Humans living in space generate wet trash which includes food residues, moist hygiene wipes and wet paper towels. For long-term space missions, these wastes must be treated to control microbial growth and avoid associated health hazards. Recovery of water in the trash will also reduce payload mass and resulting lift costs. These problems are solved by a closed-loop, forced-convection, heat-pump drying system which stops microbial activity by both pasteurization and desiccation, and recovers moisture in a gravity-independent porous media condensing heat exchanger. A computational model of the system consisting of the air heater, dryer vessel, condenser, and thermoelectric heat-pump coolers has been developed. The simulation uses a bypass factor to model drying efficiency and to predict the properties of the humid air leaving the drying vessel. The conservation equations for mass, energy, and fluid flow were applied to the condenser to give a system of partial differential equations that was solved numerically by the finite element method. The thermodynamic efficiency and power load of the thermoelectric cooler and heaters were computed for different dryer and condenser conditions. Simulation values were compared with experimental data to validate the model for various operating conditions at sea-level pressure and unit gravity. The model predicts the system performance, energy use per unit of recovered water, and effectiveness of enthalpy recovery options. This can be used to optimize the performance of the drying system for various space habitat conditions.