Application of polynomial chaos theory as an accurate and computationally efficient proxy model for heterogeneous steam-assisted gravity drainage reservoirs

Abstract

Reservoir modeling and simulation have become important elements of reservoir management. However, high computational cost associated with the use of numerical simulators make them cumbersome, especially with large-scale simulation models and complex oil recovery processes like steam-assisted gravity drainage (SAGD). A data-driven proxy model can be an alternative to predict SAGD recovery performance in real heterogeneous reservoirs, however, computationally efficient proxy model which can handle large number of input variables while providing accurate results requires further attention. In this work, a proxy model based on polynomial chaos expansion (PCE) is developed to predict the production parameters of SAGD reservoir. Karhunen–Loeve (KL) expansion is used to parameterize input variables in terms of random variables using which PCE further calculates production data for the given reservoir. To calculate coefficients of PCE, probabilistic collocation method is used. To demonstrate the functionality of the proposed approach, case study of a SAGD reservoir located in northern Alberta, Canada is shown in this paper. Various production parameters predicted from the PCE proxy model are compared with the actual simulation results and other proxy models based on radial basis functions (RBF) and artificial neural networks (ANN). From the results, it can be said that PCE proxy model demonstrates good agreement with full-physics simulation results and outperforms other proxy methods in terms of training data required and accuracy of predictions. In addition, since proposed PCE proxy model greatly reduces the computing cost, it potentially paves the way for expedited and frequent execution of uncertainty quantification, assisted history matching, and optimization workflows, resulting into efficient reservoir management and significant monetary benefits.