Transitions between liquid and gaseous phases of a fluid material are characterised by a jump in density and the coexistence of both phases during the phase change process. The jump occurs at the interface between the fluid phases and can be handled numerically by the introduction of a singular surface. This allows for a thermodynamically consistent description of mass transfer across the interface and the transition of the interfacial term towards the mass production term included in the mass balance equations. In the present article, a multicomponent and multiphasic porous aggregate is treated in a non-isothermal environment, while accounting for the thermodynamics of the fluid-phase transitions. Based on the Theory of Porous Media, this approach provides a well-founded continuum mechanical basis for the description of deformable, fluid-saturated porous solid aggregates. In particular, a bicomponent, triphasic model is proposed consisting of a thermoelastic porous solid, which is percolated by compressible gaseous and liquid fluid phases. The thermodynamical behaviour, i.e. the dependency of the fluid densities on temperature and pressure, is governed by the van der Waals equation of state and the Antoine equation for the vaporisation-condensation line. Moreover, the interface between the fluid phases is represented by a singular surface and results in jump conditions included in the balance relations of the components of the overall aggregate. The evaluation of the jump conditions leads to a formulation of the interfacial mass transfer, which basically relates the energy added to the system to the latent heat needed for the phase change in a certain amount of a substance. The mass transfer itself or the mass production, respectively, furthermore depends on interfacial areas introduced as a function of

The transition between two different phases of a substance is an everyday process, which is encountered amongst others in the geomechanical field, for example, in CO 2 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.

Supercritical CO 2 can be injected into deep saline aquifers to reduce the amount of CO 2 in the atmosphere and thus, lessen the impact on the global warming. Qualified reservoirs should be in a sufficient depth to guarantee the thermodynamical environment for the supercritical state of CO 2 and should be confined by an impermeable cap-rock layer. It is crucial to guarantee the safety of the storage site. Therefore, deformation processes and crack development of the rock matrix and the cap-rock layer, which might be induced by the high pressure injection of CO 2 , must be investigated. If cracks occur, CO 2 could migrate into shallower regions, where the temperature and pressure cannot support the supercritical condition of the CO 2 anymore. Thus, it is important to describe the phase transition process between supercritical, liquid and gaseous CO 2 . The Theory of Porous Media (TPM), see e. g. [1], provides a useful continuum-mechanical basis to describe real natural systems in a thermodynamically consistent way. Hence, the TPM is applied to model multiphasic flow of CO 2 and water and to include elasto-plastic solid deformations of the porous matrix. The Peng-Robinson equation, e. g. [2], is implemented as a cubic equation of state to describe the phase behaviour of CO 2 . However, the two-phase region cannot be represented by a continuously differentiable function such as the Peng-Robinson equation and thus, the Antoine equation provides additional information of the vapourisation curve. The Extended Finite-Element Method (XFEM) will be used to account for the discontinuities arising from crack development due to solid deformations [3]. Herein, special attention has to be paid to the matrix-fracture interaction of the fluid phases. Numerical examples are performed to investigate the injection of CO 2 into a saline aquifer. These are computed with the FE program PANDAS, which allows for solutions of strongly coupled multiphasic problems in deformable porous media.

CO2 is supposed to be one of the major greenhouse gases. Thus, the idea arose to capture and store CO2 in the subsurface. Besides other geological formations, CO2 can be injected into deep saline aquifers, where its upward migration is blocked by an almost impermeable cap‐rock layer. It is crucial to guarantee the safety of this storage and to eliminate possibilities of leakage. Therefore, deformation processes of the rock matrix and the cap‐rock layer, which might be induced by the high pressure injection of CO2, must be investigated. The deformations may lead, on the one hand, to an increase in porosity and permeability and thereby improve the storage capacity of the reservoir. On the other hand, the increase in stress results in solid deformations of the rock matrix and may cause crack development in the cap‐rock layer. Additionally, phase transition processes between supercritical, liquid and gaseous CO2 have to be taken into account when the pressure or the temperature in the reservoir changes. The phase transition can cause an increase of CO2 volume and, hence, an increase in pressure and stress.A continuum‐mechanical description of multiphasic flow including solid deformations is derived, which is based on the Theory of Porous Media (TPM). An elastic‐plastic material law is applied to account for the behaviour of the solid skeleton. Numerical examples are used to investigate the injection of CO2. Regions with high stresses can be identified and considered for crack initiation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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