Reservoir simulation: mathematical techniques in oil recovery
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, PA
SIAM, Soc. for Industrial and Applied Mathematics
2007
|
| Series: | CBMS-NSF regional conference series in applied mathematics
77 |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 205 - 213 |
| Physical Description: | XXVIII, 219 S. Ill., graph. Darst. |
| ISBN: | 9780898716405 |
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| 245 | 1 | 0 | |a Reservoir simulation |b mathematical techniques in oil recovery |c Zhangxin Chen |
| 264 | 1 | |a Philadelphia, PA |b SIAM, Soc. for Industrial and Applied Mathematics |c 2007 | |
| 300 | |a XXVIII, 219 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a CBMS-NSF regional conference series in applied mathematics |v 77 | |
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| 650 | 7 | |a Mecânica dos fluídos computacional |2 larpcal | |
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| 650 | 7 | |a Simulação (métodos) |2 larpcal | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Oil reservoir engineering |x Mathematical models | |
| 650 | 4 | |a Oil reservoir engineering |x Simulation methods | |
| 650 | 4 | |a Porous materials |x Permeability |x Mathematical models | |
| 650 | 4 | |a Transport theory |x Mathematical models | |
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| adam_text | Contents
List of Figures
xiii
List of Tables xv
List of Notation
xvii
Preface
xxvii
1
Introduction
1
1.1
Petroleum Reservoir Simulation
..................... 1
1.2
Classical Reservoir Engineering Methods
................ 1
1.2.1
Material Balance Methods
................. 1
1.2.2
Decline Curve Methods
.................. 2
1.2.3
Statistical Methods
..................... 2
1.2.4
Analytical Methods
.................... 2
1.3
Reservoir Simulation Methods
..................... 3
1.3.1
Reservoir Simulation Stages
................ 3
1.3.2
Reservoir Simulator Classifications
............ 4
1.3.3
Reservoir Simulation Applications
............ 4
1.4
SI Metric Conversion Factors
...................... 6
2
A Glossary of Petroleum Terms
7
2.1
Reservoir Rock Properties
........................ 7
2.2
Reservoir Fluid Properties
........................ 9
2.3
Wettability
................................ 12
2.4
Fluid Displacement Processes
...................... 13
2.5
Reservoir Rock/Fluid Properties
..................... 13
2.5.1
Two-Phase Relative Permeability
............. 15
2.5.2
Three-Phase Relative Permeability
............ 17
2.6
Terms Used in Numerical Simulation
.................. 20
3
Single-Phase Flow and Numerical Solution
23
3.1
Basic Differential Equations
....................... 23
3.1.1
Mass Conservation
..................... 23
3.1.2
Darcy sLaw
........................ 25
ix
Contents
3.1.3
Units
............................ 26
3.1.4
Different Forms of Flow Equations
............ 26
3.2
An Analytic Solution
........................... 31
3.3
Finite Difference Methods
........................ 34
3.3.1
First Difference Quotients
................. 34
3.3.2
Second Difference Quotients
............... 36
3.3.3
Grid Systems
........................ 38
3.3.4
Treatment of Boundary Conditions
............ 39
3.3.5
Finite Differences for Stationary Problems
........ 41
3.3.6
Finite Differences for Parabolic Problems
......... 42
3.3.7
Consistency, Stability, and Convergence
......... 44
3.3.8
Finite Differences for Hyperbolic Problems
........ 48
3.4
Numerical Solution of Single-Phase Flow
............... 51
3.4.1
Treatment of Initial Conditions
.............. 52
3.4.2
Time Discretization
.................... 52
3.4.3
Spatial Discretization
................... 53
3.4.4
Treatment of Block Transmissibility
............ 53
3.4.5
Solution Approaches in Time
............... 56
3.4.6
Material Balance Analysis
................. 63
Weil Modeling
67
4.1
Introduction
............................... 67
4.2
Analytical Formulas
