Machine Learning-Based Optimization of Well Locations and WAG Parameters under Geologic Uncertainty

Abstract The effects of well locations and control parameters on reservoir responses is important during CO2 enhanced oil recovery (CO2-EOR) and water-alternating-gas (WAG) injection. Oil recovery and CO2 storage capacity typically vary with respect to corresponding changes in WAG ratio, slug size, and injector locations. The relationships between control parameters and response variables are usually studied using compositional simulators. However, the computational expense required to run such simulators could hinder their applicability to optimization procedures requiring many evaluations. Surrogate models (proxies) provide inexpensive alternatives for approximating reservoir responses. In this study, a machine learning-based proxy is developed to predict responses to changes in location and control parameters during WAG injection. Slight adjustments in injector well locations, WAG ratio and slug size could yield dramatic changes in the objective function responses. This complex relationship between control parameters and reservoir-wide responses makes data-driven methods an attractive option. We extend a recently developed machine learning approach in which the primary predictors are physical well locations, and water and gas injection rates, and the primary response is net present value (NPV). Because of the complexity of the response surface, we augmented the predictor variables with well-to-well pairwise connectivities, injector block permeabilities and porosities, and initial injector block saturations. Connectivities are represented by ‘diffusive times of flight’ of the pressure front, which is computed using the Fast Marching Method. Training observations are obtained from a handful of compositional simulations. We then used the Extreme Gradient Boosting method (XGBoost) to build intelligent proxies for making predictions given any set of observations. We propose a hyperdimensional, simultaneous optimization of well locations and controls using a novel optimization scheme similar Mesh Adaptive Direct Search (MADS). Our optimization scheme was developed to fully take advantage of the speed and statistical output of the proxy. The proposed approach is demonstrated using a case study in which the underlying geology is uncertain. Results show significant correlation between proxy predictions and reservoir simulations, which validates application of the trained proxy. In addition, we demonstrate that simultaneous optimization of location and controls yields improvements over a sequential approach without any significant increase in computational cost.