The model equations that are solved in the Multiphase Flow in Porous Media interface are based on the mass conservation of each phase and on an extended Darcy’s law. The mass conservation equation for each phase is given by

where εp (dimensionless) is the porosity, and the vector ui should be interpreted as the volumetric flux of phase i (SI unit m3/(m2·s) or m/s). The volumetric fluxes are determined using the extended Darcy’s law (Ref. 2)

where κ denotes the permeability (SI unit: m2) of the porous medium, g the gravitational acceleration vector (SI unit m/s2), and μi the dynamic viscosity (SI unit: kg/(m·s)), pi the pressure field (SI unit: Pa), and κri the relative permeability (dimensionless) of phase i, respectively. The phase pressures pi are related through the capillary pressure functions :

One phase pressure can be chosen independently so that N − 1 capillary pressure relations are needed to define the other phase pressures. In addition it is assume that all phases together fill the pore space completely, so that we have