Ensemble-Based Closed-Loop Optimization Applied to Brugge Field

Abstract

Abstract In closed-loop reservoir management, geologic properties are updated sequentially using available data, and model-based optimization is used to search for the optimal operating strategy. Ensemble-based methods can be used to solve both data assimilation and production optimization with the gradient approximated from an ensemble. This ensemble-based closed-loop optimization method is flexible and has been illustrated using a small scale problem in Chen et al. (2008). The dimensionality of the model parameter and control parameter space are high in large scale problems. Approximating the gradient using small ensembles might result in unsatisfactory solution of the ensemble-based closed-loop optimization. In this paper the ensemble-based closed-loop optimization is applied to a large scale SPE Benchmark study. Brugge field, a synthetic reservoir, is designed as a common platform to test different methods for closed-loop reservoir management. The problem was designed to mimic real field scenarios, and as a result is by far the largest and most complex test case on closed-loop optimization. The Brugge field model consists of nine layers and the number of active cells is 44550. It has one internal fault and seven rock regions with different relative permeability and capillary pressure functions. There are 20 producers and 10 injectors in the field. Noise corrupted production data are provided monthly. Additionally, time-lapse seismic data are available at year ten. Each well has three different completions that can be controlled independently. The producing life of the reservoir is 30 years and the objective of optimization is to maximize the net present value at the end of 30 years. Due to the complexity of this test case, several advanced techniques are used in order to improve the solution of the ensemble-based closed-loop optimization. Saturation normalization is used to account for the presence of difference rock regions. Localization is used in the assimilation of production and seismic data to increase the effective size of the ensemble and to alleviate the effect of spurious correlations resulted from the small ensemble. Relative permeability curves and initial oil water contact are estimated together with the gridlock properties. Covariance inflation is used to maintain the desired variability in the ensemble. We expect that these techniques will also be critical in real field application of the ensemble-based closed-loop optimization. Introduction Closed-loop optimization combines model-based optimization with sequential data assimilation in order to operate the field in an adaptive manner (Brouwer et al., 2004; Sarma et al., 2005; Naevdal et al., 2006; Wang et al., 2007; Chen et al., 2008). The reservoir model is adjusted sequentially as production data become available in time. Field operation strategy can be optimized based on the updated reservoir model. Chen et al. (2008) introduced an ensemble-based closed-loop optimization method where the ensemble Kalman filter (EnKF) or ensemble randomized maximum likelihood (EnRML) is used to update reservoir models and the ensemble-based optimization (EnOpt) is used to optimize the production. The gradient information needed for both data assimilation and production optimization is approximated from an ensemble of model realizations, in which case the simulator only serves as a black box. Compared to adjoint-based methods this ensemble-based method is flexible and can be easily used with any reservoir simulator. Approximating the gradient from the ensemble does not require differentiability; instead it utilizes the correlation between variables to approximate a global search direction and has less chance of getting stuck at local minimum/maximum than local gradients.