Flow and transport in porous media and fractured rock: from classical methods to modern approaches
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Weinheim [u.a.]
VCH
1995
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 428 - 477 |
| Beschreibung: | XIV, 482 S. Ill., graph. Darst. |
| ISBN: | 3527292608 |
Internformat
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| 100 | 1 | |a Sahimi, Muhammad |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Flow and transport in porous media and fractured rock |b from classical methods to modern approaches |c Muhammad Sahimi |
| 264 | 1 | |a Weinheim [u.a.] |b VCH |c 1995 | |
| 300 | |a XIV, 482 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Groundwater flow |x Mathematical models | |
| 650 | 4 | |a Porous materials |x Mathematical models | |
| 650 | 4 | |a Rocks |x Permeability |x Mathematical models | |
| 650 | 4 | |a Transport theory |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804124365498875904 |
|---|---|
| adam_text | Contents
Preface vii
Chapter 1: Continuum versus Discrete Models 1
1.0 Introduction ............................. 1
1.1 A hierarchy of heterogeneities and length scales.......... 2
1.2 Long-range correlations, fractals and percolation......... 3
1.3 Continuum versus discrete models................. 5
1.4 Summary............................... 7
Chapter 2: The Equations of Change 8
2.0 Introduction ............................. 8
2.1 The equation of continuity ..................... 8
2.2 The momentum equation...................... 9
2.3 The diffusion and convective-diffusion equations.......... 10
Chapter 3: Fractal Concepts and Percolation Theory 12
3.0 Introduction ............................. 12
3.1 Box-counting method and self-similar fractals........... 13
3.2 Self-affine fractals .......................... 16
3.3 Multifractal systems......................... 16
3.4 Fractional Brownian motion and long-range correlations..... 18
3.5 Percolation processes......................... 21
3.5.1 Bond and site percolation.................. 22
3.5.2 Computer simulation of percolation on a network..... 24
3.5.3 Characterization of a percolation system.......... 25
3.5.4 Scaling theory of percolation processes........... 27
3.5.5 Formation of fractal structures in percolation systems ... 29
3.5.6 Percolation in finite systems and finite-size scaling..... 30
3.5.7 Percolation in random networks and in continua...... 31
3.6 A glance at history.......................... 33
3.7 Conclusions.............................. 35
X Contents
Chapter 4: Diagenetic Processes and Formation of Rock 36
4.0 Introduction............................. 36
4.1 Diagenetic and metasomatic processes............... 36
4.2 Continuum models of diagenetic processes............. 38
4.3 Geometrical models of diagenetic processes in granular rock ... 45
4.4 A geometrical model of carbonate rock............... 47
4.5 Diagenetic processes of fractured rock............... 49
4.6 Conclusions.............................. 50
Chapter 5: Morphology of Porous Media and Fractured Rock 52
5.0 Introduction............................. 52
5.1 Porosity, specific surface area and tortuosity............ 52
5.2 Fluid saturation, capillary pressure, and contact angle...... 53
5.3 Pore size distribution ........................ 56
5.3.1 Mercury porosimetry, network simulation and percolation 57
5.3.2 Sorption isotherms and percolation............. 73
5.3.3 Small-angle scattering.................... 77
5.3.4 Nuclear magnetic resonance................. 79
5.4 Topological properties of porous media............... 82
5.5 Fractal properties of porous media................. 88
5.5.1 Adsorption methods ..................... 88
5.5.2 Chord-length measurements................. 90
5.5.3 Correlation function method................. 95
5.5.4 Small-angle scattering methods............... 98
5.5.5 Spectral method ....................... 101
5.6 Porosity and pore size distribution of fractal porous media .... 103
5.7 Morphology of fractured rocks ................... 103
5.8 Conclusions.............................. Ill
