Mathematical Models for Poroelastic Flows [Hardcover]

The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equations). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5  15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.Isothermal Liquid Filtration.- Filtration of a compressible thermo-fluid.- Hydraulic shock in incompressible poroelastic media.- Double porosity models for a liquid filtration.- Filtration in composite incompressible media.- Isothermal acoustics in poroelastic media.- Non-isothermal acoustics in poroelastic media.- Isothermal acoustics in composite media.- Double porosity models for acoustics.- Diffusion and convection in porous media.- The Muskat problem.For each underground physical process the reader finds a set of mathematical models depending on the dimensionless criteria of the given process and describing the process with different degrees of exactness The reader may apply the suggested approach to solve many other important problems in filtration and acoustics and obtain macroscopic mathematical models, which are asymptotically exact First volume in a new series