Fluid transport in Forchheimer porous medium with spatially varying porosity and permeability

Filtration of incompressible fluid in a saturated heterogeneous porous medium is theoretically studied. A mathematical model is based on the Forchheimer equation with an additional term that takes into account the heterogeneity of the medium. The effect of spatially varying permeability and porosity on the filtration in a flat channel is numerically investigated. For simplicity, we make an assumption about the lack of correlation between porosity and permeability and take them as independent parameters of the medium. The results show that the spatial variations of permeability and porosity affect transport in porous media in different ways. In the first case, the fluid flowing around the areas with low permeability obeys the Forzheimer law. The structure of the hydrodynamic fields and the flow rate do not vary when the flow direction changes to the opposite. In the media with varying porosity, the flow asymmetry is observed: filtration rate in the direction of increasing porosity is greater than in the opposite direction...