........................... 68
4.3
Single-Layer Well Models
........................ 69
4.3.1
Square Grids
........................ 69
4.3.2
Extensions
......................... 71
4.4
Multilayer Well Models
......................... 74
4.5
Coupling of Flow and Well Equations
.................. 75
4.6
Coupling ofWellbore-Hydraulics and Reservoir Models
........ 78
4.6.1
Single-Phase Flow
..................... 78
4.6.2
Multiphase Flow
...................... 79
Two-Phase Flow and Numerical Solution
83
5.1
Basic Differential Equations
....................... 83
5.1.1
Mass Conservation
..................... 83
5.1.2
Darcy sLaw
........................ 84
5.1.3
Alternative Differential Equations
............. 85
5.1.4
Boundary Conditions
................... 89
5.2
An Analytic Solution
........................... 91
5.2.1
Analytic Solution Before Water Breakthrough
...... 91
5.2.2
Analytic Solution at the Water Front
............ 92
5.2.3
Analytic Solution After Water Breakthrough
....... 93
5.3
Numerical Solution of Two-Phase Flow
................. 94
5.3.1
Treatment of Initial Conditions
.............. 95
5.3.2
Source/Sink Terms
..................... 95
5.3.3
Spatial Discretization
................... 96
Contents
x¡
5.3.4
Treatment of
Block Transmissibility............ 97
5.3.5
Solution Approaches in Time
............... 99
6
The Black Oil Model and Numerical Solution
103
6.1
Basic Differential Equations
....................... 103
6.1.1
Mass Conservation and Darcy s Law
........... 103
6.1.2
Rock/Fluid Properties
................... 106
6.1.3
Fluid Properties
...................... 107
6.1.4
Phase States
........................ 108
6.2
Numerical Solution of the Black Oil Model
............... 109
6.2.1
Treatment of Initial Conditions
.............. 110
6.2.2
Simultaneous Solution Techniques
............ 112
6.2.3
Sequential Solution Techniques
.............. 120
6.2.4
Iterative
IMPES
Solution Techniques
........... 124
6.2.5
Adaptive Implicit Techniques
............... 127
6.2.6
Well Coupling
....................... 128
7
Transport of Multicomponents in a Fluid and Numerical Solution
131
7.1
Basic Differential Equations
....................... 132
7.2
Computation of Fluid Viscosity
..................... 133
7.3
Equations of State
............................ 134
7.4
Diffusion, Dispersion, and Tortuosity
.................. 136
7.4.1
Fick sLaw
......................... 136
7.4.2
Impact of Tortuosity on Diffusion
............. 137
7.4.3
Soret Effects and Gravity Segregation
........... 146
7.4.4
Isothermal Gravity/Chemical Equilibrium
........ 147
7.5
Numerical Solution
........................... 148
7.5.1
A Model Problem
..................... 148
7.5.2
Finite Difference Equations
................ 148
7.6
Nonisothermal Flow
........................... 151
7.7
Examples
................................. 152
7.7.1
Forced Convection
..................... 152
7.7.2
Forced Convection Plus Dispersion
............ 154
8
Compositional Flow and Numerical Solution
157
8.1
Basic Differential Equations
....................... 157
8.1.1
Mass Conservation and Darcy s Law
........... 157
8.1.2
Equations of State
..................... 159
8.2
Numerical Solution of Compositional Flow
............... 161
8.2.1
Choice of Primary Variables
................ 162
8.2.2
Finite Difference Equations
................ 164
8.3
Solution of Equilibrium Relations
.................... 170
8.3.1
Successive Substitution Method
.............. 170
8.3.2
Newton-Raphson Flash Calculation
............ 171
8.3.3
Derivatives of
Fugacity
Coefficients
........... 172
8.3.4
Solution of the PR Cubic Equation
............ 173
xü Contents
8.3.5
Practical
Considerations
..................175
9
Nonisothermal
Flow and Numerical Solution
177
9.1
Basic Differential Equations
.......................178
9.1.1
Mass Conservation and Darcy s Law
...........178
9.1.2
Energy Conservation
....................179
9.1.3
Rock Properties
