Page 11 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Contents xiii

6 A Decoupling Procedure for Simulating Fluid Mixing, Heat Transfer
and Non-Equilibrium Redox Chemical Reactions in Fluid-Saturated
Porous Rocks ................................................... 121
6.1 Statement of Coupled Problems between Fluids Mixing, Heat
Transfer and Redox Chemical Reactions ........................ 123
6.2 A Decoupling Procedure for Removing the Coupling between
Reactive Transport Equations of Redox Chemical Reactions. . ...... 126
6.3 Verification of the Decoupling Procedure . . . ..................... 128
6.4 Applications of the Proposed Decoupling Procedure to Predict
Mineral Precipitation Patterns in a Focusing and Mixing System
Involving Two Reactive Fluids . . . . ............................ 134
6.4.1 Key Factors Controlling Mineral Precipitation
Patterns in a Focusing and Mixing System Involving
Two Reactive Fluids . . . ............................... 136
6.4.2 Theoretical Analysis of Mineral Precipitation
Patterns in a Focusing and Mixing System Involving
Two Reactive Fluids . . . ............................... 138
6.4.3 Chemical Reaction Patterns due to Mixing and Focusing
of Two Reactive Fluids in Permeable Fault Zones . ......... 140
6.4.4 Numerical Illustration of Three Types of Chemical Reaction
Patterns Associated with Permeable Fault Zones . . ......... 145

7 An Equivalent Source Algorithm for Simulating Thermal and
Chemical Effects of Intruded Magma Solidification Problems ........ 153
7.1 An Equivalent Source Algorithm for Simulating
Thermal and Chemical Effects of Intruded Magma
Solidification Problems ...................................... 155
7.2 Implementation of the Equivalent Source Algorithm in the Finite
Element Analysis with Fixed Meshes ........................... 160
7.3 Verification and Application of the Equivalent Source Algorithm . . . . 163

8 The Particle Simulation Method for Dealing with Spontaneous
Crack Generation Problems in Large-Scale Geological Systems ...... 175
8.1 Basic Formulations of the Particle Simulation Method ............. 179
8.2 Some Numerical Simulation Issues Associated with the Particle
Simulation Method .......................................... 184
8.2.1 Numerical Simulation Issue Caused by the Difference
between an Element and a Particle ...................... 184
8.2.2 Numerical Simulation Issue Arising from Using the Explicit
Dynamic Relaxation Method to Solve a Quasi-Static Problem 186
8.2.3 Numerical Simulation Issue Stemming from the Loading
Procedure Used in the Particle Simulation Method ......... 189
8.3 An Upscale Theory of Particle Simulation for Two-Dimensional
Quasi-Static Problems ....................................... 194