Title: Bound-Preserving and Phase-wise Conservative Schemes for Incompressible Two-Phase Flow in Porous Media with Multiple Capillary Pressure Functions

Abstract: Two or multiple phases commonly occur as fluid mixture in petroleum industry, where oil, gas and water are often produced and transported together. As a result, petroleum reservoir engineers spent great efforts in the development and production of oil and gas reservoirs by conducting and interpolating the simulation of multiphase flows in porous geological formation. Meanwhile, environmental scientists use subsurface flow and transport models to investigate and compare for example various schemes to inject and store CO2 in subsurface geological formations, such as depleted reservoirs and deep saline aquifers. One basic requirement for accurate modeling and simulation of multiphase flow is to have the predicted physical quantities sit within a physically meaningful range. For example, the predicated saturation should sit between 0 and 1 while the predicated molar concentration should sit between 0 and the maximum value allowed by the equation of state. Unfortunately, popular simulation methods used in the industries do not preserve physical bounds. A commonly used fix to this problem is to simply apply a cut-off operator (say, to the computed saturation) at each time step, i.e., to set the saturation to be zero whenever it becomes negative, and to set it to one whenever it becomes larger than one. However, this cut-off practice does not only destroy the local mass conservation, but it also damages the global mass conservation, which seriously ruins the numerical accuracy and physical interpretability of the simulation results.