A mathematical model describing isothermal, two‐phase flow in porous media has been developed. The model, which consists of describing differential equations and algorithms for their numerical solution, was applied to the problem of vertical groundwater movement in unsaturated soils in the absence of evaporation and transpiration. The equations describing water‐air flow through porous media are second order, nonlinear partial differential equations. These equations were converted to finite difference form and were solved with the aid of a digital computer using an iterative implicit procedure. The model includes effective permeabilities of each phase and capillary pressure as functions of liquid saturation. The properties of the porous media may be varied in the model as functions of position. A comparison was made between computed results and experimental field data on moisture movement beneath a shallow surface pond. Water was added to the pond at controlled rates to maintain an approximately constant head for a set time period. Following this wetting period the pond was kept dry, but covered to reduce evaporation. At different times during the wetting and drying periods, neutron logs were run to measure water saturation versus depth at depths of up to 22 feet. The experiment was simulated with the computer model and excellent agreement between calculated results and the data was obtained; thus the mathematical model could be used to describe soil moisture movement during wetting and drying periods.
Water Resources Research – Wiley
Published: Jun 1, 1970
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