Pore-Level Analysis of the Relationship Between Porosity, Irreducible Water Saturation, and Permeability of Clastic Rocks

Abstract

Abstract Permeability is one of the most important, most spatially variable, most uncertain, and hence least predictable transport properties of porous media. Various empirical models, such as Tixier's, Timur's and Coates' equations, are widely used to quantify permeability from well-log calculations of porosity and irreducible water saturation. However, these models do not explicitly include the role played by rock structure, spatial fluid distribution in the pore space, wettability, or clay mineral distribution on permeability. We present a pore-scale approach to investigate the influence of these factors on the permeability of clastic rocks for explicit pore geometries of brine-saturated granular rocks. Synthetic pore-scale models are constructed to represent granular sands with variable grain-size distributions. These models include the structural effects of compaction, cementation, and distribution of dispersed hydrated clay minerals. Irreducible water is geometrically distributed on grain surfaces of the synthetic rocks. Permeability is calculated from lattice-Boltzmann flow simulations. A nonlinear relationship between permeability, porosity, and irreducible water saturation is established for these computer-generated rocks. We compare calculated permeability values of computer-generated rocks and laboratory measurements of core samples to those estimated from different empirical approaches, such as Tixier, Coates, and Timur models. It is found that the latter models cannot be applied to general cases of clastic rocks even if their free parameters are adjusted to fit core measurements. Our simulations also show that spatial distributions of clay minerals and irreducible water play a fundamental role in establishing an accurate correlation between permeability, porosity, and irreducible water saturation. Specific deterministic equations must be established for rock formations that exhibit distinct grain-size distributions, clay types, structural clay distributions, and grain cementation. Introduction Permeability governs the displacement of fluids through the pore space of porous media. It is one of the most important and least predictable transport properties of porous media in reservoir characterization. Permeability is usually evaluated from core samples and/or well tests. However, core samples and well-test data are often only available from few wells in a reservoir while well logs are available from the majority of wells. Therefore, accurate and reliable evaluation of permeability from well-log data embodies a significant technical and economic advantage.1 Various empirical models have been proposed to infer permeability from well-log data, based on calculations of porosity, water saturation, capillary pressure, and formation resistivity factor.2-6 Permeability is estimated via correlations among other rock petrophysical properties. In many cases, there may exist deterministic relationships among these properties, but such correlations usually are empirically derived for a given formation in a given area, are often statistical in nature and, therefore, cannot be applied to general cases.7