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History Matching in Metric Space
An extremely useful aspect of MDS is that we can visualize the location of the true reservoir (yellow "cross" in the figure below) and compare it to the set of reservoir models in space. This comparison is useful for pre-history match screening.
One should remember though that we can only visualize in 2 or 3 dimensions, but the true dimension of the MDS space may be much higher, depending on the distance measure.
For history matching, we can go beyond this screening process and examine the input parameters which went into the creation of the reservoir models. To do this, we first cluster the reservoir models, and find the cluster which contains the true reservoir (yellow cluster in figure). The models which are in the same cluster as the true reservoir will have the best overall match to the historical data used in the distance measure. We then examine the distribution (histogram) of the parameter values in the yellow cluster, then compare that with the global distribution of the parameter values. An example of this analysis is shown in the figure below.
The figure below illustrates the essential information which comes from this analysis. First, we can determine easily the parameter distribution of the models which are in the same cluster as the true reservoir (labeled "history" below). This identifies what parameter values all the reservoir models in the "history" cluster have in common. For example, the reservoir models in the "history" cluster have a value of 90 for the "Angle" parameter (top left). When comparing the "history" cluster distribution to the overall distribution (labeled "global"), we know which parameter values have a high impact on the history match. For example, the "Angle" value is certainly influential in the quality of the history match, but the "Sorw" and the "Corr Length" parameters seem to have a low impact. One useful consequence of this analysis is that if the engineer wished to create more reservoir models close to history, one would sample from the "history" cluster distributions. In this way, diversity in parameter values would be maintained where the parameter values are insensitive to the history match, yet at the same time sample correctly from the parameters which are important for history matching.