Upscaling coupled heterogeneous diffusion reaction equations in porous media

In this work, the periodic homogenization method is applied to a system of two equations of diffusion coupled through heterogeneous chemical reactions at the solid-fluid interface. This upscaling is discussed according to the order of magnitude of the Damkohler number. For large values of Damkohler number, a new homogenized diffusion reaction model coupling chemical reaction and diffusion is obtained. The homogenized diffusion and co-diffusion tensors are function of the heterogeneous reaction rate coefficients. The relevance of this homogenized model is analysed with respect to the order of magnitude of the Damkohler number. Some numerical simulations using this homogenized model are carried out and compared to numerical simulations at pore scale.

Automated summary

In this work, the periodic homogenization method is used to study a system of two diffusion equations coupled through heterogeneous chemical reactions. The upscaling is discussed based on the magnitude of the Damkohler number. For large Damkohler numbers, a new homogenized diffusion reaction model that couples chemical reaction and diffusion is obtained. The homogenized diffusion and co-diffusion tensors depend on the heterogeneous reaction rate coefficients. The relevance of this homogenized model is analyzed in relation to the magnitude of the Damkohler number. Numerical simulations using this homogenized model are conducted and compared to simulations at the pore scale.