Non-isothermal two-phase flow in deformable porous media: systematic open-source implementation and verification procedure

We propose a formulation for non-isothermal two-component two-phase flow through deformable porous media. The approach covers phase transitions among both phases, i.e. liquid phase components evaporate into the gas phase while gas phase components dissolve or condensate into the liquid phase. These phase transitions always take place in thermodynamic equilibrium. The set of model equations is thereby largely independent of the specific constitutive relations. Starting from general equilibrium equations, we show the evolution of the system of weak formulations of all governing equations, which are then discretised with Taylor-Hood elements in a standard finite element approach. The model equations and the construction of the constitutive equilibria are implemented in the open-source simulator OpenGeoSys, which can be freely used and modified. To verify the implementation, we have selected a number of complementary test cases covering a wide range of process couplings. The numerical model is compared with analytical and semi-analytical solutions of these problems as well as with experimental results. It is shown in the paper that by including thermodynamic effects, solid mechanics, and phase transition processes, the proposed numerical model covers many characteristic features of unsaturated geomaterials and can be employed for the description of a broad range of problems encountered in geotechnical engineering. Article highlights An open-source FEM tool for non-isothermal two-phase flow in deformable porous or fractured media is presented in detail. The model features phase transitions across both fluid phases based on simple equilibrium conditions. A variety of benchmark tests is presented and compared to other software results and to exact solutions.