Two reduced models for reactive flows in fractured porous media

In the simulation of many porous media applications, such as geothermal energy, CO2 and nuclear waste storage and groundwater management, transport and reaction processes are fundamental to make accurate and reliable predictions. Moreover, the fractures present in the undeground, with their physical properties (high/low conductivity) and complex geometry are of paramount importance, on one side, but extremely complex to handle on the other. We propose two models based on a geometrical reduction procedure that approximate fractures as objects of lower dimension forming thus a system of mixed-dimensional partial differential equation. The first model describes a thermal reactive flow problem in both the fractures and porous media, coupled with suitable interface conditions. Chemical reactions can change porosity and fracture aperture with dissolution and precipitation of minerals. To obtain the solution for each time step, we consider a splitting strategy so that each physical process is solved sequentially ensuring, at the discrete level, mass conservation.  The second model in addition accounts for a thin layer of porous media surrounding the fractures where the effect of chemical reactions is prevalent, approximating it with a line/surface coupled with the fracture. Its thickness, which may change in time, is estimated with a mono-dimensional equation solved in the direction normal to the fracture. Comparison with the equi-dimensional problem ensure the quality of the proposed models.