Computational Geosciences

, Volume 13, Issue 2, pp 181–186 | Cite as

Comparison between neuro-fuzzy and fractal models for permeability prediction

Original paper


We have used different techniques for permeability prediction using porosity core data from one well at the Maracaibo Lake, Venezuela. One of these techniques is statistical and uses neuro-fuzzy concepts. Another has been developed by Pape et al. (Geophysics 64(5):1447–1460, 1999), based on fractal theory and the Kozeny–Carman equations. We have also calculated permeability values using the empirical model obtained in 1949 by Tixier and a simple linear regression between the logarithms of permeability and porosity. We have used 100% of the permeability–porosity data to obtain the predictor equations in each case. The best fit, in terms of the root mean-square error, was obtained with the statistical approach. The results obtained from the fractal model, the Tixier equation or the linear approach do not improve the neuro-fuzzy results. We have also randomly taken 25% of the porosity data to obtain the predictor equations. The increase of the input data density for the neuro-fuzzy approach improves the results, as is expected for a statistical analysis. On the contrary, for the physical model based on the fractal theory, the decrease in the data density could allow reaching the ideal theoretical Kozeny–Carman model, on which are based the fractal equations, and hence, the permeability prediction using these expressions is improved.


Porosity Permeability Neuro-fuzzy Fractal theory Prediction Linear regretion Empirical General Pape equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pape, H., Clauser, C., Iffland, J.: Permeability prediction based on fractal pore-space geometry. Geophysics 64(5), 1447–1460 (1999)CrossRefGoogle Scholar
  2. 2.
    Finol, J., Guo, Y.K., Jing, X.D.: A rule based fuzzy model for the prediction of petrophysical rock parameters. J. Pet. Sci. Eng. 29, 97–113 (2001)CrossRefGoogle Scholar
  3. 3.
    Balan, B., Mohaghegh, S., Ameri, S.: State-of-the-art in permeability determination from well log data, part 1: a comparative study, model development. In: Proceedings, SPE Eastern Regional Conference and Exhibition. SPE30978, pp. 1–10, Morgantown, 19–21 September 1995Google Scholar
  4. 4.
    Nelson, P.H.: Permeability–porosity relationships in sedimentary rocks. Log Anal. 35(3), 38–62 (1994)Google Scholar
  5. 5.
    Shenhav, H.: Lower cretaceous sandstone reservoirs, Israel: petrography, porosity, permeability. AAPG Bull. 55, 2194–2224 (1971)Google Scholar
  6. 6.
    Dandekar, A.Y.: Petroleum Reservoir Rock and Fluid Properties, vol. 488. CRC, Taylor & Francis, London (2006)Google Scholar
  7. 7.
    Pape, H., Clauser, C., Iffland, J.: Permeability-porosity relationship in sandstone based on fractal pore space geometry. Pure Appl. Geophys. 157, 603–619 (2000)CrossRefGoogle Scholar
  8. 8.
    Jang, J.: ANFIS: adaptive network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 23, 665–685 (1993)CrossRefGoogle Scholar
  9. 9.
    Wong, K.W., Wong, P.M., Gedeon, T.D., Fung, C.C.: A state-of-art review of fuzzy logic for reservoir evaluation. APPEA J. 43, 587–593 (2003)Google Scholar
  10. 10.
    Finol, J., Jing, X.D.: Permeability prediction in shaly formations: the fuzzy modelling approach. Geophysics 67(3), 817–829 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Laboratorio de Física Teórica de Sólidos, CEFITEC, Escuela de FísicaUniversidad Central de VenezuelaCaracasVenezuela
  2. 2.Instituto de Nanociencia de Aragón (INA)Universidad de ZaragozaZaragozaSpain
  3. 3.Dpto. de Ciencias de la TierraUniversidad Simón Bolívar (USB)CaracasVenezuela
  4. 4.Dpto. de Ciencias Básicas, UNEXPOAntonio José de Sucre La YaguaraCaracasVenezuela

Personalised recommendations