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Mathematical and Numerical Modeling in Porous Media: Applications in Geosciences [Kõva köide]

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  • Formaat: Hardback, 370 pages, kõrgus x laius: 246x174 mm, kaal: 902 g
  • Sari: Multiphysics Modeling
  • Ilmumisaeg: 24-Jul-2012
  • Kirjastus: CRC Press
  • ISBN-10: 041566537X
  • ISBN-13: 9780415665377
Teised raamatud teemal:
Mathematical and Numerical Modeling in Porous Media: Applications in GeosciencesSuurem pilt
  • Formaat: Hardback, 370 pages, kõrgus x laius: 246x174 mm, kaal: 902 g
  • Sari: Multiphysics Modeling
  • Ilmumisaeg: 24-Jul-2012
  • Kirjastus: CRC Press
  • ISBN-10: 041566537X
  • ISBN-13: 9780415665377
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780415665377.html
Märksõnad:
"This volume presents a collection of prominent research contributions on applications of physics of porous media in Geosciences selected from two recent international workshops providing a state of the art on mathematical and numerical modeling in Enhanced Oil Recovery, Transport, Flow, Waves, Geostatistics and Geomechanics. The subject matters are of general interest for the porous media community, in particular to those seeking quantitative understanding of the physics of phenomena with its Mathematical Model and its subsequent solution through Numerical Methods"--

Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete understanding of the physical processes involved in fluid flow and transport. This fact can be attributed to the complexity of the phenomena which include multicomponent fluids, multiphasic flow and rock-fluid interactions. Since its formulation in 1856, Darcy’s law has been generalized to describe multi-phase compressible fluid flow through anisotropic and heterogeneous porous and fractured rocks. Due to the scarcity of information, a high degree of uncertainty on the porous medium properties is commonly present. Contributions to the knowledge of modeling flow and transport, as well as to the characterization of porous media at field scale are of great relevance. This book addresses several of these issues, treated with a variety of methodologies grouped into four parts:

I Fundamental concepts
II Flow and transport
III Statistical and stochastic characterization
IV Waves

The problems analyzed in this book cover diverse length scales that range from small rock samples to field-size porous formations. They belong to the most active areas of research in porous media with applications in geosciences developed by diverse authors.

This book was written for a broad audience with a prior and basic knowledge of porous media. The book is addressed to a wide readership, and it will be useful not only as an authoritative textbook for undergraduate and graduate students but also as a reference source for professionals including geoscientists, hydrogeologists, geophysicists, engineers, applied mathematicians and others working on porous media.

About the book series vii
Editorial board of the book series ix
Preface xxi
Acknowledgements xxiii
About the editors xxv
Contributors xxvii
Section 1 Fundamental concepts
1 Relative permeability
3(24)
T.J.T. Spanos
1.1 Introduction
3(1)
1.2 Darcy's equation
4(2)
1.3 Heterogeneity
6(3)
1.4 Lubrication theory
9(2)
1.5 Multiphase flow in porous media
11(4)
1.6 Dispersion
15(5)
1.7 Few comments about the associated thermodynamics
20(1)
1.8 Conclusions
20(7)
1.A Appendix
20(1)
1.A.1 Solid properties
20(2)
1.A.2 Fluid properties
22(1)
1.A.3 Reciprocity
22(3)
References
25(2)
2 From upscaling techniques to hybrid models
27(26)
I. Battiato
D.M. Tartakovsky
2.1 Introduction
27(1)
2.2 From first principles to effective equations
28(4)
2.2.1 Classification of upscaling methods
28(1)
2.2.2 Flow: From Stokes to Darcy/Brinkman equations
29(1)
2.2.3 Transport: From advection-diffusion to advection-dispersion equation
30(2)
2.3 Applicability range of macroscopic models for reactive systems
32(6)
2.3.1 Diffusion-reaction equations: mixing-induced precipitation processes
32(1)
2.3.2 Preliminaries
33(1)
