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Physicochemical Fluid Dynamics in Porous Media: Applications in Geosciences and Petroleum Engineering [Hardback]

  • Formāts: Hardback, 400 pages, height x width x depth: 249x175x23 mm, weight: 907 g
  • Izdošanas datums: 09-Jan-2019
  • Izdevniecība: Blackwell Verlag GmbH
  • ISBN-10: 3527342354
  • ISBN-13: 9783527342358
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Physicochemical Fluid Dynamics in Porous Media: Applications in Geosciences and Petroleum EngineeringPalielināt
  • Formāts: Hardback, 400 pages, height x width x depth: 249x175x23 mm, weight: 907 g
  • Izdošanas datums: 09-Jan-2019
  • Izdevniecība: Blackwell Verlag GmbH
  • ISBN-10: 3527342354
  • ISBN-13: 9783527342358
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783527342358.html
Keywords:
A unique and timely book on understanding and tailoring the flow of fluids in porous materials

Porous media play a key role in chemical processes, gas and water purification, gas storage and the development of new multifunctional materials. Understanding hydrodynamics in porous media is decisive for enabling a wide range of applications in materials science and chemical engineering. This all-encompassing book offers a timely overview of all flow and transport processes in which chemical or physicochemical phenomena such as dissolution, phase transition, reactions, adsorption, diffusion, capillarity, and surface phenomena are essential. It brings together both theoretical and experimental results and includes important industrial applications.

Physicochemical Fluid Dynamics in Porous Media: Applications in Geoscience and Petroleum Engineering explains the thermodynamics of phase equilibria for multicomponent fluids, physicochemical models of single-phase and immiscible two-phase flow, based on the macroscopic theory of oil displacement by water. It also covers the theory of two-phase flow with partial miscibility and describes partially miscible flows with phase transitions by means of the negative saturation approach. The final chapters are devoted to flow with chemical reactions, based on the example of in-situ leaching of uranium, and flow with bio-chemical reactions in terms of the underground storage of hydrogen.

-Brings together the theoretical and experimental results necessary for the understanding of hydrodynamics in porous media -Covers important industrial applications such as underground leaching of uranium and underground storage of hydrogen -Presents a state-of-the-art overview and summarizes the research results usually found only scattered in the literature

Physicochemical Fluid Dynamics in Porous Media: Applications in Geoscience and Petroleum Engineering will appeal to chemical engineers, materials scientists, applied physicists, and mechanical engineers.
Preface xv
Introduction xvii
1 Thermodynamics of Pure Fluids
1(12)
1.1 Equilibrium of Single-phase Fluids -- Equation of State
2(3)
1.1.1 Admissible Classes of EOS
2(1)
1.1.2 Van der Waals EOS
3(1)
1.1.3 Soave-Redlish-Kwong EOS
3(2)
1.1.4 Peng-Robinson EOS
5(1)
1.1.5 Mixing Rules for Multicomponent Fluids
5(1)
1.2 Two-phase Equilibrium of Pure Fluids
5(8)
