Mathematical modeling and simulation of water-alternating-gas (WAG) injection

Water-alternating-gas (WAG) injection is a relatively mature oil recovery technique in hydrocarbon reservoirs that has attracted the interest of the oil and gas industry due to its successful performance. The main goal of a WAG process is to control the mobility and to decrease the problem of viscous fingering, leading to improved oil recovery by combining the benefits of gas injection (GI) and waterflooding (WF). Mathematical modeling and simulation of three-phase flow in porous media involve complexities related to the three-phase relative permeability, capillary pressure, and hysteresis effects that are cycle-dependent. Extensive theoretical studies are available in the literature, simulating immiscible and miscible WAG processes; however, the simulation study on near-miscible WAG is overlooked. Also, the majority of WAG simulation studies lack the cycle-dependent three-phase hysteresis that appears in the relative permeability and capillary pressure models. Production from naturally fractured reservoirs (NFRs) is more complicated (compared to homogeneous reservoirs) due to the flow communication between the matrix and fracture in fractured porous media. The implementation of water-alternating-gas (WAG) injection in NFRs also features inherent complexities related to the three-phase flow, the saturation history, and cycle-dependent hysteresis of the individual phases. Moreover, the experimental evaluation of WAG injection in a fractured system is expensive and time-consuming, if not impractical. In this research work, the three-phase flow modeling of near-miscible WAG process for enhanced oil recovery (EOR) implication is studied, using implicit pressure explicit saturation (IMPES) method. The mathematical model simulates a WAG case study in a strongly water-wet Berea core, using synthetic oil and brine at 38ﾟC and 12.7 MPa. The recovery data from the mathematical model is in excellent agreement with the experimental data of near-miscible WAG process. For instance, the absolute relative error is less than 1.7% while estimating the ultimate recovery factor of the oil in WF and GI stages of all three cycles. The effects of main variables such as injection rate, WAG ratio, slug size (PV) injection, crude oil viscosity, and core absolute permeability on the WAG performance are also studied. The findings from this study can help for better understanding of WAG injection at near-miscible condition for various scenarios under various conditions in terms of operational condition and rock and fluid’s characteristics. This work is also intended to simulate WAG injection in a fractured system through a computational fluid dynamics (CFD) approach. We evaluate the impacts of hysteresis, fracture characteristics (aperture, orientation, and fracture density in the network), and the three-phase relative permeability of phases during the WAG injection using COMSOL Multiphysics®. The model simulates an immiscible WAG injection, and the modeling results are compared to the experimental data in a strong water-wet sand-pack. Similar to the experiments, we simulate Maroon crude as the oil phase, synthetic brine, and pure CO₂ at 100ﾟC and atmospheric pressure. The results from our model are in excellent agreement with the experimental data. The absolute relative error is less than 12 % while predicting the ultimate recovery factors (RF) of the oil in water flooding (WF) and gas injection (GI) cycles. Including three-phase hysteresis significantly increases the accuracy of a WAG process simulation. Excluding the hysteresis remarkably decreases the instantaneous RFs at each cycle (especially GI cycles) and also the ultimate RF by 4%. The simulation results can help to manage and design the optimum operation of immiscible WAG in fractured reservoirs. In the fourth phase of the work, a total number of 1457 data points to predict three sets of two-phase relative permeabilities involved in the WAG injection process, and in a strongly water-wet sandstone core where smart tools such as least squares-support vector machine (LSSVM) and adaptive network-based fuzzy inference system (ANFIS) are employed. The statistical parameters including coefficient of determination, root mean square error, mean error, and standard deviation are used to examine the predictive models. The LSSVM shows a better performance compared to ANFIS in estimating relative permeabilities. The analysis based on relative importance of parameters shows that for the LSSVM model, water saturation is the most influencing input for gas-water and oil-water systems, while gas saturation is the most important input parameter in the gas-oil system. Final RF of WAG process after three cycles of water-and gas injection is 93.6%. Forecasting WAG flooding performance using fast and robust models is of great importance to obtain a better understanding of the process future, optimize the operational design procedure, and avoid high-cost blind tests in laboratory or pilot scales. In the last phase of this work, a novel correlation to predict the performance of near-miscible WAG injection is presented in strongly water-wet sandstones. An analytical correlation using gene expression programming (GEP) technique is developed. Dimensional analysis technique is applied and generated dimensionless numbers using eight key parameters with the aid of the Buckingham’s π theorem. Based on the error analysis, the newly developed GEP-based correlation leads to the predictions, which are in a good match with the target data so that R²= 92.85 % and MSE=1.38e-3 are obtained for the training phase; and the testing phase results in R²= 91.93 % and MSE=4.30e-3. The correlation proposed in this phase can be used to forecast the RF of a WAG injection process before committing to expensive and time-consuming laboratory and pilot tests.

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