Chapter 6: Models of Porous Media 112
6.0 Introduction ............................. 112
6.1 Models of macroscopic porous media................ 112
6.1.1 One-dimensional models................... 113
6.1.2 Spatially-periodic models................... 113
6.1.3 Bethe lattice models..................... 116
6.1.4 Network models........................ 117
6.1.5 Continuum models...................... 120
6.2 Models of pore surface roughness.................. 123
6.3 Models of megascopic porous media................ 127
6.3.1 Random hydraulic conductivity models........... 128
6.3.2 Fractal models ........................ 129
6.3.3 Multifractal models...................... 130
6.4 Interpolation schemes and conditional simulation......... 132
6.5 Conclusions.............................. 134
Contents XI
Chapter 7: Models of Fractured Rock 135
7.0 Introduction............................. 135
7.1 Continuum approach: The multi-porosity models......... 135
7.2 Network models........................... 137
7.2.1 Two-dimensional fracture networks............. 137
7.2.2 Three-dimensional fracture networks............ 141
7.2.3 Continuum representation of fracture networks....... 142
7.2.4 Percolation properties of fracture networks ........ 144
7.3 Simulated annealing model..................... 145
7.4 Synthetic fractal models....................... 147
7.5 Mechanical fracture models..................... 150
7.6 Conclusions.............................. 157
Chapter 8: Flow and Transport in Porous Media 158
8.0 Introduction............................. 158
8.1 The volume-averaging method and derivation of Darcy s law . . . 158
8.2 The Brinkman and Forchheimer equations............. 161
8.3 Predicting the permeability, conductivity and diffusivity..... 162
8.3.1 Continuum models: Exact results and rigorous bounds . . 163
8.3.2 Continuum models: Field-theoretic and perturbation meth-
ods ............................... 167
8.3.3 Exact formulation and effective-medium approximations . 169
8.3.4 Position-space renormalization group methods....... 180
8.3.5 Renormalized effective-medium approximation....... 186
8.3.6 The Bethe lattice model................... 187
8.3.7 Critical path analysis..................... 189
8.3.8 Transfer matrix method................... 194
8.3.9 Random walk methods ................... 196
8.3.10 Network simulation ..................... 200
8.4 Fractal transport and non-local formulation of diffusion ..... 201
8.5 Derivation of Archie s law...................... 205
8.6 Relation between permeability and electrical conductivity .... 209
8.7 Relation between permeability and nuclear magnetic resonance . 210
8.8 Dynamic permeability........................ 212
8.9 Conclusions.............................. 213
Chapter 9: Dispersion in Porous Media 215
9.0 Introduction............................. 215
9.1 The phenomenon of dispersion................... 215
9.2 Mechanisms of dispersion processes................. 216
9.3 The convective-diffusion equation.................. 217
9.4 Measurement of dispersion coefficients............... 218
9.5 Dispersion in simple systems.................... 220
9.5.1 Dispersion in a capillary tube................ 222
XII Contents
9.5.2 Dispersion in spatially-periodic models of porous media . . 223
9.6 Dependence of dispersion coefficients on the Péclet number . . . 224
9.7 Models of dispersion in macroscopic porous media........ 227
9.7.1 Continuum models: The volume-averaging method .... 227
9.7.2 Continuum models: Statistical-kinetic approach...... 229
9.7.3. Continuum models: Fluid-mechanical models........ 230
9.7.4 Network models....................... 233
9.8 Long-time tails: Dead-end pores versus disorder.......... 235
9.9 Dispersion in short porous media.................. 237
9.10 Dispersion in porous media with percolation disorder....... 239
9.11 Dispersion in megascopic porous media .............. 246
9.11.1 Continuum models: Large-scale volume-averaging..... 248
9.11.2 Continuum models: Stochastic-spectral methods...... 249
9.11.3 Discrete models and Monte Carlo methods ........ 252
9.11.4 Fractal models........................ 253