1.2.1 Pseudo-liquid/Pseudo-gas and True Liquid/Gas
6(1)
1.2.2 Equilibrium Conditions in Terms of Chemical Potentials
6(1)
1.2.3 Explicit Relationship for Chemical Potential
7(1)
1.2.4 Equilibrium Conditions in Terms of Pressure and Volumes
8(1)
1.2.5 Solvability of the Equilibrium Equation -- Maxwell's Rule
9(1)
1.2.6 Calculation of Gas-Liquid Coexistence
10(1)
1.2.7 Logarithmic Representation for Chemical Potential -- Fugacity
11(2)
2 Thermodynamics of Mixtures
13(18)
2.1 Chemical Potential of an Ideal Gas Mixture
13(4)
2.1.1 Notations
13(1)
2.1.2 Definition and Properties of an Ideal Gas Mixture
14(1)
2.1.3 Entropy and Enthalpy of Ideal Mixing
15(1)
2.1.4 Chemical Potential of Ideal Gas Mixtures
16(1)
2.2 Chemical Potential of Nonideal Mixtures
17(3)
2.2.1 General Model for Chemical Potential of Mixtures
17(2)
2.2.2 Chemical Potential of Mixtures Through Intensive Parameters
19(1)
2.3 Two-phase Equilibrium Equations for a Multicomponent Mixture
20(6)
2.3.1 General Form of Two-phase Equilibrium Equations
20(1)
2.3.2 Equilibrium Equations in the Case of Peng-Robinson EOS
21(2)
2.3.3 AT-values
23(1)
2.3.4 Calculation of the Phase Composition ("flash")
24(1)
2.3.5 Expected Phase Diagrams for Binary Mixtures
24(2)
2.4 Equilibrium in Dilute Mixtures
26(5)
2.4.1 Ideal Solution
26(1)
2.4.2 Chemical Potential for an Ideal Solution
27(1)
2.4.3 Equilibrium of Ideal Gas and Ideal Solution: Raoult's Law
27(1)
2.4.4 Equilibrium of Dilute Solutions: Henry's Law
28(1)
2.4.5 /C-values for Ideal Mixtures
28(1)
2.4.6 Calculation of the Phase Composition
29(2)
3 Chemistry of Mixtures
31(26)
3.1 Adsorption
31(5)
3.1.1 Mechanisms of Adsorption
31(1)
3.1.2 Langmuir's Model of Adsorption
32(2)
3.1.3 Types of Adsorption Isotherms
34(1)
3.1.4 Multicomponent Adsorption
35(1)
3.2 Chemical Reactions: Mathematical Description
36(3)
3.2.1 Elementary Stoichiometric System
36(1)
3.2.2 Reaction Rate
37(1)
3.2.3 Particle Balance Through the Reaction Rate in a Homogeneous Reaction
37(1)
3.2.4 Particle Balance in a Heterogeneous Reaction
38(1)
3.2.5 Example
39(1)
3.3 Chemical Reaction: Kinetics
39(3)
3.3.1 Kinetic Law of Mass Action: Guldberg-Waage Law
39(1)
3.3.2 Kinetics of Heterogeneous Reactions
40(1)
3.3.3 Reaction Constant
41(1)
3.4 Other Nonconservative Effects with Particles
42(1)
3.4.1 Degradation of Particles
42(1)
3.4.2 Trapping of Particles
42(1)
3.5 Diffusion
42(15)
3.5.1 Fick's Law
43(1)
3.5.2 Properties of the Diffusion Parameter
44(1)
3.5.3 Calculation of the Diffusion Coefficient in Gases and Liquids
45(1)
3.5.3.1 Diffusion in Gases
45(1)
3.5.3.2 Diffusion in Liquids
46(1)
3.5.4 Characteristic Values of the Diffusion Parameter
46(1)
3.5.5 About a Misuse of Diffusion Parameters
47(1)
3.5.5.1 A Misuse of Nondimensionless Concentrations
47(1)
3.5.5.2 Diffusion as the Effect of Mole Fraction Anomaly but not the Number of Moles
47(1)
3.5.6 Stefan-Maxwell Equations for Diffusion Fluxes
48(9)
4 Reactive Transport with a Single Reaction
57(14)
4.1 Equations of Multicomponent Single-Phase Transport
51(5)
4.1.1 Material Balance of Each Component
51(1)
4.1.2 Closure Relationships
52(1)
4.1.2.1 Chemical Terms
52(1)
4.1.2.2 Total Flow Velocity -- Darcy's Law
53(1)
