Multi-objective optimization of WAG injection using machine learning and data-driven Proxy models

In complex optimization processes such as CO2-water alternating gas (CO2-WAG), several iterative steps are needed before finding an optimal or sub-optimal set of solutions. This leads to time-consuming operations, especially when the simulation is run with a compositional simulator. Proxy models have been used to tackle this issue as they can replicate efficiently and accurately reservoir simulators in specific studies. However, the construction of such a proxy model, its basic database in particular, differs according to the designer and the objective function(s).In this study, a hybrid algorithm was designed that combined Artificial Neural Networks (ANN) and NSGA-II to find optimum solutions for a CO2-WAG injection process. The proxy model was developed based on a specific sampling method that considered the total injection time of a WAG cycle equal to one year and characterized by a new parameter, gas water injection time ratio (GWITR). The Latin Hypercube Design (LHD) is used to sample the inputs (bottom-hole flowing pressure of the producers, and water and gas injection rates) and the outputs are the cumulative oil recovery factor (FOE) and Net Present Value (NPV). After the proxy model was assessed, it was combined with Non-dominated Sorting Genetic Algorithm II (NSGA-II) to find the Pareto Front of the optimum solutions.The developed ANN model was able to predict the two outputs simultaneously with an R2 higher than 0.999 and an MSE of 6.5E-5. The found Pareto front, with good diversity and convergence, provided the operator with various solutions for decision-making.