Mathematical analysis and numerical simulation of multi-phase multi-component flow in heterogeneous porous media

Multi-phase multi-component flow processes are fundamental to engineering applications in hydrocarbon and geothermal reservoirs but also to many classical geological processes. This review will highlight recent developments in the mathematical modelling and numerical simulations of the underlying physical processes from the pore- to the reservoir scale. Many modern approaches now rely on integrating numerical and analytical methods and incorporate results across the different length scales. This provides new insights into the fundamental properties of multi-phase multi-component flow and helps to mitigate some of the inherent difficulties in quantifying them in subsurface reservoirs.