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E-grāmata: Mathematics of Fluid Flow Through Porous Media

(University of Wyoming)
  • Formāts: PDF+DRM
  • Izdošanas datums: 27-May-2021
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9781119663867
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Mathematics of Fluid Flow Through Porous MediaPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 27-May-2021
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9781119663867
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"The book will fill a gap that has emerged as computational modeling has become a standard tool in porous media research. As the field has advanced, early-career researchers such as graduate students understandably gloss over some mathematical fundamentals to begin working on computational problems at the frontiers. The proposed book will furnish a pathway by which these researchers can efficiently acquire the fundamentals needed to become well-informed users and designers of computational models. The book will introduce several advanced techniques, such as the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis in a self-contained fashion that will be accessible to students who have not previously encountered these concepts. The author has taught a course based on this material four times to audiences that included graduate students from Mathematics, Civil Engineering, Petroleum Engineering, Soil Science, and Geophysics. The course has received highly favorablestudent reviews"--

Master the techniques necessary to build and use computational models of porous media fluid flow 

In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop and mathematically rigorous source of the foundational principles of porous medium flow modeling. The book shows readers how to design intelligent computation models for groundwater flow, contaminant transport, and petroleum reservoir simulation.  

Discussions of the mathematical fundamentals allow readers to prepare to work on computational problems at the frontiers of the field. Introducing several advanced techniques, including the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis, The Mathematics of Fluid Flow Through Porous Media is an indispensable resource for students who have not previously encountered these concepts and need to master them to conduct computer simulations. 

Teaching mastery of a subject that has increasingly become a standard tool for engineers and applied mathematicians, and containing 75 exercises suitable for self-study or as part of a formal course, the book also includes: 

  • A thorough introduction to the mechanics of fluid flow in porous media, including the kinematics of simple continua, single-continuum balance laws, and constitutive relationships 
  • An exploration of single-fluid flows in porous media, including Darcy’s Law, non-Darcy flows, the single-phase flow equation, areal flows, and flows with wells 
  • Practical discussions of solute transport, including the transport equation, hydrodynamic dispersion, one-dimensional transport, and transport with adsorption 
  • A treatment of multiphase flows, including capillarity at the micro- and macroscale 

Perfect for graduate students in mathematics, civil engineering, petroleum engineering, soil science, and geophysics, The Mathematics of Fluid Flow Through Porous Media also belongs on the bookshelves of any researcher who wishes to extend their research into areas involving flows in porous media. 

