The process by which rocks are formed from the burial of a fresh sediment involves the coupled effects of mechanical compaction and geochemical reactions. Both of them affect the porosity and permeability of the rock and, in particular, geochemical reactions can significantly alter them, since dissolution and precipitation processes may cause a structural transformation of the solid matrix. Often, the differential problems that arise from the modeling of these chemical reactions may present a discontinuous right hand side, where the discontinuity depends on the solution itself. In this work we have developed a numerical model to simulate this complex multi-physics problem by treating the discontinuous right hand side with a specially tailored event-driven numerical scheme. We show the performance of this strategy in terms of positivity and mass conservation, also in comparison with a more traditional approach that relies on a regularization of the discontinuous terms.@en

The present work deals with the numerical simulation of porous media subject to the coupled effects of mechanical compaction and reactive flows that can significantly alter the porosity due to dissolution, precipitation or transformation of the solid matrix. These chemical processes can be effectively modelled as ODEs with discontinuous right hand side, where the discontinuity depends on time and on the solution itself. Filippov theory can be applied to prove existence and to determine the solution behaviour at the discontinuities. From the numerical point of view, tailored numerical schemes are needed to guarantee positivity, mass conservation and accuracy. In particular, we rely on an event-driven approach such that, if the trajectory crosses a discontinuity, the transition point is localized exactly and integration is restarted accordingly.@en