Heat Transfer in Porous Media Heated From Above With Evaporation, Condensation, and Capillary Effects

Heat and mass transfer characteristics of a sand-water-steam system heated at the top and cooled at the bottom were studied. It was found that at steady-state conditions the system segregated into three regions. The top region was conduction-dominated with the voids containing a stationary superheated steam. The middle region was convection-dominated, nearly isothermal, and exhibited an upward flow of the liquid by capillary forces and a downward flow of steam due to a slight pressure gradient. The bottom portion contained a stationary compressed liquid and was also conduction dominated. The length of the two-phase convection zone was evaluated through the application of Darcy’s equations for two-phase flow and correlations of relative permeabilities and capillary pressure data. The model was in excellent agreement with the observed results, predicting a decreasing two-phase zone length with increasing heat flux. The thermodynamics of the two-phase zone were also analyzed. It was found that the vapor phase was in a superheated state as described by the Kelvin equation for vapor pressure lowering. Also, it was evident that the liquid must also be superheated for thermodynamic equilibrium to result. A stability analysis demonstrated that the superheated liquid can exist in an unconditionally stable state under conditions typical of porous systems. The degree of liquid superheat within the two-phase zone of these experiments was obtained.