Using Metric Space Methods to Analyse Reservoir Uncertainty

In mathematics, a metric space is a set where a distance (called a metric) is defined between elements of the set. In this paper, we introduce the concept of a metric space in the framework of reservoir modelling and reservoir uncertainty. The distance between two models is a single measure that can be easily understood by the reservoir team, and can be tailored to the application of interest. We describe how placing an ensemble of reservoir models in metric space allows for novel methods for model visualization and analysis. Example applications are presented in the context of uncertainty quantification, sensitivity analysis, and history matching. Although established methods exist in these domains, placing the reservoir models in metric space allows for a complementary approach which has several advantages compared to traditional methods.