Variation of Permeability with Porosity in Sandstone Diagenesis Interpreted with a Fractal Pore Space Model

Abstract—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.

[1]  E. Teller,et al.  ADSORPTION OF GASES IN MULTIMOLECULAR LAYERS , 1938 .

[2]  Christoph Clauser,et al.  Permeability prediction based on fractal pore‐space geometry , 1999 .

[3]  Jürgen R. Schopper.  EXPERIMENTELLE METHODEN UND EINE APPARATUR ZUR UNTERSUCHUNG DER BEZIEHUNGEN ZWISCHEN HYDRAU‐LISCHEN UND ELEKTRISCHEN EIGENSCHAFTEN LOSER UND KUNSTLICH VERFESTIGTER POROSER MEDIEN * , 1967 .

[4]  Yves Guéguen,et al.  Effective medium theory and network theory applied to the transport properties of rock , 1990 .

[5]  H. Pape,et al.  The Role of Fractal Quantities, as Specific Surface and Tortuosities, for physical properties of porous media , 1984 .

[6]  J. Brakel.  Pore space models for transport phenomena in porous media review and evaluation with special emphasis on capillary liquid transport , 1975 .

[7]  G. E. Archie.  The electrical resistivity log as an aid in determining some reservoir characteristics , 1942 .

[8]  E. C. Childs,et al.  Soil geometry and soil-water equilibria , 1948 .

[9]  H. Pape,et al.  Theory of self‐similar network structures in sedimentary and igneous rocks and their investigation with microscopical and physical methods , 1987 .

[10]  E. Oelkers,et al.  Porosity prediction in quartzose sandstones as a function of time, temperature, depth, stylolite frequency, and hydrocarbon saturation , 1998 .

[11]  C. David,et al.  Geometry of flow paths for fluid transport in rocks , 1993 .

[12]  T. Wong,et al.  Network modeling of permeability evolution during cementation and hot isostatic pressing , 1995 .

[13]  Brian Evans,et al.  Permeability, porosity and pore geometry of hot-pressed calcite , 1982 .

[14]  Alan S. Michaels,et al.  Permeability of Kaolinite , 1954 .

[15]  Lutz Riepe,et al.  Interlayer conductivity of rocks — a fractal model of interface irregularities for calculating interlayer conductivity of natural porous mineral systems , 1987 .

[16]  Bernhard M. Krooss,et al.  Experimental characterisation of the hydrocarbon sealing efficiency of cap rocks , 1997 .

[17]  H. Pape,et al.  A Pigeon-hole Model For Relating Permeability To Specific Surface , 1982 .

[18]  T. Wong,et al.  Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust , 1994 .

[19]  B. Zinszner,et al.  Hydraulic and acoustic properties as a function of porosity in Fontainebleau Sandstone , 1985 .

[20]  P. Carman.  Fluid flow through granular beds , 1997 .