A new procedure for generating data covariance inflation factors for ensemble smoother with multiple data assimilation. (May 2021) - Silva, Thiago M.D.; Pesco, Sinesio; Barreto Jr., Abelardo; Onur, Mustafa
Abstract: 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. Highlights: We propose a new method to generate ES-MDA inflation factors. The first and last factors are computed using the method of Rafiee and Reynolds. The other inflation factors are computed geometrically in decreasing order. The new method achieves better ES-MDA outcomes with fewer assimilations.