Analysis and upscaling of a reactive transport model in fractured porous media with nonlinear transmission condition

Abstract

We consider a reactive transport model in a fractured porous medium. The particularity appears in the conditions imposed at the interface separating the block and the fracture, which involves a nonlinear transmission condition. Assuming that the fracture has thickness ε, we analyze the resulting problem and prove the convergence toward a reduced model in the limit ε↘0. The result is a model defined on an interface (the reduced fracture) and acting as a boundary condition for the equations defined in the block. Using both formal and rigorous arguments, we obtain the reduced models for different flow regimes, expressed through a moderate or a high Péclet number.