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Water Resources

, Volume 40, Issue 7, pp 767–775 | Cite as

Methods of modeling hydraulic heterogeneity of sedimentary formations

  • V. A. BakshevskayaEmail author
  • S. P. Pozdnyakov
Methodology and Methods of Studies

Abstract

The approaches and methods now in use for simulating the hydraulic heterogeneity of sedimentary rocks are reviewed, classified, and described. Special attention is paid to the statistical (geostatistical) models, including the most promising hydrofacies simulation methods.

Keywords

hydraulic heterogeneity stochastic modeling kriging Markov chains hydrofacies flow and transport in porous media 

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References

  1. 1.
    Baidariko, E.A., and Pozdnyakov, S.P., Simulation of liquid waste buoyancy in a deep heterogeneous aquifer, Geoekologiya, 2010, no. 6, pp. 544–554.Google Scholar
  2. 2.
    Bezrukov, A.V., Rykus, M.V., Davletova, A.R., and Savichev, V.I., Issues of ntroduction of multiple-point statistical methods, Nauchn.-Tekhn. vestn. OAO “NK “Rosneft’”, 2010, no. 2, pp. 2–8.Google Scholar
  3. 3.
    Dem’yanov, V.V., and Savel’eva, E.A., Geostatistika: teoriya i praktika (Geostatistics: Theory and Practice), Moscow: Nauka, 2010.Google Scholar
  4. 4.
    Dyubrul, O., Ispol’zovanie geostatistiki dlya vklyucheniya v geologicheskuyu model’ seismicheskikh dannykh (The Use of Geostatistics to Incorporate Seismic Data in Geological Models), Zeist: EAGE, 2002.Google Scholar
  5. 5.
    Dyubryul’, O., Geostatistika v neftyanoi geologii (Geostatistis in Petroleum Geology), Moscow: Inst. Komp. Issled., NITs “Regul. khaot. dinam., 2009.Google Scholar
  6. 6.
    Pinus, O.V., and Pairazyan, K.V., Geological modeling of productive strata of fluvial origin, Geol. Nefti Gaza, 2008, no. 1, pp. 25–30.Google Scholar
  7. 7.
    Pozdnyakov, S.P., and Bakshevskaya, V.A., Numerical analysis of macrodispersion during the pumping of a solute into an aquifer containing low-permeability inclusions, in Problemy gidrogeologii XXI veka: Nauka i obrazovanie (Issues of Geohydrology of the XXI Century: Science and Education), Moscow: RUDN, 2003, pp. 156–170.Google Scholar
  8. 8.
    Pozdnyakov, S.P., Bakshevskaya, V.A., