Langmuir isotherm curve used for this study. ........................................... 42

Figure 3-20: Impact of adsorption on gas production rate with time (100 days) for

conventional gas reservoirs; using grid blocks of (11x11x1) and (110x110x10). ......... 42

Figure 3-21: Semi-log plot showing the impact of adsorption on cumulative gas

production with time (1000 days) for conventional gas reservoirs; using grid blocks of

(11x11x1) and (110x110x10). ........................................................................................ 43

Figure 3-22: Impact of adsorption on gas-in-place with time (100 days) for conventional

gas reservoirs; using grid blocks of (11x11x1) and (110x110x10). ............................... 43

Figure 3-23: Gas-in-place of two states of gas with time (100 days) for conventional gas

reservoirs; using grid blocks of (11x11x1) and (110x110x10). ..................................... 44

Figure 3-24: Impact of adsorption on gas production rate with time (50 years) for shale

formations; using grid blocks of (11x11x1) and (110x110x10)..................................... 44


production with time (50 years) for shale formations; using grid blocks of (11x11x1)

and (110x110x10)........................................................................................................... 45

Figure 3-26 : Impact of adsorption on gas-in-place with time (50 years) for shale

formations; using grid blocks of (11x11x1) and (110x110x10)..................................... 45

Figure 3-27: Gas-in-place of two states of gas with time (50 years) for shale formations;

using grid blocks of (11x11x1) and (110x110x10). ....................................................... 46

Figure 3-28: Impact of adsorption on gas production rate in the first year for shale

formations with fractures; using grid blocks of (11x11x1) and (110x110x10).............. 46

Figure 3-29: Impact of adsorption on gas production rate with time (50 years) for shale



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production with time (50 years) for shale formations with fractures; using grid blocks of

(11x11x1) and (110x110x10). ........................................................................................ 47

Figure 3-31: Impact of adsorption on gas-in-place with time (50 years) for shale


Figure 3-32: Gas-in-place of two states of gas with time (50 years) for shale formations

with fractures; using grid blocks of (11x11x1) and (110x110x10). ............................... 48

Figure 3-33: Comparison of adsorption effects on gas production rate with time (100

days) for conventional gas reservoirs and shale formations; using grid size of (11x11x1)

and (110x110x10)........................................................................................................... 49

Figure 3-34: Impact of molecular diffusion by concentration gradient on gas-in-place

with time (100 days) for conventional gas reservoirs; using grid blocks of (11x11x1)

and (110x110x10)........................................................................................................... 57


with time (50 years) for shale formations; using grid blocks of (11x11x1) and

(110x110x10). ................................................................................................................ 57


with time (50 years) for shale formations with fractures; using grid blocks of (11x11x1)

and (110x110x10)........................................................................................................... 58

Figure 3-37: Impact of molecular diffusion on gas production rate with time (100 days)

for conventional gas reservoirs; using grid blocks of (11x11x1) and (110x110x10)..... 58

Figure 3-38: Impact of molecular diffusion on gas in place with time (100 days) for

conventional gas reservoirs; using grid blocks of (11x11x1) and (110x110x10). ......... 59


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Figure 3-39: Impact of molecular diffusion on cumulative gas production with time

(1000 days) for conventional gas reservoirs; using grid blocks of (11x11x1) and

(110x110x10). ................................................................................................................ 59

Figure 3-40: Impact of molecular diffusion on gas production rate with time (50 years)

for shale formations; using grid blocks of (11x11x1) and (110x110x10). ..................... 60

Figure 3-41: Impact of molecular diffusion on gas in place with time (50 years) for

shale formations; using grid blocks of (11x11x1) and (110x110x10). .......................... 60

Figure 3-42: Semi-log plot showing the impact of molecular on cumulative gas

production with time (50 years) for shale formations; using grid size of (11x11x1) and

(110x110x10). ................................................................................................................ 61

Figure 3-43: Impact of molecular diffusion on gas production rate in the first year for

shale formations with fractures; using grid blocks of (11x11x1) and (110x110x10). ... 61

Figure 3-44: Impact of molecular diffusion on gas production rate with time (50 years)

for shale formations with fractures; using grid blocks of (11x11x1) and (110x110x10).

........................................................................................................................................ 62

Figure 3-45: Impact of molecular diffusion on gas in place with time (50 years) for

shale formations with fractures; using grid blocks of (11x11x1) and (110x110x10). ... 62

Figure 3-46: Impact of molecular diffusion on cumulative gas production with time (50

years) for shale formations with fractures; using grid blocks of (11x11x1) and

(110x110x10). ................................................................................................................ 63

Figure 3-47: Comparison of molecular diffusion effects on gas production rate with

time (100 days) for conventional gas reservoirs and shale formations; using grid size of

(11x11x1) and (110x110x10). ........................................................................................ 63


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Figure 3-48: Impacts of different transport mechanisms on gas production rate with time

(100 days) for conventional gas reservoirs; using grid blocks of (110x110x10). .......... 67

Figure 3-49: Impact of different transport mechanisms on gas in place with time (100

days) for conventional gas reservoirs; using grid blocks of (110x110x10). .................. 67

Figure 3-50: Semi-log plot showing the impact of different transport mechanisms on

cumulative gas production with time (1000 days) for conventional gas reservoirs; using

grid blocks of (110x110x10). ......................................................................................... 68


(50 years) for shale formations; using grid size of (110x110x10). ................................ 68

Figure 3-52: Impact of different transport mechanisms on gas-in-place with time (50

years) for shale formations; using grid size of (110x110x10). ....................................... 69

Figure 3-53: Semi-log plot showing the impact of different transport mechanism on

cumulative gas production with time (50 years) for shale formations; using grid size of

(110x110x10). ................................................................................................................ 69

Figure 3-54: Impacts of different transport mechanisms on gas production rate in the

first year for shale formations with fractures; using grid size of (110x110x10). ........... 70


(50 years) for shale formations with fractures; using grid size of (110x110x10). ......... 70

Figure 3-56: Impacts of different transport mechanisms on gas in place with time (50

years) for shale formations with fractures; using grid size of (110x110x10). ................ 71

Figure 3-57: Impacts of different transport mechanisms on cumulative gas production

with time (50 years) for shale formations with fractures; using grid size of

(110x110x10). ................................................................................................................. 71


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Figure C-1: gas production rate for different permeability cases.90

Figure C-2: reservoir pressure for different permeability cases.90


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Abstract

Production from tight formations introduces different flow mechanisms, which

makes the prediction of production more complex than conventional reservoirs. Themuch smaller pore diameters in the range of mostly nanometers rather than micrometers

results in an extremely low formation permeability in range of nanodarcy. As a result

of such small pore diameter, large surface area is exposed in the porous media with

larger volume of gas adsorbing on the pore surface, which in turn allows more gas

production from desorption mechanism if the pressure change is favorable.

