Variation of Permeability with Porosity in Sandstone Diagenesis Interpreted with a Fractal Pore Space Model
Permeability is one of the key rock properties for the management of hydrocarbon and geothermal reservoirs as well as for aquifers. The fundamental equation for estimating permeability is the Kozeny-Carman equation. It is based on a capillary bundle model and relates permeability to porosity, tortuosity and an effective hydraulic pore radius which is defined by this equation. Whereas in clean sands the effective pore radius can be replaced by the specific surface or by the grain radius in a simple way, the resulting equations for permeability cannot be applied to consolidated rocks. Based on a fractal model for porous media, equations were therefore developed which adjust the measure of the specific surface and of the grain radius to the resolution length appropriate for the hydraulic process. These equations are calibrated by a large data set for permeability, formation factor, and porosity determined on sedimentary rocks. This fractal model yields tortuosity and effective pore radius as functions of porosity as well as a general permeability-porosity relationship, the coefficients of which are characteristic for different rock types. It can be applied to interpret the diagenetic evolution of the pore space of sedimentary rocks due to mechanical and chemical compaction with respect to porosity and permeability.