Premium
Thermodynamically consistent description of mass transfer in porous media by a singular surface
Author(s) -
Häberle Kai,
Ehlers Wolfgang
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510186
Subject(s) - mass transfer , porous medium , phase transition , thermodynamics , isothermal process , mechanics , porosity , heat transfer , thermoelastic damping , jump , materials science , physics , quantum mechanics , thermal , composite material
Phase transition processes are important and ubiquitous physical phenomena. These processes are not limited to systems like batch reactors, but can also appear inside porous solids such as in the sequestration of CO 2 or in the food industry. In these processes, mainly first‐order transitions between the liquid and the gaseous phases of a certain fluid occur and are characterised by a jump in density and the coexistence of both phases during phase change. This jump is numerically handled by introducing a singular surface, which allows for a thermodynamically consistent description of the mass transfer during phase transition. The mass transfer is driven by the change in internal energy and couples the two mass balance relations of the two fluid phases. The formulation of a model for a multiphasic porous aggregate in a non‐isothermal environment, while accounting for the thermodynamics of the fluids and the phase transition, requires a potent theory for its description. Here, the Theory of Porous Media (TPM) provides a well‐founded, continuum‐mechanical basis to model deformable, fluid‐saturated porous media. In this particular case, a three‐phasic model is proposed, consisting of the thermoelastic solid phase, which is percolated by the compressible gaseous and liquid fluid phases. The representation of the interface between the fluid phases by a singular surface results in additional terms in the balance relations. The evaluation of these terms leads to a consistent formulation of the mass transfer, which basically compares the energy added to the system with the latent heat of the phase transition. This mass‐transfer term is furthermore dependent on the interfacial area, a factor defined by porosity and saturation. Finally, the proposed model for phase transition inside a porous medium is based on the mixture momentum balance, the volume balances of the fluid phases and the energy balance. Consequently, the four primary variables are the solid deformation, the effective pore pressures of the two fluid phases and the temperature. The numerical simulation of condensation or evaporation of CO 2 in a porous solid rock, which can be either caused by changes in temperature or in pressure, allows for the demonstration of possible application areas for the presented model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)