Efficient Multi-Objective History-Matching Using Gaussian Processes
H. Hamdi, I. Couckuyt, T. Dhaene and M. Costa Sousa
Event name: ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery
Session: ECMOR XVI Poster Session 1
Publication date: 03 September 2018
Info: Extended abstract, PDF ( 1.22Mb )
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In a multiobjective optimization approach, a trade-off is sought to balance between the optimality of different objectives. In this paper, we introduce a new efficient multiobjective optimization approach using sequential Gaussian Process (GP) modeling that can quickly find the Pareto solutions in a minimal number of model evaluations. This is the first time that we present this approach for history-matching. The difference with other optimization algorithms is elucidated for the cases where we can only afford to run a limited number of simulations. Unlike other surrogate-based methods, we do not aim for a greedy approach by minimizing the surface itself as there can be a large uncertainty in the surrogate approximations. Instead, statistical criteria are introduced to account for both proxy model uncertainty as well as its extrema. This multiobjective optimization approach has been successfully applied for the first time to history match the production data (i.e. pressure, water and hydrocarbon rates) from a multi-fractured horizontal well in a tight formation. A GP surface is constructed for each misfit, to provide the predictions and the associated uncertainty for any unknown location. Multiobjective criteria, i.e., the hypervolume-based Probability of Improvement (PoI) and Expected Improvement (EI), are developed to account for the uncertainty of the misfit surfaces. The maximization of these statistical criteria ensures to balance between exploration and exploitation, even in higher dimensions. As such, a new point is selected whose values in different objectives are predicted to hopefully extend or dominate the solutions in the current Pareto set.