......................180
9.1.4
Fluid Properties
......................181
9.2
Numerical Solution of Nonisothermal Flow
...............182
9.2.1
Choice of Primary Variables
................183
9.2.2
Finite Difference Equations
................184
10
Practical Topics in Reservoir Simulation
193
10.1
Design of Study Objectives
.......................193
10.2
Analysis of Reservoir Data
.......................195
10.2.1
Geophysical Data
.....................196
10.2.2
Geological Data
......................197
10.2.3
Engineering Data
.....................197
10.3
Development of Simulation Models
...................198
10.3.1
Model Selection
......................198
10.3.2
Grid Selection
.......................200
10.4
History Matching
............................203
10.5
Prediction of Reservoir Performance
..................204
Bibliography
205
Index
215
|
| adam_txt |
Contents
List of Figures
xiii
List of Tables xv
List of Notation
xvii
Preface
xxvii
1
Introduction
1
1.1
Petroleum Reservoir Simulation
. 1
1.2
Classical Reservoir Engineering Methods
. 1
1.2.1
Material Balance Methods
. 1
1.2.2
Decline Curve Methods
. 2
1.2.3
Statistical Methods
. 2
1.2.4
Analytical Methods
. 2
1.3
Reservoir Simulation Methods
. 3
1.3.1
Reservoir Simulation Stages
. 3
1.3.2
Reservoir Simulator Classifications
. 4
1.3.3
Reservoir Simulation Applications
. 4
1.4
SI Metric Conversion Factors
. 6
2
A Glossary of Petroleum Terms
7
2.1
Reservoir Rock Properties
. 7
2.2
Reservoir Fluid Properties
. 9
2.3
Wettability
. 12
2.4
Fluid Displacement Processes
. 13
2.5
Reservoir Rock/Fluid Properties
. 13
2.5.1
Two-Phase Relative Permeability
. 15
2.5.2
Three-Phase Relative Permeability
. 17
2.6
Terms Used in Numerical Simulation
. 20
3
Single-Phase Flow and Numerical Solution
23
3.1
Basic Differential Equations
. 23
3.1.1
Mass Conservation
. 23
3.1.2
Darcy'sLaw
. 25
ix
Contents
3.1.3
Units
. 26
3.1.4
Different Forms of Flow Equations
. 26
3.2
An Analytic Solution
. 31
3.3
Finite Difference Methods
. 34
3.3.1
First Difference Quotients
. 34
3.3.2
Second Difference Quotients
. 36
3.3.3
Grid Systems
. 38
3.3.4
Treatment of Boundary Conditions
. 39
3.3.5
Finite Differences for Stationary Problems
. 41
3.3.6
Finite Differences for Parabolic Problems
. 42
3.3.7
Consistency, Stability, and Convergence
. 44
3.3.8
Finite Differences for Hyperbolic Problems
. 48
3.4
Numerical Solution of Single-Phase Flow
. 51
3.4.1
Treatment of Initial Conditions
. 52
3.4.2
Time Discretization
. 52
3.4.3
Spatial Discretization
. 53
3.4.4
Treatment of Block Transmissibility
. 53
3.4.5
Solution Approaches in Time
. 56
3.4.6
Material Balance Analysis
. 63
Weil Modeling
67
4.1
Introduction
. 67
4.2
Analytical Formulas
. 68
4.3
Single-Layer Well Models
. 69
4.3.1
Square Grids
. 69
4.3.2
Extensions
. 71
4.4
Multilayer Well Models
. 74
4.5
Coupling of Flow and Well Equations
. 75
4.6
Coupling ofWellbore-Hydraulics and Reservoir Models
. 78
4.6.1
Single-Phase Flow
. 78
4.6.2
Multiphase Flow
. 79
Two-Phase Flow and Numerical Solution
83
5.1
Basic Differential Equations
. 83
5.1.1
Mass Conservation
. 83
5.1.2
Darcy'sLaw
. 84
5.1.3
Alternative Differential Equations
. 85
5.1.4
Boundary Conditions
. 89
5.2
An Analytic Solution
. 91
5.2.1
Analytic Solution Before Water Breakthrough
. 91
5.2.2
Analytic Solution at the Water Front
. 92
5.2.3
Analytic Solution After Water Breakthrough
. 93
5.3
Numerical Solution of Two-Phase Flow
. 94
5.3.1
Treatment of Initial Conditions
. 95
5.3.2
Source/Sink Terms
. 95
5.3.3
Spatial Discretization
. 96
Contents
x¡
5.3.4
Treatment of
Block Transmissibility. 97
5.3.5
Solution Approaches in Time
. 99
6
The Black Oil Model and Numerical Solution
103
6.1
Basic Differential Equations
. 103
6.1.1
Mass Conservation and Darcy's Law
. 103
6.1.2
Rock/Fluid Properties
. 106
6.1.3
Fluid Properties
. 107
6.1.4
Phase States
. 108
6.2
Numerical Solution of the Black Oil Model
. 109
6.2.1
Treatment of Initial Conditions