9.11.5 Long-range correlated percolation model.......... 255
9.12 Dispersion in stratified porous media................ 259
9.13 Conclusions.............................. 260
Chapter 10: Flow and Dispersion in Fractured Rock 261
10.0 Introduction............................. 261
10.1 Flow in a single fracture: Continuum and discrete models .... 262
10.2 Flow in fractured rock........................ 263
10.2.1 Continuum approach: The multi-porosity models..... 264
10.2.2 Network models: Exact formulation and EMAs...... 269
10.2.3 Anisotropie EMA and the permeability of fracture networks279
10.3 Dispersion in a single fracture.................... 282
10.4 Dispersion in fractured rock..................... 283
10.5 Conclusions.............................. 286
Chapter 11: Miscible Displacements 287
11.0 Introduction............................. 287
11.1 Factors affecting miscible displacement processes......... 288
11.2 Viscous fingering........................... 290
11.3 Continuum models of miscible displacements in Hele-Shaw cells . 292
11.4 Continuum models of miscible displacements in porous media . . 299
11.4.1 Numerical simulation of miscible displacements in porous
media............................. 305
11.4.2 Stability analysis of miscible displacements........ 305
11.5 Discrete models of miscible displacements............. 310
11.5.1 Diffusion-limited aggregation models............ 311
11.5.2 The dielectric breakdown model .............. 314
11.5.3 The gradient-governed growth model............ 315
11.5.4 The two-walker model.................... 315
Contents XIII
11.5.5 Probabilistic models..................... 316
11.5.6 Deterministic network models................ 320
11.6 Crossover from fractal to compact displacement.......... 322
11.7 Miscible displacements in megascopic porous media........ 324
11.8 Conclusions.............................. 325
Chapter 12: Immiscible Displacements and Multiphase Flows 327
12.0 Introduction............................. 327
12.1 Wettability, contact angles and their measurement........ 327
12.1.1 Sessile drop method..................... 329
12.1.2 Amott method........................ 330
12.1.3 U.S. Bureau of Mines method................ 331
12.2 The effect of surface roughness on contact angles......... 331
12.3 Dependence of dynamic contact angle and capillary pressure on
capillary number........................... 332
12.4 Fluids on fractal surfaces: Hypodiffusion and hyperdiffusion . . . 334
12.5 Effect of wettability on capillary pressure............. 336
12.6 Immiscible displacement processes................. 339
12.6.1 Spontaneous imbibition................... 342
12.6.2 Quasi-static imbibition ................... 342
12.6.3 Imbibition at constant flow rates.............. 343
12.6.4 Dynamic invasion at constant flow rates.......... 344
12.6.5 Trapping of blobs ...................... 344
12.6.6 Displacement of blobs: Choke-off and pinch-off...... 346
12.7 Models of two-phase flow and displacement............ 348
12.7.1 Continuum equations and relative permeabilities..... 349
12.7.2 Measurement of relative permeability ........... 350
12.7.3 The effect of wettability on relative permeability..... 351
12.7.4 Fractional flows and the Buckley-Leverett equation .... 352
12.8 Discrete models of capillary-controlled two-phase flow ...... 355
12.8.1 Random-percolation models................. 356
12.8.2 Random site-correlated bond percolation models..... 359
12.8.3 Invasion percolation..................... 359
12.8.4 Random percolation with trapping............. 362
12.9 Crossover from fractal to compact displacement.......... 364
12.10 Pinning of an interface: Dynamic scaling of rough surfaces .... 366
12.11 Finite-size effects and Devil s staircase............... 370
12.12 Displacement under the influence of gravity: Gradient percolation 372
12.14 Dispersion in two-phase flows.................... 373
12.13 A phase diagram for displacement processes............ 376
12.15 Scaling laws for relative permeability and dispersion coefficients . 377
12.16 Network models of immiscible displacements at finite capillary
