The effects of transient temperature gradients on soil moisture dynamics

Abstract

The remediation of non-mobile non-aqueous phase liquid (NAPL) from the unsaturated zone involves a number of physical processes that may be functions of temperature. The coupled mechanism of soil moisture (liquid and vapour) and thermal energy transfer in a partially saturated porous medium has been investigated through the use of mathematical modelling. The physical flow processes involved in this analysis are liquid, vapour and adsorbed liquid flow, heat conduction, heat convection, latent heat and heat of wetting transfer. A mixed form of both the moisture and the thermal energy equations is utilized, ensuring a mass and energy conservative formulation. The Galerkin finite element method is employed for the spatial integration of the governing equations while temporal integration is achieved by a fully implicit finite difference method with a variable time-stepping scheme. The two-dimensional coupled equations of moisture and thermal energy flow are assembled through the use of a simultaneous solution approach, resulting in a non-linear system of equations which is linearized at each time-step using a full Newton-Raphson iteration scheme. The proposed model was tested on a variety of problems which verified that it was formulated properly. Simulation results indicate that transient temperature gradients affect the moisture velocity and water pressure fields, due mainly to viscosity effects on the hydraulic properties of the medium. The effects of pressure gradients on the temperature distribution are minimal, indicating that heat conduction is the dominant mechanism associated with thermal energy transport. This present study is a step toward the non-isothermal analysis of the transport of contaminant gases in the unsaturated zone and in the dissolution kinetics of residual organics which may lead to a better understanding of remedial actions that involve thermal processes.