Equation of state for relative permeability, including hysteresis and wettability alteration

Commercial compositional simulators commonly apply correlations or empirical relations that are based on fitting experimental data to calculate phase relative permeabilities. These relations cannot adequately capture the effects of hysteresis, fluid compositional variations, and rock-wettability alteration. Furthermore, these relations require phases to be labeled, which is not accurate for complex miscible or near-miscible displacements with multiple hydrocarbon phases. Therefore, these relations can be discontinuous for compositional processes, causing inaccuracies and numerical problems in simulation. This paper develops for the first time an equation-of-state (EOS) to model robustly and continuously the relative permeability as a function of phase saturations and distributions, fluid compositions, rock-surface properties, and rock structure. Phases are not labeled; instead, the phases in each gridblock are ordered on the basis of their compositional similarity. Phase compositions and rock-surface properties are used to calculate wettability and contact angles. The model is tuned to measured two-phase relative permeability curves with very few tuning parameters and then is used to predict relative permeability away from the measured experimental data. The model is applicable to all flow in porous-media processes, but is especially important for low-salinity polymer, surfactant, miscible gas, and water-alternating-gas (WAG) flooding. The results show excellent ability to match measured data, and to predict observed trends in hysteresis and oil-saturation trapping, including those from Land's model and for a wide range in wettability. The results also show that relative permeabilities are continuous at critical points and yield a physically correct numerical solution when incorporated within a compositional simulator (PennSim 2013). The model has very few tuning parameters, and the parameters are directly related to physical properties of rock and fluid, which can be measured. The new model also offers the potential for incorporating results from computedtomography (CT) scans and pore-network models to determine some input parameters for the new EOS.