Preface xi
1 Introduction
1(6)
1.1 Historical Setting
1(1)
1.2 Partial Differential Equations (PDEs)
2(2)
1.3 Dimensions and Units
4(1)
1.4 Limitations in Scope
5(2)
2 Mechanics
7(26)
2.1 Kinematics of Simple Continua
7(3)
2.1.1 Referential and Spatial Coordinates
7(2)
2.1.2 Velocity and the Material Derivative
9(1)
2.2 Balance Laws for Simple Continua
10(6)
2.2.1 Mass Balance
11(2)
2.2.2 Momentum Balance
13(3)
2.3 Constitutive Relationships
16(4)
2.3.1 Body Force
17(1)
2.3.2 Stress in Fluids
17(2)
2.3.3 The Navier-Stokes Equation
19(1)
2.4 Two Classic Problems in Fluid Mechanics
20(4)
2.4.1 Hagen-Poiseuille Flow
21(2)
2.4.2 The Stokes Problem
23(1)
2.5 Multiconstituent Continua
24(9)
2.5.1 Constituents
25(1)
2.5.2 Densities and Volume Fractions
26(3)
2.5.3 Multiconstituent Mass Balance
29(1)
2.5.4 Multiconstituent Momentum Balance
30(3)
3 Single-fluid Flow Equations
33(34)
3.1 Darcy's Law
33(6)
3.1.1 Fluid Momentum Balance
34(1)
3.1.2 Constitutive Laws for the Fluid
35(2)
3.1.3 Filtration Velocity
37(1)
3.1.4 Permeability
38(1)
3.2 Non-Darcy Flows
39(3)
3.2.1 The Brinkman Law
39(1)
3.2.2 The Forchheimer Equation
40(1)
3.2.3 The Klinkenberg Effect
41(1)
3.3 The Single-fluid Flow Equation
42(2)
3.3.1 Fluid Compressibility and Storage
43(1)
3.3.2 Combining Darcy's Law and the Mass Balance
44(1)
3.4 Potential Form of the Flow Equation
44(7)
3.4.1 Conditions for the Existence of a Potential
45(1)
3.4.2 Calculating the Scalar Potential
46(1)
3.4.3 Piezometric Head
47(1)
3.4.4 Head-Based Flow Equation
48(1)
3.4.5 Auxiliary Conditions for the Flow Equation
49(2)
3.5 Areal Flow Equation
51(4)
3.5.1 Vertically Averaged Mass Balance
52(2)
3.5.2 Vertically Averaged Darcy's Law
54(1)
3.6 Variational Forms for Steady Flow
55(3)
3.6.1 Standard Variational Form
55(2)
3.6.2 Mixed Variational Form
57(1)
3.7 Flow in Anisotropic Porous Media
58(9)
3.7.1 The Permeability Tensor
58(1)
3.7.2 Matrix Representations of the Permeability Tensor
59(2)
3.7.3 Isotropy and Homogeneity
61(1)
3.7.4 Properties of the Permeability Tensor
62(2)
3.7.5 Is Permeability Symmetric?
64(3)
4 Single-fluid Flow Problems
67(28)
4.1 Steady Areal Flows with Wells
67(8)
4.1.1 The Dupuit-Thiem Model
67(3)
4.1.2 Dirac S Models
70(3)
4.1.3 Areal Flow in an Infinite Aquifer with One Well
73(2)
4.2 The Theis Model for Transient Flows
75(9)
4.2.1 Model Formulation
75(1)
4.2.2 Dimensional Analysis of the Theis Model
76(3)
4.2.3 The Theis Drawdown Solution
79(1)
4.2.4 Solving the Theis Model via Similarity Methods
80(4)
4.3 Boussinesq and Porous Medium Equations
84(11)
4.3.1 Derivation of the Boussinesq Equation
86(2)
4.3.2 The Porous Medium Equation
88(1)
4.3.3 A Model Problem with a Self-similar Solution
89(6)
5 Solute Transport
95(26)
5.1 The Transport Equation
95(5)
5.1.1 Mass Balance of Miscible Species
96(1)
5.1.2 Hydrodynamic Dispersion
97(3)
5.2 One-Dimensional Advection
100(6)
5.2.1 Pure Advection and the Method of Characteristics
101(2)
5.2.2 Auxiliary Conditions for First-Order PDEs
103(1)
5.2.3 Weak Solutions
104(2)
5.3 The Advection-Diffusion Equation
106(5)
5.3.1 The Moving Plume Problem
106(2)
5.3.2 The Moving Front Problem
108(3)
5.4 Transport with Adsorption
111(10)
5.4.1 Mass Balance for Adsorbate
112(1)
5.4.2 Linear Isotherms and Retardation
113(1)
5.4.3 Concave-down Isotherms and Front Sharpening
114(2)
5.4.4 The Rankine-Hugoniot Condition
116(5)
6 Multifluid Flows
121(46)
6.1 Capillarity
122(7)
6.1.1 Physics of Curved Interfaces
122(3)
6.1.2 Wettability
125(2)
6.1.3 Capillarity at the Macroscale
127(2)
6.2 Variably Saturated Flow
129(5)
6.2.1 Pressure Head and Moisture Content
129(2)
6.2.2 The Richards Equation
131(1)
6.2.3 Alternative Forms of the Richards Equation
132(1)
6.2.4 Wetting Fronts
133(1)
6.3 Two-fluid Flows
134(5)
6.3.1 The Muskat-Meres Model
134(2)
6.3.2 Two-fluid Flow Equations
136(1)
6.3.3 Classification of Simplified Flow Equations
137(2)
6.4 The Buckley-Leverett Problem
139(10)
6.4.1 The Saturation Equation
139(2)
6.4.2 Welge Tangent Construction
141(5)
6.4.3 Conservation Form
146(1)
6.4.4 Analysis of Oil Recovery
146(3)
6.5 Viscous Fingering
149(5)
6.5.1 The Displacement Front and Its Perturbation
150(2)
6.5.2 Dynamics of the Displacement Front
152(1)
6.5.3 Stability of the Displacement Front
153(1)
6.6 Three-fluid Flows
154(4)
6.6.1 Flow Equations
156(1)
6.6.2 Rock-fluid Properties
157(1)
6.7 Three-fluid Fractional Flow Analysis
158(9)
6.7.1 A Simplified Three-fluid System
159(1)
6.7.2 Classification of the Three-fluid System
160(2)
6.7.3 Saturation Velocities and Saturation Paths
162(2)
6.7.4 An Example of Three-fluid Displacement
164(3)
7 FLows With Mass Exchange
167(14)
7.1 General Compositional Equations
168(4)
7.1.1 Constituents, Species, and Phases
168(1)
7.1.2 Mass Balance Equations
169(1)
7.1.3 Species Flow Equations
170(2)
7.2 Black-oil Models
172(3)
7.2.1 Reservoir and Stock-tank Conditions
172(1)
7.2.2 The Black-oil Equations
173(2)
7.3 Compositional Flows in Porous Media
175(3)
7.3.1 A Simplified Compositional Formulation
175(1)
7.3.2 Conversion to Molar Variables
176(2)
7.4 Fluid-phase Thermodynamics
178(3)
7.4.1 Flash Calculations
178(1)
7.4.2 Equation-of-state Methods
179(2)
Appendix A Dedicated Symbols
181(2)
Appendix B Useful Curvilinear Coordinates
183(6)
B.1 Polar Coordinates
183(1)
B.2 Cylindrical Coordinates
184(2)
B.3 Spherical Coordinates
186(3)
Appendix C The Buckingham Pi Theorem
189(4)
C.1 Physical Dimensions and Units
189(1)
C.2 The Buckingham Theorem
190(3)
Appendix D Surface Integrals
193(4)
D.1 Definition of a Surface Integral
193(1)
D.2 The Stokes Theorem
194(1)
D.3 A Corollary to the Stokes Theorem
195(2)
Bibliography 197(10)
Index 207
Myron B. Allen, is Professor Emeritus of Mathematics at the University of Wyoming in Laramie, Wyoming, USA. He is the author of Continuum Mechanics: The Birthplace of Mathematical Models and co-author of the first and second editions of Numerical Analysis for Applied Science.
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