Polynomial-Chaos-Expansion Based Integrated Dynamic Modelling Workflow for Computationally Efficient Reservoir Characterization: A Field Case Study

Abstract

Abstract Assisted history matching which integrates production data dynamically in reservoir modelling has been used to reduce uncertainty in reservoir geological properties which leads to credible production forecasting. For largescale heterogeneous heavy oil reservoirs, typically thousands of full physics simulation runs of multimillion grid reservoir models might be required to accurately probe the posterior probability space given the production history of reservoir, therefore not practical. In this paper, a unique approach for computationally efficient dynamic data integration is presented which includes construction of a proxy model that can replace reservoir simulator. Realizations are first parameterized using Karhunen-Loeve (KL) transformation and represented in terms of few uncorrelated random variables. Considering these random variables as input and production parameters as output, a mathematical model based on Polynomial Chaos Expansion (PCE) is constructed using deterministic coefficients and orthogonal polynomials which is further employed in assisted history matching instead of computationally expensive reservoir simulator. History matching of a SAGD field located in northern Alberta is performed using proposed KL-PCE framework and results are compared with the base case that uses commercial reservoir simulator. Ensemble Kalman Filter (EnKF) is used for assisted history matching due to its ability to assimilate data in large-scale nonlinear systems. Effectiveness of proposed idea is evaluated based on the following criteria: (1) Does KL-PCE framework reduce computational cost significantly, and (2) does proposed workflow produce satisfactory history matching results? It is observed that KL-PCE based proxy model provides similar performance as a commercial simulator in terms of ensemble convergence. Also, uncertainty in geological parameters is reduced significantly which is evident from convergence of updated ensemble towards the true value. Furthermore, computing cost of assisted history matching is reduced by almost 95% as training of PCE needs only few full physics simulations. Finally, proposed surrogate-accelerated integrated dynamic modelling can be used in greenfield closed-loop optimization workflows and uncertainty assessment with minimal use of numerical simulator which ultimately maximize the benefit in monetary terms.