Rigorous Performance Evaluation of Stochastic Optimization for Water Injection Strategies

This paper presents an approach to optimize field water injection strategies using stochastic methods under uncertainty. For many fields, voidage replacement was the dictating factor of setting injection strategies. Determining the optimum injection-production ratio (IPR) requires extensive experience taking into consideration all the operational facility constraints. We present the outcome of a study, in which several optimization techniques were used to find the optimum field IPR values and then elaborate on the techniques? strengths and weaknesses. The synthetic reservoir simulation model, with millions of grid blocks and significant numbers of producers and injectors, was divided into seven IPR regions based on a streamline study. Each region was assigned an IPR value with an associated uncertainty interval. An ensemble of fifty probabilistic scenarios was generated by experimental design, using Latin Hypercube sampling of IPR values within tolerance limits. Scenarios were used as the main sampling domain to evaluate a family of optimization engines: population-based methods of artificial intelligence (AI), such as Genetic algorithms and Evolutionary strategies, Bayesian inference using sequential or Markov chain Monte Carlo, and proxy-based optimization. The optimizers were evaluated based on the recommended IPR values that meet the objective of minimizing the water cut by maximizing oil production and minimizing water production. The speed of convergence of the optimization process was also a subject of evaluation. To ensure unbiased sampling of IPR values and to prevent oversampling of boundary extremes, a uniform triangular distribution was designed. The results of the study show a clear improvement of the objective function, compared to the initial sampled cases. As a direct search method, the Evolutionary strategies with covariance matrix adaptation (ES-CMA) yielded the optimum IPR value per region. While examining the effect of applying these IPR values in the reservoir simulation model, a significant reduction of water production from the initial cases without an impact on the oil production was observed. Compared to ESCMA, other optimization methods have dem