Modelling of cyclic hysteresis of three-phase relative permeability during water-alternating-gas (WAG) injection

Multiphase flow takes place in many petroleum reservoirs in particular mature fields and reservoirs under fluid (e.g., gas, WAG) injection. The numerical simulation of such reservoirs requires knowledge of flow functions (i.e. relative permeability and capillary pressure). Since experimental measurement of fluid permeabilities in particular under three-phase flow conditions is very time consuming and difficult, many correlations and models have been developed and are widely used instead of measured data. In this study, we have used the results of a comprehensive set of water-alternating-gas (WAG) injection coreflood experiments performed under different wettability conditions and core permeability values in order 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 modelling of cyclic hysteresis of three-phase relative permeability during WAG injection. This technique is a direct method which uses measured three-phase k_r data obtained from first cycle of WAG to predict the relative permeability of the subsequent cycles. The integrity of this technique has been validated against the three-phase k_r data obtained from our WAG experiments We also assess the validity of the WAG hysteresis model available in reservoir simulators against our three-phase relative permeability data in order to evaluate its performance.