In mathematics, a metric space is a set where a distance (called a metric) is defined between elements of the set. Metric space methods have been employed for decades in various applications, for example in internet search engines, image classification, or protein classification. In petroleum reservoir modelling however, metric space methods are not widely known. In this paper, we introduce the concept of a metric space in the framework of reservoir modelling. The metric space is formed by calculating a distance between two models. The distance is analogous to the well-known concept of an objective function in optimization, with the exception that the distance is not only evaluated between the model response and historical data, but also between two reservoir model responses. We describe how placing an ensemble of reservoir models in metric space allows for novel methods for visualization and analysis of model ensembles, reservoir uncertainty, and data integration.


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