Investigation on the production data frequency for assimilation with ensemble smoother

Abstract

Underestimating posterior variances is a critical problem in using iterative ensemble smoothers for data assimilation in reservoir models. This issue limits the method’s capacity to assimilate large amounts of data and results in inaccurate evaluations of uncertainty for future performance predictions. This underestimation may be attributed to various factors, such as the parametrization of the problem, the characterization of the prior and data uncertainties and deficiencies in the ability of the forward model to reproduce the system’s dynamic behavior. Unfortunately, limitations inherent in the ensemble smoother formulation, mainly related to using small ensembles, also contribute to variance underestimation. To address this issue, we devise a synthetic reservoir data assimilation problem that isolates variance underestimation to the ensemble smoother. Using this test problem, we explore the impact of altering the production data setup to counteract the premature loss of ensemble variance. Our tests indicate that reducing data frequency is a relatively straightforward and robust approach to implement in practice. In addition, we propose implementing a distinct truncation scheme for singular values, which helps to mitigate the undesirable variance loss. Furthermore, we present six supplementary test problems, including four actual field cases, to provide additional empirical evidence that it is possible to reduce the variance loss without compromising the data-match quality.