Heat and Mass Transport in Unsaturated-Saturated Porous Media Including Water Suspension and Inner Heat Exchange

Abstract

Water suspension with heat transport into unsaturated-saturated porous media is analyzed. The numerical modeling includes the infiltration of silt. Moreover, the heat energy of suspension is exchanged with the heat energy of the matrix. The deposited silt influence the porosity and hydraulic permeability. The flow model is based on Richard's type equation and empirical van Genuchten - Mualem model describing capillarity driving force and saturation-pressure relation governing the flow in unsaturated part of porous media. The developed numerical method is usable for solving inverse problems determining some model parameters. The numerical method is based on flexible time discretization and a finite volume method in space variables. The nonlinearity in the flow part of the model is solved by iterative linearization based on the idea in Celia et all. The correctness of the numerical approximation is justified also by a different numerical approximation based on space discretization leading to the reduction of the whole system to the solution of ordinary differential equations. But this method requires significantly more computation time. This is not suitable for solving inverse problems. The used method is justified in numerical experiments solving the direct problem.