Condensation in a porous medium

One-dimensional, steady-state heat and mass transfer with phase change are studied, for a two-phase zone in a water-saturated porous medium. A model problem for the saturation and fluid pressures is formulated, and an explicit temperature dependence for the saturation vapour pressure, together with an explicit saturation dependence for the capillary pressure allows us to solve the model problem for temperature and saturation profiles within the two-phase zone. A boundary layer analysis identifies existing models as approximations to the full model in the large vapour-pressure gradient limit. This approximation yields an uncoupled problem for saturation and temperature, and asymptotic analysis shows that a singularity is introduced if we accept the approximate model over the full model. An iterative method is described which allows both the full and outer models of the two-phase zone to be coupled to the two single-phase zones, and computations are performed with realistic control parameters for the entire three-zone system. Numerical solutions for both the two-phase zone and the three-zone system show excellent agreement between the full and outer formulations.Science, Faculty ofMathematics, Department ofGraduat