Application of the Picard–Newton Method to Simulate Enhanced Oil Recovery in Heterogeneous Reservoirs: AWAG Injection Study Using Sequential Gaussian Simulation for Permeability Modeling

Water Alternating Gas (WAG) injection is a well-established enhanced oil recovery technique that improves sweep efficiency by combining the favorable displacement characteristics of waterflooding and gas injection. This work presents a sequential Picard–Newton formulation for simulating three-phase flow under WAG conditions in heterogeneous petroleum reservoirs. The mathematical model considers slightly compressible, immiscible oil, water, and gas phases under isothermal conditions, discretized using the finite volume method. Reservoir heterogeneity is represented through geostatistical permeability fields generated by Sequential Gaussian Simulation, capturing the spatial correlations and anisotropy characteristic of subsurface formations. The methodology is applied to investigate WAG performance in two heterogeneous reservoir models with mean permeabilities of 100 mD and 200 mD under identical 1:1 injection ratios. The numerical results successfully reproduce the cyclic saturation and production behavior characteristic of WAG processes. Comparative analysis reveals that higher permeability enhances injectivity and cumulative recovery but accelerates water breakthrough and production decline, illustrating the trade-off between displacement efficiency and sweep control. These findings demonstrate that the proposed framework provides an efficient and physically consistent tool for evaluating WAG strategies in heterogeneous reservoirs, with potential application to field-scale optimization of advanced recovery operations.