Impact of Relative Permeability Hysteresis on the Numerical Simulation

Abstract Pore-scale physics, laboratory investigations, and field experience, dictate that three-phase relative permeabilities exhibit strong dependence on the saturation path and the saturation history. Such dependence is especially relevant in immiscible wateralternating-gas (WAG) processes, which are characterized by a sequence of three-phase drainage and imbibition cycles. In this paper, we study the influence of relative permeability hysteresis on the field-scale predictions of WAG injection. Because their measurement is difficult and time-consuming, three-phase relative permeabilities are usually interpolated from two-phase data. The errors associated with this procedure have been investigated by Oak (SPE 20183), who reported that interpolated values might differ significantly from experimental ones. The effect of using different interpolation models in field-scale simulations has been illustrated by a number of authors, who found that recovery predictions could be significantly different depending on the three-phase relative permeability model. Here, we study the impact of using history-dependent saturation functions in reservoir simulations. First, we investigate the degree of accuracy with which different hysteretic models reproduce Oak's three-phase relative permeability data. In doing so, we assess the validity of existing models, and we identify the model parameters subject to most uncertainty. Our analysis suggests that current models account for some of the hysteretic behavior observed experimentally, but do not reproduce experimental measurements adequately during cyclic water/gas injection. Second, we illustrate how the use of a hysteretic relative permeability model affects reservoir simulations. We use a synthetic model of a quarter five-spot pattern in a homogenous reservoir, and a more realistic heterogeneous reservoir modified from the PUNQ-S3 model. We find that there is striking disparity in the simulation results depending on whether a hysteretic or a nonhysteretic model is employed. Therefore, we conclude that (1) it is essential to incorporate hysteresis in the relative permeabilities in order to obtain accurate predictions of realistic immiscible WAG processes; and (2) enhancements are needed to improve the predictive capabilities of current relative permeability hysteresis models.