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Computational Geosciences

, Volume 19, Issue 4, pp 821–844 | Cite as

Assessment of ordered sequential data assimilation

  • Kristian FossumEmail author
  • Trond Mannseth
ORIGINAL PAPER

Abstract

Ensemble based data assimilation methods, such as the (sequential) ensemble Kalman Filter (EnKF) and the (non-sequential) ensemble smoother (ES), are widely used for history matching petroleum reservoir models. In a recent study (Fossum and Mannseth, Inverse Probl. 30(11):114002-3, [2014]), investigating the difference between sequential and non-sequential assimilation, it was shown that, for a series of weakly non-linear data, the sequential assimilation strategy outperformed the non-sequential approach, especially if the data were ordered according to ascending degree of non-linearity. In this paper, we assess, numerically, various assimilation strategies. Here, we consider numerous data types representing a large variation in the degree of non-linearity, and we consider both simple and complex forward models. The numerical study is divided into two parts. Firstly, the assimilation methods are assessed for problems that allow a controllable variation in the degree of data non-linearity. This investigation is conducted by toy models to ensure that a sufficiently large range of non-linear data is tested. Secondly, considering a 2D synthetic reservoir case, the assimilation methods are assessed for different production strategies and reference models. The numerical experiments show that for most models, considering data with a suitable degree of non-linearity, assimilating the data ordered after ascending degree of non-linearity produce the lowest approximation error. Two counter examples illustrate that the optimal assimilation strategy cannot be determined for all cases, especially if the degree of non-linearity depends greatly on the position in parameter space.

Keywords

Sequential estimation Data assimilation Ensemble methods Numerical assessment 

Mathematics Subjects Classification (2010)

62L12 65C05 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Uni Research CIPRBergenNorway
  2. 2.Department of MathematicsUniversity of BergenBergenNorway

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