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Geofluids
Volume 2017, Article ID 1361289, 11 pages
https://doi.org/10.1155/2017/1361289
Research Article

Characterization of Aquifer Multiscale Properties by Generating Random Fractal Field with Truncated Power Variogram Model Using Karhunen–Loève Expansion

1Department of Oil-Gas Field Development, College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China
2State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing 102249, China
3State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Sinopec Group, Beijing 100083, China
4Department of Hydrosciences, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, China

Correspondence should be addressed to Tongchao Nan; nc.ude.ujn@nanct

Received 29 June 2017; Revised 31 October 2017; Accepted 28 November 2017; Published 19 December 2017

Academic Editor: Walter A. Illman

Copyright © 2017 Liang Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. A. Sudicky, “A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process,” Water Resources Research, vol. 22, no. 13, pp. 2069–2082, 1986. View at Publisher · View at Google Scholar · View at Scopus
  2. P. Dietrich and C. Leven, “Direct push-technologies,” in Groundwater Geophysics, R. Kirsch, Ed., pp. 347–366, Springer, Berlin, Germany, 2006. View at Google Scholar
  3. S. J. Berg and W. A. Illman, “Three-dimensional transient hydraulic tomography in a highly heterogeneous glaciofluvial aquifer-aquitard system,” Water Resources Research, vol. 47, no. 10, Article ID W10507, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Dagan, Flow and Transport in Porous Formations, Springer, New York, NY, USA, 1989.
  5. L. W. Gelhar, Stochastic Subsurface Hydrology, Prentice-Hall, Englewood Cliffs, NJ, USA, 1993.
  6. J. P. Delhomme, “Spatial variability and uncertainty in groundwater flow parameters: A geostatistical approach,” Water Resources Research, vol. 15, no. 2, pp. 269–280, 1979. View at Publisher · View at Google Scholar · View at Scopus
  7. R. J. Hoeksema and P. K. Kitanidis, “Prediction of transmissivities, heads, and seepage velocities using mathematical modeling and geostatistics,” Advances in Water Resources, vol. 12, no. 2, pp. 90–102, 1989. View at Publisher · View at Google Scholar · View at Scopus
  8. R. A. Carlson and J. L. Osiensky, “Geostatistical analysis and simulation of nonpoint source groundwater nitrate contamination: A case study,” Environmental Geosciences, vol. 5, no. 4, pp. 177–186, 1998. View at Publisher · View at Google Scholar · View at Scopus
  9. C. V. Deutsch and A. G. Journel, GSLIB: Geostatistical Software Library and User’s Guide, Applied Geostatistics Series, Oxford University Press, Oxford, UK, 2nd edition, 1997.
  10. S. P. Neuman, “Universal scaling of hydraulic conductivities and dispersivities in geologic media,” Water Resources Research, vol. 26, no. 8, pp. 1749–1758, 1990. View at Publisher · View at Google Scholar · View at Scopus
  11. L. W. Gelhar, C. Welty, and K. R. Rehfeldt, “A critical review of data on field‐scale dispersion in aquifers,” Water Resources Research, vol. 28, no. 7, pp. 1955–1974, 1992. View at Publisher · View at Google Scholar · View at Scopus
  12. F. J. Molz and G. K. Boman, “Further evidence of fractal structure in hydraulic conductivity distributions,” Geophysical Research Letters, vol. 22, no. 18, pp. 2545–2548, 1995. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Painter, “Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations,” Water Resources Research, vol. 32, no. 5, pp. 1183–1195, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. L. Tennekoon, M. C. Boufadel, D. Lavallee, and J. Weaver, “Multifractal anisotropic scaling of the hydraulic conductivity,” Water Resources Research, vol. 39, no. 7, pp. 113–117, 2003. View at Google Scholar · View at Scopus
  15. J. Egglestön and S. Rojstaczer, “Inferring spatial correlation of hydraulic conductivity from sediment cores and outcrops,” Geophysical Research Letters, vol. 25, no. 13, pp. 2321–2324, 1998. View at Publisher · View at Google Scholar · View at Scopus
  16. M. C. Boufadel, S. Lu, F. J. Molz, and D. Lavallee, “Multifractal scaling of the intrinsic permeability,” Water Resources Research, vol. 36, no. 11, pp. 3211–3222, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. H. H. Liu and F. J. Molz, “Discrimination of fractional Brownian movement and fractional Gaussian noise structures in permeability and related property distributions with range analyses,” Water Resources Research, vol. 32, no. 8, pp. 2601–2605, 1996. View at Publisher · View at Google Scholar · View at Scopus
  18. F. Ruan and D. McLaughlin, “An efficient multivariate random field generator using the fast Fourier transform,” Advances in Water Resources, vol. 21, no. 5, pp. 385–399, 1998. View at Publisher · View at Google Scholar · View at Scopus