2.3.3 Upscaling via volume averaging
34(2)
2.3.4 Advection-diffusion-reaction equation
36(2)
2.4 Hybrid models for transport in porous media
38(10)
2.4.1 Intrusive hybrid algorithm
38(3)
2.4.2 Taylor dispersion in a fracture with reactive walls
41(1)
2.4.3 Hybrid algorithm
42(1)
2.4.4 Numerical results
43(1)
2.4.5 Non-intrusive hybrid algorithm
44(4)
2.5 Conclusions
48(5)
References
49(4)
3 A tensorial formulation in four dimensions of thermoporoelastic phenomena
53(12)
M.C. Suarez Arriaga
3.1 Introduction
53(1)
3.2 Theoretical and experimental background
53(2)
3.3 Model of isothermal poroelasticity
55(2)
3.4 Thermoporoelasticity model
57(1)
3.5 Dynamic poroelastic equations
58(1)
3.6 The finite element method in the solution of the thermoporoelastic equations
58(1)
3.7 Solution of the model for particular cases
58(1)
3.8 Discussion of results
59(2)
3.9 Conclusions
61(4)
References
62(3)
Section 2 Flow and transport
4 New method for estimation of physical parameters in oil reservoirs by using tracer test flow models in Laplace space
65(14)
J. Ramirez-Sabag
O.C. Valdiviezo-Mijangos
M. Coronado
4.1 Introduction
65(1)
4.2 Numerical laplace transformation of sample data
65(3)
4.3 The laplace domain optimization procedure
68(1)
4.4 The real domain optimization procedure
68(1)
4.5 The optimization method
68(1)
4.6 The validation procedure
69(4)
4.6.1 Employed mathematical models
69(1)
4.6.2 Generation of synthetic data
70(1)
4.6.3 Result with synthetic data
70(3)
4.7 Reservoir data cases
73(3)
4.7.1 A homogeneous reservoir (Loma Alta Sur
73(1)
4.7.2 A fractured reservoir (Wairakei field
74(2)
4.8 Summary and concluding remarks
76(3)
References
76(3)
5 Dynamic porosity and permeability modification due to microbial growth using a coupled flow and transport model in porous media
79(18)
M.A. Diaz-Viera
A. Moctezuma-Berthier
5.1 Introduction
79(1)
5.2 The flow and transport model
80(5)
5.2.1 Conceptual model
80(1)
5.2.2 Mathematical model
81(3)
5.2.3 Numerical model
84(1)
5.2.4 Computational model
85(1)
5.3 Numerical simulations
85(7)
5.3.1 Reference study case description: a waterflooding test in a core
85(1)
5.3.2 Modeling of secondary recovery by water injection
86(2)
5.3.3 Modeling of enhanced recovery by water injection with microorganisms and nutrients
88(2)
5.3.4 Porosity and permeability modification due to microbial activity
90(2)
5.4 Final remarks
92(5)
References
95(2)
6 Inter-well tracer test models for underground formations having conductive faults: development of a numerical model and comparison against analytical models
97(16)
M. Coronado
J. Ramirez-Sabag
O. Valdiviezo-Mijangos
6.1 Introduction
97(1)
6.2 Description of the analytical models
98(5)
6.2.1 The closed fault model
99(2)
6.2.2 The open fault model
101(2)
6.3 The numerical model
103(3)
6.4 Numerical results
106(1)
6.5 Comparison of the analytical models against numerical simulations
107(3)
6.5.1 Injection-dominated flow case
108(1)
6.5.2 Fault-dominated flow case
108(1)
6.5.3 Closed fault case
109(1)
6.6 Summary and final conclusions
110(3)
References
111(2)
7 Volume average transport equations for in-situ combustion
113(20)
A.G. Vital-Ocampo
O. Cazarez-Candia
7.1 Introduction
113(1)
7.2 Study system
114(3)
7.2.1 Local mass, momentum and energy equations
115(1)
7.2.2 Jump conditions
115(2)
7.3 Average volume
117(1)
7.4 Average equations
118(2)
7.5 Physical model
120(1)
7.6 Equations for in-situ combustion
121(5)
7.7 Numerical solution
126(1)
7.8 Solution
126(2)
7.9 Results
128(2)
7.10 Conclusions
130(3)
7.A Appendix
131(1)
7.A.1 Oil vaporization
131(1)
References
131(2)
8 Biphasic isothermal tricomponent model to simulate advection-diffusion in 2D porous media
133(40)
A. Moctezuma-Berthier
8.1 Introduction
133(1)
8.2 Model description
133(36)
8.2.1 General considerations
133(1)
8.2.2 Mathematical model
134(5)
8.2.3 Numerical model
139(5)
8.2.4 Solution of the system
144(4)
8.2.5 Management of the partials derivatives
148(11)
8.2.6 Solution scheme
159(4)
8.2.7 Treating the boundary conditions
163(5)
8.2.8 Initial conditions for the fluid flow and the tracer systems
168(1)
8.3 Validation of biphasic flow system
