Probabilistic history matching using discrete Latin Hypercube sampling and nonparametric density estimation

Abstract

This paper describes a new iterative procedure for probabilistic history matching using a discrete Latin Hypercube (DLHC) sampling method and nonparametric density estimation. The iterative procedure consists of selecting a set of models based on the history matching quality (normalized misfit) to generate histograms. The histograms are smoothed and used to estimate marginal probability densities of reservoir attributes. Three selection methods are evaluated. One of them is based on a global objective function (GOF) and the others are based on a local objective function (LOF), which is composed of influenced reservoir responses identified with the aim of a correlation matrix. The methodology was successfully applied to the UNISIM-I-H benchmark case, which is a reservoir model based on Namorado field, Campos basin, Brazil. Eight iterations with 450 combinations for each one were adequate to address the problem studied in this paper. To demonstrate the robustness of the proposed method and the consistency of the results, the iterative process was repeated 10 times and the discrepancy among the results was very small. The proposed method exhibited good convergence along the iterations, reducing the variability of the objective function (average normalized misfit) by approximately 90% from the first to the last iteration. Robustness, efficiency and facility of implementation are the key features of the proposed methodology.