  19. P. R. Kramer, O. Kurbanmuradov, and K. Sabelfeld, “Comparative analysis of multiscale Gaussian random field simulation algorithms,” Journal of Computational Physics, vol. 226, no. 1, pp. 897–924, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. C. Cameron, “Relative efficiency of Gaussian stochastic process sampling procedures,” Journal of Computational Physics, vol. 192, no. 2, pp. 546–569, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. V. Di Federico and S. P. Neuman, “Scaling of random fields by means of truncated power variograms and associated spectra,” Water Resources Research, vol. 33, no. 5, pp. 1075–1085, 1997. View at Publisher · View at Google Scholar · View at Scopus
  22. L. Xue and D. Zhang, “A multimodel data assimilation framework via the ensemble Kalman filter,” Water Resources Research, vol. 50, no. 5, pp. 4197–4219, 2014. View at Publisher · View at Google Scholar · View at Scopus
  23. F. Heße, V. Prykhodko, S. Schlüter, and S. Attinger, “Generating random fields with a truncated power-law variogram: Acomparison of several numerical methods,” Environmental Modeling and Software, vol. 55, pp. 32–48, 2014. View at Publisher · View at Google Scholar · View at Scopus
  24. T. Dieker, Simulation of fractional Brownian motion [M.S., thesis], Department of Mathematical Sciences, University of Twente, Enschede, The Netherlands, 2004.
  25. H. Li and D. Zhang, “Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods,” Water Resources Research, vol. 43, pp. 6627–6632, 2007. View at Google Scholar
  26. H. Li, H. Chang, and D. Zhang, “Stochastic collocation methods for efficient and accurate quantification of uncertainty in multiphase reservoir simulations,” in Proceedings of the SPE Reservoir Simulation Symposium 2009, pp. 509–520, February 2009. View at Scopus
  27. Q. Liao and D. Zhang, “Probabilistic collocation method for strongly nonlinear problems: 1. Transform by location,” Water Resources Research, vol. 49, no. 12, pp. 7911–7928, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Chang and D. Zhang, “A comparative study of stochastic collocation methods for flow in spatially correlated random fields,” Communications in Computational Physics, vol. 6, no. 3, pp. 509–535, 2009. View at Google Scholar · View at Scopus
  29. S. Strebelle, “Conditional simulation of complex geological structures using multiple-point statistics,” Mathematical Geology, vol. 34, no. 1, pp. 1–21, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. T. Hewett, “Fractal Distributions of Reservoir Heterogeneity and Their Influence on Fluid Transport,” in Proceedings of the SPE Annual Technical Conference and Exhibition, New Orleans, LA, USA, 1986. View at Publisher · View at Google Scholar
  31. S. Painter and L. Paterson, “Fractional Lévy motion as a model for spatial variability in sedimentary rock,” Geophysical Research Letters, vol. 21, no. 25, pp. 2857–2860, 1994. View at Publisher · View at Google Scholar · View at Scopus
  32. A. G. Guzman and S. Neuman, “Field air injection experiments,” in Apache Leap Tuff INTRAVAL Experiments: Results and Lessons Learned, T. Rasmussen, S. Rhodes, A. Guzman, and S. Neuman, Eds., Nuclear Regulatory Commission, 1996. View at Google Scholar
  33. F. J. Molz, H. Rajaram, and S. Lu, “Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions,” Reviews of Geophysics, vol. 42, no. 1, 2004. View at Google Scholar · View at Scopus
  34. D. Veneziano and A. K. Essiam, “Nonlinear spectral analysis of flow through multifractal porous media,” Chaos, Solitons & Fractals, vol. 19, no. 2, pp. 293–307, 2004. View at Publisher · View at Google Scholar · View at Scopus
  35. V. Ganti, A. Singh, P. Passalacqua, and E. Foufoula-Georgiou, “Subordinated Brownian motion model for sediment transport,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 80, no. 1, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Siena, A. Guadagnini, M. Riva, and S. P. Neuman, “Extended power-law scaling of air permeabilities measured on a block of tuff,” Hydrology and Earth System Sciences, vol. 16, no. 1, pp. 29–42, 2012. View at Publisher · View at Google Scholar · View at Scopus
  37. A. Guadagnini, S. P. Neuman, M. G. Schaap, and M. Riva, “Anisotropic statistical scaling of soil and sediment texture in a stratified deep vadose zone near Maricopa, Arizona,” Geoderma, vol. 214-215, pp. 217–227, 2014. View at Publisher · View at Google Scholar · View at Scopus
  38. B. Jafarpour and M. Khodabakhshi, “A probability conditioning method (PCM) for nonlinear flow data integration into multipoint statistical facies simulation,” Mathematical Geosciences, vol. 43, no. 2, pp. 133–164, 2011. View at Publisher · View at Google Scholar · View at Scopus