Predictive Modeling of Relative Permeability using a GeneralizedEquation-of-State

摘要

Reliable simulation of enhanced oil recovery processes depends on an accurate description of fluidtransport in the subsurface.Current empirical transport models of rock-fluid interactions are fit to limitedexperimental data for specific rock types,fluids,and boundary conditions.In this paper,a general equation-of-state(EoS)approach is developed for relative permeability(kr)based on a set of geometric stateparameters:normalized Euler characteristic(connectivity)and saturation.Literature data and pore-networkmodeling(PNM)simulations are used to examine the functional form of the EoS.Our results show that the new kr-EoS matches experimental data better than the conventional Coreyform,especially for highly nonlinear relative permeabilities at low saturations.Using hundreds of PNMsimulations,relative permeability scanning curves show a locus of residual saturation and connectivitywhich defines an important limit for the physical kr region.The change of this locus is also considered fortwo contact angles.PNM data further allows for the estimation of the relative permeability partial derivativeswhich are used as inputs in the EoS.Linear functions of these partials in the connectivity-saturation spacerenders a quadratic response of kr,which shows excellent predictions.Unlike current empirical models thatare based on only one residual saturation,the state function approach allows for dynamic residual conditionscritical for capturing hysteresis in relative permeability.