Homogenization approach to the upscaling of a reactive flow through particulate filters with wall integrated catalyst

Catalytic membranes can degrade gaseous pollutants to clean gas via a catalytic reaction to achieve green emissions. Further, a catalytic membrane is a three scale porous medium. Membranes used in catalytic filters usually have thicknesses of centimeters or millimeters, and consist of active (washcoat) particles, inert material and microscale, micron size, pores. The washcoat particles are porous material with nanoscale pores. The catalytic reactions are heterogeneous (surface reactions) and they occur on the surface of the nanopores. Obviously, simulations at fully resolved pore scale are not feasible, and upscaling techniques have to be applied. It is known that the same microscale problem can be upscaled to different macroscale equations depending on the characteristic numbers. In this paper we study the homogenization of reactive flow in the presence of strong absorption in the washcoat particles. Two reactive transport regimes are studied, where in both the reaction dominates over the convection and the diffusion. Péclet's number in the first one is of order 1, and in the second one it is proportional to the ratio of the thickness of the catalytic membrane and the characteristic length of the microscale pores. Two different upscaled equations are obtained, respectively. Direct numerical simulation at microscale is used to validate these derived macroscale equations.