Relative Permeability Rock Typing Through Clustering Combined With Heuristic Optimization
Authors: Martins Compan Andre Luiz , Couto Paulo , Bodstein Gustavo Cesar Rachid 
Published: June 2014

Abstract
Rock classification is an important task to reservoir characterization and simulation. There are many methods used in the petroleum industry to classify rocks within groups, most of them designed to be applied generically to all petrophysical properties. Some authors, however, point out that these generic classifications may not be able to capture the complexity of the relative permeability, resulting on high-spread relative permeability groups. These authors use correlations between petrophysical data and relative permeability points to obtain these two-phase dynamic rock-types through a manual process. This work presents a systematic method to determine relative permeability classes (rock-types) from relative permeability lab data in a generic and semi-automatic way, using a clustering method associated with an optimization method.
Clustering methods are able to classify elements according to its similarities in an n-dimensional space of characteristics, but it is not enough to obtain clusters with little dispersion of relative permeability; these clusters should be related with rock characteristics available in the reservoir model. The proposed method 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) until the clusters become representative dynamic classes with minimum spread of relative permeability curves. The optimization process can minimize the clusters spread by changing the relative weight of parameters that form the clustering n-dimensional space or by changing constants of the equations that relate rock properties. In such case these equations, and not the properties themselves, are the clustering space basis. By changing the parameters of these equations, the optimization method can also find functional relations between petrophysical and geological characteristics with relative permeability curves.
The first set of results show an important reduction of the dispersion found among the relative permeability curves within the groups, what makes the method a good option to reduce uncertainty of the relative permeability used in the reservoir simulation.

Introduction
Except in cases of " homogeneous" reservoirs, it is almost impossible to fully characterize petrophysical properties of the reservoir, what makes rock classification a fundamental step to a proper reservoir characterization and flow simulation. Rock classification can be done in many ways and receive many names, each one with its own advantages and limitations. Archie (1950) already proposed in 1950 a rock classification, naming it " Type of Rock", as " ... a formation whose parts have been deposited under similar conditions and have undergone similar process of later weathering, cementation or re-solution…" According to Archie rock classified as being of the same rock type will have similar pore size distributions, permeability-porosity relationship, capillary pressure curves and connate water saturation. Rushing, et al. (2008) divides the rock types as Depositional, Petrographic and Hydraulic, and summarize other classifications like Lithofacies, Petrofacies and Electrofacies. These classifications mainly take into account static and quasi-static properties or single-phase flow characteristics to rock clustering. Hamon & Bennes (2004) have shown that these rock types may not be able to capture all variability of multi-phase flow, represented by the relative permeability curves. Rebele, et al. (2009) agrees with Hamon & Bennes and use a specific rock type for the relative permeability curves calling it as " Dynamic Rock-Type".