4.1.2.3 Diffusion Flux -- Fick's Law
53(1)
4.1.3 Transport Equation
53(2)
4.1.4 Transport Equation for Dilute Solutions
55(1)
4.1.5 Example of Transport Equation for a Binary Mixture
55(1)
4.1.6 Separation of Flow and Transport
56(1)
4.2 Elementary Fundamental Solutions of ID Transport Problems
56(8)
4.2.1 Convective Transport -- Traveling Waves
57(1)
4.2.2 Transport with Diffusion
58(1)
4.2.3 Length of the Diffusion Zone
59(1)
4.2.4 Peclet Number
59(1)
4.2.5 Transport with Linear Adsorption -- Delay Effect
60(1)
4.2.6 Transport with Nonlinear Adsorption: Diffusive Traveling Waves
60(2)
4.2.7 Origin of Diffusive Traveling Waves
62(1)
4.2.8 Transport with a Simplest Reaction (or Degradation/Trapping)
62(1)
4.2.9 Macrokinetic Effect: Reactive Acceleration of the Transport
63(1)
4.3 Reactive Transport in Underground Storage of CO2
64(7)
4.3.1 Problem Formulation and Solution
65(1)
4.3.2 Evolution of CO2 Concentration
66(1)
4.3.3 Evolution of the Concentration of Solid Reactant
67(1)
4.3.4 Evolution of the Concentration of the Reaction Product
67(1)
4.3.5 Mass of Carbon Transformed to Solid
68(3)
5 Reactive Transport with Multiple Reactions (Application to In Situ Leaching)
71(20)
ISL Technology
71(2)
5.1 Coarse Monoreaction Model of ISL
73(2)
5.1.1 Formulation of the Problem
73(1)
5.1.2 Analytical Solution
74(1)
5.2 Multireaction Model of ISL
75(5)
5.2.1 Main Chemical Reactions in the Leaching Zone
75(2)
5.2.2 Transport Equations
77(1)
5.2.3 Kinetics of Gypsum Precipitation
78(1)
5.2.4 Definite Form of the Mathematical Model
79(1)
5.3 Method of Splitting Hydrodynamics and Chemistry
80(11)
5.3.1 Principle of the Method
80(1)
5.3.2 Model Problem of In Situ Leaching
81(1)
5.3.3 Analytical Asymptotic Expansion: Zero-Order Terms
82(1)
5.3.4 First-Order Terms
83(1)
5.3.5 Solution in Definite Form
84(1)
5.3.6 Case Without Gypsum Deposition
84(1)
5.3.7 Analysis of the Process: Comparison with Numerical Data
85(1)
5.3.8 Experimental Results: Comparison with Theory
86(2)
5.3.9 Recovery Factor
88(3)
6 Surface and Capillary Phenomena
91(632)
6.1 Properties of an Interface
91(4)
6.1.1 Curvature of a Surface
91(1)
6.1.2 Signed Curvature
92(2)
6.1.3 Surface Tension
94(1)
6.1 A Tangential Elasticity of an Interface
95(1)
6.2 Capillary Pressure and Interface Curvature
96(7)
6.2.1 Laplace's Capillary Pressure
96(1)
6.2.2 Young-Laplace Equation for Static Interface
97(2)
6.2.3 Soap Films and Minimal Surfaces
99(2)
6.2.4 Catenoid as a Minimal Surface of Revolution
101(1)
6.2.5 Plateau's Configurations for Intercrossed Soap Films
102(1)
6.3 Wetting
103(667)
6.3.1 Fluid-Solid Interaction: Complete and Partial Wetting
103(1)
6.3.2 Necessary Condition of Young for Partial Wetting
104(2)
6.3.3 Hysteresis of the Contact Angle
106(1)
6.3.4 Complete Wetting -- Impossibility of Meniscus Existence
106(1)
6.3.5 Shape of Liquid Drops on Solid Surface
107(2)
6.3.6 Surfactants -- Significance of Wetting for Oil Recovery
109(61)
6.4 Capillary Phenomena in a Pore
110(1)
6.4.1 Capillary Pressure in a Pore
110(2)
6.4.2 Capillary Rise
112(1)
6.4.3 Capillary Movement -- Spontaneous Imbibition
113(1)
6.4.4 Menisci in Nonuniform Pores -- Principle of Pore Occupancy
114(1)
