Advertisement

Mathematical Geology

, Volume 26, Issue 8, pp 985–994 | Cite as

Model-free estimation of fracture aperture with neural networks

  • Marek Kacewicz
Article

Abstract

The feedforward backpropagation technique provides a model-free estimation with neural networks. The algorithm was used to estimate fracture aperture of natural fractures in three dimensional space. A three-layer neural network with at least 5 nodes in a hidden layer was trained on a data set consisting of formation imaging microscanner logs (FMS)from horizontal boreholes. Sensitivity studies were performed to account for the rate of learning convergence, convergence to local error minima, etc. Among the factors contributing mostly to the overall good or bad performance of the network, the following are worth mentioning: number of data points, data spacing, and data variability. It is shown that a smoothing operation applied to aperture data along the wellbore often helps to reduce ‘disorientation’ of the network and to switch from oscillations or chaotic ‘jumps’ to convergence.

Key words

naturally fractured reservoirs fracture networks fracture apertures neural networks feedforward backpropagation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barton, C. C., 1992, Fractal Analysis of the Scaling and Spatial Clustering of Fracture Rocks: Fractals and Their Application to Geology, Proceedings of the 1988 GSA Annual Meeting.Google Scholar
  2. Barton, C. C., and Larsen, E., 1985, Fractal Geometry of Two-Dimensional Fracture Networks at Yucca Mountain, Southwestern Nevada: Proceedings of the Int. Symp. on Fundamental of Rock Joints, Bjorkliden, p. 77–84.Google Scholar
  3. Belfield. W. C., 1994, Multifractal Characteristics of Natural Fracture Apertures: Geophys. Res. Lett. (in press).Google Scholar
  4. Belfield, W. C., and Sovich, J., 1994, Fracture Statistics from Horizontal Wellbores: Paper HWC94-37, Canadian SPE/CIM/CANMET Int. Conf. on Advances in Horizontal Well Applications, Calgary, Canada.Google Scholar
  5. Chiles, J. P., 1988, Fractal and Geostatistical Methods for Modeling a Fracture Network, Math. Geol., v. 20, 6, p. 631–654.Google Scholar
  6. Chiles, J. P., 1989, Modélisation Géostalistique de Réseaux de Fractures,in M. Armstrong, ed.,Geostatistics (Vol. 1) Kluwer Academic Pub., Dordrecht, p. 57–76.Google Scholar
  7. Chiles. J., and de Marsily, G., 1993, Stochastic Models of Fracture Systems and Their Use in Flow and Transport Modeling, in J. Bear, Ch. Tsang, and G. de Marsily, eds., Flow and Contaminant Transport in Fractured Rocks: Academic Press, p. 169–236.Google Scholar
  8. Dowd, P. A., 1994, The Use of Neural Networks for Spatial Simulation,in R. Dimitrakopoulos, ed.,Geostatistics for the Next Century: Kluwer Academic Pub., Dordrecht, p. 173–184.Google Scholar
  9. Jacquin, C. G., and Adler, P. M., 1987, Fractal Porous Media. II. Geometry of Porous Geological Structures: Trans. Porous Media, v. 2, p. 571–596.Google Scholar
  10. Kosko. B., 1992,Neural Networks and Fuzzy Systems — A Dynamical Systems Approach to Machine Intelligence: Prentice Hall, 449 p.Google Scholar
  11. La Pointe, P. R., 1980, Analysis of Spatial Variation in Rock Mass Properties Through Geostatistics: Proceedings of the 21st U.S. Symp. on Rock Mechanics, Rolla, Missouri, p. 570–580.Google Scholar
  12. Long, J. C., and Billaux, D. M., 1987, From Field Data To Fracture Network Modeling and Example Incorporating Spatial Structure: An Example Incorporating Spatial Structure: Water Res. Res. v. 27, n. 7, p. 1201–1216.Google Scholar
  13. Miller, S. M., 1979, Geostatistical Analysis for Evaluating Spatial Dependence of Fracture Set Characteristics: Proceedings of the 16th APCOM Symp., New York, p. 537–545.Google Scholar
  14. Neretnieks, I., 1993, Solute Transport in Fractured Rock—Applications to Radionuclide Waste Repositories, in J. Bear, Ch. Tsang, and G. de Marsily, eds.,Flow and Contaminant Transport in Fractured Rocks; Academic Press, p. 39–127.Google Scholar
  15. Pao, Y., 1989,Adaptive Pattern Recognition and Neural Networks: Addison-Wesley, 309 p.Google Scholar
  16. Parker, D. B., 1982, Learning Logic, Invention Report S81-64, File 1. Office of Technology Licensing, Stanford University, Stanford, CA.Google Scholar
  17. Penn, B. S., Gordon, A. J., and Wendlandt, R. F., 1993, Using Neural Networks to Locate Edges and Linear Features in Satellite Images: Comput. Geosci., v 19, 10, p. 1545–1565.Google Scholar
  18. Rogers. S. J., Fang, J. H., Karr, C. L., and Stanley, D. A., 1992, Determination of Lithology from Well Logs Using a Neural Network: Am. Assoc. Petrol. Geol. Bull., v. 76, n. 5, p. 731–739.Google Scholar
  19. Rumelhart, D. E., Hinton, G. E., and Williams, R. J., 1986, Learning Internal Representations by Error Propagation,in, Parallel Distributed Processing: Explorations in the Microstructures of Cognition (Vol. 1) J. L. McClelland and D. E. Rumelhart, eds., MIT Press, p. 318.Google Scholar
  20. Thomas, A., 1987, tStructure Fractale de l'Architecture de Champs de Fractures en Milieu Rocheux, Comptes Rendus (Vol. 304, Ser II, no. 4) Acad. Sci., Paris, p. 181–186.Google Scholar
  21. Werbos, P. J., 1974, Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences: Ph.D. dissertation in Statistics, Harvard University.Google Scholar
  22. Wu, X., and Zhou, Y., 1993, Reserve Estimation Using Neural Network Techniques: Comp. Geosci., v. 19, n. 4, p. 567–575.Google Scholar

Copyright information

© International Association for Mathematical Geology 1994

Authors and Affiliations

  • Marek Kacewicz
    • 1
  1. 1.ARCO Exploration and Production TechnologyPlano

Personalised recommendations