Improving pseudo-optimal Kalman-gain localization using the random shuffle method

In present days, Iterative ensemble smoothers (IES) are among the main methods to perform ensemble-based history matching in petroleum reservoirs. Generally, some localization technique is applied to the IES to prevent ensemble collapse, which is the consequence of an excessive reduction of the posterior ensemble variance. When the standard distance-based localization is applied, the assimilation of non-local parameters is difficult, and besides that, this kind of methodology has also several intrinsic parameters that need to be defined before the assimilation. In contrast, adaptive localization methods aim to overcome the noticed problems of distance-based localization, by using some statistical method to define the localization. This article proposes a novel adaptive localization scheme, on top of two preexisting techniques: pseudo-optimal and correlation-based localizations. The motivation here is to further improve the adaptive localization scheme, by combining the strengths of these two preexisting techniques. The efficacy of the proposed localization scheme is tested in one 2D and one 3D case studies, whereas the latter case study involves a field-scale reservoir model with both local and non-local parameters, which often impose challenges on the conventional localization schemes. In comparison to other evaluated localization schemes, our results indicate that the proposed adaptive localization scheme achieves improved history matching performance. •Novel adaptive localization method by combining correlation and pseudo-optimal localization methods.•The methodology proposed by inflating the pseudo-optimal equation using the noise level obtained by the random-shuffle method.•The proposed method showed good performance to remove spurious correlations.•Improvement in terms of preserving the posterior ensemble variance.