Relations between pores, throats and permeability: A petrographic/physical analysis of some carbonate grainstones and packstones

Abstract

Some physical properties of carbonate rocks are sensitive to mineralogy, others are functions of porosity, and still others are related to the distribution and configuration of porosity. Properties associated with transmissivity (permeability, electrical conductivity) fall in the latter category. Porosity is distributed in rocks as a three-dimensionally interconnected network with large voids (pores) connected at small constrictions (pore throats). Thin sections carry only pore information. A new methodology termed Petrographic Image Analysis consists of a systematic procedure which determines pore/throat relationships. These data are sufficient to construct precise physical models for calculating permeability and formation factor. Petrographic Image Analysis involves: (1) acquisition of digital images of porosity from thin section, (2) measurement of the size and geometric complexity of that porosity, and (3) objective determination of pore types using a pattern-recognition/pore-classification procedure. Once classified, the size, relative proportions and number of pores per unit volume of each pore type can be calculated. Regression procedures provide a first-order model between mercury saturation as a function of pressure and pore type proportion, and thus between pore type and throat size. Analysis of the deviations from regression refine the throat-size assignments on a sample-by-sample basis. From this, permeability and electrical conductivity can be calculated based on Darcy’s and Ohm’s Laws respectively. The models agree with measured properties with high precision. Both models are additive in that the contribution of each pore type is calculated separately. Therefore, the relative mobility of phases occupying different portions of the pore system can be assessed. These principles are illustrated by analysis of the pore/throat system of a suite of carbonate pelletal packstones and peloidal grainstones from a Middle-East limestone reservoir, and the derivation of statistical and physical models estimating the permeability of these rocks. Derivation of formation factor (to be discussed in a later paper) can be done by a similar method due to the close relationship between Darcy’s Law and Ohm’s Law.