Furthermore, due to the tight nature of permeability, flow from pressure gradient due to

convection is limited. As a result, flow contribution from diffusion becomes more

significant. Some new flow mechanisms like Knudsen diffusion and surface diffusion

also come into play in these smaller pore size reservoirs.

While it is clearly understood that flow mechanisms in tight formations differs

significantly from conventional reservoirs, most studies on tight formations have not

accurately incorporated these new flow mechanisms. Furthermore, there has been no or

very limited study on the impact of each of these flow mechanisms on the total

production in order to determine the relative importance of each mechanism.

In this study, we focus on determining the relative importance of convection,

desorption and molecular diffusion on the production from tight formations and

compare these contributions to those in conventional reservoirs. In order to focus on the

impact of flow mechanisms, we use single gas component (methane) system with a

single porosity model to simulate flow. Convection is defined by Darcys Law, as is

defined in conventional reservoirs. For adsorption/desorption mechanism, Langmuir


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isotherm model is applied to describe the process. Two models for describing molecular

diffusion are used, one based on concentration drive and another based on chemical

potential drive. In addition, we also study the effect of grid size on the flow simulations

as numerical dispersion becomes more significant as the pore size becomes smaller.

The results indicate that adsorption/desorption mechanism plays an important role in

shale formations only when the reservoir pressure drops to a low values. Secondly, the

contribution of molecular diffusion in shale formations is significant because the low

permeability and pressure drop cause a small amount of convection and desorption.

Thirdly, the grid size effects are very important in this simulation work, especially besignificant for shale formation model because of numerical dispersion. Finally,

molecular diffusion driven by concentration gradient model is not applicable to this

single gas component system study.


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Chapter 1: IntroductionAs a result of the high development of modern society, more fossil energy resources are

required to meet the basic demand of human beings. In most of the world, the petroleum

industry produces oil and gas from conventional reservoirs. However, unconventional

resources, including tight-sand, coalbed methane, and shale formations, have drawn

considerable attention in recent years due to the vast reserve and long-term production

potential (Kawata et al., 2001; Holditch, 2006). Table 1-1 shows the World distribution

of unconventional gas resources (Holdith, 2006). It shows that there is extensive amount

of gas in unconventional reservoirs with more emphasis in shale formations, especially

in the United States. While there are considerable challenges in producing from these

resources, recent technological development in geological evaluation, drilling,

stimulation, and production operations are enabling engineers to overcome many of

these challenges to allow economical production from these resources. These resources

have boosted natural gas production by 30% in the United States. In 2009, gas

production, in the United States, from unconventional resources exceeded the gas

production from conventional reservoirs.

After investigating a large sample of shale rocks over 10 years, Bustin et al. (2008) gave

the definition of shale as: shale has come to refer to any very fine-grained rocks

capable of storing significant amount of gas and as such strata referred to as gas shales

range from rocks that are true shales sensu stricto to rocks that grade into tight sands.

Rock property, pore structure, and flow characteristics vary significantly between

different shale formations due to the wide definition of shale. To date, there are no

standard experimental methods and simulation models specific to shale. Some recent


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researches have estimated the shale gas-in-place (Ambrose et al., 2012; Hartman, et al.,

2011; Das et al., 2012), the gas flow in shale (Javadpour et al., 2007; Javadpour, 2009;

Freeman et al., 2010; Blasingame, 2008), and shale gas production (Biswas, 2011;

Wattenbarger et al., 1998). However, these methods all have their assumptions which

present limitations to their application.

RegionCoalbedMethane

(Tcf)Shale Gas

(Tcf)

Tight-sand Gas

(Tcf)Total(Tcf)

North America 3,017 3,840 1,371 8,228

Latin America 39 2,116 1,293 3,448

Western Europe 157 509 353 1,019

Central and Eastern Europe 118 39 78 235

Former Soviet Union 3,957 627 901 5,485

Middle East and North Africa 0 2,547 823 3,370

Sub-Saharan Africa 39 274 784 1,097

Centrally planned 1,215 3,526 353 5,094

Asia and China Pacific(Organization for EconomicCooperation and Development)

470 2,312 705 3,487

Other Asia Pacific 0 313 549 862

South Asia 39 0 196 235

World 9,051 16,103 7,406 32,560

Table 1-1: The distribution of worldwide unconventional gas resources. (Holdith,

2006)

1.1 Properties of shale formations

Unlike conventional gas reservoirs, the pore size in shale formations range from a few

nanometers to a few micrometers, and the number of nanopores (diameter smaller than

1 m) is much higher than micropores (diameter is larger than 1 m). The combination

of nano-scale pore network with micro-scale pore network dominates the gas flow in


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shale. Figure 1-1 shows the comparison of pore distribution between conventional gas

reservoirs and shale formations, which indicates shale is composed mainly of nanopores

with small distribution of micropores, while conventional reservoirs show an opposite

trend with majority of micropores and small amount of nanopores.

Figure 1-1 Pore distribution in conventional gas reservoirs and shale formations.

(Javadpour et al., 2007)

This pore distribution gives rise to three different features of shale formations:

1. These nanopores cause very low permeabilities. Bustin et al. (2008) measured

a large sample of shale permeabilities which fell within the range of 1 to 103

nd. Their samples were from a large range of formations, including soft clay-

rich Colorado Group shales from the Western Canadian Sedimentary Basin

and brittle, silica-rich shale from Muskwa Formation in Northeastern British

Columbia and Woodford. Javadpour et al. (2007) measured permeability of

152 shale samples from nine reservoirs by pulse decay technique (Figure 1-2)

showing that 90% of measured permeabilities are less than 150 nd and the

mode of the permeability is 54 nd.

2. Nano-scale pores have a larger-exposed area compared to micropores, and will

allow more gas adsorption on pore surfaces. Beliveau (1993) indicates that the

ratio of free gas to adsorbed gas storage capacity decreases as pore size


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decreasing. When the diameter of pore goes down to 0.01 m, the adsorbed

gas will exceed free gas storage.

3. The flow transport mechanisms deviate far from the conventional gas

reservoirs. Convection will not be the only dominant mechanism in gas flow,

and some other transport mechanisms should be considered as well, like gas

adsorption/desorption (desorbing as pressure depletion), molecular diffusion

(significant contribution when convection flow is low), surface diffusion

(happens in adsorption layers of small pores), and Knudsen diffusion (happens

in small pores at low pressures).

Figure 1-2: Frequency versus permeability of 152 shale gas samples from nine

reservoirs. (a) permeability distribution, (b) cumulative frequency distribution.

