Challenges of PCE-based proxy modeling and multi-objective optimization of wAg injection in carbonate reservoirs

Water-Alternating-Gas (WAG) injection could be an efficient way to improve recovery factors in fractured carbonate reservoirs. However, there are many geological uncertainties and engineering designs that influence the efficiency of the WAG process. In this study, we explore the challenges of combining polynomial chaos expansion (PCE)-based proxy modelling with multi-objective optimization using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to optimize the design of a WAG injection method under pseudo-miscible conditions for a fractured carbonate reservoir that is an analogue for the Arab D formation. A range of realistic geological uncertainties and engineering parameters are considered. Our results show that the order of the PCE-based proxy model needs to be carefully established for each geological scenario in a fractured reservoir. Likewise, the iterative enrichment of the proxy-model is non-monotonic, and each geological scenario requires its own evaluation of the proxy model during iterative enrichment. The convergence of the proxy is independent of the degree at which the reservoir is fractured but depends on the dimensions of the parameter space. The more engineering controls are considered, the more iterations are needed. Without a continuous and careful evaluation of the proxy model, the resulting simulation estimates may deviate significantly from full-physics simulations.