A Novel Application of Mahalanobis Distance Calculation in Assisted History Matching

Abstract

Summary The Mahalanobis distance is a statistical distance and is often used in various machine learning tasks to perform clustering analysis. This paper presents its application to history matching. This new extension, so-called rock typing coupled with the adjoint method, is proposed to maintain the geological consistency between model parameters of different rock types. The rock types have different porosity and permeability ranges, relative permeability curves, and different connate water and residual oil saturation. In general, most gradient-based history matching tools honour the minimum and maximum geological constraints, but the link between the different rock type-dependent parameters may not be maintained. This leads to questionable geological admissibility of the entire model and, thus, calls for the necessity of removing or minimising inconsistencies. This paper shows how the use of Mahalanobis distance calculation can suggest better and more plausible results. It presents the theory, applied methodology and the applicability of Mahalanobis distance calculation in a new history matching workflow that improves geological consistency, including the rock types. The rock type is changed with corresponding parameters at the grid-block level based on the porosity and horizontal permeability change with the rock typing history matching workflow. The so-called rock-typing extension of the history matching workflow allows parameters to be modified co-dependently according to the rock type definition based on the porosity and the permeability adjustments suggested by adjoint-based sensitivity calculations. The Mahalanobis distance is associated with the rock types through their porosity and permeability correlations. Therefore, it guides the correction step and determines the appropriate rock type based on the underlying statistical information. History matching was performed on a simple synthetic model, a quarter of a five-spot pattern with the standard and the rock-typing extended workflow. Comparison results show significant improvements in history matching quality in terms of geological consistency with fewer iterations or within the same number of iterations but with favourable objective function values. With the help of Mahalanobis distance, the novel approach has successfully preserved the geological consistency of the models during the history matching process.