Hydraulic permeability and electrical conductivity of sedimentary rocks are predicted from the microscopic geometry of the pore space. The cross-sectional areas and perimeters of the individual pores are estimated from two-dimensional scanning electron micrographs of rock sections. The hydraulic and electrical conductivities of the individual pores are determined from these geometrical parameters, using Darcys law. The effective medium theory from solid-state physics is then used to determine an effective average conductance of each pore. Finally, the pores are assumed to be arranged on a cubic lattice, which allows the calculation of overall macroscopic values for the permeability and the electrical conductivity. Preliminary results using Berea, Boise, Massilon and Saint-Gilles sandstones show reasonably close agreement between the predicted and measured transport properties.
The determination of hydrologic parameters that characterize fluid flow through rock masses on a large scale (e.g., hydraulic conductivity, capillary pressure, and relative permeability) is crucial to activities such as the planning and control of enhanced oil recovery operations, and the design of nuclear waste repositories . Results of numerical simulation experiments performed to quantify the effects of the release and migration of non-condensible gas in water-saturated fractured formations highlight the impact of macroscopic transport properties such as intrinsic permeability, relative permeability, and capillary pressure (Schlueter and Pruess 1990). Indeed, a simulation is only as good as the underlying reservoir description, and therefore depends heavily on the physical properties as defined. Consequently, there is a need for a first-principle understanding of how pore morphology and other related factors can be used to predict basic hydraulic properties. The macroscopic transport properties of porous and fractured media depend critically upon processes at the pore level, the connectivity and geometry of the pore space being most influential. The main objective of this research is to understand, through analysis and experiment, how fluids in pores affect the hydraulic and electrical properties of rocks, and to develop equations relating these macroscopic properties to the microscopic geometry and structure of the pore space. It has been our aim to assemble a comprehensive picture of a rock based on a geologically sound and physically accurate framework. In this study, two-dimensional scanning electron microscope (SEM) micrographs of rock cross-sections have been employed to infer the hydraulic and electrical conductances of the individual pores. We assume that the pores are cylindrical tubes of varying radius, and that they are arranged on a cubic lattice with a coordination number of 6. The hydraulic conductance of each tube is estimated from its area and perimeter, using the hydraulic radius approximation and the Hagen-Poiseuille equation, while the electrical conductance is related only to the cross-sectional area of the tube. In the section under consideration, the pore cross-sections are assumed to be randomly oriented with respect to the directions of the channel axes. The orientation effect has been corrected by means of geometrical and stereological considerations. Account is also taken of possible variation of the cross-sectional area along the length of each tube, e.g., pore necks and bulges.
