Evaluation of Distance-space Proxy Models for Inference of Reserves Distribution

When evaluating oil and gas field development plans, it is often necessary to construct a reserves distribution given only a very limited number of reservoir model realizations, in which case traditional (parameter–space) proxy modeling does not always provide a sufficiently accurate approximation to the true distribution. For example, a problem may arise in a situation where models corresponding to a few different geological scenarios are calibrated using the historical data, but it is expensive to explore the parametric space “between” these model realizations.

In this work we investigate the validity of a proxy modeling method—which we term distance-space modeling—that aims to address this issue by generating a model based on the characteristic production profiles from the available realizations of the reservoir models. The chief distinction between the two methods is that in parameter–space modeling, the proxy model is built in the parameter-space; that is to say that the coordinates assigned to a realization in the interpolation space are precisely its parameter values. Whereas in the proposed method, the coordinates of the realization are obtained in such a way that the proximity of any two realizations is in some way representative of the similarity of the output of the dynamic reservoir simulator (e.g., predictions of the bottom hole pressure, fluid production rates, ratios etc.).

We verify the proposed distance-space method against the “true” distribution of the total produced oil from a test reservoir and parameter-space proxy models. The “true” distribution was obtained by running a large number of model realizations in a reservoir simulator. For a small number of runs used to construct the proxy model, the distance-space approach seems to offer a valid alternative to traditional proxy-modeling, with comparable or better results. As the number of runs is increased, however, the performance of the distance proxy model does not seem to improve and can even deteriorate. This is in contrast to the results of parameter-space modeling, which tend to improve as the number of runs is increased.