Fast evaluation of well placements in heterogeneous reservoir models using machine learning

Abstract

Surrogate models, or proxies, provide computationally inexpensive alternatives for approximating reservoir responses. Proxy models are routinely developed to generate spatially-varying output such as field pressures and saturations, or well responses such as production rates and bottom- hole pressures. In this study, a machine learning approach is adopted to predict reservoir responses based on injector well locations. The proxy developed in this work is trained to reproduce reservoir-wide objective functions, i.e., total profit, cumulative oil/gas produced, or net CO2 stored. Because of the geological complexity of most reservoirs, slight adjustments in injector well locations could yield dramatic changes in the objective function responses. Hence, most proxies do not include well locations as inputs in their formulation. This complex relationship between well locations and reservoir-wide responses makes nonparametric, machine learning-based methods an attractive option. We introduce a machine learning approach in which the primary predictors are physical well locations, and the primary response is a defined objective function such as NPV. The complexity of the response surface with respect to well locations necessitates that we augment the predictor variables with well-to-well pairwise connectivities, injector block permeabilities and porosities, and initial injector block saturations. Introducing well-to-well connectivities yields significant improvements in prediction accuracy. Connectivities are represented by 'diffusive times of flight' of the pressure front, which is computed using the Fast Marching Method. A handful of training observations are obtained from numerical reservoir simulations. The Extreme Gradient Boosting method is then used to build an intelligent model for making predictions given any set of observations. The proposed approach is demonstrated using five synthetic case studies: i) a homogeneous reservoir waterflood, ii) a channelized reservoir waterflood, iii) a 20-model ensemble waterflood, iv) a CO2 flood in a heterogeneous reservoir, v) a CO2 flood in a heterogeneous reservoir with complex topography. Results show a significant correlation between proxy predictions and reservoir simulation results.