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 hydroc arbon and geothermal reservoirs as well as for aquifers. The fundamental eq uation for estimating permeability is the Kozeny-Carman equation. It is bas ed on a capillary bundle model and relates permeability to porosity, tortuo sity and an effective hydraulic pore radius which is defined by this equati on. 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 equ ations for permeability cannot be applied to consolidated rocks. Based on a fractal model for porous media, equations were therefore developed which a djust the measure of the specific surface and of the grain radius to the re solution length appropriate for the hydraulic process. These equations are calibrated by a large data set for permeability, formation factor, and poro sity determined on sedimentary rocks. This fractal model yields tortuosity and effective pore radius as functions of porosity as well as a general per meability-porosity relationship, the coefficients of which are characterist ic for different rock types. It can be applied to interpret the diagenetic evolution of the pore space of sedimentary rocks due to mechanical and chem ical compaction with respect to porosity and permeability.