6.4.5 Capillary Trapping -- Principle of Phase Immobilization
115(1)
6.4.6 Effective Capillary Pressure
116(2)
6.5 Augmented Meniscus and Disjoining Pressure
118(1)
6.5.1 Multiscale Structure of Meniscus
118(1)
6.5.2 Disjoining Pressure in Liquid Films
119(1)
6.5.3 Augmented Young-Laplace Equation
120(3)
7 Meniscus Movement in a Single Pore
123(1)
7.1 Asymptotic Model for Meniscus near the Triple Line
123(7)
7.1.1 Paradox of the Triple Line
123(1)
7.1.2 Flow Model in the Intermediate Zone (Lubrication Approximation)
124(1)
7.1.3 Tanner's Differential Equation for Meniscus
125(2)
7.1.4 Shape of the Meniscus in the Intermediate Zone
127(1)
7.1.5 Particular Case of Small 0: Cox-Voinov Law
128(1)
7.1.6 Scenarios of Meniscus Spreading
128(2)
7.2 Movement of the Augmented Meniscus
130(3)
7.2.1 Lubrication Approximation for Augmented Meniscus
130(2)
7.2.2 Adiabatic Precursor Films
132(1)
7.2.3 Diffusive Film
132(1)
7.3 Method of Diffuse Interface
133(1)
7.3.1 Principle Idea of the Method
133(1)
7.3.2 Capillary Force
134(1)
7.3.3 Free Energy and Chemical Potential
135(2)
7.3.4 Reduction to Cahn-Hilliard Equation
137(2)
8 Stochastic Properties of Phase Cluster in Pore Networks
139(1)
8.1 Connectivity of Phase Clusters
139(5)
8.1.1 Connectivity as a Measure of Mobility
139(1)
8.1.2 Triple Structure of Phase Cluster
140(1)
8.1.3 Network Models of Porous Media
140(2)
8.1.4 Effective Coordination Number
142(1)
8.1.5 Coordination Number and Medium Porosity
143(1)
8.2 Markov Branching Model for Phase Cluster
144(611)
8.2.1 Phase Cluster as a Branching Process
144(1)
8.2.2 Definition of a Branching Process
145(2)
8.2.3 Method of Generating Functions
147(1)
8.2.4 Probability of Creating a Finite Phase Cluster
148(1)
8.2.5 Length of the Phase Cluster
149(1)
8.2.6 Probability of an Infinite Phase Cluster
150(1)
8.2.7 Length-Radius Ratio Y: Fitting with Experimental Data
151(2)
8.2.8 Cluster of Mobile Phase
153(1)
8.2.9 Saturation of the Mobile Cluster
154(1)
8.3 Stochastic Markov Model for Relative Permeability
155(1)
8.3.1 Geometrical Model of a Porous Medium
155(1)
8.3.2 Probability of Realizations
156(1)
8.3.3 Definition of Effective Permeability
156(1)
8.3.4 Recurrent Relationship for Space-Averaged Permeability
157(1)
8.3.5 Method of Generating Functions
158(1)
8.3.6 Recurrent Relationship for the Generating Function
159(1)
8.3.7 Stinchcombe's Integral Equation for Function F(x)
160(1)
8.3.8 Case of Binary Distribution of Permeabilities
161(1)
8.3.9 Large Coordination Number
162(3)
9 Macroscale Theory of Immiscible Two-Phase Flow
165(1)
9.1 General Equations of Two-Phase Immiscible Flow
165(1)
9.1.1 Mass and Momentum Conservation
165(2)
9.1.2 Fractional Flow and Total Velocity
167(1)
9.1.3 Reduction to the Model of Kinematic Waves
167(1)
9.2 Canonical Theory of Two-Phase Displacement
168(1)
9.2.1 ID Model of Kinematic Waves (the Buckley-Leverett Model)
168(1)
9.2.2 Principle of Maximum
169(1)
9.2.3 Nonexistence of Continuous Solutions
170(1)
9.2.4 Hugoniot-Rankine Conditions at a Shock
171(1)
9.2.5 Entropy Conditions at a Shock
172(2)
9.2.6 Entropy Condition for Particular Cases
174(1)
9.2.7 Solution Pathway
175(1)
9.2.8 Piston-Like Shocks
176(1)
9.3 Oil Recovery
177(1)
