Elliptic regions in porous media flow: Effect of relative permeability on loss of strict hyperbolicity in three-phase porous media flow
A.S. Markensteijn · Research Repository (Delft University of Technology) · 2016
Reservoir simulation is a widely used means for prediction and optimization of oil recovery from a reservoir and it is based on the multiphase porous media flow model. For one dimensional, incompressible, immiscible three-phase flow in a homogeneous medium without gravity and capillary pressure, loss of strict hyperbolicity can occur for certain relative permeability models causing problems when solving the three-phase flow model numerically. To avoid loss of strict hyperbolicity, a set of three curves is used to determine the existence of an elliptic region and modelling three-phase relative permeability is seen as an interpolation problem between two two-phase relative permeabilities. This results in a new type of three-phase relative permeability model where the relative permeabilities of all three phases depend on both the water and gas saturation. The new relative permeability models are able to avoid loss of strict hyperbolicity in some cases where the existing relative permeability models resulted in an elliptic region, however, the new relative permeability models do not guarantee strict hyperbolicity for all situations. This leads to the view that a relative permeability model must be chosen for each situation separately.