169(1)
8.4 Conclusions
170(3)
References
170(3)
Section 3 Statistical and stochastic characterization
9 A 3D geostatistical model of Upper Jurassic Kimmeridgian facies distribution in Cantarell oil field, Mexico
173(22)
R. Casar-Gonzalez
M.A. Diaz-Viera
G. Murillo-Muneton
L. Velasquillo-Martinez
J. Garcia-Hernandez
E. Aguirre-Cerda
9.1 Introduction
173(2)
9.2 Methodological aspects of geological and petrophysical modeling
175(2)
9.2.1 The geological model
175(2)
9.2.2 The petrophysical model
177(1)
9.3 Conceptual geological model
177(6)
9.3.1 Geological setting
177(1)
9.3.2 Sedimentary model and stratigraphic framework
177(2)
9.3.3 The conceptual geological model definition
179(1)
9.3.4 Analysis of the structural sections
180(1)
9.3.5 Description of the stratigraphic correlation sections
181(1)
9.3.6 Lithofacies definition
181(2)
9.4 Geostatistical modeling
183(10)
9.4.1 Zone partition
183(1)
9.4.2 Stratigraphic grid definition
183(1)
9.4.3 CA facies classification
184(1)
9.4.4 Facies upscaling process
184(1)
9.4.5 Statistical analysis
184(5)
9.4.6 Geostatistical simulations
189(4)
9.5 Conclusions
193(2)
References
193(2)
10 Trivariate nonparametric dependence modeling of petrophysical properties
195(10)
A. Erdely
M.A. Diaz-Viera
V. Hernandez-Maldonado
10.1 Introduction
195(2)
10.1.1 The problem of modeling the complex dependence pattern between porosity and permeability in carbonate formations
195(1)
10.1.2 Trivariate copula and random variables dependence
196(1)
10.2 Trivariate data modeling
197(1)
10.3 Nonparametric regression
198(4)
10.4 Conclusions
202(3)
References
203(2)
11 Joint porosity-permeability stochastic simulation by non-parametric copulas
205(26)
V. Hernandez-Maldonado
M.A. Diaz-Viera
A. Erdely-Ruiz
11.1 Introduction
205(1)
11.2 Non-conditional stochastic simulation methodology by using Bernstein copulas
205(1)
11.3 Application of the methodology to perform a non-conditional simulation with simulated annealing using bivariate Bernstein copulas
206(12)
11.3.1 Modeling the petrophysical properties dependence pattern, using non-parametric copulas or Bernstein copulas
207(1)
11.3.2 Generating the seed or initial configuration for simulated annealing method, using the non-parametric simulation algorithm
208(2)
11.3.3 Defining the objective function
210(1)
11.3.4 Measuring the energy of the seed, according to the objective function
210(1)
11.3.5 Calculating the initial temperature, and the most suitable annealing schedule of simulated annealing method to carry out the simulation
211(2)
11.3.6 Performing the simulation
213(2)
11.3.7 Application of the methodology for stochastic simulation by bivariate Bernstein copulas to simulate a permeability (K.) profile A case of study
215(3)
11.4 Comparison of results using three different methods
218(9)
11.4.1 A single non-conditional simulation, and a median of 10 non-conditional simulations of permeability
219(2)
11.4.2 A single 10% conditional simulation, and a median of 10, 10% conditional simulations of permeability
221(3)
11.4.3 A single 50% conditional simulation, and a median of 10, 50% conditional simulations of permeability
224(2)
11.4.4 A single 90% conditional simulation, and a median of 10, 90% conditional simulations of permeability
226(1)
11.5 Conclusions
227(4)
References
229(2)
12 Stochastic simulation of a vuggy carbonate porous media
231(20)
R. Casar-Gonzalez
V. Suro-Perez
12.1 Introduction
231(1)
12.2 X-ray computed tomography (CT
231(2)
12.3 Exploratory data analysis of X-Ray computed tomography
233(1)
12.4 Transformation of the information from porosity values to indicator variable
233(2)
12.5 Spatial correlation modeling of the porous media
235(2)
12.6 Stochastic simulation of a vuggy carbonate porous media
237(1)
12.7 Simulation annealing multipoint of a vuggy carbonate porous media
238(2)
12.8 Simulation of continuous values of porosity in a vuggy carbonate porous medium
240(2)
12.9 Assigning permeability values based on porosity values
242(2)
12.10 Application example: effective permeability scaling procedure in vuggy carbonate porous media
244(2)
