Miscible Displacement

Abstract

Fluid flow in porous media was discussed in the preceding chapters. How to derive macro Darcy-type laws from micro laws, such as Stokes equations or its generalizations was demonstrated. It is natural to ask how one can use those results and apply them to miscible displacement problems. In soil physics or soil chemistry, e.g., it is of great importance to combine the homogenization techniques, described so far, with problems of diffusion, dispersion, and convection of chemical species that are transported in the fluid flowing in the pore space of a porous medium. In principle, it turns out that all the mathematical methods developed can easily be applied to such problems. In particular, there is no difficulty in taking chemical reactions into consideration, because, usually, these are described by undifferentiated terms in the differential equations. Therefore, they are basically unmodified during the homogenization process.