(Javadpour et al., 2007)


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1.2 Adsorption in shale formations

Large surface areas of nanopores in shale cause a large fraction of gas to be adsorbed on

the surface. Many recent researches about shale gas-in-place estimation indicate that

there is a large amount of gas in shale existing in the adsorbed state (Das et al., 2012;

Leahy-Dios et al., 2011; Mengal et al., 2011; Hartman et al., 2011). On the other hand,

the desorption process also contributes a large amount of gas to the total gas flow in the

production process (Mengal et al., 2011). Desorption from the surface of shale

formations happens when there is considerable depletion of free gas and pressure drop.

From past study on coalbed methane adsorption mechanism, the Langmuirs isotherm

model is typically applied to calculate the amount of gas adsorption/desorption at

different pressures:

(Equation1-1)where is the adsorbed gas volume per rock weight (in e.g., scf / ton) at any pressureP (psi), is maximum Langmuir volume, and is Langmuir pressure, defined as thepressure value at which the adsorbed gas content is equal to , (psi). These twoparameters ( ) relate the gas storage capacity of a reservoir rock to pressure anddepend on the temperature, rank, and the moisture content. They can be measured in

experiments using core samples. Figure 1-3 shows a typical Langmuir isotherm curve.

As it shows, the amount of adsorbed gas per unit rock weight increases as pressure

increases until it plateaus at a maximum value (VL). Nowadays, researchers apply

Langmuir isotherm model to simulate adsorption in both shale formations and coalbed

methane (CBM) because of their similarity in gas storage mechanism (free gas in pore


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space and adsorbed gas on pore surface). (Economides et al., 2010; Leahy-Dios et al.,

2011)

For the multi-component gas system, it is necessary to consider the effect of the gas

phase composition. The extended Langmuir model is commonly used for the prediction

of mixed gas adsorption behavior in shale:

(Equation 1-2)where is the adsorbed volume of component i at partial pressure . and isthe Langmuir volume constant and Langmuir pressure constant of component i. which

can be determined by pure gas experiments in the laboratory.

Figure 1-3: A typical Langmuir isotherm curve. (Das et al., 2012)

In summary, adsorption exists mostly in the very small pores (nanopores), because the

larger exposed areas allow more gas adsorbing on the surface. In addition, the adsorbed

gas storage capacity of reservoir rocks depends on reservoir pressure and the type of

reservoir rocks (rank, temperature of reservoir, moisture content). The gas desorption is

determined by the extent of change in pressure, actual pressures, and Langmuir


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isotherm pressure-volume relationship. Hence, there is very limited amount of adsorbed

gas in conventional reservoirs. While unconventional reservoirs have large amount of

adsorbed gas due to existence of nanopores, due to their low permeability, there might

not be sufficient change in pressure to allow the large amount of adsorbed gas to be

produced.

1.3 Gas flow mechanisms in shale formations

1.3.1 Flow in micropores

In micropores of shale, gas flow is dominated by convective pressure-driven flow which

can be treated as in conventional gas reservoirs. The flow flux is caused by a pressure

gradient, and dominates all other forms of transport in magnitude. Darcys equation can

describe the gas flow in the large pore system.

(Equation 1-3)where Q is the gas flow rate (m3/s), k is Darcys permeability (m2), A is the cross-

sectional area to flow (m2), is flow viscosity (Pas), and is the pressure gradient(Pa/m).

From equation 1-3, one can see that convection flow is determined by pressure gradient,

permeability, and viscosity. Viscosity of gas only is related to the temperature, so there

are only two factors determine the convection flow in isothermal gas systempressure

gradient and permeability. Because the permeability of shale formations is much less

than conventional gas reservoirs, the magnitude of convection flow in shale formations

will be much smaller at the same pressures.


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1.3.2 Flow in nanopores

Javadpour (2009) described the gas molecules transportation in tight gas formations.

There are three forms of gas existing in the shale pore system: freely compressed gas in

pore space, adsorbed gas on the pore surface, and dissolved gas in the kerogen

materials. These three types of gas are in an equilibrium state in the pore system. Figure

1-4 shows the three types of gas and how they are transported in the production process.

When production starts, the equilibrium will be disturbed and gas molecules start

flowing toward the low pressure zone. Free gas is firstly produced and the pressure

draws down (process 1 in Figure 1-4). Then the adsorbed gas desorbs from the surface

to the pore space which cause the pressure to increase (process 2 in Figure 1-4). At last,

concentration equilibrium changes between the kerogen bulk and surface, and gas

molecules will move from kerogen bulk to its surface (process 3 in Figure 1-4).

Potential gas transportation mechanisms in this process involve convective flow,

molecular diffusion in pore space, Knudsen diffusion, and surface diffusion.

Figure 1-4: Gas molecules movements in shale formations. (Javadpour, 2009)


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1.3.2.1 Knudsen numberBefore discussing these distinctive mechanisms in detail, it is necessary to introduce the

concept of Knudsen number. Due to the extremely small pore volume in shale

formations, conventional Darcys law cannot describe gas flow transport in shale

formations. The Knudsen number can be used for measuring the degree ofrarefaction of gases in porous media. It is defined by the ratio of the gas molecular

mean-free-path and the pore diameter dpore.

(Equation 1-4)The mean-free-path is given by Cunnigham and Williams (1980):

(Equation 1-5)where is the Boltzmann constant, and is the collision diameter.

(Equation 1-6)where Vc is the critical volume of gas components in cm

3/mol.

For Knudsen number:

less than 0.001: viscous flow, which can be described by the conventional

Darcys law;

from 0.001 to 0.1: slip flow. The flow velocity near the pore walls is not zero

and the viscous flow model needs to incorporate Klinkenberg slippage factor to

account for this phenomena;

from of 0.1 to 10: transition flow where the molecular-wall collision becomes

significant;


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larger than 10, the gas flow should be recognized as a swarm of discrete

particles which is called free-molecular flow.

When Knudsen number is larger than 0.001 (not viscous flow), the Darcy-permeability

should be corrected into apparent permeability to estimate gas flow in reservoirs.

Florence et al. (2007) studied the apparent permeability prediction for low-permeability

sands. The methods are shown in appendix C.

1.3.2.2 Molecular diffusionMolecular diffusion is the most well-understood diffusion type for gas transportation in

porous media. Dutta et al. (2009) and Poling et al. (2000) summarize that molecular

diffusion can be caused by different types of driving forces, including pressure

gradients (pressure diffusion), temperature gradients (thermal diffusion), external force

fields (forced diffusion), and concentration gradients.

