A concurrent efficient global optimization algorithm applied to polymer injection strategies

One of the major difficulties in applying optimization to reservoir engineering problems is that each function evaluation requires a complete simulation which is computationally expensive. Moreover, some problems are known to be multimodal with several local minima. A common approach to tackle these problems is to construct cheap global approximation models of the responses often called metamodels or surrogates. These are based on simulation results obtained for a limited number of designs using data fitting. The optimization algorithm is coupled to the cheap metamodel. In this study a two-stage approach is employed based on the efficient global optimization algorithm, EGO, due to Jones. First an initial sample of designs is obtained using Latin hypercube. Parallel simulation runs for the initial sample are used to construct a Kriging metamodel. In the second stage the metamodel is used to guide the search for promising designs which are added to the sample in order to update the model until a suitable termination criterion is fulfilled. The selection of designs which are adaptively added to the sample is based on the maximization of the expected improvement merit function which balances the need for improving the value of the objective function with that of improving the quality of the metamodel prediction. In this study the original EGO algorithm is modified to exploit parallelism. The modified algorithm is applied to a polymer injection optimization problem. This eight-variable problem maximizes economical return by controlling the starting time and slug duration in each injector well. In the presented example a parametric study was conducted varying oil price. It is concluded that polymer flooding is feasible for oil prices above US$20.00/STB and gains increase with oil price.