Transport by Oscillatory Flow in Soils with Rate-Limited Mass Transfer: 1. Theory

Oscillatory flow of fluid in a porous medium can generate a one-way transport of heat or chemicals if there is a gradient of temperature or chemical concentration and a rate-limited heat or mass transfer between the moving fluid and an immobile phase. For chemical transport in soils, the immobile phase can occur in stagnant porosity, by sorption, or by dissolution of a vapor in the pore water. As a function of oscillation frequency, the transport rate has a broad peak near the value omega tau(c) = 1, where omega is the angular frequency of oscillation and tau(c) is the characteristic equilibration time of the mobile phase. The transport rate is proportional to the gradient and to the square of the amplitude of periodic fluid displacement. A unique diffusivity derived from the analysis enables prediction of the long-term transport by a diffusion calculation without fluid flow, thereby providing a tool for estimating the removal of contaminant vapors by passive soil vapor extraction (PSVE). We compared predictions of the analytic theory with numerical simulations of PSVE. The mobile-immobile model is also applicable to transport in other cases of oscillatory flow in porous media, including cyclic motion of water or gas due to tidal aquifers or earth tides.