9.3.1 Recovery Factor and Average Saturation
177(1)
9.3.2 Breakthrough Recovery
178(1)
9.3.3 Another Method of Deriving the Relationship for the Recovery Factor
179(1)
9.3.4 Graphical Determination of Breakthrough Recovery
179(1)
9.3.5 Physical Structure of Solution. Structure of Nondisplaced Oil
180(1)
9.3.6 Efficiency of Displacement
181(1)
9.4 Displacement with Gravity
182(1)
9.4.1 1D-model of Kinematic Waves with Gravity
182(1)
9.4.2 Additional Condition at Shocks: Continuity w.r.t. Initial Data
183(2)
9.4.3 Descending Flow
185(1)
9.4.4 Ascending Flow
186(1)
9.5 Stability of Displacement
187(1)
9.5.1 Saffman-Taylor and Raleigh-Taylor Instability and Fingering
187(1)
9.5.2 Stability Criterion
188(1)
9.6 Displacement by Immiscible Slugs
189(1)
9.6.1 Setting of the Problem
190(1)
9.6.2 Solution of the Problem
191(1)
9.6.3 Solution for the Back Part
192(1)
9.6.4 Matching Two Solutions
192(1)
9.6.5 Three Stages of the Evolution in Time
192(4)
9.7 Segregation and Immiscible Gas Rising
196(1)
9.7.1 Canonical ID Model
196(1)
9.7.2 Description of Gas Rising
197(1)
9.7.3 First Stage of the Evolution: Division of the Forward Bubble Boundary
198(1)
9.7.4 Second Stage: Movement of the Back Boundary
199(1)
9.7.5 Third Stage: Monotonic Elongation of the Bubble
200(3)
10 Nonlinear Waves in Miscible Two-phase Flow (Application to Enhanced Oil Recovery)
203(54)
Expected Scenarios of Miscible Gas-Liquid Displacement
203(2)
10.1 Equations of Two-Phase Miscible Flow
205(4)
10.1.1 General System of Equations
205(1)
10.1.2 Formulation Through the Total Velocity and Fractional Flow
206(1)
10.1.3 Ideal Mixtures; Volume Fractions
207(1)
10.1.4 Conversion to the Model of Kinematic Waves
208(1)
10.1.5 Particular Case of a Binary Mixture
209(1)
10.1.5.1 Conclusion
209(1)
10.2 Characterization of Species Dissolution by Phase Diagrams
209(61)
10.2.1 Thermodynamic Variance and Gibbs `Phase Rule
209(61)
Example
210(1)
10.2.2 Ternary Phase Diagrams
211(2)
10.2.3 Tie Lines
213(1)
10.2.4 Tie-Line Parametrization of Phase Diagrams (Parameter α)
214(2)
10.2.5 Saturation of Gas
216(1)
10.2.6 Phase Diagrams for Constant K-Values
216(4)
10.2.7 Phase Diagrams for Linear Repartition Function: β = -γα
219(2)
10.3 Canonical Model of Miscible EOR
221(1)
10.3.1 Problem Setting
221(1)
10.3.2 Fractional Flow of a Chemical Component
222(2)
10.4 Shocks
224(8)
10.4.1 Hugoniot-Rankine and Entropy Conditions at a Shock. Admissible Shocks
225(1)
10.4.2 Mechanical Shock (C-shock) and Its Graphical Image
226(1)
10.4.3 Chemical Shock (Cα-shock) and Its Graphical Image
227(1)
10.4.4 Shocks of Phase Transition
228(2)
10.4.5 Weakly Chemical Shock
230(1)
10.4.6 Three Methods of Changing the Phase Composition
231(1)
10.4.7 Solution Pathway
231(1)
10.5 Oil Displacement by Dry Gas
232(7)
10.5.1 Description of Fluids and Initial Data
232(1)
10.5.2 Algorithm of Selecting the Pathway
233(2)
10.5.3 Behavior of Liquid and Gas Composition
235(1)
10.5.4 Behavior of Liquid Saturation
236(1)
10.5.5 Physical Behavior of the Process
237(2)
10.5.6 EOR Efficiency
239(1)
10.6 Oil Displacement by Wet Gas
239(7)
10.6.1 Formulation of the Problem and the Pathway
239(1)
10.6.2 Solution to the Problem. Physical Explanation
240(2)
