Picard-Newton Method for Water-Alternating-Gas Injection Simulation in Heterogeneous Reservoirs

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 addresses slightly compressible, immiscible oil, water, and gas phases under constant-temperature conditions, with the governing equations discretized in space and time 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 heterogeneous reservoir models with mean permeabilities of 100, 200, and 400 × 10${}^{-15}$ m${}^2$ 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 gas breakthrough and, in the highest-permeability case, water breakthrough, as well as 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.