Proposal
A numerical scheme is unstable when the result, during the solution procedure, becomes unbounded. Explicit schemes, such as IMPES, are limited by stability conditions. Robust stability criteria can help in understanding the numerical scheme's behavior and can also be used as switching criteria for adaptive implicit models. In this paper, general stability criteria are derived for black-oil and compositional models with various levels of implicitness, including pressure implicit, pressure and saturation implicit and fully implicit.
Unlike the existing stability analyses for reservoir simulation models, we start with the most general multiphase multicomponent model framework and derive stability criteria using Fourier stability analysis on the equations to which explicit schemes are applied. Our approach takes into account all of the major mechanisms governing fluid flow, i.e., convection, diffusion, capillary forces, gravity, fluid and rock compressibility, vapor-liquid equilibrium in compositional models and solubility in black-oil models. The derived criteria can provide a reasonable measure in the most general models. Black-oil models are treated as special cases of compositional models.
Our approach is compared to existing approaches; its application within ExxonMobil's reservoir simulator, EMpower, is discussed.
