Correlation-Based Localization Effective in Ensemble-Based History Matching
Authors: Carpenter Chris 
Published: March 2019

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 191305, “Correlation-Based Adaptive Localization for Ensemble-Based History Matching Applied to the Norne Field Case Study,” by Xiaodong Luo, SPE, Rolf Lorentzen, SPE, Randi Valestrand, SPE, and Geir Evensen, SPE, International Research Institute of Stavanger, prepared for the 2018 SPE Norway One Day Seminar, Bergen, Norway, 18 April. The paper has been peer reviewed and published in the October 2018 SPE Journal.
Ensemble-based methods are considered to be state-of-the-art history-matching algorithms. However, in practice, they often suffer from ensemble collapse, a phenomenon that deteriorates history-matching performance. An ensemble history-matching algorithm is equipped customarily with a localization scheme to prevent ensemble collapse. To enhance the applicability of localization to various history-matching problems, the authors adopt an adaptive localization scheme that exploits the correlations between model variables and observations.
Introduction
In the current work, the authors focus on adopting an efficient adaptive localization scheme, previously established in the literature, for the full Norne Field case study. The adaptive localization scheme exploits the information of sample correlation coefficients between an ensemble of model variables and the corresponding realizations of simulated observations. The adaptive localization scheme uses a data-selection procedure; however, instead of physical distances between the locations of model variables and observations being used for data selection, the magnitudes of the sample correlation coefficients are used for data selection through a hard-thresholding strategy (i.e., keep or kill).
To conduct data selection in the adaptive localization scheme, one specifies a positive correlation-threshold value. For a given observation, if the magnitude of the sample correlation coefficient between a model variable and the simulated observation is greater than the threshold value, then the observation will be used to update that model variable. Otherwise, one discards the observation in the update of that model variable.
This described data-selection procedure essentially means that a given model variable is updated using only the observations that have significant correlations with the model variable. The rationale behind this hard-thresholding strategy is the interpretation of the magnitude of the correlation coefficient as a measure to detect the causal relation between a model variable and an observation, and the effect is the suppression of spurious correlations caused by a finite sample size.
Correlation-based localization can overcome or alleviate the issues arising in distance-based localization, such as the use of nonlocal and time-lapse observations, the need of physical locations for model variables and measurements, and the different degrees of correlations or sensitivities of model variables to observations. Because data selection depends on the magnitudes of sample correlation coefficients between model variables and the corresponding simulated observations, the measurements need not have associated physical locations.
Model variables are thus selected by using those observations that exhibit strong-enough correlations, regardless of the physical distances between observations and model variables. As a result, correlation-based localization can be used to localize nonlocal observations. The changes of correlations caused by the effect of time-lapse observations or different types of model variables will be taken into account automatically in correlation-based localization, and this makes the proposed localization scheme more-adaptive and more-flexible in various situations.