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Soares, Ricardo Vasconcellos (NORCE Norwegian Research Centre and University of Bergen) | Luo, Xiaodong (NORCE Norwegian Research Centre) | Evensen, Geir (NORCE Norwegian Research Centre and Nansen Environmental and Remote Sensing Center (NERSC)) | Bhakta, Tuhin (NORCE Norwegian Research Centre)
Summary In applications of ensemble-based history matching, it is common to conduct Kalman gain or covariance localization to mitigate spurious correlations and excessive variability reduction resulting from the use of relatively small ensembles. Another alternative strategy not very well explored in reservoir applications is to apply a local analysis scheme, which consists of defining a smaller group of local model variables and observed data (observations), and perform history matching within each group individually. This work aims to demonstrate the practical advantages of a new local analysis scheme over the Kalman gain localization in a 4D seismic history-matching problem that involves big seismic data sets. In the proposed local analysis scheme, we use a correlation-based adaptive data-selection strategy to choose observations for the update of each group of local model variables. Compared to the Kalman gain localization scheme, the proposed local analysis scheme has an improved capacity in handling big models and big data sets, especially in terms of computer memory required to store relevant matrices involved in ensemble-based history-matching algorithms. In addition, we show that despite the need for a higher computational cost to perform model update per iteration step, the proposed local analysis scheme makes the ensemble-based history-matching algorithm converge faster, rendering the same level of data mismatch values at a faster pace. Meanwhile, with the same numbers of iteration steps, the ensemble-based history-matching algorithm equipped with the proposed local analysis scheme tends to yield better qualities for the estimated reservoir models than that with a Kalman gain localization scheme. As such, the proposed adaptive local analysis scheme has the potential of facilitating wider applications of ensemble-based algorithms to practical large-scale history-matching problems.
Silva Neto, Gilson Moura (Petrobras, University of Campinas, and NORCE Norwegian Research Centre) | Soares, Ricardo Vasconcellos (NORCE Norwegian Research Centre, University of Bergen) | Evensen, Geir (NORCE Norwegian Research Centre and Nansen Environmental and Remote Sensing Center) | Davolio, Alessandra (University of Campinas) | Schiozer, Denis José (University of Campinas)
Summary Time-lapse-seismic-data assimilation has been drawing the reservoir-engineering community's attention over the past few years. One of the advantages of including this kind of data to improve the reservoir-flow models is that it provides complementary information compared with the wells' production data. Ensemble-based methods are some of the standard tools used to calibrate reservoir models using time-lapse seismic data. One of the drawbacks of assimilating time-lapse seismic data involves the large data sets, mainly for large reservoir models. This situation leads to high-dimensional problems that demand significant computational resources to process and store the matrices when using conventional and straightforward methods. Another known issue associated with the ensemble-based methods is the limited ensemble sizes, which cause spurious correlations between the data and the parameters and limit the degrees of freedom. In this work, we propose a data-assimilation scheme using an efficient implementation of the subspace ensemble randomized maximum likelihood (SEnRML) method with local analysis. This method reduces the computational requirements for assimilating large data sets because the number of operations scales linearly with the number of observed data points. Furthermore, by implementing it with local analysis, we reduce the memory requirements at each update step and mitigate the effects of the limited ensemble sizes. We test two local analysis approaches: one distance-based approach and one correlation-based approach. We apply these implementations to two synthetic time-lapse-seismic-data-assimilation cases, one 2D example, and one field-scale application that mimics some of the real-field challenges. We compare the results with reference solutions and with the known ensemble smoother with multiple data assimilation (ES-MDA) using Kalman gain distance-based localization. The results show that our method can efficiently assimilate time-lapse seismic data, leading to updated models that are comparable with other straightforward methods. The correlation-based local analysis approach provided results similar to the distance-based approach, with the advantage that the former can be applied to data and parameters that do not have specific spatial positions.
Luo, Xiaodong (International Research Institute of Stavanger) | Lorentzen, Rolf J. (International Research Institute of Stavanger) | Valestrand, Randi (International Research Institute of Stavanger) | Evensen, Geir (International Research Institute of Stavanger and Nansen Environmental and Remote Sensing Center)
Summary Ensemble‐based methods are among the state‐of‐the‐art history‐matching algorithms. However, in practice, they often suffer from ensemble collapse, a phenomenon that deteriorates history‐matching performance. It is customary to equip an ensemble history‐matching algorithm with a localization scheme to prevent ensemble collapse. Conventional localization methods use distances between the physical locations of model variables and observations to modify the degree of the observations’ influence on model updates. Distance‐based localization methods work well in many problems, but they also suffer from dependence on the physical locations of both model variables and observations, the challenges in dealing with nonlocal and time‐lapse measurements, and the nonadaptivity to handling different types of model variables. To enhance the applicability of localization to various history‐matching problems, we adopt an adaptive localization scheme that exploits the correlations between model variables and simulated observations. We elaborate how correlation‐based adaptive localization can overcome or mitigate issues arising in conventional distance‐based localization. To demonstrate the efficacy of correlation‐based adaptive localization, we adopt an iterative ensemble smoother (iES) with the proposed localization scheme to history match the real production data of the Norne Field model, and we compare the history‐matching results with those obtained by using the iES with distance‐based localization. Our study indicates that when compared with distance‐based localization, correlation‐based localization not only achieves close or better performance in terms of data mismatch, but also is more convenient to use in practical history‐matching problems. As a result, the proposed correlation‐based localization scheme might serve as a viable alternative to conventional distance‐based localization.
Abstract Ensemble-based methods are among the state-of-the-art history matching algorithms. In practice, they often suffer from ensemble collapse, a phenomenon that deteriorates history matching performance. To prevent ensemble collapse, it is customary to equip an ensemble history matching algorithm with a certain localization scheme. Conventional localization methods use distances between physical locations of model variables and observations to modify the degree of observations' influence on model updates. Distance- based localization methods work well in many problems, but they also suffer from some long-standing issues, including, for instance, the dependence on the presence of physical locations of both model variables and observations, the challenges in dealing with nonlocal and time-lapse observations, and the non-adaptivity to handle different types of model variables. To enhance the applicability of localization to various history matching problems, we propose to adopt an adaptive localization scheme that exploits the correlations between model variables and observations for localization. We elaborate how correlation-based adaptive localization can mitigate or overcome the noticed issues arising in conventional distance-based localization. To demonstrate the efficacy of correlation-based adaptive localization, we apply it to history-match the real production data of the full Norne field model using an iterative ensemble smoother (iES), and compare the history matching results to those obtained by using the same iES but with distance-based localization. Our study indicates that, in comparison to distance-based localization, correlation- based localization not only achieves close or better performance in terms of data mismatch, but also is more convenient to implement and use in practical history matching problems. As a result, the proposed correlation-based localization scheme may serve as a viable alternative to conventional distance-based localization.
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.