Phreatic eruptions are non-magmatic explosions consisting in the sudden expansions of groundwater due to the input of hot magmatic ¿¿uids and heat. Although such eruptions are intrinsically less hazardous than magmatic eruptions (i.e. the energy released in the process is relatively low) the lack of clear and early precursory signals increases the associated risks. Moreover, the priming mechanisms of phreatic eruption are still not completely understood. In this work we propose a physical model for the priming mechanism of phreatic eruptions. This model is based on the mixture theory and describes the dynamic and energetic evolution of a two-phases ¿¿uid composed of several chemical species within a porous matrix. In particular, we decided to not use the Darcy ¿¿ow approximation as momentum conservation equation in order to relax a set of assumptions. The system must be coupled with an equation of state in order to describe the relations between thermodynamic properties of the ¿¿uid and phase transitions. The complexity of this model requires the solution to be numerical. In this regard, we created Phreer, a module for the ¿¿nite-element solver Alya. To the present date, the model is coupled with an equation of state capable of describing the thermodynamic properties of a water-carbon dioxide mixture with pressures up to 10.0 GPa and temperatures in the range of 673.15 K and 2573.15 K, i.e. the pressure-temperature ranges we expect to observe within volcanic domains.