Subspace Ensemble Randomized Maximum Likelihood with Local Analysis for Time-Lapse-Seismic-Data Assimilation

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.