2012-simulating effects of adsorption, diffusion, and convection in tight formations
TRANSCRIPT
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
1/108
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
2/108
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
3/108
Copyright by JIAZUN LI 2012
All Rights Reserved.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
4/108
To Mom, Dad, Grandma, and Grandpa
I love you so much!
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
5/108
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
6/108
v
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
7/108
vi
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
8/108
vii
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
9/108
viii
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
10/108
ix
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
11/108
x
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
Figure 3-8: Semi-log plot shows the impact of grid size on cumulative gas production
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
formations with fractures................................................................................................ 33
Figure 3-13: Semi-log plot shows the impact of grid size on cumulative gas production
with time (50 years) for shale formations....................................................................... 34
Figure 3-14: Impact of grid size on reservoir pressure with time (50 years) for shale
formations with fractures................................................................................................ 34
Figure 3-15: Impact of grid size on gas in place with time (50 years) for shale
formations with fractures................................................................................................ 35
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
12/108
xi
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
Figure 3-25: Semi-log plot showing the impact of adsorption on cumulative gas
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
formations with fractures; using grid blocks of (11x11x1) and (110x110x10).............. 47
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
13/108
xii
Figure 3-30: Semi-log plot showing the impact of adsorption on cumulative gas
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
formations with fractures; using grid blocks of (11x11x1) and (110x110x10).............. 48
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
Figure 3-35: Impact of molecular diffusion by concentration gradient on gas-in-place
with time (50 years) for shale formations; using grid blocks of (11x11x1) and
(110x110x10). ................................................................................................................ 57
Figure 3-36: Impact of molecular diffusion by concentration gradient on gas-in-place
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
14/108
xiii
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
15/108
xiv
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
Figure 3-51: Impacts of different transport mechanisms on gas production rate with time
(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
Figure 3-55: Impacts of different transport mechanisms on gas production rate with time
(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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
16/108
xv
Figure C-1: gas production rate for different permeability cases.90
Figure C-2: reservoir pressure for different permeability cases.90
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
17/108
xvi
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
18/108
xvii
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
19/108
1
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
20/108
2
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
21/108
3
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
22/108
4
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)
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
23/108
5
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
24/108
6
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
25/108
7
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
26/108
8
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)
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
27/108
9
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;
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
28/108
10
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).
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
29/108
11
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
30/108
12
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
31/108
13
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
32/108
14
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
33/108
15
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
34/108
16
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
35/108
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;
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
36/108
18
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
37/108
19
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
38/108
20
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
39/108
21
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
40/108
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
41/108
23
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 8 11111 54 nd yes
Case 9 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
Case 15 11111 54 nd yes 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
Case 25 11011010 54 nd yes 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
Case 30 11011010 54 nd yes yes
Table 2-3: Specifications of simulation cases in this study.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
42/108
24
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
43/108
25
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
44/108
26
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).
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
45/108
27
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
initial gasproduction
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
initial gasproduction
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
46/108
28
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
47/108
29
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
48/108
30
Figure 3-5: Impact of grid size on reservoir pressure with time (100 days) for
conventional gas reservoirs.
Figure 3-6: Impact of grid size on gas-in-place with time (100 days) for
conventional gas reservoirs.
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
49/108
31
Figure 3-7: Impact of grid size on gas production rate with time (50 years) for
shale formations.
Figure 3-8: Semi-log plot shows the impact of grid size on cumulative gas
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
50/108
32
Figure 3-9: Impact of grid size on reservoir pressure with time (50 years) for shale
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
51/108
33
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
11x11x1, k= 54nd+frac
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
52/108
34
Figure 3-13: Semi-log plot shows the impact of grid size on cumulative gas
production with time (50 years) for shale formations.
Figure 3-14: Impact of grid size on reservoir pressure with time (50 years) for shale
formations with fractures.
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
11x11x1, 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
11x11x1, k= 54nd+frac
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
53/108
35
Figure 3-15: Impact of grid size on gas in place with time (50 years) for shale
formations with fractures.
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
11x11x1, k= 54nd+frac
0
1000
2000
3000
4000
5000
0 25 50 75 100
Reservoirpressure(psia)
Time (day)
case 1
case 2
case 3
case 4
case 5
case 16
case 17
case 18
case 19
case 20
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
54/108
36
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
Reservoirpressure(psia)
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
Reservoirpressure(psia)
Time (year)
case 11
case 12
case 13
case 14
case 15
case 26
case 27
case 28
case 29
case 30
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
55/108
37
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
56/108
38
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
57/108
39
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
58/108
40
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
59/108
41
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.
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
60/108
42
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
Normalizedgasproductionrate
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
61/108
43
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).
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
11X11X1, k= 5.4 md, pure adsp
110X110X10, k=5.4 md
110X110X10, k=5.4 md, 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 25 50 75 100
Normalizedgasinplace
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
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
62/108
44
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
Normalizedgasinplace
Time (day)
Total gas, 11x11x1, pure adsp
Free gas, 11x11x1, pure adsp
Adsorbing gas, 11x11x1, pure adsp
Total gas, 110x110x10, 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
Normalizedgasproductionrate
Time (day)
11X11X1, k=54 nd
11X11X1, k= 54 nd, pure adsp
110x110x10, k=54 nd
110x110x10, k=54 nd, pure adsp
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
63/108
45
Figure 3-25: Semi-log plot showing the impact of adsorption on cumulative gas
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
11X11X1, k= 54 nd, pure adsp
110x110x10, k=54 nd
110x110x10, k=54 nd, pure adsp
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
Normalizedgasinplace
Time (year)
11X11X1, k=54 nd
11X11X1, k= 54 nd, pure adsp
110x110x10, k=54 nd
110x110x10, k=54 nd, pure adsp
-
7/30/2019 2012-Simulating Effects of Adsorption, Diffusion, And Convection in Tight Formations
64/108
46
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
Normalizedgasinplace
Time (year)
Total gas, 11x11x1, pure adsp
Free gas, 11x11x1, pure adsp
Adsorbing gas, 11x11x1, pure adsp
Total gas, 110x110x10, pure adsp
Free gas, 110x110x10, pure adsp
Adsorbing gas, 110x110x10, pure adsp
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