In general, concentration gradient is considered in gas transportation in porous media

and Ficks Law is applied to model this process:

(Equation 1-7) is the molar flux of component i per unit area; c is the total molar concentration givenby ; is the molar volume of the mixture; is the mole fraction ofcomponent i;

is the gradient in the direction of flow; is the diffusion coefficient of

component i in mixtures. The diffusion coefficient presents the proportional relationship

between the flux J i relative to a plane of no net molar flow and the gradient . Forthe mixtures system with n components, the independent diffusion fluxes are and diffusion coefficients are (Cussler, 1984; Taylor and Krishna, 1993).


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When , , where is the self-diffusion coefficient of component i inpure i. Self-diffusion can model the one component gas transportation process.

Gas diffusion coefficients used in diffusion calculations can be determined from

experimental studies where possible. Dawson et al. (1970) and Helbaek et al. (1996)

measured the self-diffusion coefficient of methane at different pressures and

temperatures using Nuclear Magnetic Resonance technique. Several investigations of

diffusion coefficients of the multi-component gas system in porous media condition

were conducted in laboratory (Sigmund, 1976; Sigmund, 1976; Grogan et al., 1988;

Islas-Juarez et al., 2004).

On the other hand, it is possible to use kinetic theory to describe molecular diffusion in

binary gas. The Chapman-Enskog model (Chapman and Cowling, 1970), resulting from

solving the Boltzmann equation, is usually used for the theoretical estimation of

gaseous diffusion coefficients as:

(Equation 1-8)

where is the binary diffusion coefficient in cm2/s, T is temperature in K, P ispressure in atm, is the collision diameter in and is the diffusion collisionintegral, and

* ( ) ( )+

(Equation 1-9)

where

and

are the molecular weights of A and B in gm/mol. The above model is

only accurate at low to moderate pressure range usually below 1 MPa (Wesselingh

and Krishna, 2000). The key to applying Equation 1-7 is to estimate the value ofand which usually causes the complexity of Chapman-Enskog model.


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Several proposed methods for coping with the complexity were developed with

empirical constants based on experimental data. One method is developed by Wilke and

Lee (1955):

*( )+ (Equation 1-10)where is the binary diffusion coefficient in cm2/s, T is temperature in K, P ispressure in bar, is the collision diameter in and is the diffusion collisionintegral, and are the molecular weights of A and B in gm/mol. M AB =2[(1/MA)+(1/MB)]

-1.

Fuller, et al. (1965, 1966, 1969) modified Equation 1-8 to

(Equation 1-11)where is the binary diffusion coefficient in cm2/s, T is temperature in K, P ispressure in bar, is the sum of atomic diffusion volumes for each component (Fulleret al., 1969),

and

are the molecular weights of A and B in gm/mol. MAB =

2[(1/MA)+(1/MB)]-1.

Pollin et al. (2001) shows the comparison of diffusion coefficients between

experimental results and these theoretical methods. Values of the diffusion coefficient

determined by the theoretical methods generally have an average absolute error within 4

to 10%. Other evaluations by Elliott and Watts (1972), Gotoh et al., (1973), (1974), and

Lugg (1968) have demonstrated that both Fuller and Wilke-Lee method yields the

smallest average error.

Ficks law is widely used to model tight gas/shale gas diffusion due to its simplicity.

For the single component gas system, the concentration gradient is very small at high


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pressure condition. So Ficks law fails to describe the gas molecular diffusion in these

situations. A more accurate model is used to describe the molecular diffusion in some

commercial software (ECLIPSE* technical description, 2011).

[ ] (Equation 1-12) is the activity-corrected diffusion coefficient of component i, is the thermaldiffusion coefficient of component i, is the molecular weight of component i, isthe gravitational acceleration, is the mole fraction of component i, is the height, is the reference height, is the gas constant, is the temperature, and is the chemicalpotential of component i, given by

(Equation 1-13)where is the reference chemical potential, and is the component fugacity.At high pressure conditions, it is necessary to consider the component chemical

potential (the first term in Equation 1-12), gravity potential which drives the heavy

species to the bottom of the reservoir (the second term in Equation 1-12), and the

temperature gradient which drive those species with a low enthalpy / high entropy to the

hottest parts of the reservoir (the last term in Equation 1-12). When the first two terms

are equal, equilibrium will reach. The last term accounts for the diffusion caused by a

temperature gradient in reservoirs. The activity-corrected diffusion coefficient can be

expressed as:

(Equation 1-14) is the activity-corrected diffusion coefficient of component i, is the concentrationgradient driving diffusion coefficient for component i, is the mole fraction of


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component i, and is the component fugacity. The detail of the relationship betweenthe two diffusion coefficients is presented in appendix B.

In summary, molecular diffusion happens in both conventional gas reservoir and shale

formations. For the single gas component and isothermal system, pressure and diffusion

coefficients are factors to determine gas diffusion. However, as the experimental

measurements of diffusion coefficients indicate, the molecular diffusion is small and its

contribution mainly depends on the magnitude of other mechanisms.

1.3.2.3 Knudsen diffusionKnudsen diffusion occurs in very small pores, usually in order of 10nm to 100nm and at

very low pressures. Under this condition, the mean free path (the distance between

molecular collisions) is greater than the nanopore diameter, which will cause gas

molecules to collide with the pore wall and not frequently collide with other molecules.

In shale formations, Knudsen diffusion is significant at the low pressures because the

pore diameter is very small which falls into the level of nanometers. But it can hardly

happen in conventional gas reservoirs due to the micropore system.

The Knudsen diffusion coefficient can be expressed as (Javadpour, 2007): (Equation 1-15)

where dpore is the diameter of the nanopore, is the gas constant, is the temperature,

is the gas molecular weight.1.3.2.4 Surface diffusionIf there are gas layers adsorbing on the surface of small pore walls, the gas molecules

will transport primarily through the physically adsorbed layer other than the pore space.


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This is because gas molecules, in small pores, can barely escape the adsorption layer

and the diffusion process is relatively fast. This type of transport is called surface

diffusion (Cussler, 1984). Shale formations are known for adsorbed gas on the kerogen

surface and the nanopore system. In shale gas production process, the surface diffusion

includes rapid gas desorption, rapid transport along the surface layer, and rapid gas

adsorption. Some research work showed that surface diffusion may be an important

contribution to the total gas flow (Fathi and Akkutlu, 2009). However, due to the

complexity of surface diffusion, no proper model is available to describe this

phenomenon.


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Chapter 2:Modeling of Gas Transport in Conventional GasReservoirs and Tight Gas Reservoirs/Shales

2.1 Objective

The basic principle of gas flow in conventional gas reservoirs and shale formations was

introduced in chapter 1. In the large pore space of conventional gas reservoir, the gas

flow is dominated by convective flow which can be described by Darcys equation.

When it comes to shale formations, the nanopore system introduces other transport

mechanisms, including gas adsorption/desorption, and molecular diffusion. The

mechanisms of adsorption/desorption and molecular diffusion can be modeled by some

commercial software, like ECLIPSE* by Schlumberger.

