The ensemble smoother with multiple data assimilation (ES-MDA) has gained much attention as a powerful tool for history matching problems. Previous studies showed that it could provide both a good match of data and estimates of model parameters. In the original ES-MDA formulation, the number of data assimilation and covariance inflation factors are determined in advance. Selecting them in a decreasing order may improve the final results. Moreover, recent studies propose some theoretical and practical methods to select inflation factors based on the discrepancy principle. This work aims to introduce a new method for generating the data covariance inflation factors for ES-MDA. In the new method, the first inflation factor is generated using a Levenberg–Marquardt regularizing scheme. The last inflation factor is set by a parameter that limits its magnitude, computed using the singular values of the dimensionless sensitivity matrix estimated from the prior ensemble. As a result, the method computes the correct number of data assimilations that produces inflation factors such that the sum of their inverse is equal to one, as required by ES-MDA. It is shown through a synthetic two-dimensional water flooding history matching problem that the proposed methodology achieves both better model parameter match and data match with a smaller number of assimilations than the methods available in the literature.

具有多个数据同化功能的集成平滑器（ES-MDA）作为解决历史记录匹配问题的强大工具而受到了广泛的关注。先前的研究表明，它既可以提供数据的良好匹配，又可以提供模型参数的估计值。在原始的ES-MDA公式中，数据同化和协方差膨胀因子的数量是预先确定的。以降序选择它们可能会改善最终结果。此外，最近的研究提出了一些基于差异原理来选择通胀因子的理论和实践方法。这项工作旨在介绍一种为ES-MDA生成数据协方差膨胀因子的新方法。在新方法中，使用Levenberg-Marquardt正则化方案生成第一个膨胀因子。最后一个膨胀因子由一个限制其大小的参数设置，该参数使用从先前合奏估计的无量纲灵敏度矩阵的奇异值计算得出。结果，该方法计算出产生通货膨胀因子的数据同化的正确数量，以使它们的逆之和等于1，如ES-MDA所要求的。通过一个合成的二维注水历史匹配问题表明，与文献中可用的方法相比，所提出的方法以较少的同化量实现了更好的模型参数匹配和数据匹配。该方法可以计算出产生通货膨胀因子的数据同化的正确数量，以使它们的逆之和等于1，如ES-MDA所要求的。通过一个合成的二维注水历史匹配问题表明，与文献中可用的方法相比，所提出的方法以较少的同化量实现了更好的模型参数匹配和数据匹配。该方法可以计算出产生通货膨胀因子的数据同化的正确数量，以使它们的逆之和等于1，如ES-MDA所要求的。通过一个合成的二维注水历史匹配问题表明，与文献中可用的方法相比，所提出的方法以较少的同化量实现了更好的模型参数匹配和数据匹配。