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Optimization of the water-flooding process in the oilfields is inherently subject to several uncertainties arising from the imperfect reservoir subsurface model and inadequate data. On the other hand, the uncertainty of economic conditions due to oil price fluctuations puts the decision-making process at risk. It is essential to handle optimization problems under both geological and economic uncertainties. In this study, a Pareto-based Multi-Objective Particle Swarm Optimization (MOPSO) method has been utilized to maximize the short-term and long-term production goals, robust to uncertainties. Some modifications, including applying a variable in the procedure of leader determination, namely crowding distance, a corrected archive controller, and a changing boundary exploration, are performed on the MOPSO algorithm. These corrections led to a complete Pareto front with enough diversity on the investigated model, covering the entire solution space. Net Present Value (NPV) is considered the first goal that represents the long-term gains, while a highly discounted NPV (with a discount rate of 25%) has been considered short-term gains since economic uncertainty risk grows with time. The proposed optimization method has been used to optimize water flooding on the Egg benchmark model. Geological uncertainty is represented with ensembles, including 100 model realizations. The  k -means clustering method is utilized to reduce the realizations to 10 to reduce the computing cost. The Pareto front is obtained from Robust Optimization (RO) by maximizing average NPV over the ensembles, as the conservative production plan. Results show that optimization over the ensemble of a reduced number of realizations by the  k -means technique is consistent with all realizations’ ensembles results, comparing their cumulative density functions. Furthermore, 10 oil price functions have been considered to form the economic uncertainty space. When SNPV and LNPV are optimized, considering uncertainty in oil price scenarios, the Pareto front’s production scenarios are robust to oil price fluctuations. Using the robust Pareto front of LNPV  versus  SNPV in both cases, one can optimize production strategy conservatively and update it according to the current reservoir and economic conditions. This approach can help a decision-maker to handle unexpected situations in reservoir management.

Model-based production optimization under geological and economic uncertainties using multi-objective particle swarm method