numbers................................ 378
12.18 Two-phase flow in megascopic and stratified rock......... 385
XIV Contents
12.18.1 Continuum models and large-scale averaging .......386
12.19 Two-phase flow in fractured rock..................388
12.20 Conclusions..............................389
Chapter 13: Flow and Transport in Unconsolidated Porous Media390
13.0 Introduction.............................390
13.1 Morphology of random and regular packings of particles.....390
13.2 Flow and conduction in unconsolidated porous media.......394
13.2.1 Exact results.........................395
13.2.2 Experimental data, empirical correlations and numerical
simulation...........................400
13.3 Dispersion in unconsolidated porous media............402
13.4 Two-phase flow in unconsolidated porous media..........404
13.4.1 Countercurrent flows.....................405
13.4.2 Cocurrent downflows.....................407
13.4.3 Cocurrent upflows......................407
13.5 Modelling two-phase flows in unconsolidated porous media .... 409
13.5.1 Continuum models......................409
13.5.2 Network models.......................411
13.6 Conclusions..............................414
Chapter 14: Advances in Computational Methods 415
14.0 Introduction.............................415
14.1 Finite-difference methods......................416
14.2 Lattice-gas simulation of fluid flow.................419
14.3 Lattice-Boltzmann simulation of fluid flow.............422
14.4 LGA and LBA simulation of single-phase flow in porous media . 424
14.5 LG and LB simulation of two-phase flow in porous media .... 426
14.6 Conclusions..............................427
References 428
Index 478
|
| any_adam_object | 1 |
| author | Sahimi, Muhammad |
| author_facet | Sahimi, Muhammad |
| author_role | aut |
| author_sort | Sahimi, Muhammad |
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| ctrlnum | (OCoLC)32049710 (DE-599)BVBBV009990356 |
| dewey-full | 530.4/15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/15 |
| dewey-search | 530.4/15 |
| dewey-sort | 3530.4 215 |
| dewey-tens | 530 - Physics |
| discipline | Geowissenschaften Physik |
| format | Book |
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| id | DE-604.BV009990356 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:44:30Z |
| institution | BVB |
| isbn | 3527292608 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006621779 |
| oclc_num | 32049710 |
| open_access_boolean | |
| owner | DE-29T DE-29 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-20 DE-703 DE-92 DE-12 DE-706 DE-634 DE-83 DE-188 |
| owner_facet | DE-29T DE-29 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-20 DE-703 DE-92 DE-12 DE-706 DE-634 DE-83 DE-188 |
| physical | XIV, 482 S. Ill., graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | VCH |
| record_format | marc |
| spelling | Sahimi, Muhammad Verfasser aut Flow and transport in porous media and fractured rock from classical methods to modern approaches Muhammad Sahimi Weinheim [u.a.] VCH 1995 XIV, 482 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 428 - 477 Eau souterraine - Écoulement - Modèles mathématiques Eaux souterraines - Écoulement - Modèles mathématiques ram Matériaux poreux - Fluides, Dynamique des - Modèles mathématiques Matériaux poreux - Modèles mathématiques ram Mecanica e dinamica dos fluidos larpcal Roches - Perméabilité - Modèles mathématiques Roches - Perméabilité - Modèles mathématiques ram Transport, Théorie du - Modèles mathématiques Transport, Théorie du - Modèles mathématiques ram dynamique fluide inriac matériau poreux inriac milieu poreux inriac mécanique rupture inriac mécanique sol inriac simulation inriac théorie transport inriac Mathematisches Modell Groundwater flow Mathematical models Porous materials Mathematical models Rocks Permeability Mathematical models Transport theory Mathematical models Bruchtektonik (DE-588)4146728-0 gnd rswk-swf Poröser Stoff (DE-588)4046811-2 gnd rswk-swf Strömung (DE-588)4058076-3 gnd rswk-swf Gestein (DE-588)4020734-1 gnd rswk-swf Gestein (DE-588)4020734-1 s Bruchtektonik (DE-588)4146728-0 s