. 110
6.2.2
Simultaneous Solution Techniques
. 112
6.2.3
Sequential Solution Techniques
. 120
6.2.4
Iterative
IMPES
Solution Techniques
. 124
6.2.5
Adaptive Implicit Techniques
. 127
6.2.6
Well Coupling
. 128
7
Transport of Multicomponents in a Fluid and Numerical Solution
131
7.1
Basic Differential Equations
. 132
7.2
Computation of Fluid Viscosity
. 133
7.3
Equations of State
. 134
7.4
Diffusion, Dispersion, and Tortuosity
. 136
7.4.1
Fick'sLaw
. 136
7.4.2
Impact of Tortuosity on Diffusion
. 137
7.4.3
Soret Effects and Gravity Segregation
. 146
7.4.4
Isothermal Gravity/Chemical Equilibrium
. 147
7.5
Numerical Solution
. 148
7.5.1
A Model Problem
. 148
7.5.2
Finite Difference Equations
. 148
7.6
Nonisothermal Flow
. 151
7.7
Examples
. 152
7.7.1
Forced Convection
. 152
7.7.2
Forced Convection Plus Dispersion
. 154
8
Compositional Flow and Numerical Solution
157
8.1
Basic Differential Equations
. 157
8.1.1
Mass Conservation and Darcy's Law
. 157
8.1.2
Equations of State
. 159
8.2
Numerical Solution of Compositional Flow
. 161
8.2.1
Choice of Primary Variables
. 162
8.2.2
Finite Difference Equations
. 164
8.3
Solution of Equilibrium Relations
. 170
8.3.1
Successive Substitution Method
. 170
8.3.2
Newton-Raphson Flash Calculation
. 171
8.3.3
Derivatives of
Fugacity
Coefficients
. 172
8.3.4
Solution of the PR Cubic Equation
. 173
xü Contents
8.3.5
Practical
Considerations
.175
9
Nonisothermal
Flow and Numerical Solution
177
9.1
Basic Differential Equations
.178
9.1.1
Mass Conservation and Darcy's Law
.178
9.1.2
Energy Conservation
.179
9.1.3
Rock Properties
.180
9.1.4
Fluid Properties
.181
9.2
Numerical Solution of Nonisothermal Flow
.182
9.2.1
Choice of Primary Variables
.183
9.2.2
Finite Difference Equations
.184
10
Practical Topics in Reservoir Simulation
193
10.1
Design of Study Objectives
.193
10.2
Analysis of Reservoir Data
.195
10.2.1
Geophysical Data
.196
10.2.2
Geological Data
.197
10.2.3
Engineering Data
.197
10.3
Development of Simulation Models
.198
10.3.1
Model Selection
.198
10.3.2
Grid Selection
.200
10.4
History Matching
.203
10.5
Prediction of Reservoir Performance
.204
Bibliography
205
Index
215 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Chen, Zhangxin |
| author_facet | Chen, Zhangxin |
| author_role | aut |
| author_sort | Chen, Zhangxin |
| author_variant | z c zc |
| building | Verbundindex |
| bvnumber | BV023278108 |
| callnumber-first | T - Technology |
| callnumber-label | TN871 |
| callnumber-raw | TN871 |
| callnumber-search | TN871 |
| callnumber-sort | TN 3871 |
| callnumber-subject | TN - Mining Engineering and Metallurgy |
| classification_rvk | SI 196 |
| classification_tum | MAT 650f GEO 326f |
| ctrlnum | (OCoLC)155757193 (DE-599)BVBBV023278108 |
| dewey-full | 622/.3382015118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 622 - Mining and related operations |
| dewey-raw | 622/.3382015118 |
| dewey-search | 622/.3382015118 |
| dewey-sort | 3622 103382015118 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Geowissenschaften Bergbau / Hüttenwesen Mathematik |
| discipline_str_mv | Geowissenschaften Bergbau / Hüttenwesen Mathematik |
| format | Book |
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| id | DE-604.BV023278108 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:38:37Z |
| indexdate | 2024-07-09T21:14:47Z |
| institution | BVB |
| isbn | 9780898716405 |
| language | English |
| lccn | 2007061749 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016462953 |
| oclc_num | 155757193 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-703 DE-91G DE-BY-TUM |
| physical | XXVIII, 219 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | SIAM, Soc. for Industrial and Applied Mathematics |
| record_format | marc |
| series | CBMS-NSF regional conference series in applied mathematics |
| series2 | CBMS-NSF regional conference series in applied mathematics |
