# Evaluating prior predictions of production and seismic data

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## Abstract

It is common in ensemble-based methods of history matching to evaluate the adequacy of the initial ensemble of models through visual comparison between actual observations and data predictions prior to data assimilation. If the model is appropriate, then the observed data should look plausible when compared to the distribution of realizations of simulated data. The principle of data coverage alone is, however, not an effective method for model criticism, as coverage can often be obtained by increasing the variability in a single model parameter. In this paper, we propose a methodology for determining the suitability of a model before data assimilation, particularly aimed for real cases with large numbers of model parameters, large amounts of data, and correlated observation errors. This model diagnostic is based on an approximation of the Mahalanobis distance between the observations and the ensemble of predictions in high-dimensional spaces. We applied our methodology to two different examples: a Gaussian example which shows that our shrinkage estimate of the covariance matrix is a better discriminator of outliers than the pseudo-inverse and a diagonal approximation of this matrix; and an example using data from the Norne field. In this second test, we used actual production, repeat formation tester, and inverted seismic data to evaluate the suitability of the initial reservoir simulation model and seismic model. Despite the good data coverage, our model diagnostic suggested that model improvement was necessary. After modifying the model, it was validated against the observations and is now ready for history matching to production and seismic data. This shows that the proposed methodology for the evaluation of the adequacy of the model is suitable for large realistic problems.

## Keywords

Prior predictive distribution Model criticism Model improvement Mahalanobis distance Production data RFT data Acoustic impedance Seismic inversion Correlated observation error History matching Norne field## Notes

### Acknowledgements

The authors thank Equinor (operator of the Norne field) and its license partners Eni Norge and Petoro for the release of the Norne data. The authors acknowledge the Center for Integrated Operations at NTNU for cooperation and coordination of the Norne Cases. The view expressed in this paper are the views of the authors and do not necessarily reflect the views of Equinor and the Norne license partners.

We are grateful to Geovariances for providing a license for the use of Isatis for factorial co-kriging, and to Schlumberger for providing Eclipse and Petrel licenses.

### Funding information

This study is supported by the CIPR/IRIS cooperative research project “4D Seismic History Matching” which is funded by industry partners Eni Norge, Petrobras, and Total, as well as the Research Council of Norway through the Petromaks2 program.

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