Strömung (DE-588)4058076-3 s DE-604 Poröser Stoff (DE-588)4046811-2 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006621779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sahimi, Muhammad Flow and transport in porous media and fractured rock from classical methods to modern approaches Eau souterraine - Écoulement - Modèles mathématiques Eaux souterraines - Écoulement - Modèles mathématiques ram Matériaux poreux - Fluides, Dynamique des - Modèles mathématiques Matériaux poreux - Modèles mathématiques ram Mecanica e dinamica dos fluidos larpcal Roches - Perméabilité - Modèles mathématiques Roches - Perméabilité - Modèles mathématiques ram Transport, Théorie du - Modèles mathématiques Transport, Théorie du - Modèles mathématiques ram dynamique fluide inriac matériau poreux inriac milieu poreux inriac mécanique rupture inriac mécanique sol inriac simulation inriac théorie transport inriac Mathematisches Modell Groundwater flow Mathematical models Porous materials Mathematical models Rocks Permeability Mathematical models Transport theory Mathematical models Bruchtektonik (DE-588)4146728-0 gnd Poröser Stoff (DE-588)4046811-2 gnd Strömung (DE-588)4058076-3 gnd Gestein (DE-588)4020734-1 gnd |
| subject_GND | (DE-588)4146728-0 (DE-588)4046811-2 (DE-588)4058076-3 (DE-588)4020734-1 |
| title | Flow and transport in porous media and fractured rock from classical methods to modern approaches |
| title_auth | Flow and transport in porous media and fractured rock from classical methods to modern approaches |
| title_exact_search | Flow and transport in porous media and fractured rock from classical methods to modern approaches |
| title_full | Flow and transport in porous media and fractured rock from classical methods to modern approaches Muhammad Sahimi |
| title_fullStr | Flow and transport in porous media and fractured rock from classical methods to modern approaches Muhammad Sahimi |
| title_full_unstemmed | Flow and transport in porous media and fractured rock from classical methods to modern approaches Muhammad Sahimi |
| title_short | Flow and transport in porous media and fractured rock |
| title_sort | flow and transport in porous media and fractured rock from classical methods to modern approaches |
| title_sub | from classical methods to modern approaches |
| topic | Eau souterraine - Écoulement - Modèles mathématiques Eaux souterraines - Écoulement - Modèles mathématiques ram Matériaux poreux - Fluides, Dynamique des - Modèles mathématiques Matériaux poreux - Modèles mathématiques ram Mecanica e dinamica dos fluidos larpcal Roches - Perméabilité - Modèles mathématiques Roches - Perméabilité - Modèles mathématiques ram Transport, Théorie du - Modèles mathématiques Transport, Théorie du - Modèles mathématiques ram dynamique fluide inriac matériau poreux inriac milieu poreux inriac mécanique rupture inriac mécanique sol inriac simulation inriac théorie transport inriac Mathematisches Modell Groundwater flow Mathematical models Porous materials Mathematical models Rocks Permeability Mathematical models Transport theory Mathematical models Bruchtektonik (DE-588)4146728-0 gnd Poröser Stoff (DE-588)4046811-2 gnd Strömung (DE-588)4058076-3 gnd Gestein (DE-588)4020734-1 gnd |
| topic_facet | Eau souterraine - Écoulement - Modèles mathématiques Eaux souterraines - Écoulement - Modèles mathématiques Matériaux poreux - Fluides, Dynamique des - Modèles mathématiques Matériaux poreux - Modèles mathématiques Mecanica e dinamica dos fluidos Roches - Perméabilité - Modèles mathématiques Transport, Théorie du - Modèles mathématiques dynamique fluide matériau poreux milieu poreux mécanique rupture mécanique sol simulation théorie transport Mathematisches Modell Groundwater flow Mathematical models Porous materials Mathematical models Rocks Permeability Mathematical models Transport theory Mathematical models Bruchtektonik Poröser Stoff Strömung Gestein |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006621779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sahimimuhammad flowandtransportinporousmediaandfracturedrockfromclassicalmethodstomodernapproaches |