Numerical Modeling of the Drying of Porous Materials

Abstract

The drying of porous materials represents a challenging class of problems involving several nonlinear transport mechanisms operative in both the liquid and vapor phases. The difficulties encountered in attempting to solve such problems have led most researchers to simplify their models in one of two ways: either 1) moisture migration is ssumed to proceed only in the liquid phase towards a drying surface where it then evaporates, or 2) evaporation occurs at a stationary liquid-vapor interface and is transported to the drying surface as a vapor (evaporation front model). Although there are some situations in which one of these models may be adequate, most drying problems involve the transport of both phases simultaneously. The disposal of nuclear waste canisters in partially saturated geological formations offers a good example of this class of problems, a class for which presently existing solution methods are inadequate.

This paper presents a one-dimensional numerical solution technique for the transport of water, water vapor, and an inert gas through a porous medium. The fundamental equations follow from the application of volume averaging theory. These transient equations are finite differenced and solved using a predictor-type time integration scheme especially formulated to provide stable solutions of the resulting strongly coupled nonlinear equations. Solutions are presented for a simple problem involving the drying of a bed of sand, for which experimental data is available. The inclusion of vapor phase transport for this problem is shown to lead naturally to a prediction of the constant rate and falling rate periods of drying. Results are seen to be especially sensitive to the choice of a function representing the relative permeability of the bed for low saturations.