Constitutive relation for the mass transfer during a gas‐liquid phase transition in porous media

Abstract

AbstractThe transition between two different phases of a substance is an everyday process, which is encountered amongst others in the geomechanical field, for example, in CO2 storage. The transition from the liquid to the gaseous phase and vice versa crosses the so‐called two‐phase region, where both phases coexist for specific temperature and pressure conditions. In this context, two mass‐balance equations are defined for both fluid phases, respectively. These two equations are coupled by the mass‐production term, which describes the mass transfer between the two phases during phase transition. A great variety of models exist to describe phase transition processes in zero dimensional systems, e. g., batch reactors. However, only a few articles can be found, where phase changes inside a porous medium are discussed. An approach to the latter case can be based on the well‐founded, continuum‐mechanical Theory of Porous Media (TPM), which allows to describe multi‐phasic flow inside a deformable porous medium. By evaluating the entropy inequality, a constitutive relation for the mass production term can be derived. This term compares to the two‐film theory, the standard model for the description of mass transfer in a two‐phase system. Adapting this relation to porous media leads to a mass transfer coefficient, which represents the kinetic behaviour of the molecules of the substance under consideration and the influence of the solid porous material on the phase transition process. For lack of experimental data, the mass transfer coefficient will be composed of the transfer coefficient from classical thermodynamics and geometrical information of the porous‐media structure. The thermodynamical behaviour of the fluid is described by, e. g., the Redlich‐Kwong‐Soave equation of state. Simulations conducted with either changing temperature or pressure boundary conditions are compared with simulations, where only one mass balance is used for both fluid phases and the mass transition is only visible by the jump in density. This allows for the verification of the derived constitutive relation. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)