12.11 Scaling effective permeability with average power technique
246(1)
12.12 Scaling effective permeability with percolation model
246(2)
12.13 Conclusions and remarks
248(3)
References
248(3)
13 Stochastic modeling of spatial grain distribution in rock samples from terrigenous formations using the plurigaussian simulation method
251(16)
J. Mendez-Venegas
M.A. Diaz-Viera
13.1 Introduction
251(1)
13.2 Methodology
251(5)
13.2.1 Data image processing
252(1)
13.2.2 Geostatistical analysis
252(4)
13.3 Description of the data
256(3)
13.4 Geostatistical analysis
259(1)
13.4.1 Exploratory data analysis
259(1)
13.4.2 Variographic analysis
259(1)
13.5 Results
259(5)
13.6 Conclusions
264(3)
References
266(1)
14 Metadistances in prime numbers applied to integral equations and some examples of their possible use in porous media problems
267(22)
H. Ortiz-Tapia
14.1 Introduction
267(2)
14.1.1 Some reasons for choosing integral equation formulations
267(1)
14.1.2 Discretization of an integral equation with regular grids
267(1)
14.1.3 Solving an integral equation with MC or LDS
268(1)
14.2 Algorithms description
269(2)
14.2.1 Low discrepancy sequences
269(1)
14.2.2 Halton LDSs
269(1)
14.2.3 What is a "metadistance"
270(1)
14.2.4 Refinement of mds
271(1)
14.3 Numerical experiments
271(13)
14.3.1 Fredholm equations of the second kind in one integrable dimension
271(1)
14.3.2 Results in one dimension
272(1)
14.3.3 Choosing a problem in two dimensions
273(2)
14.3.4 Transformation of the original problem
275(2)
14.3.5 General numerical algorithm
277(1)
14.3.6 MC results, empirical reseating
278(1)
14.3.7 Halton results, empirical reseating
278(2)
14.3.8 MDs results, empirical rescaling
280(2)
14.3.9 MC results, systematic rescaling
282(1)
14.3.10 Halton results, systematic rescaling
282(1)
14.3.11 MDs results, systematic rescaling
282(1)
14.3.12 Accuracy goals
282(2)
14.3.13 Rate of convergence
284(1)
14.4 Conclusions
284(5)
References
284(5)
Section 4 Waves
15 On the physical meaning of slow shear waves within the viscosity-extended Biot framework
289(14)
T.M. Muller
P.N. Sahay
15.1 Introduction
289(1)
15.2 Review of the viscosity-extended biot framework
290(2)
15.2.1 Constitutive relations, complex phase velocities, and characteristic frequencies
290(2)
15.2.2 Properties of the slow shear wave
292(1)
15.3 Conversion scattering in randomly inhomogeneous media
292(3)
15.3.1 Effective wave number approach
292(2)
15.3.2 Attenuation and dispersion due to conversion scattering in the slow shear wave
294(1)
15.4 Physical interpretation of the slow shear wave conversion scattering process
295(3)
15.4.1 Slow shear conversion mechanism as a proxy for attenuation due to vorticity diffusion within the viscous boundary layer
295(2)
15.4.2 The slow shear wave conversion mechanism versus the dynamic permeability concept
297(1)
15.5 Conclusions
298(5)
15.A Appendix
299(1)
15.A.1 α and β matrices
299(1)
15.A.2 Inertial regime
300(1)
References
301(2)
16 Coupled porosity and saturation waves in porous media
303(32)
N. Udey
16.1 Introduction
303(1)
16.2 The governing equations
303(3)
16.2.1 Variables and definitions
303(1)
16.2.2 The equations of continuity
304(1)
16.2.3 The equations of motion
305(1)
16.2.4 The porosity and saturation equations
305(1)
16.3 Dilatational waves
306(7)
16.3.1 The Helmholtz decomposition
306(1)
16.3.2 The dilatational wave equations
307(2)
16.3.3 The dilatational wave operator matrix equation
309(2)
16.3.4 Wave operator trial solutions
311(2)
16.4 Porosity waves
313(3)
16.4.1 The porosity wave equation
313(2)
16.4.2 The dispersion relation
315(1)
16.4.3 Comparison with pressure diffusion
315(1)
16.5 Saturation waves
316(3)
16.5.1 The wave equations
317(2)
16.5.2 The dispersion relation
319(1)
16.6 Coupled porosity and saturation waves
319(5)
16.6.1 The dispersion relation
319(2)
16.6.2 Factorization of the dispersion relation
321(3)
16.7 A numerical illustration
324(7)
16.7.1 The porosity wave
324(3)
16.7.2 The saturation wave
327(4)
16.8 Conclusion
331(4)
References
332(3)
Subject index 335(4)
Book series page 339
Martin A. Diaz Viera, Pratap Sahay, Manuel Coronado, Arturo Ortiz Tapia