Model Error Estimation Improves Forecasting
Authors: Carpenter Chris 
Published: March 2020

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 19142, “Improved Estimation and Forecast Through Model Error Estimation—Norne Field Example,” by Minjie Lu and Yan Chen, Total, prepared for the 2019 International Petroleum Technology Conference, Beijing, 26–28 March. The paper has not been peer reviewed. Copyright 2019 International Petroleum Technology Conference. Reproduced by permission.
Ensemble-based methods have proved to be effective in calibrating multiple reservoir models with historical production data. However, because of the complex nature of hydrocarbon reservoirs, the model calibration is always a simplified version of reality with coarse representation and unmodeled physical processes. This flaw in the model that causes mismatch between actual observations and simulated data when “perfect” model parameters are used as model input is known as model error. The results of the authors’ research showed a promising benefits from use of a systematic procedure of model diagnostics, model improvement, and model-error quantification during data assimilations.
Introduction
For reservoir history matching using ensemble-based methods, typically the model error is either ignored or treated by inflating the observation error co-variance beyond the actual measurement errors. This simple inflation of measurement error, however, does not account for the correlated structure of the model error and can result in suboptimal analysis. In this paper, the authors investigate and modify a work flow proposed previously in the literature for addressing model errors in assimilation of production data. The correlated total error for various time series of production data is estimated from the data residual after a standard history-matching process using the Levenberg-Marquardt form of iterative ensemble smoother (LM-EnRML). Then the history-matching process is repeated using LM-EnRML with the estimated total error. To the best of the authors’ knowledge, this is the first real field application of quantifying model error through data residual for improved estimation and forecasting.
Methodology
In this study, LM-EnRML is chosen for history matching because it does not require the perturbation of dobs using inflated noises sampled from the covariance of the observation noise (CD) at each iteration, which simplifies computation and increases stability of the model update when CD is estimated from data residual. Furthermore, LM-EnRML uses the magnitude of data mismatch as a stopping criterion without requiring a prespecified number of iterations. This feature is convenient for ensuring that data are matched to an appropriate level, especially when some degree of model error exists.
A Full-Cycle Work Flow. Typically, before the start of history matching, the initial simulated model responses should be checked against the observed data for any inconsistency through various model diagnostic measures. Then, a model improvement process should be carried out to improve consistency. With this improved model, the first model calibration begins. After a routine history-matching procedure, one should check if a large discrepancy exists between the simulated data (after history matching) and historical observations. If a large discrepancy exists, the simulation model used should be revisited and improved (e.g., by adding physically motivated model parameters or deleting abnormal observation data). Some model errors or observation biases are likely to remain despite the efforts to improve the model. Thus, one should no longer use the measurement error (CD) to weigh observations, but to estimate a total error covariance that consists of both the model error and the measurement error. Often, model structural errors or biased observations result in spatially or temporally correlated data residuals; therefore, the total error covariance cannot typically be considered as a diagonal matrix. The methodology of estimating CD is provided in the complete paper.