Ranking of geostatistical models and uncertainty quantification using Signal Detection Principle (SDP)

The selection of an optimal model from a set of multiple realizations for dynamic reservoir modelling and production forecasts has been a persistent issue for reservoir modelers and decision makers. Current evidence has shown that many presumably good reservoir models which originally matched the true historic data did not always perform well in predicting the future of the reservoir as a result of uncertainties.
In this paper, a new method for optimal model selection using Signal Detection Principle (SDP) approach is presented. In principle, SDP approach models the dissimilarity between various realizations as a crossfunction of spatial distance, statistical correlation and the inherent noise level in the model; while the existing methods estimate the dissimilarity between parameter values of different realizations as a function of distance
(statistical or spatial distance) or quality factor. SDP approach fills the model divergence gap by way of classifying the information-bearing patterns in a model as signals, and identifying random patterns which bears no information as noise. Thus, it quantifies the mismatch uncertainty and the inherent fudge in every realization as a measure of the model’s reliability. The SDP approach has been validated with historical data, and the results show that the reliability factor of the best model has a value of one. Thus, if the strongest reservoir model has a reliability factor of one, then that model will make approximately the closest and best predictions as the true system in every forecast; whereas if the reliability factor of the model is less than or greater than one, its predictions will always disperse from historical data and is unsuitable for reservoir
forecasts. Two examples based on real field data are used to demonstrate the application of SDP approach. In these case examples SDP was used to analyse the difference between the reservoir models in a set of multiple realizations. The target variable in this study was STOIIP (Stock Tank Oil Initially in Place). The results show
that the models with a lower reliability factor made similar predictions as the real reservoir data in almost all the forecasts. Similarly, the models with higher reliability factors made dissimilar and more unreliable predictions in most of the forecasts.