Energy Equation for Volatile Liquid Transport in Porous Media

Abstract

Two energy balance equations widely used to describe simultaneous transfer of heat and mass in porous media are inconsistent with control volume energy conservation. Potential energy, enthalpy, and internal energy terms are involved in the discrepancies. Energy within a volume is properly counted as the sum of internal, potential, and kinetic energy. However, one equation uses enthalpy where internal energy should have been used. In the other, potential energy and shifts in internal energy associated with heat of wetting are not included. Energy conservation for a control volume dictates summing convective fluxes of internal, potential, and kinetic energy at the control volume surface along with conducted heat and work crossing the boundary. The pressure–volume (pv) work at the volume surface may be combined with internal energy convection so that flow of enthalpy is used in the flux term. Examples of energy change versus work input in adiabatic processes illustrate the error introduced when enthalpy rather than internal energy is used to compute control volume energy content. For porous media flows kinetic energy can be dropped. A consistent equation based on the control volume approach is presented. It includes effects due to internal energy, potential energy, heat of wetting, conducted heat, non-pv work, enthalpy, and mass flow. Substantial temperature changes due to heat of wetting have been found experimentally in a separate work. A comparison is needed of the experiments and a numerical simulation based on the new equation.