Nowadays, researchers start to incorporate adsorption/desorption, molecular diffusion,

and Knudsen diffusion in their work. (Javadpour et al., 2007; Javadpour et al., 2009;

Freeman et al., 2010; Mengal et al., 2011) Multi-porosity and/or dual permeability

models are typically applied in their works to account for reservoir fractures.

Researchers usually incorporate these transport mechanisms into their multi-component

gas system models. Consequently, the effects of fractures, gas content and components

are brought in their works which do not allow the effect of each transport mechanism to

be clearly.

In our study, we first use ECLIPSE 300* to build up a single porosity model for

conventional reservoirs and shale formations. Then we will simulate the effects of

transport mechanisms: adsorption/desorption, diffusion driven by concentration

gradient, and diffusion driven by chemical potential gradient. All of these are included

with the base case where only the convective flow in the single component gas system


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17

is present. In such system, the effects of gas content and component will be eliminated.

The grid block numbers of (11x11x1) and (110x110x10) in x, y, and z directions will be

applied for studying the grid size effects on our models. At last, we will incorporate the

effect of grid size on each single transport mechanism.

The objectives of this study include:

Comparing grid size effects on conventional reservoirs and shale formations due

to numerical dispersion;

Simulating and comparing pure adsorption/desorption mechanism and pure

molecular diffusion mechanism (two different models) impacts on conventional

reservoirs and shale formations;

Comparing grid size effects on adsorption/desorption mechanism and molecular

diffusion mechanism in conventional reservoirs and shale formations;

Simulating the multi-mechanisms of convection, adsorption and diffusion on

conventional reservoirs and shale formations.

2.2 Model specification

The following assumptions are made as the basic characteristics applying for this

research work:

1. Single gas component (methane) system with water component;

2. Homogeneous reservoir matrix with uniform rock properties in single porosity

models;

3. No gas condensate in the system;

4. Isothermal system;


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5. The same Langmuir isotherm values to both conventional gas reservoirs and

shale formations;

6. Knudsen diffusion is ignored because gas molecule-wall collision only happens

in low pressures (Fathi et al., 2012), while the pressure in our model (5000 psia)

is much higher. Figure 2-1 shows that when pressure is larger than 1000 psia

(less than 0.001 in the x-axis), the effect of wall-molecular collisions will

become nearly zero. In addition, we can estimate the Knudsen number and

apparent permeability of our models to see whether Knudsen diffusion is

important. The Knudsen numbers of shale formation models at differentconditions are 0.747, 0.0779, and 0.112; the apparent permeabilities are 86.27,

86.63, 102.4 nd. We also simulated our shale gas models in these three models,

and show the gas production rate in Figure C-1 and C-2. Although the gas rates

change as much as twice, the magnitude of the gas rate is still very small. The

changes do not show an apparent difference for different mechanisms effects.

The details are presented in appendix C. Thus, it is reasonable for our study to

ignore Knudsen diffusion. To keep consistency, we still use the permeability of

54 nd for shale formations.

7. There is only one vertical producing well located in the corner of the reservoir

and penetrating through all the reservoir thickness. The reservoir physical model

is shown in Figure 2-2;

8. The well produces at constant-BHP constraint. It has been completed in the first

year and started to produce from the 2nd year for 50 years.


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The assumptions 1 to 4 are made for simplification. The reason for using the same

Langmuir isotherm values in all cases is to keep the same original gas in place when

adding adsorption mechanism in our models. With the same initial conditions, the effect

of adsorption/desorption can be observed and compared more straightforwardly. We use

the typical relative permeability and capillary pressure curves for tight reservoir, shown

in Figure 2-3. The model parameters are listed in Table 2-1. These data were first

obtained from literature reviews (Bahrami et al., 2011; Ambrose et al., 2010, Leahy-

Dios et al., 2011; Economides et al., 2010; Das et al., 2012) and then modified to fit our

model. We reduced the irreducible water and gas saturations, and increase initial gassaturation, to enhance the gas production rate from shale formations. We use

compositional mode in ECLIPSE 300* and choose to use the Peng-Robinson equation

of state. The detail of Peng-Robinson equation of state is demonstrated in ECLIPSE*

Technical Description (2011). The critical properties for running the EOS model are

listed in Table 2-2.

Due to the very small gas rate in shale formations, we added hydraulic fracture in our

shale formation models to enhance the production rate and pressure drop. We first

rearrange the grid size in our models to keep the production well in the same location.

Then keeping the same number of grid blocks, we changed the entire row of grid

cellswhere the production well locatedalong x-axis into fracture cells. Finally, the

permeability of fracture is updated. The specifications of cases which we simulated in

our study are listed in Table 2-3.


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Figure 2-1: Simulation and experimental results showing the impact of pore

pressure on the interactions between gas molecules and pore wall. (Fathi et al.,

2012)

Figure 2-2: Dimensions and grid blocks for reservoir models; using grid blocks of

(11x11x1) and (110x110x10); (X, Y, Z) orders.


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Figure 2-3: The relative permeability curve (top) and capillary pressure curve

(bottom) used in this study.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Relativepermea

bility

Water saturation

krw

krg

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1

Pc,psi

Water saturation

Pc


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22

SI units Field unitsdepth of reservoir top Dr 1253.6 m 4113 ft

x 51 m 167.3 ftreservoir dimensions y 51 m 167.3 ft

z 18 m 59 ft

conventional reservoir permeability kc 5.4 mdshale matrix permeability ks 54 ndshale fracture permeability kf 15000 mdporosity 8%fracture width width 0.08 m 3.15 inreservoir temperature Tr 82

oC 179.6 oFinitial reservoir pressure Pinitial 345 bar 5003.8 psiabottom hole pressure BHP 50 bar 725.2 psiaskin factor s 0initial gas saturation Sgi 0.75

initial water saturation Swi 0.25diffusion coefficient Di 0.0078 m2/day

Langmuir isothermLangmuir pressure PL 44.816 barLangmuir volume VL 0.00299654 sm

3/kg

Table 2-1: Model parameters in this study.

component namegas molecular weight

methane16.043 g/mol

OmegaA 0.45723553

OmegaB 0.07779607critical temperature 215.66 Kcritical pressure 81.296 barcritical volume 0.065588 m3/molcritical z-factor 0.29738shift parameters 0.0742789acentric factors 0.46931binary interaction coefficients 0component parachor 74.92

Lorentz-Bray-Clark viscosity correlation coefficientsa 0.1023

b 0.023364c 0.058533d -0.040758e 0.0093324

Table 2-2: Critical properties of methane for running the one component

compositional model.


