Changes in the porosity and permeability of a porous medium due to melting are modeled. A frozen phase, which initially fills a part of the porous medium, melts and gets dissolved in the injected hot solvent. The amount of melted material, the rate of melting as well as the profiles of temperature, porosity, and concentration are analyzed to understand the nature of this naturally and industrially important phenomenon. Four reference scenarios corresponding to instantaneous thermal equilibrium, no heat transfer to the frozen phase, no-melting, and instantaneous melting conditions are solved analytically and the effects of different parameters are discussed. Numerical simulation results show that the profiles of the fluid temperature, porosity of the medium, and solvent concentration, form three fronts moving at different rates. it is found that for heat transfer coefficients above a certain value, the rate of melting is independent of this parameter and the system can be considered to have reached instantaneous thermal equilibrium. Moreover, slow heat transfer in the medium is shown to increase the rate of melting at long time periods by involving larger areas in the melting process. Heterogeneous scenarios are also analyzed by introducing frozen blocks of different geometries. The ability of the flow to bypass the frozen region involves a new heat transfer mechanism identified as outer-boundary convection. The effects of the geometry of the block along with the other parameters on the melting process are examined. Furthermore a generalizing scheme is proposed to predict the melt production for different block geometries and values of the saturation of the frozen phase. (C) 2015 Elsevier Ltd. All rights reserved.