Homogenization theory applied to soil vapor extraction in aggregated soils

Abstract

The macroscale equations governing the convective diffusion of a volatile organic compound during soil vapor extraction in the vadose zone composed of aggregated soils are derived systematically. Although the macroscale effective equations of flow and chemical transport can be developed by intuitive arguments, a formal derivation is presented by the theory of homogenization in order to prescribe precisely the underlying assumptions and the degree of accuracy, and to prepare grounds for further extensions to three-scaled media. Specifically the basic assumptions are (i) the soil matrix is composed of a nearly periodic array of spherical aggregates, (ii) within an aggregate water is immobile because of capillarity and viscous forces, (iii) the aggregates are much smaller than the macroscale. and (iv) diffusion in the aggregates is much weaker than that in the pore air. Local equilibrium is confirmed as a limiting case of the present theory when the aggregate diffusion time is much shorter than the global advection time. © 1996 American Institute of Physics.