| spelling | Chen, Zhangxin Verfasser aut Reservoir simulation mathematical techniques in oil recovery Zhangxin Chen Philadelphia, PA SIAM, Soc. for Industrial and Applied Mathematics 2007 XXVIII, 219 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier CBMS-NSF regional conference series in applied mathematics 77 Literaturverz. S. 205 - 213 Mecânica dos fluídos computacional larpcal Modelos matemáticos larpcal Simulação (métodos) larpcal Mathematisches Modell Oil reservoir engineering Mathematical models Oil reservoir engineering Simulation methods Porous materials Permeability Mathematical models Transport theory Mathematical models Erdöllagerstätte (DE-588)4125182-9 gnd rswk-swf Erdölgewinnung (DE-588)4139144-5 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Erdöllagerstätte (DE-588)4125182-9 s Erdölgewinnung (DE-588)4139144-5 s Simulation (DE-588)4055072-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 CBMS-NSF regional conference series in applied mathematics 77 (DE-604)BV000016696 77 http://www.loc.gov/catdir/enhancements/fy0805/2007061749-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0805/2007061749-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0805/2007061749-t.html Table of contents only Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016462953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Zhangxin Reservoir simulation mathematical techniques in oil recovery CBMS-NSF regional conference series in applied mathematics Mecânica dos fluídos computacional larpcal Modelos matemáticos larpcal Simulação (métodos) larpcal Mathematisches Modell Oil reservoir engineering Mathematical models Oil reservoir engineering Simulation methods Porous materials Permeability Mathematical models Transport theory Mathematical models Erdöllagerstätte (DE-588)4125182-9 gnd Erdölgewinnung (DE-588)4139144-5 gnd Simulation (DE-588)4055072-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4125182-9 (DE-588)4139144-5 (DE-588)4055072-2 (DE-588)4114528-8 |
| title | Reservoir simulation mathematical techniques in oil recovery |
| title_auth | Reservoir simulation mathematical techniques in oil recovery |
| title_exact_search | Reservoir simulation mathematical techniques in oil recovery |
| title_exact_search_txtP | Reservoir simulation mathematical techniques in oil recovery |
| title_full | Reservoir simulation mathematical techniques in oil recovery Zhangxin Chen |
| title_fullStr | Reservoir simulation mathematical techniques in oil recovery Zhangxin Chen |
| title_full_unstemmed | Reservoir simulation mathematical techniques in oil recovery Zhangxin Chen |
| title_short | Reservoir simulation |
| title_sort | reservoir simulation mathematical techniques in oil recovery |
| title_sub | mathematical techniques in oil recovery |
| topic | Mecânica dos fluídos computacional larpcal Modelos matemáticos larpcal Simulação (métodos) larpcal Mathematisches Modell Oil reservoir engineering Mathematical models Oil reservoir engineering Simulation methods Porous materials Permeability Mathematical models Transport theory Mathematical models Erdöllagerstätte (DE-588)4125182-9 gnd Erdölgewinnung (DE-588)4139144-5 gnd Simulation (DE-588)4055072-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mecânica dos fluídos computacional Modelos matemáticos Simulação (métodos) Mathematisches Modell Oil reservoir engineering Mathematical models Oil reservoir engineering Simulation methods Porous materials Permeability Mathematical models Transport theory Mathematical models Erdöllagerstätte Erdölgewinnung Simulation |
| url | http://www.loc.gov/catdir/enhancements/fy0805/2007061749-b.html http://www.loc.gov/catdir/enhancements/fy0805/2007061749-d.html http://www.loc.gov/catdir/enhancements/fy0805/2007061749-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016462953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016696 |
| work_keys_str_mv | AT chenzhangxin reservoirsimulationmathematicaltechniquesinoilrecovery |