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E-raamat: Physical and Chemical Dissolution Front Instability in Porous Media: Theoretical Analyses and Computational Simulations

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Physical and Chemical Dissolution Front Instability in Porous Media: Theoretical Analyses and Computational SimulationsSuurem pilt
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This monograph provides state-of-the-art theoretical and computational findings from investigations on physical and chemical dissolution front instability problems in porous media, based on the author’s own work. Although numerical results are provided to complement theoretical ones, the focus of this monograph is on the theoretical aspects of the topic and those presented in this book are applicable to a wide range of scientific and engineering problems involving the instability of nonlinear dynamic systems. To appeal to a wider readership, common mathematical notations are used to derive the theoretical solutions. The book can be used either as a useful textbook for postgraduate students or as a valuable reference book for computational scientists, mathematicians, engineers and geoscientists.
1 Introduction 1(14)
1.1 Thermodynamic Instability
2(1)
1.2 Chemical Dynamic Instability
3(1)
1.3 Physical Surface (Including Dissolution Front) Instability
4(2)
1.4 The Contextual Arrangements of This Monograph
6(2)
References
8(7)
2 Fundamental Theory for Chemical Dissolution-Front Instability Problems in Fluid-Saturated Porous Media 15(34)
2.1 Mathematical Theory for Simulating Chemical Dissolution-Front Instability Problems in Fluid-Saturated Porous Media
17(13)
2.1.1 A General Case of Reactive Multi-Chemical-Species Transport with Consideration of Porosity/Permeability Feedback
17(2)
2.1.2 A Particular Case of Reactive Single-Chemical-Species Transport with Consideration of Porosity/Permeability Feedback
19(11)
2.2 Computational Theory for Simulating the Morphological Evolution of a Chemical Dissolution Front
30(6)
2.2.1 Formulation of the Segregated Algorithm for Simulating the Evolution of Chemical Dissolution Fronts
30(2)
2.2.2 Derivation of the Finite Element Equations of the Problem
32(4)
2.3 Verification of the Proposed Numerical Algorithm for Simulating the Evolution of Chemical Dissolution Fronts
36(6)
2.4 An Application Example for Simulating the Morphological Evolution of Chemical Dissolution Fronts
42(4)
References
46(3)
3 Effects of Particle Reactive Surface Areas on Chemical Dissolution-Front Instability in Fluid-Saturated Porous Media 49(22)
3.1 Theoretical Analysis of the Effect of Particle Shapes on Chemical Dissolution-Front Instability in Fluid-Saturated Porous Media
51(5)
3.2 Numerical Modeling of the Chemical Dissolution-Front Evolution Within Fluid-Saturated Porous Media Consisting of Different Particle Shapes
56(14)
References
70(1)
4 Effects of Mineral Dissolution Ratios on Chemical Dissolution-Front Instability in Fluid-Saturated Porous Media 71(22)
4.1 Theoretical Considerations of the Problem
72(5)
4.2 Numerical Simulation of the Problem
77(3)
4.3 Effects of Mineral Dissolution Ratios on the Evolution Patterns of Chemical Dissolution Fronts During Propagation in Fluid-Saturated Porous Media
80(10)
References
90(3)
5 Effects of Solute Dispersion on Chemical Dissolution-Front Instability in Fluid-Saturated Porous Media 93(30)
5.1 Mathematical Model for Chemical Dissolution-Front Instability Problems in Fluid-Saturated Porous Media Including Solute Dispersion Effects
95(3)
5.2 Theoretical Consideration of the Effects of Solute Dispersion on Chemical Dissolution-Front Instability in Two-Dimensional Fluid-Saturated Porous Media
98(14)
