Methodology for Numerical Simulation With Cycle-Dependent Relative Permeabilities

Multiphase flow involving saturation oscillations should be modeled with history-dependent, relative permeability functions. Earlier approaches have been based on two-phase flow. The main assumptions have been that the imbibition process is reversible. Moreover, scanning curves were developed only for saturations between some extreme values. Several tertiary oil recovery processes have shown cycle-dependent hysteresis for relative permeability. When saturation oscillations occur during three-phase flow such as water alternating gas (WAG), the two-phase hysteresis models will generally not be able to describe relative permeabilities obtained from corefloods. For three-phase flow, local hysteresis effects may also be important. New relative permeability representations that account for local hysteresis effects are presented. Hysteresis models for both wetting and nonwetting phase permeabilities have been developed. The new models account for reduced mobility and irreversible hysteresis loops during three-phase flow. The models depend on the initial saturation at the start of the given process. An algorithm is presented for implementing the nonwetting phase hysteresis model in a numerical simulator. The new three-phase models use experimental wetting and nonwetting relative permeabilities as input, and knowledge of relations between maximum nonwetting saturation and trapped nonwetting saturation.