Permeability prediction based on fractal pore‐space geometry

Estimating permeability from grain-size distributions or from well logs is attractive but difficult. In this paper we present a new, generally applicable, and relatively inexpensive approach which yields permeability information on the scale of core samples and boreholes. The approach is theoretically based on a fractal model for the internal structure of a porous medium. It yields a general and petrophysically justified relation linking porosity to permeability, which may be calculated either from porosity or from the pore-radius distribution. This general relation can be tuned to the entire spectrum of sandstones, ranging from clean to shaly. The resulting expressions for the different rock types are calibrated to a comprehensive data set of petrophysical and petrographical rock properties measured on 640 sandstone core samples of the Rotliegend Series (Lower Permian) in northeastern Germany. With few modifications, this new straight-forward and petrophysically motivated approach can also be applied to metamorphic and igneous rocks. Permeability calculated with this procedure from industry porosity logs compares very well with permeability measured on sedimentary and metamorphic rock samples.

[1]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[2]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range , 1956 .

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

[4]  Günter Zimmermann,et al.  Integrated log interpretation in the German Continental Deep Drilling Program: Lithology, porosity, and fracture zones , 1997 .

[5]  Amos Nur,et al.  Porosity reduction and crustal pore pressure development , 1984 .

[6]  C. Jacquin,et al.  Fractal porous media II: Geometry of porous geological structures , 1987 .

[7]  A. H. Thompson,et al.  The microgeometry and transport properties of sedimentary rock , 1987 .

[8]  Thompson,et al.  Fractal sandstone pores: Implications for conductivity and pore formation. , 1985, Physical review letters.

[9]  Hansen,et al.  Fractal pore space and rock permeability implications. , 1988, Physical review. B, Condensed matter.

[10]  P. Adler.  Transport processes in fractals—I. Conductivity and permeability of a leibniz packing in the lubrication limit , 1985 .

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

[12]  Gary Mavko,et al.  The effect of a percolation threshold in the Kozeny‐Carman relation , 1997 .

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

[14]  J. B. Walsh,et al.  The effect of pressure on porosity and the transport properties of rock , 1984 .

[15]  S. Tarafdar,et al.  Archie's law from a fractal model for porous rocks , 1997 .

[16]  Jean Paul Rigaut,et al.  An empirical formulation relating boundary lengths to resolution in specimens showing ‘non‐ideally fractal’ dimensions , 1984 .

[17]  J. Lauterjung,et al.  The German Continental Deep Drilling Program KTB: Overview and major results , 1997 .

[18]  J. P. D. Plessis,et al.  Electrical conduction and formation factor in isotropic porous media , 1996 .

[19]  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 .

[20]  Zehui Huang,et al.  Permeability prediction with artificial neural network modeling in the Venture gas field, offshore eastern Canada , 1996 .

[21]  D. L. Johnson,et al.  Permeability and borehole Stoneley waves: Comparison between experiment and theory , 1989 .

[22]  Heinrich Soffel,et al.  Petrophysical properties of the 9-km-deep crustal section at KTB , 1997 .

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