ABSTRACT
Most descriptions of migration processes in the subsurface are based on the continuum mechanics approach to porous media. In this approach, the medium is viewed as consisting of solid matrix and void spaces, occupied by one or more fluids (e.g., water, air, oil, etc.), which represent different phases at the microscopic level. The values of state variables, and of material parameters or coefficients of the phase, can be assigned to every point within the domain. In the continuum representation of a porous medium, the state variables and properties describing the system, which are discontinuous at the pore scale, are replaced by the variables and properties that are continuous at the macroscopic level (Bear, 1972). Thus, the porous medium is replaced by a model represented as overlapping continua of solid and fluid phases. The value of any variable for each point in this continuum space is obtained by averaging the actual physical property over a representative elementary volume (REV). These averaged variables (e.g., porosity, density, pressure, temperature, concentration etc.) are referred to as macroscopic values of the considered physical properties. The macroscopic balance equations are derived using spatial averaging methods (Bear and Bachmat, 1990; Hassanizadeh and Gray, 1979a, 1979b, 1980; Whitaker, 1999; and Sorek et al., 2005, 2010). This chapter presents the derivations of the basic equations needed to describe fluid flow, solute and heat transport in porous media, assuming a non-deformable solid matrix.
