Correlating Microstructure to the Petrophysical Properties of Porous Rocks
Authors: Roberts A.P. , Bentz Dale P. , Knackstedt Mark A. 
Published: December 2007

Abstract
We generate model random porous media which give a realistic representation of the complex microstructure observed in porous rocks. The freedom in specifying the parameters of the model allows the modeling of petrophysical media with diverse pore morphologies. The model qualitatively accounts for the principal features of a variety of sedimentary rocks. We derive the conductivity and permeability for the model porous materials. Excellent agreement with experimentally measured properties of sedimentary samples is obtained. The agreement provides a strong hint that it is now possible to correlate effective physical properties of rocks to microstructure.

Introduction
Rocks are heterogeneous. From a microscopic viewpoint the pore geometry is complex and difficult to enumerate. Determination of the precise solid-fluid boundary in anything but the simplest rocks is a difficult, if not impossible, task. For this reason many believe a quantitative approach to the problem might never be attained. Yet, understanding the inter-relationship between rock microstructure and its expression in geophysical and petrophysical data is necessary for enhanced characterisation of petroleum reservoirs. When studied at a macroscopic level, correlation of rock properties to rock characteristics have been noted. In particular, transport properties (conductivity and permeability) of porous rocks have been correlated to the volume fraction of pore space (porosity) of the solid. An empirical equation that links the conductivity of a brine saturated rock (r) to the porosity was first proposed by Archie:
(1)
Here F is the formation factor, w is the conductivity of the brine, is the porosity of the porous media and m the cementation exponent. Most experimental and theoretical work has been devoted to establishing the correlation variables m and C for different classes of rock. In these equations all the explicit microstructural information describing the porous solid is subsumed in the porosity and details of the microstructure are ignored. Changes in bulk porosity alone cannot explain the main features of the conductivity data. Microstructural parameters relative to the porous network must be included in a detailed analysis of the transport properties of rocks. Past theoretical attempts to relate macroscopic physical properties to a description of microstructure of the porous material have been limited. Most methods use oversimplified representations of the pore structure for which properties can be analytically evaluated. Examples include simple micro-porous models (dilute spheres, cylindrical tubes, periodic media) and effective medium approaches. These models do not explicitly account for microstructure. Therefore, to correlate the model to experimental data, these models must incorporate parameters which are poorly defined (e.g. shape factors). A major factor in attempts to understand the macroscopic behaviour of porous solids is the ability to generate, and to characterize, realistic model microstructures.
In this paper we describe a model which gives a realistic representation of general porous media microstructure. The model is based on level cuts of a Gaussian random field with arbitrary spectral density. The freedom in specifying the parameters of the model allows the modeling of petrophysical media with diverse pore morphologies. The model qualitatively accounts for the principal features of a wide variety of sedimentary rocks. We calculate the conductivity and permeability for the model porous materials. Excellent agreement with experimentally measured properties of sedimentary samples is obtained. The agreement provides a strong hint that it is now possible to correlate effective physical properties of rocks to microstructure.
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