5.2.1 Derivation of Dimensionless Governing Equations for the Theoretical Problem
98(2)
5.2.2 Derivation of Base Solutions for the Dimensionless Governing Equations of the Theoretical Problem in the Limit Case of the Mineral Dissolution Ratio Approaching Zero
100(6)
5.2.3 Derivation of the Critical Condition for Unstable Chemical Dissolution-Fronts in Two-Dimensional Fluid-Saturated Porous Media Including Solute Dispersion Effects
106(5)
5.2.4 Theoretical Understanding of the Effects of Solute Dispersion on Chemical Dissolution-Front Instability in Two-Dimensional Fluid-Saturated Porous Media
111(1)
5.3 Application of the Present Theoretical Solutions
112(8)
References
120(3)
6 Effects of Medium Permeability Anisotropy on Chemical Dissolution-Front Instability in Fluid-Saturated Porous Media 123(28)
6.1 Mathematical Governing Equations for Chemical Dissolution-Front Instability Problems in Fluid-Saturated Porous Media Including Medium Anisotropy Effects
125(3)
6.2 Theoretical Analyses of Medium Permeability Anisotropy Effects
128(12)
6.2.1 Derivation of Dimensionless Governing Equations
129(1)
6.2.2 Derivation of Base Solutions for the Dimensionless Governing Equations of the Theoretical Problem Including the Consideration of Medium Orthotropic Effects (in the Case of s -> 0)
130(3)
6.2.3 Derivation of the Critical Condition for Unstable Chemical Dissolution-Fronts in Two-Dimensional Fluid-Saturated Porous Media Including Medium Orthotropic Effects (in the Case of e -> 0)
133(7)
6.3 Application of the Present Theoretical Solutions
140(9)
6.3.1 Theoretical Understanding of the Effects of Medium Permeability Anisotropy on Chemical Dissolution-Front Instability in Two-Dimensional Fluid-Saturated Porous Media
140(2)
6.3.2 Effects of Medium Permeability Anisotropy on the Morphological Evolution of the Chemical Dissolution Front in Two-Dimensional Fluid-Saturated Porous Media
142(7)
References
149(2)
7 Effects of Medium and Pore-Fluid Compressibility on Chemical Dissolution-Front Instability in Fluid-Saturated Porous Media 151(48)
7.1 Theoretical Considerations of the Chemical Dissolution-Front Instability Problem in Deformable Fluid-Saturated Porous Media
152(10)
7.1.1 Dimensional and Dimensionless Governing Equations of the Problem
152(5)
7.1.2 Analytical Solutions Derived from Using a Fully-Compressible Pore-Fluid Model
157(1)
7.1.3 Analytical Solutions When the Pore-Fluid in the Upstream Region Is Incompressible
158(4)
7.2 Effects of Pore-Fluid Compressibility on the Evolution of a Chemical Dissolution Front in Subcritical Chemical Dissolution Systems
162(10)
7.2.1 Derivation of Analytical Solutions for the Benchmark Problem in the Subcritical Chemical Dissolution System of a Finite Domain
162(4)
7.2.2 Evaluation of the Dimensionless Propagating Speed of the Chemical Dissolution Front Associated with the Derived Analytical Solutions for the Benchmark Problem
166(2)
7.2.3 Effects of Pore-Fluid Compressibility on the Evolution of a Chemical Dissolution Front in Subcritical Chemical Dissolution Systems
168(4)
7.3 Computational Theory for Simulating the Morphological Evolution of a Chemical Dissolution Front with the Consideration of Pore-Fluid and Medium Compressibility
172(16)
7.3.1 Derivation of the Finite Difference Equations of the Problem
174(1)
7.3.2 Derivation of the Proposed Porosity-Gradient Replacement Approach
175(3)
7.3.3 Derivation of the Finite Element Equations of the Problem
178(5)
7.3.4 Verification of the Proposed Numerical Procedure
183(5)
7.4 Effect of Pore-Fluid Compressibility on the Morphological Evolution of a Chemical Dissolution Front in the Supercritical Chemical Dissolution System
188(2)
