Permeability Hysteresis in Gravity Counterflow Segregation
Pavel Bedrikovetsky | Schaerer , Christian | Sarkis , Marcus | Marchesin , Dan
relative permeability | hysteresis | Riemann problem | conservation laws | two-phase flow in porous media | Godunov method laws | two-phase flow in porous media | Godunov method
Hysteresis effects in two-phase flow in porous media are important in applications such as waterflooding or gas storage in sand aquifers. In this paper, we develop a numerical scheme for such a flow where the permeability hysteresis is modelled by a family of reversible scanning curves enclosed by irreversible imbibition and drainage permeability curves. The scheme is based on associated local Riemann solutions and can be viewed as a modification of the classical Godunov method. The Riemann solutions necessary for the scheme are presented, as well as the criteria that guarantee the well-posedness of the Riemann problem with respect to perturbations of left and right states. The numerical and analytical results show strong influence of the permeability hysteresis on the flow. In addition, the numerical scheme reproduces accurately the available experimental data once hysteresis is taken into account in the model.