Correlation-Based Adaptive Localization With Applications to Ensemble-Based 4D-Seismic History Matching

Abstract

Summary Ensemble-based history-matching methods have received much attention in reservoir engineering. In real applications, small ensembles are often used in reservoir simulations to reduce the computational costs. A small ensemble size may lead to ensemble collapse, a phenomenon in which the spread of the ensemble of history-matched reservoir models becomes artificially small. Ensemble collapse is not desired for an ensemble-based history-matching method because it not only deteriorates the capacity in uncertainty quantification, but also forces the ensemble-based method to later stop updating reservoir models. In practice, distance-based localization is thus introduced to tackle ensemble collapse. Distance-based localization works well in many problems. However, one prerequisite in using distance-based localization is that the observations have associated physical locations. In certain circumstances with complex observations, this may not be true, and it thus becomes challenging to apply distance-based localization. In this work, we propose a correlation-based adaptive localization scheme that does not rely on the physical locations of the observations. Instead, we use the spatial distributions of the correlations between model variables and the corresponding simulated observations. In the course of history matching, we update model variables by only using the observations that have relatively high correlations with them, while excluding those that have relatively low correlations. This is equivalent to introducing a data-selection procedure to the history-matching algorithm. As a result, the threshold values for data selection play an essential role in the proposed adaptive localization scheme, and we develop both ideal and practical approaches to the choices of the threshold values. We demonstrate the efficacy of the proposed localization scheme using seismic history-matching problems—one 2D and one 3D—in which ensemble collapse is severe in the presence of large amounts of observational data, but distance-based localization may not be applicable because of the lack of physical locations of the seismic data in use. In contrast, correlation-based localization works well to prevent ensemble collapse and also renders good history-matching results. We also note some practical conveniences of the proposed localization scheme, including the applicability to nonlocal observations, the relative simplicity in implementation, the transferability of the same codes among different (either 2D or 3D) case studies, and the adaptivity to different types of observations and petrophysical parameters.

Efficient Assimilation of Crosswell Electromagnetic Data Using an Ensemble-Based History-Matching Framework

“…Localization is one of the most common regularization techniques used in ensemble-based historymatching applications (Oliver and Chen, 2011). In general, localization methods fall into two categories: distance-based (Chen and Oliver, 2010;Emerick and Reynolds, 2011) and non-distance-based (Zhang and Oliver, 2010;Luo et al, 2018) localization methods. In distance-based localization, one assumes that any covariance beyond a certain distance is purely a result of sampling errors.…”

Iterative static modeling of channelized reservoirs using history-matched facies probability data and rejection of training image

“…1 because they do not consider the geological meaning of reservoir parameters. It has been reported that this problem can be solved by techniques such as localization in many studies (Watanabe and Datta-Gupta 2012;Luo et al 2018;Jung et al 2018). Since this research is not a study to improve the ensemble-based method, only the standard ensemble-based methods are used as a comparison of the proposed method.…”

A Fuzzy-Logic-Based Covariance Localization Method in Data Assimilation

“…However, small ensembles can cause a series of problems, including rank deficiency, distanced spurious correlations, and Monte Carlo sampling errors [6][7][8][9]. Therefore, a number of auxiliary techniques have been developed and reported in the literature, including covariance inflation, as well as localization and hybrid covariances [10][11][12][13][14].…”

“…In addition, in certain circumstances, model variables or the corresponding observation may not have associated physical locations, which may violate the principles of distance-based methods. Therefore, some adaptive localization methods, which may not be based on physical distances, have been proposed [14,22,24]. For instance, De La Chevrotiere and Harlim [24] proposed a data-driven method for improving the poorly estimated sample correlation by using a linear map.…”