Dissolution of an immobile phase during flow in porous media

In this paper we examine the problem of the dissolution of an immobile phase during flow in porous media with the objective of deriving an evolutionary transport equation for the volume fraction of the immobile phase. Both the speed of displacement of the phase interface and the interfacial mass-transfer coefficient are represented in terms of mapping variables that are determined by the solution of two closure problems. Other problems of this type include the dissolution and phase change of solids and liquids which can occur because of concentration and temperature gradients. The dissolution of solids is of interest to geologists concerned with transport in sedimentary basins, while engineers are often confronted with freezing and melting processes in multiphase systems. The analysis presented in this paper provides a theoretical framework for the solution of these problems.