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Parity in Rock Typing for Geology, Petrophysics and Engineering by Tackling Interconnectivity with a Fractal Leaky-Tubes Description

Abstract

Modified form of Kozeny-Carman equation was the basis of “hydraulic (or flow) units” methodology introduced in 1990s for rock typing. The original study proposed an algebraic manipulation of the equation to derive groups of similarities in porosity-permeability relations. The attempt was for managing the statistical non-representative nature of limited number of samples in a given study, by assuming similar capillary bundles would govern fluid flow in a similar manner. In this study, capillary-bundle approximation is replaced with leaky-tube hydraulics that is bounded by pigeon-hole fractal model of pore space. By addressing interconnectivity of flow-paths through leaky-tube hydraulics and using fractal dimensions for identifying similarities, the shortcomings of capillary-bundle assumption is inhibited; making the revised rock-typing a common-denominator between petrophysics, engineering and geology. The original “hydraulic units” approach was devised for sample selection for core analysis providing better coverage of the spectrum of rock properties; hence, the simplification of porosity-permeability relation did not affect the outcome. However, the methodology was extended by practitioners into modeling and prediction of rock properties that were fed into static models with a non-trivial failure rate throughout the years. Although, the methodology served as a great simplifier of data management and manipulation, the capillary bundle assumption has been the culprit of the failure of modeling and prediction of rock properties for heterogeneous rocks that violate the very assumption of capillary bundles. In this study, more progressive modification of original methodology for rock-typing is proposed to circumvent the shortcomings of basic assumptions in Kozeny-Carman relation of pore space and flow- controls. The modifications require additional Wireline data that are becoming standard logging suites of today. The sought-after agreement in rock typing between disciplines and proper modelling and propagation of rock properties for a field, justify the incremental cost of required data for pivotal wells in a field.