Introduction to modelling of transport phenomena in porous media.

*(English)*Zbl 0743.76003
Theory and Applications of Transport in Porous Media 4. Dordrecht etc.: Kluwer Academic Publishers (ISBN 0-7923-0557-4/hbk). xxiv, 553 p. (1990).

The main objective of this book is to present, in a systematic way, a methodology for constructing mathematical models of transport problems in a porous medium domain on the basis of the continuum approach.

The book is divided into two parts: Part A, consisting of three chapters, presents the general theory of modelling transport phenomena in a porous medium domain. The first chapter presents the continuum approach, defines microscopic and macroscopic levels of description, introduces the concept of spatial averaging and defines some macroscopic characteristics of porous media and their constituents. Chapter 2 continues to develop this approach by presenting a description of transport phenomena at the microscopic level, and by deriving averaging rules for transforming the microscopic level of description of any transport problem to a macroscopic one, in which all state variables and parameters are macroscopic quantities. The various laws that govern the macroscopic fluxes of extensive quantities in a porous medium domain, are also derived. Thermodynamic concepts and quantities are introduced whenever necessary. Finally, by adding macroscopic initial and boundary conditions, a complete mathematical statement, or mathematical model, of any transport problem at the macroscopic level of description is obtained. This is discussed in Chapter 3.

In Part B, the general theory presented in Part A is applied to specific problems of transport of mass and volume of a phase, mass of a component and heat in single and multiphase fluid systems in a porous medium domain. The appropriate models are developed at the macroscopic level.

The mathematical models developed in this part are applicable to problems such as water flow and transport of pollutants in aquifers and in the unsaturated zone, flow of oil, water and gas in petroleum reservoirs, radioactive waste disposal in deep geological formations, land subsidence due to pumping from aquifers, heat storage in aquifers and solute transport in reactors in the chemical industry. Only a limited number of basic models are considered. However, the examples presented should also enable the reader to develop models for other applications.

The book is divided into two parts: Part A, consisting of three chapters, presents the general theory of modelling transport phenomena in a porous medium domain. The first chapter presents the continuum approach, defines microscopic and macroscopic levels of description, introduces the concept of spatial averaging and defines some macroscopic characteristics of porous media and their constituents. Chapter 2 continues to develop this approach by presenting a description of transport phenomena at the microscopic level, and by deriving averaging rules for transforming the microscopic level of description of any transport problem to a macroscopic one, in which all state variables and parameters are macroscopic quantities. The various laws that govern the macroscopic fluxes of extensive quantities in a porous medium domain, are also derived. Thermodynamic concepts and quantities are introduced whenever necessary. Finally, by adding macroscopic initial and boundary conditions, a complete mathematical statement, or mathematical model, of any transport problem at the macroscopic level of description is obtained. This is discussed in Chapter 3.

In Part B, the general theory presented in Part A is applied to specific problems of transport of mass and volume of a phase, mass of a component and heat in single and multiphase fluid systems in a porous medium domain. The appropriate models are developed at the macroscopic level.

The mathematical models developed in this part are applicable to problems such as water flow and transport of pollutants in aquifers and in the unsaturated zone, flow of oil, water and gas in petroleum reservoirs, radioactive waste disposal in deep geological formations, land subsidence due to pumping from aquifers, heat storage in aquifers and solute transport in reactors in the chemical industry. Only a limited number of basic models are considered. However, the examples presented should also enable the reader to develop models for other applications.

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76S05 | Flows in porous media; filtration; seepage |

76T99 | Multiphase and multicomponent flows |

86A60 | Geological problems |