Petrography and Reservoir Physics III: Physical Models for Permeability and Formation Factor (1)

Abstract

Permeability and formation factor are physical properties of porous rocks useful for assessing reservoirs. Neither property varies consistently as porosity varies. The relationship of both properties to porosity is complex, being sensitive to the structure of the porous microstructure, i.e., the sizes of pore throats, the numbers and sizes of pores, and the relationships between pores and throats. Physical models to account for these factors require parameters that describe physically relevant properties of the microstructure. A partial characterization of the relationship between pores and throats is embodied in the relationship between pore type and throat size. This relationship is derived by combining data obtained from thin sections, from which pore types are derived via image analysis, and mercury injection porosimetry, which quantifies throat size information. Parameters derived from such a combination are sufficient to construct simple physical models for permeability and electrical conductivity (inverse formation factor). These models assume a porous medium that has large numbers of flow paths parallel to the potential gradient, such that flow has little tortuosity (i.e., flow parallel to bedding). The contributions of each pore type to permeability and electrical conductivity are computed. Calculated values are close to measurement values. A constant of proportionality is the same for all samples from a reservoir, but can vary between reservoirs, is required, and must have values ranging (for sandstones) from about 2.5 to 3.5 for permeability an 5.0 to 7.0 for conductivity. These values are consistent for an efficiently packed fabric. One result of such modeling is a physical model of Archie's cementation exponent m as the ratio of the logarithms of the cross sectional throat area to pore area (per unit area).