10.6.3 Comparison with Immiscible Gas Injection
242(1)
10.6.4 Injection of Overcritical Gas
243(2)
10.6.5 Injection of Overcritical Gas in Undersaturated Single-Phase Oil
245(1)
10.7 Gas Recycling in Gas-Condensate Reservoirs
246(11)
10.7.1 Techniques of Enhanced Condensate Recovery
246(1)
10.7.2 Case I: Dry Gas Recycling: Mathematical Formulation
247(1)
10.7.3 Solution to the Problem of Dry Gas Recycling
247(2)
10.7.4 Case II: Injection of Enriched Gas
249(2)
10.7.4.1 Conclusion
251(1)
10.8 Chemical Flooding
251(1)
10.8.1 Conservation Equations
251(1)
10.8.2 Reduction to the Model of Kinematic Waves
252(1)
10.8.3 Diagrams of Fractional Flow of Water F(s, c)
253(1)
10.8.4 Shocks and Hugoniot-Rankine Conditions
253(2)
10.8.5 Solution of the Riemann Problem
255(1)
10.8.6 Impact of the Adsorption
256(1)
11 Counter Waves in Miscible Two-phase Flow with Gravity (Application to CO2 & H2 Storage)
257(14)
Introducing Notes
257(1)
11.1 Two-component Two-phase Flow in Gravity Field
258(7)
11.1.1 Formulation
259(2)
11.1.2 Solution Before Reaching the Barrier
261(1)
11.1.3 Reverse Wave Reflected from Barrier
261(2)
11.1.4 Calculation of the Concentrations at the Shocks
263(1)
11.1.5 Rate of Gas Rising and Bubble Growth Under the Barriers
264(1)
11.1.6 Comparison with Immiscible Two-phase Flow
264(1)
11.2 Three-component Flow in Gravity Field
265(6)
11.2.1 Problem Setting
265(1)
11.2.2 Solution of the Riemann Problem
266(2)
11.2.3 Propagation of the Reverse Wave Under the Barrier
268(3)
12 Flow with Variable Number of Phases: Method of Negative Saturations
271(20)
12.1 Method NegSat for Two-phase Fluids
271(11)
12.1.1 Interface of Phase Transition and Nonequilibrium States
271(2)
12.1.2 Essence of the Method Negsat
273(2)
12.1.3 Principle of Equivalence
275(1)
12.1.4 Proof of the Equivalence Principle
276(1)
12.1.5 Density and Viscosity of Fictitious Phases
277(1)
12.1.6 Extended Saturation -- Detection of the Number of Phases
277(2)
12.1.7 Equivalence Principle for Flow with Gravity
279(1)
12.1.8 Equivalence Principle for Flow with Gravity and Diffusion
279(2)
12.1.9 Principle of Equivalence for Ideal Mixing
281(1)
12.1.10 Physical and Mathematical Consistency of the Equivalent Fluids
282(1)
12.2 Hyperbolic-parabolic Transition
282(9)
12.2.1 Phenomenon of Hyperbolic-parabolic Transition (HP Transition)
282(2)
12.2.2 Derivation of the Model (12.23)
284(1)
12.2.3 Purely Hyperbolic Case
284(1)
12.2.4 Case of Hyperbolic-parabolic Transition
285(2)
12.2.5 Generalization of Hugoniot-Rankine Conditions for a Shock of HP-transition
287(1)
12.2.6 Regularization by the Capillarity
288(2)
12.2.7 Reduction to VOF or Level-set Method for Immiscible Fluids
290(1)
13 Biochemical Fluid Dynamics of Porous Media
291(48)
13.1 Microbiological Chemistry
291(9)
13.1.1 Forms of Existence of Microorganisms
291(1)
13.1.2 Bacterial Metabolism
292(1)
13.1.3 Bacterial Movement
293(1)
13.1.4 Chemotaxis
294(1)
13.1.5 Population Dynamics
295(1)
13.1.6 Kinetics of Population Growth and Decay: Experiment
295(1)
13.1.6.1 Population Decay
295(1)
13.1.6.2 Population Growth
296(1)
13.1.7 Kinetics of Population Growth: Mathematical Models
297(1)
13.1.8 Coupling Between Nutrient Consumption and Bacterial Growth
