A Relative Permeability Rock-Typing Methodology With a Clustering Method Combined With a Heuristic Optimization Procedure

Abstract

Summary Many methods are used to group and classify rocks, most of them designed to be applied to all petrophysical properties, in general. Some authors, however, point out that these generic classifications may not be able to capture the complexity of the relative permeability property, resulting in highly spread relative permeability groups. These authors use correlations between petrophysical data and relative permeability curves to obtain two-phase dynamic rock types through a manual process. The present work describes a general, systematic, and semiautomatic methodology to determine the relative permeability classes (rock types) from relative permeability experimental data, by use of a clustering method associated with an optimization procedure. Clustering methods are able to classify elements according to their similarities in an n-dimensional space of characteristics, but they may not be able to produce clusters with little data scattering of relative permeability, because these clusters must be related to the rock characteristics available in the reservoir model. The method proposed in this investigation uses a clustering method to obtain groups of reservoir-model rock characteristics associated with an optimization method to deform the space of characteristics (clustering space) such that the clusters become representative dynamic classes with minimum spread of relative permeability curves. The results show a significant decrease of the data scattering found among the relative permeability curves within the groups, therefore reducing the uncertainty of the relative permeability used in reservoir simulations. In our methodology, the relative permeability boundaries of each group are also defined, such that every group has its own set of relative permeability curves with some uncertainty for the curve that represents the group. The associated confidence interval of each curve is evaluated with the Student's-t distribution to determine the relative permeability optimistic and pessimistic curves for each group. These boundaries allow optimistic and pessimist scenarios to be drawn.