Thirtieth Annual Robert J. Melosh Competition - "Modeling Flow, Reactive Transport and Geomechanics in Porous Media"

In this presentation, we discuss enriched Galerkin (EG) algorithms for modeling Darcy flow, reactive transport, and geomechanics in porous media. This approach involves enriching the continuous Galerkin finite element method with discontinuous elements. For transport EG is coupled with entropy residual stabilization for transport. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele-Shaw cells are illustrated as well as results for two phase flow. Here dynamic adaptive mesh refinement is applied in order to save computational cost for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents any spurious oscillations. Applications of EG to acidizing in carbonate reservoirs and coupling with mechanics using fixed stress is also discussed. This work was done in collaboration with Sanghyun Lee at Florida State and Rencheng Dong at UT-Austin.