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case

Number ofgrid blocks in

x, y, and zdirections

Permeability Adsorption

concentrationgradientdriving

diffusion

chemicalpotentialgradientdriving

diffusion

Conventional

gasreservoirs

Case 1 11111 5.4 md

Case 2 11111 5.4 md yes

Case 3 11111 5.4 md yes

Case 4 11111 5.4 md yes

Case 5 11111 5.4 md yes yes

Shale

formations

Case 6 11111 54 nd

Case 7 11111 54 nd yes



Case 10 11111 54 nd yes yes

Shaleformations

withfractures Case 11 11111 54 nd

Case 12 11111 54 nd yes

Case 13 11111 54 nd yes

Case 14 11111 54 nd yes


Conventional

gasreservoirs

Case 16 11011010 5.4 md

Case 17 11011010 5.4 md yes

Case 18 11011010 5.4 md yes

Case 19 11011010 5.4 md yes

Case 2011011010 5.4 md yes yes

Shale

formations

Case 21 11011010 54 nd

Case 22 11011010 54 nd yes

Case 23 11011010 54 nd yes

Case 24 11011010 54 nd yes


Sh

aleformations

w

ithfractures

Case 26 11011010 54 nd

Case 27 11011010 54 nd yes

Case 28 11011010 54 nd yes

Case 29 11011010 54 nd yes


Table 2-3: Specifications of simulation cases in this study.


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Chapter 3:Results and DiscussionResults are analyzed by plotting charts of gas production rate vs. time, cumulative gas

production vs. time, and gas-in-place vs. time. For conventional gas reservoirs, the gasproduction rate drop to 0.1% of initial value after 100 day ofproduction, and continues

to drop around 0.007% per day. This indicates that gas flow has become steady-state

flow after 100 producing days. As a result, presenting results up to 100 production day

is enough for conventional gas reservoirs. For shale formations, we use the typical life

for production well of 50 years to compare the results due to its very low production

rates. For shale formations with fractures, because the initial gas rate is so high that

cannot be presented in the same charts with the gas rate after 1-year production, we plot

the production rate in the first year, and the following 49 years separately. As figure 3-1

shows the gas production rate of different models base cases are not in the same

magnitude, we normalize the data by dividing the larger initial or ultimate value among

all the comparing cases for each plot in order to be able to compare results.

3.1 Grid size

Among various parameters affecting the simulation results in the compositional model

of ECLIPSE 300*, grid size is one of the most important. The reason is that ECLIPSE*

uses the numerical finite-difference scheme to perform simulation which are

intrinsically affected by numerical dispersion. And the finite difference in the numericalsimulations is first order. In Figure 3-1, for example, we show the pressure gradient in

our reservoir model of different grid sizes at the 40 th day. The pressure drop faster with

time in larger grid size model, but the pressure gradient is smaller than smaller grid size


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model. As a result, gas will move faster in smaller grid size model. In this section, we

compare the 121 (11111) grid blocks model with the 121000 (11011010) grid

blocks model for conventional gas reservoirs and shale formations. Table 3-1 shows

some results of case 1 and case 16 (conventional reservoirs); case 6 and case 21 (shale

formations); case 11 and case 26 (shale formations with fractures).

Figure 3-2 to 3-5 show the impact of grid size on conventional gas reservoirs. First, the

initial gas production rate of smaller grid size model is 14% larger than the larger grid

size. However, the production rate of smaller grid size model drops faster than larger

grid size, and such that the larger grid size produces faster after the 8

th

day. Second, gridsize effects do not change the initial gas-in-place and total gas production, although

smaller grid size reach the ultimate recovery faster by about 10 days. In addition, the

gas-in-place curves have almost the same trends as pressure curve because there is only

convection flow in the base cases.

Figure 3-6 to 3-9 show that the grid size effects on shale formations are much more

significant than conventional gas reservoirs. The initial gas production rate of smaller

grid size is 57% larger than larger grid size. It also drops much faster in the first 5 years

than the gas rate of larger grid size model. At the last day of the 50 th year, the difference

of their gas production rates reduced to 16%. Consequently, the smaller grid size

produced 19% more natural gas than the larger grid size after 50 years. Similarly, the

original gas-in-place does not change in different grid size of shale formation models,

and the trends of pressure drop curves and the gas-in-place curves are the same.

One can see the grid effects on shale formations with fractures from Figure 3-10 to 3-

14. The initial gas production rate of smaller grid size is 19% higher than larger grid


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size. However, the gas rate of smaller grid size drops drastically at the very beginning

time, and they would surpass each other after 150 days production. At the last day, the

difference becomes to -6%. As a result, they will produce the same amount of gas at the

6th year and finally larger grid size can produce 4% more gas after 50 years

production, and 4% more pressure drop. And the grid size does not change the original

gas-in-place as well. Some noisy production data can be observed in the last several

years. The reason is that the iteration in ECLIPSE* does not converge when adding

small grid block of fractures into the shale formation models.

In Figure 3-16 to 3-18, we plot all pressure curves of each model in the same chart. Andthe results indicate that the differences of pressure drops are not very large in the same

model when adding diffusion and/or adsorption mechanism. For conventional

reservoirs, the pressure drop from 5004 psia to 780 psia; for shale formations, the

pressure goes from 5004 psia to average 4860 psia and average 3400 psia (with

fractures).


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model case

initial gasproduction

rate(ft3/day)

gasproduction

rate at 8thday

(ft3/day)

cumulativegas

production(ft3)

reservoirpressuredrop after100 days'

production

(psia)

conventionalgas reservoirs

case 1 3,083,846 938,266 24,270,670 4253

case 16 3,588,277 928,639 24,269,388 4269

grid sizeeffects

14% -1% 0% 0.4%

model case


rate(ft3/day)

gasproductionrate at last

day(ft3/day)

cumulativegas

production(ft3)

reservoirpressuredrop after50 years'

production(psia)

Shaleformations

case 6 93 36.56 756,089 143case 21 220 43.54 934,646 177grid sizeeffects

57% 16% 19% 19%

model case


rate(ft3/day)

gasproductionrate at last

day(ft3/day)

cumulativegas

production(ft3)

reservoirpressuredrop after50 years'

production(psia)

Shaleformations

with fractures

case 11 59,633 205 8,133,276 1472case 26 73,500 192 7,801,123 1408grid sizeeffects

19% -6% -4% -4%

Table 3-1: Grid size effects on conventional gas reservoirs and shale formations.


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Figure 3-1: gas production rate in different models

Figure 3-2: Pressure gradient in different grid size models.

800

1,000

1,200

1,400

1,600

1,800

0 10 20 30 40 50

Reservoirpressure,psia

Distance, m

110x110x10

11x11x1


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Figure 3-3: Impact of grid size on gas production rate with time (100 days) for

conventional gas reservoirs.

