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

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 e, we analyze the resulting problem and prove the convergence towards a reduced model in the limit e ¿ 0. The resulting 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. Keywords: Fractured porous media; Upscaling; Reactive transport; Nonlinear transmission conditions