Permeability prediction based on fractal pore‐space geometry

Geophysics - Tập 64 Số 5 - Trang 1447-1460 - 1999
H. Pape1, Christoph Clauser1, Joachim Iffland1
1Rheinische Frederich- Whilhelms-Universitat, Bonn, Federal Republic of Germany

Tóm tắt

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 straightforward 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.

Từ khóa


Tài liệu tham khảo

10.1016/0301-9322(85)90007-2

10.2118/942054-G

10.1029/96JB03396

10.1121/1.1908241

10.1121/1.1908241

10.1029/JB090iB13p11524

10.1021/ja01269a023

Bryant, W. R., Hottmann, W., and Trabant, P., 1974, Permeability of unconsolidated and consolidated marine sediments, Gulf of Mexico: Texas A&M Univ., Report.

Carman P. C., 1937, Trans. Inst. Chem. Eng., 15, 150

1948, Some physical aspects of water flow in porous media: Discuss. Faraday Soc.3, 78.

1956, Flow of gases through porous media: Butterworth Scientific Publ.

10.1190/1.1443971

Clauser, C., 1992, Permeability of crystalline rocks: EOS:73, No. 21, 233, 237.

Debschütz, W., 1995, Hydraulische Untersuchungen an Sediment‐ und Kristallingesteinen unter variablen hydro‐ und lithostatischen Druckbedingungen: Trennung strömungs‐characterisierender Kenngrößen und Korrelation mit anderen petrophysikalischen Größen: Ph.D. dissertation, Tech. Univ. Clausthal.

10.1016/0309-1708(96)00001-2

Emmermann R., 1997, J. Geophys. Res., 102, 18 178

10.1103/PhysRevB.38.2635

10.1190/1.1443970

Iffland, J., and Voigt, H.D., 1996, Porositäts‐ und Permea bilitäts‐verhalten von Rotliegendsandsteinen unter Überlagerungsdruck: DGMK-Berichte, Tagungsbericht 9602.

Jaquin C. G., 1987, Transport in Porous Media, 2, 571

10.1103/PhysRevLett.54.1325

Kenyon, B., Kleinberg, R., Straley, C., Gubelin, G., and Morriss, C., 1995, Nuclear magnetic resonance imaging—technology for the 21st century: Schlumberger Oilfield Review, Autumn 1995, 19–33.

Köhler, M., Pape, H., Pasternak, M., and Schmidt, R., 1993, Natural gas reserves in the Ems estuary region, Part I: Reservoir engineering (in German): Geological Survey of Lower Saxony, internal report no. 110986, Hannover, Germany.

Korvin, G., 1992, Fractal models in the earth sciences: Elsevier Science Publ. Co., Inc.

Kozeny, J., 1927, Über die kapillare Leitung des Wassers im Boden (Aufstieg Versickerung und Anwendung auf die Bewässerung): Sitz. Ber. Akad. Wiss. Wien, Math. Nat. (Abt. IIa),136a, 271–306.

Kulenkampff, J., 1994, Die komplexe elektrische Leitfähigkeit poröser Gesteine im Frequenz‐bereich von 10 Hz bis 1 Mhz: Einflüsse von Porenstruktur und Porenfüllung: Ph.D. dissertation, Tech. Univ. Clausthal.

Leder, F., and Park, W. C., 1986, Porosity reduction in sandstone by quartz overgrowth: AAPG Bull.70, 1713–1728.

Luffel, D. L., Howard, W. E., and Hunt, E. R., 1991, Travis Peak core permeability and porosity relationships at reservoir stress: SPE Form. Eval.6, 310–318.

Mandelbrot, B. B., 1977, Fractals—form, chance and dimensions: W. H. Freeman & Co.

10.1190/1.1444251

10.1021/ie50534a041

Nelson, P. H., 1994, Permeability‐porosity relationships in sedimentary rocks: The Log Analyst,35, No. 3, 38–62.

Pape, H., 1999, Fractal geometry and fractal “music of the Earth” (according to a term of H. Cloos): Zbl. Geol. Paläont. I,9/10, 969–979.

Pape, H., and Schopper, J. R., 1987, Fractal description of the Falkenberg granite microfissure system as derived from petrophysical and microscopical investigations: Geol. Jahrbuch,E39, 149–166.

1988, Relations between physically relevant geometrical properties of a multifractal porous system,inUnger, K. K., Rouquerol, J., Sing, K. S. W., and Kral, H., eds. Characterization of porous solids: Elsevier Science Publ. Co., Inc., 473–482.

Pape, H., and Vogelsang, D., 1996, Fractal evaluation of induced polarization logs in the KTB-Oberpfalz HB: Geol. Jb.E54, 3–27.

10.1016/0166-6622(87)80136-1

10.1016/0166-6622(87)80136-1

10.1016/0166-6622(87)80136-1

10.1016/0166-6622(87)80136-1

10.1029/96JB03802

Richardson, L. F., 1961, The problem of contiguity: An appendix to statistics of deadly quarrels: General Systems Yearbook,6, 139–187.

10.1111/j.1365-2818.1984.tb00461.x

Schlömer, S., and Krooss, B. M., 1997, Experimental characterization of the hydrocarbon sealing efficiency of cap rocks: Marine and Petroleum Geology,14, 565–580.

10.1111/j.1365-2478.1967.tb01809.x

Serra, O., 1984, Fundamentals of well‐log interpretation: 1. The acquisition of data. Elsevier Science Publ. Co., Inc.

10.1103/PhysRevB.55.8038

Shenhav, H., 1971, Lower Cretaceous sandstone reservoirs, Israel: Petrography, porosity, permeability: AAPG Bull.55, 2194–2224.

10.1080/00018738700101062

Timur, A., 1968, An investigation of permeability, porosity and residual water saturation relations for sandstone reservoirs: The Log Analyst,9, No. 4, 8–17.

1969, Effective porosity and permeability of sandstones investigated through nuclear magnetic resonance principles: The Log Analyst,10, No. 1, 3–11.

Ungerer, P., Burrus, J., Doligez, B., Chénet, P. Y., and Bessis, F., 1990, Basin evaluation by integrated two‐dimensional modeling of heat transfer, fluid flow, hydrocarbon generation, and migration: AAPG Bull.74, 309–335.

10.1029/JB089iB13p11539

10.1029/JB089iB11p09425

10.1190/1.1442578

Zawisza, L., 1993, Simplified method of absolute permeability estimation of porous beds: Archives of Mining Sciences,38, 342–352.

Zimmermann, G., 1991, Integrierte Auswertung von Bohrlochmessungen der Kontinentalen Tiefbohrung (KTB) mit Verfahren der multivariaten Statistik: Ph.D. dissertation, Tech. Univ. Berlin.

Zimmermann, G., Burkhardt, H., and Melchert, M., 1992, Estimation of porosity in crystalline rock by a multivariate statistical approach: Sci. Drill.3, 27–35.

Thông tin
Thông tin xuất bản

Geophysics

Tập 64 Số 5

1447-1460

Thông tin tác giả