Figure 3-4: Semi-log plot shows the impact of grid size on cumulative gas

production with time (1000 days) for conventional gas reservoirs.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1 10 100 1000

N

ormalizedcumulativegasproduc

tion

Time (day)

110X110X10, k=5.4 md

11X11X1, k=5.4 md


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Figure 3-5: Impact of grid size on reservoir pressure with time (100 days) for


Figure 3-6: Impact of grid size on gas-in-place with time (100 days) for


0

1,000

2,000

3,000

4,000

5,000

0 25 50 75 100

reservoirpressure,psia

Time (day)

110X110X10, k=5.4 md

11X11X1, k=5.4 md


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Figure 3-7: Impact of grid size on gas production rate with time (50 years) for

shale formations.


production with time (50 years) for shale formations.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 5 10 15 20 25 30 35 40 45 50 55

Normalizedgasproduction

rate

Time (year)

110x110x10, k=54 nd

11X11X1, k=54 nd

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1 10 100 1000 10000 100000

Normalizedcumulativegasprodu

ction

Time (day)

110x110x10, k=54 nd

11X11X1, k=54 nd


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32


formations.

Figure 3-10: Impact of grid size on gas-in-place with time (50 years) for shale

formations.

4800

4840

4880

4920

4960

5000

0 5 10 15 20 25 30 35 40 45 50 55

Reservoirpressure(p

sia)

Time (year)

110x110x10, k=54 nd

11X11X1, k=54 nd

0.96

0.97

0.98

0.99

1.00

0 5 10 15 20 25 30 35 40 45 50 55

Normalizedgasinplace

Time (year)

110x110x10, k=54 nd

11X11X1, k=54 nd


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Figure 3-11: Impact of grid size on gas production rate in the first year for shale

formations with fractures.

Figure 3-12: Impact of grid size on gas production rate with time (50 years) for

shale formations with fractures.

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

0 90 180 270 360

Gasproductionrate(ft3/d

ay)

Time (day)

110x110x10, k=54nd+frac

11x11x1, k= 54nd+frac

0.00

0.20

0.40

0.60

0.80

1.00

0 5 10 15 20 25 30 35 40 45 50 55

Normalizedgasproductionrate

Time (year)

110x110x10, k=54nd+frac



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production with time (50 years) for shale formations.



0.00

0.20

0.40

0.60

0.80

1.00

1 10 100 1000 10000 100000

Normalizedcumulativegasprod

uctionrate

Time (day)

110x110x10, k=54nd+frac


3000

3500

4000

4500

5000

0 5 10 15 20 25 30 35 40 45 50 55

Reservoirpressure(psia)

Time (year)

110x110x10, k=54nd+frac



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Figure 3-15: Impact of grid size on gas in place with time (50 years) for shale


Figure 3-16: Pressure drop in conventional reservoirs for 100 days

0.60

0.70

0.80

0.90

1.00

0 5 10 15 20 25 30 35 40 45 50 55

Normalizedgasinplac

e

Time (year)

110x110x10, k=54nd+frac


0

1000

2000

3000

4000

5000

0 25 50 75 100


Time (day)

case 1

case 2

case 3

case 4

case 5

case 16

case 17

case 18

case 19

case 20


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Figure 3-17: Pressure drop in shale formations for 50 years

Figure 3-18: Pressure drop in shale formations with fractures for 50 years

4,750

4,800

4,850

4,900

4,950

5,000

0 5 10 15 20 25 30 35 40 45 50 55


Time (year)

case 6

case7

case 8

case 9

case 10

case 21

case 22

case 23

case 24

case 25

3,000

3,500

4,000

4,500

5,000

0 5 10 15 20 25 30 35 40 45 50 55


Time (year)

case 11

case 12

case 13

case 14

case 15

case 26

case 27

case 28

case 29

case 30


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3.2 Adsorption

As discussed in chapter 1, adsorption/desorption is a contributing mechanism of gas

flow in shale. ECLIPSE 300* applies Langmuir isotherm model (Equation 1-1) to

simulate adsorption/desorption of a single component system. For our one component

gas (methane) system, we obtained the Langmuir isotherm data of methane in shale

formations by doing literature review (Jacobi et al. 2008; Mengal et al., 2011; Das et al.,

2012; Economides, 2010). They used experimental methods to measure the Langmuir

isotherm data from various shale samples. The data measured in these researches are

listed in Table 3-2. Finally, we decided to use the Langmuir isotherm pressure of 44.82

bars (650 psia) and the Langmuir isotherm volume of 0.00299654 sm3/kg (Mengal et

al., 2011) because it is close to the average value of experimental results of Das et al.

(2012). The Langmuir isotherm curve in our study is shown in Figure 3-19.

From Figure 3-20 to 3-23, one can see the grid size and adsorption/desorption effects on

conventional gas reservoirs. First of all, around 17% more original gas-in-place results

from gas adsorption for both grid sizes due to the Langmuir isotherm data in this study.

The remaining part is the free gas existing in pore space, which has the same volume as

the free gas in models without adsorption. When pressure drops, the adsorbed gas will

desorb from the pore surface which will enhance the initial gas flow rate for 1%. As

pressure depletion, more and more gas will be released from the pore surface which will

increase the gas production rate. Consequently, approximately 6% more gas was

produced in 100 days. Grid size effects are close to the base case: the smaller grid size

results in larger initial gas production rates (14%), faster gas rate drop, and shorter time

(10 days) to achieve the ultimate recovery.


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Figure 3-24 to 3-27 show that the adsorption mechanism has very little impacts on shale

gas production. The reason is that the very small pressure drop inside reservoir pores

cannot cause significant gas desorbing from reservoir rock, see Figure 3-18. Even after

50 years production, pure adsorption mechanism only enhances 1% gas production.

Considering the grid size effects, the smaller grid size can cause 58% larger initial gas

production rate and 19% more cumulative gas production after 50 years, which are the

same as the base case.

One can see, as hydraulic fractures were induced in shale formations, the gas production

rate and pressure drop become larger which lead to adsorption gas releasing from shaleformations. Figure 3-28 to 3-32 show the adsorption/desorption effects on shale

formations with fractures. When adding adsorption/desorption mechanism, one can see

that initial gas production rates are enhanced by 1% and the rate keeps higher in the

entire production life for both grid sizes. The free gas in pore space was first produced

which cause the reservoir pressure depletion. Then, the desorption process happens and

increases pore pressure. As a result, 3% more gas is produced, and pressure drops 1%

less after 50 years production. However, as the reservoir pressure decreases from 5003

psia to 3500 psia, the desorption gas is still in a small amount when compared to free

gas production, see figure 3-19 and 3-32. For the grid size effects, the initial gas

production rate is enhanced by 17% in smaller grid size, but the cumulative pressure is

4% less due to numerical dispersion.