298(2)
13.1.9 Experimental Data on Bacterial Kinetics
300(1)
13.2 Bioreactive Waves in Microbiological Enhanced Oil Recovery
300(8)
13.2.1 The Essence of the Process
300(2)
13.2.2 Metabolic Process
302(1)
13.2.3 Assumptions
303(1)
13.2.4 Mass Balance Equations
303(1)
13.2.5 Description of the Impact of the Surfactant
304(1)
13.2.6 Reduction to the Model of Kinematic Waves
304(1)
13.2.7 ID MEOR Problem
305(1)
13.2.8 Solution and Analysis of the MEOR Problem
305(3)
13.3 Nonlinear Waves in Microbiological Underground Methanation Reactors
308(10)
13.3.1 Underground Methanation and Hydrogen Storage
308(1)
13.3.2 Biochemical Processes in an Underground Methanation Reactor
309(2)
13.3.3 Composition of the Injected Gas
311(1)
13.3.4 Mathematical Model of Underground Methanation
311(2)
13.3.5 Kinematic Wave Model
313(1)
13.3.6 Asymptotic Model for Biochemical Equilibrium
314(1)
13.3.7 Particular Case of Biochemical Equilibrium
315(1)
13.3.8 Solution of the Riemann Problem
315(2)
13.3.9 Comparison with the Case Without Bacteria. Impact of Bacteria
317(1)
13.4 Self-organization in Biochemical Dynamical Systems (Application to Underground Methanation)
318(7)
13.4.1 Integral Material Balance in the Underground Reactor
318(1)
13.4.2 Reduction to a Dynamical System
319(1)
13.4.3 Singular Point Analysis -- Oscillatory Regimes
320(1)
13.4.4 Existence of a Limit Cycle -- Auto-oscillations
321(2)
13.4.5 Phase Portrait of Auto-oscillations
323(2)
13.5 Self-organization in Reaction-Diffusion Systems
325(14)
13.5.1 Equations of Underground Methanation with Diffusion
325(2)
13.5.2 Turing's Instability
327(1)
13.5.3 Limit Space Oscillatory Waves at ε = 0
328(1)
13.5.4 Three Types of Limit Patterns at Large Times
329(1)
13.5.5 Exact Analytical Solution of Problem (13.52). Estimation of Parameters
330(1)
13.5.6 Limit Two-scale Spatial Oscillatory Patterns at ε > 0
331(2)
13.5.7 Two-scale Asymptotic Expansion of Problem (13.59)
333(1)
13.5.7.1 Two-scale Formulation
333(1)
13.5.7.2 Two-scale Expansion
334(1)
13.5.7.3 Zero-order Terms c0 and n0
334(1)
13.5.7.4 First-order Term n1
335(1)
13.5.7.5 Second-order Term c2
336(1)
13.5.8 2D Two-scale Spatial Patterns
336(3)
A Chemical Potential of a Pure Component from the Homogeneity of Gibbs Energy 339(2)
B Chemical Potential for Cubic EOS 341(2)
C Chemical Potential of Mixtures from the Homogeneity of Gibbs Energy 343(4)
D Calculation of the Integral in (2.25a) 347(2)
E Hugoniot-Rankine Conditions 349(2)
F Numerical Code (Matlab) for Calculating Phase Diagrams of a Pure Fluid 351(4)
Bibliography 355(8)
Index 363
Mikhail Panfilov, D.Sc., is Professor at the Institute of Mathematics Elie Cartan - University of Lorraine/CNRS, and at the Institute Jean le Rond d'Alembert - Sorbonne University/CNRS. Born and studied in Moscow. He is twice graduated in applied mathematics/mechanics and petroleum engineering. He worked at the Oil & Gas Research Institute of the Academy of Sciences in Moscow. In 2000 he moved to France. He published more than 80 papers in international reviews and two monographs. He is a State Prize Laureate of Russia for Science (1997) and several Excellence Awards of the French Ministry of Higher Education and Research.