7.5 Effect of Medium Compressibility on the Morphological Evolution of a Chemical Dissolution Front in the Supercritical Chemical Dissolution System
190(6)
References
196(3)
8 Computational Simulation of Three-Dimensional Behaviour of Chemical Dissolution-Front Instability in Fluid-Saturated Porous Media 199(24)
8.1 Governing Equations of the Problem and the Proposed Numerical Procedure
202(4)
8.1.1 Governing Equations of the Problem
202(2)
8.1.2 The Proposed Numerical Procedure
204(2)
8.2 Verification of the Proposed Numerical Procedure
206(9)
8.3 Morphological Evolution of Three-Dimensional Chemical-Dissolution Fronts in Fluid-Saturated Porous Media
215(4)
References
219(4)
9 Fundamental Theory for Nonaqueous-Phase-Liquid Dissolution-Front Instability Problems in Fluid-Saturated Porous Media 223(44)
9.1 Mathematical Modeling of NAPL Dissolution Problems in Two-Dimensional Fluid-Saturated Porous Media
224(3)
9.2 Theoretical Analysis of NAPL Dissolution Induced Instability Problems in Two-Dimensional Fluid-Saturated Porous Media
227(18)
9.2.1 Previous Approach
227(7)
9.2.2 Current Approach
234(10)
9.2.3 Theoretical Understanding of the Effects of Solute Dispersion on NAPL Dissolution-Front Instability in Two-Dimensional Fluid-Saturated Porous Media
244(1)
9.3 Computational Simulation of NAPL Dissolution-Front Instability Problems in Two-Dimensional Fluid-Saturated Porous Media
245(12)
9.3.1 Formulation of the Proposed Numerical Procedure for Simulating the Evolution of NAPL Dissolution Fronts
246(3)
9.3.2 Verification of the Proposed Numerical Procedure for Simulating the Evolution of NAPL Dissolution Fronts
249(8)
9.4 Three Different Kinds of Modes Associated with Morphological Evolution of NAPL Dissolution Fronts in Supercritical Systems
257(6)
9.4.1 The Fundamental Mode
259(1)
9.4.2 The Fingering Mode
259(2)
9.4.3 The Fractal Mode
261(2)
References
263(4)
10 Effects of Domain Shapes and Mesh Discretization Error on the Morphological Evolution of Nonaqueous-Phase-Liquid Dissolution Fronts in Fluid-Saturated Porous Media 267(48)
10.1 Governing Equations of NAPL Dissolution Problems in Two-Dimensional Fluid-Saturated Porous Media
270(7)
10.2 Effects of Domain Shapes on the Morphological Evolution of NAPL Dissolution Fronts in Supercritical Systems
277(12)
10.3 Effects of Mesh Discretization Error on the Morphological Evolution of NAPL Dissolution Fronts in Supercritical Systems
289(22)
10.3.1 The Theoretical Basis of Mesh Discretization Error Estimation for NAPL Dissolution Problems
290(9)
10.3.2 Corner and Mesh Discretization Effects on the Morphological Evolution of NAPL Dissolution Fronts in Supercritical Systems of Trapezoidal Domains
299(12)
References
311(4)
11 Fundamental Theory for Acidization Dissolution-Front Instability in Fluid-Saturated Carbonate Rocks 315(30)
11.1 Mathematical Analysis of the Acidization Dissolution Problem
317(14)
11.1.1 Determination of the Propagation Speed of the Acidization Dissolution Front in a Fluid-Saturated Carbonate Rock
319(3)
11.1.2 Instability Analysis of the Acidization Dissolution Front in a Fluid-Saturated Carbonate Rock
322(9)
11.2 Theoretical Understanding of Some Fundamental Characteristics of Acidization Dissolution-Front Instability Problems
331(5)
11.2.1 The Intrinsic Time and Length Scales of an Acidization Dissolution System
331(1)
11.2.2 The Asymptotic Behavior of an Acidization Dissolution System under Two Limit Conditions
332(1)
11.2.3 Effects of Several Factors on the Critical Zhao Number of an Acidization Dissolution System
333(2)
11.2.4 Effects of Several Factors on the Propagation Speed of an Acidization Dissolution Front
335(1)
11.3 Application of the Proposed Theory
336(6)
References
342(3)
Summary Statements 345(6)
Index 351
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