Summary Water alternating gas (WAG) is a well-established enhanced-oil-recovery process where gas and water are injected in alternating fashion. Good volumetric sweep is achieved as water and gas target both the oil residing in low and high portions of the reservoir, respectively. Other important features in three-phase hysteretic flow include phase trapping, which is believed to be more strongly associated with the gas phase. With these aspects in mind, a vast simulation study has been performed investigating immiscible WAG injection focusing on mechanisms such as mobility, gravity, injected volume fractions, reservoir heterogeneity, gas entrapment, and relative permeability hysteresis. The aim of our work is to investigate the interplay between these mechanisms for a model system with sufficient complexity to be of relevance and then scale recovery performance using a new dimensionless number that incorporates the relevant model input parameters. A horizontally layered reservoir is considered where oil is displaced by water and gas alternately injected toward a producer. The model is a modified black-oil type, where hysteresis in the gas phase is modeled using the Land (1968) model for trapping and the Carlson (1981) model for relative permeability hysteresis. It is seen that gravity segregation in uniform models and increased heterogeneity in no-gravity models both lead to lower oil recovery. However, in heterogeneous models, gravity can divert flow from high-permeability layers into low-permeability layers and improve recovery. Hysteresis lowers gas mobility and hence improves gas/oil mobility ratio and reduces gravity segregation. The first effect is always positive, but the second is mainly positive in more uniform reservoirs where gravity segregation has a negative effect on recovery. In heterogeneous reservoirs, reducing gravity segregation can lead to the oil in low-permeability layers remaining unswept. The newly derived characteristic dimensionless number is effectively a WAG mobility ratio, termed M*, expressing how well the injected-fluid mixture is able to displace oil, whether it is because of fluid mobilities, heterogeneity, or other effects. At a value of M* near unity, optimal recovery is achieved, whereas logarithmic increase of M* reduces recovery.

In this study, we solve the challenge of predicting oil recovery factor (RF) in layered heterogeneous reservoirs after 1.5 pore volumes of water-, gas- or water-alternating-gas (WAG) injection. A dataset of ~2500 reservoir simulations is analyzed based on a Black Oil 2D Model with different combinations of reservoir heterogeneity, WAG hysteresis, gravity influence, mobility ratios and WAG ratios. In the first model MOD1, RF is correlated with one input (an effective WAG mobility ratio M*). Good correlation (Pearson coefficient −0.94), but with scatter, motivated a second model MOD2 using eight input parameters: water–oil and gas–oil mobility ratios, water–oil and gas–oil gravity numbers, a reservoir heterogeneity factor, two hysteresis parameters and water fraction. The two mobility ratios exhibited the strongest correlation with RF (Pearson coefficient −0.57 for gas-oil and −0.48 for water-oil). LSSVM was applied in MOD2 and trained using different optimizers: PSO, GA, GWO and GSA. A physics-based adaptation of the dataset was proposed to properly handle the single-phase injection. A total of 70% of the data was used for training, 15% for validation and 15% for testing. GWO and PSO optimized the model equally well (R2 = 0.9965 on the validation set), slightly better than GA and GSA (R2 = 0.9963). The performance metrics for MOD1 in the total dataset were: RMSE = 0.050 and R2 = 0.889; MOD2: RMSE = 0.0080 and R2 = 0.998. WAG outperformed single-phase injection, in some cases with 0.3 units higher RF. The benefits of WAG increased with stronger hysteresis. The LSSVM model could be trained to be less dependent on hysteresis and the non-injected phase during single-phase injection.

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