The Statistical Reservoir Model: calibrating faults and fractures, and predicting reservoir response to water flood

This paper describes the new concept of a ‘Statistical Reservoir Model’ to determine significant well-pair correlations. We solve this conceptual problem using a predictive error filter, combined with Bayesian methods that identify those well pairs that are related to each other with statistical significance, for the Gullfaks reservoir in the North Sea. Significant, long-range, correlations in the whole field are found at an optimal time lag of one month. The correlation function for significantly-correlated well pairs, after normalization for the distribution of available wells, shows a long-range power-law decay that is consistent with a critical-point response at the reservoir scale. A principal component analysis shows a strong correlation with the location and orientation of faults that intersect the main producing horizon. A predictive experiment shows that the model performs very well both in history matching and predictive mode on a time scale of about one month.