Ensemble-based methods have become the state-of-the-art approaches to reservoir data assimilation (RDA). In practical applications, however, they suffer from issues imposed by the limited ensemble size. Among others, one noticeable problem is significant sampling error in the sample covariance estimator when the ensemble size is substantially small relative to the dimensionality of an RDA problem. Therefore, in practical applications, enhancing the estimation accuracies of sample covariance matrices is crucial for improving the performance of ensemble-based data assimilation. In this article, we propose a novel approach, called the covariance scaling method, to mitigating sampling errors in sample covariance matrices. This approach aims to find the optimal regularization parameter that minimizes the difference between a true covariance and its sample estimate. In contrast to other similar methods in the literature, such as the covariance shrinkage method, covariance scaling can be applied to minimize the errors in approximating a generic covariance matrix, including the cross-covariance matrix, which is of particular interest to ensemble-based methods. In addition, since the optimal regularization parameter of covariance scaling depends on the true, yet unknown covariance matrix, we propose an approximate formula to calculate the regularization parameter based on some sample covariance and cross-covariance matrices, and we further extend this approximate formula to derive an alternative, tuning-free method for adaptive localization. The covariance scaling method was evaluated and compared with other similar techniques in several experiments, showing improved performance in terms of both cross-covariance estimation and ensemble data assimilation.
Mês: março 2026
Model-Based Decision Analysis of Production Strategy for Heavy-Oil Field Development and Management Under Uncertainty: Waterflooding, Polymer Flooding, and Intelligent Wells
The decision-making procedure to develop and manage a production strategy is challenging because it requires a high investment and is performed under uncertainty. Heavy-oil reservoirs present low mobility and a high production of water under waterflooding. However, intelligent wells with ICVs (inflow control valves) and polymer flooding can improve the field’s performance. This work proposes a decision analysis to select the best strategy for the development of a heavy-oil field, evaluating and comparing the feasibility of waterflooding, polymers, and ICVs. We complement the nominal optimization accomplished for the base case in previous works by considering a probabilistic procedure with uncertainties, which includes the following: the generation of uncertain scenarios, the initial risk evaluation, the optimization of production strategies, a risk curve analysis, and the selection of the best strategy. A model-based reservoir simulation is used to perform the procedure, with the Expected Monetary Value (EMV) quantifying the economic returns. The case study is a sandstone heavy-oil reservoir (13° API) that represents a real Brazilian offshore field. Based on the EMV, we selected the polymer flooding strategy for this case study. However, since better water management was achieved with small differences to the polymer strategy, the option of using the ICVs in combination with polymer could be attractive depending on the various objectives of an oil field.