Modeling of Cyclic Hysteresis of Three-Phase Relative Permeability During Water-Alternating-Gas Injection

Multiphase flow takes place in many petroleum reservoirs-in particular, mature fields and reservoirs under fluid [e.g., gas, water-alternating-gas (WAG)] injection. The numerical simulation of such reservoirs requires knowledge of flow functions (i.e., relative permeability and capillary pressure). Because experimental measurement of fluid permeabilities (in particular) under three-phase-flow conditions is very time-consuming and difficult, many correlations and models were developed and these are widely used instead of measured data. In this study, we have used the results of a comprehensive set of WAG-injection coreflood experiments performed under different wettability conditions and core-permeability values to obtain relative permeabilites of oil, water, and gas under reservoir pressure and temperature. Three-phase relative permeability of each phase was obtained by history matching the measured production and differential pressure obtained in the laboratory. The results of the experiments revealed significant cyclic hysteresis effects in gas and oil relative permeability. We proposed new formulations and methodology for the modeling of cyclic hysteresis of three-phase relative permeability during WAG injection. This technique is a direct method that uses measured three-phase k(r) data obtained from the first cycle of WAG injection to predict the relative permeability of the subsequent cycles. The integrity of this technique was validated against the three-phase k(r) data obtained from our WAG experiments. We also assess the validity of the WAG-injection hysteresis model available in reservoir simulators against our three-phase relative permeability data to evaluate its performance.