Figure 3-33 shows the comparison of adsorption effects between conventional gas

reservoirs and shale formations. In order to be able to compare them in one chart, we

normalized every curve by dividing the initial number of each curve. The adsorption


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effects are most significant on conventional gas reservoirs. And for shale formations,

more obvious effects can be observed for models with fractures. This results from the

pressure drop difference among the three models. As we assume the adsorption gas

storage capacity is the same in all cases by giving the same Langmuir isotherm value,

pressure gradient become the only factor to affect gas desorption. Thus, the smaller is

the final reservoir pressure, the desorption mechanism is more significant. This result

accords with the theory we discussed in chapter 1.


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sample

PL VL

psia bar scf/ton sm3/kg

Das et al., 2012 1 900 62.05 70 0.002185

2 800 55.16 70 0.002185

3 525 36.20 73 0.0022794 650 44.82 78 0.002435

5 800 55.16 78 0.002435

6 900 62.05 81 0.002528

7 750 51.71 69.5 0.002169

8 900 62.05 67.5 0.002107

9 780 53.78 45 0.001405

10 1000 68.95 52 0.001623

11 600 41.37 42 0.001311

12 850 58.61 118 0.003683

13 800 55.16 44 0.00137314 1080 74.46 49 0.001529

15 650 44.82 43 0.001342

16 930 64.12 102 0.003184

average 807 55.65 68 0.002111

Economides et al.,

2010930 64.12 46 0.001436

Mengal et al., 2011 650 44.82 96 0.002997

Table 3-2: Langmuir isotherm data of methane in shale formations from literature

review.


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model caseinitial gas

production(ft3/day)

originalgas-in-place

(ft3)

cumulativegas

productionfor 100 days

(ft3)

reservoir pressuredrop after 100 days'production (psia)

conventionalgas

reservoirs

case 1 3,083,846 28,298,220 24,118,937 4253

case 2 3,102,376 34,082,973 25,747,637 4278adsorption

effects1% 17% 6% 1%

case 16 3,588,277 28,298,216 24,216,618 4269case 17 3,614,046 34,082,969 26,401,379 4254

adsorptioneffects

1% 17% 8% -0.4%

grid sizeeffects

14% 0% 2.5% -0.6%

model case

initial gas

production(ft3/day)

original

gas-in-place (ft3)

cumulativegas

productionfor 50 years

(ft3)

reservoir pressure

drop after 50 years'production (psia)

shaleformations

case 6 93 28,298,220 756,088 143case 7 93 34,082,973 758,776 140

adsorptioneffects

0% 17% 0.4% -2%

case 21 220 28,298,216 934,646 177case 22 220 34,082,969 939,112 173

adsorptioneffects

0% 17% 0.5% -2%

grid sizeeffects 58% 0% 19% 19%

model caseinitial gas

production(ft3/day)

originalgas-in-

place (ft3)

cumulativegas

productionfor 50 years

(ft3)

reservoir pressuredrop after 50 years'production (psia)

shaleformations

withfractures

case 11 59,663 28,298,220 8,133,276 1472

case 12 60,065 34,082,973 8,378,384 1453adsorption

effects0.7% 17% 3% -1.3%

case 26 73,500 28,298,216 7,801,123 1408

case 27 72,510 34,082,973 8,060,926 1392adsorption

effects-1.3% 17% 3% -1.1%

Grid sizeeffects

17% 0% -4% -4%

Table 3-3: Adsorption/desorption effects on conventional gas reservoirs and shale

formations.


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Figure 3-19: Langmuir isotherm curve used for this study.

Figure 3-20: Impact of adsorption on gas production rate with time (100 days) for

conventional gas reservoirs; using grid blocks of (11x11x1) and (110x110x10).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 25 50 75 100


Time (day)

11X11X1, k=5.4 md

11X11X1, k= 5.4 md, pure adsp

110X110X10, k=5.4 md

110X110X10, k=5.4 md, pure adsp


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production with time (1000 days) for conventional gas reservoirs; using grid blocks

of (11x11x1) and (110x110x10).

Figure 3-22: Impact of adsorption on gas-in-place with time (100 days) for

conventional gas reservoirs; using grid blocks of (11x11x1) and (110x110x10).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1 10 100 1000

Normalizedcumulativegaspr

oduction

Time (day)

11X11X1, k=5.4 md


110X110X10, k=5.4 md


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 25 50 75 100


Time, day

11X11X1, k=5.4 md


110X110X10, k=5.4 md



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Figure 3-23: Gas-in-place of two states of gas with time (100 days) for conventional

gas reservoirs; using grid blocks of (11x11x1) and (110x110x10).

Figure 3-24: Impact of adsorption on gas production rate with time (50 years) for

shale formations; using grid blocks of (11x11x1) and (110x110x10).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 25 50 75 100


Time (day)

Total gas, 11x11x1, pure adsp

Free gas, 11x11x1, pure adsp

Adsorbing gas, 11x11x1, pure adsp


Free gas, 110x110x10, pure adspAdsorbing gas, 110x110x10, pure adsp

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 5 10 15 20 25 30 35 40 45 50 55


Time (day)

11X11X1, k=54 nd

11X11X1, k= 54 nd, pure adsp

110x110x10, k=54 nd

110x110x10, k=54 nd, pure adsp


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production with time (50 years) for shale formations; using grid blocks of

(11x11x1) and (110x110x10).

Figure 3-26 : Impact of adsorption on gas-in-place with time (50 years) for shale

formations; using grid blocks of (11x11x1) and (110x110x10).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1 10 100 1,000 10,000 100,000

Normalizedcumulativegasprod

uction

Time (day)

11X11X1, k=54 nd


110x110x10, k=54 nd


0.70

0.75

0.80

0.85

0.90

0.95

1.00

0 5 10 15 20 25 30 35 40 45 50 55


Time (year)

11X11X1, k=54 nd


110x110x10, k=54 nd



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Figure 3-27: Gas-in-place of two states of gas with time (50 years) for shale

formations; using grid blocks of (11x11x1) and (110x110x10).

Figure 3-28: Impact of adsorption on gas production rate in the first year for shale

formations with fractures; using grid blocks of (11x11x1) and (110x110x10).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 5 10 15 20 25 30 35 40 45 50 55


Time (year)







0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

0 90 180 270 360

Gasproductionrate,ft3/day

Time (day)

110x110x10, k=54nd+frac 110x110x10, k=54 nd+frac, adsp

11x11x1, k= 54nd+frac 11x11x1, k=54 nd+frac, adsp

7/30/201

2012-simulating effects of adsorption, diffusion, and convection in tight formations

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