On the development of a relative permeability equation of state

Standard compositional simulators use composition-dependent cubic equations of state (EoS), but saturation-dependent relative permeability and capillary pressure. This discrepancy causes discontinuities, increasing computational time and reducing accuracy. In addition, commonly used empirical correlations, such as the Corey relative permeability model, show a sole dependence of relative permeability on phase saturation, lumping the effect of other pore-scale phenomena into one tuning exponent. To rectify this problem, relative permeability has been recently defined as a state function, so that it becomes compositional dependent and single valued. Such a form of the relative permeability EoS can significantly improve the convergence in compositional simulation for both two- and three-phase flows. This paper revisits the recently developed EoS for relative permeability by defining relevant state variables and deriving functional forms of the partial derivatives in the state function. The state variables include phase saturation, phase connectivity, wettability index, capillary number, and pore topology. The developed EoS is constrained to key physical boundary conditions. The model coefficients are estimated through linear regression on data collected from a pore-scale simulation study that estimates relative permeability based on micro-CT image analysis. The results show that a simple quadratic expression with few calibration coefficients gives an excellent match to two-phase flow simulation measurements from the literature. The goodness of fit, represented by the coefficient of determination (R²) value, is 0.97 for relative permeability at variable phase saturation and phase connectivity, and constant wettability, pore structure, and capillary number (∼ 10^{− 4}). The quadratic response for relative permeability also shows excellent predictive capabilities.