Numerical Modeling of the Drying of Porous Materials
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 resea
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G. Ronald Hadley Fluid and Thermal Sciences Department Sandia National Laboratories Albuquerque, New Mexico, USA
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 assumed 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 thi$ 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. 1. INTRODUCTION When a partially saturated porous material dries, the coupled transport of heat, liquid water, water vapor, and air is often involved. Although this fact has been known for some time, a complete solution of drying problems has been severely hampered, due primarily to two factors: the coupling of the transport equations, and the strong nonlinearities in each equation. The equation R. Toei et al. (eds.), Drying ’85 © Springer-Verlag Berlin Heidelberg 1985
describing the transport of the liquid phase contains nonlinear terms arising primarily from the shape of the capillary pressure curve. The gas transport equations are non-linear due to the inclusion of Darcy's law, and the heat equation due to temperature-dependent transport properties. The equations are coupled as a result of evaporation/condensation, the influence of gas pressure gradients on liquid motion, and convective cooling by all three fluid phases. These complications have rendered analytic solutions impossible for all but the simplest drying problems. Although the advent of the high-speed computer has opened up new possiblilties for numerical solu
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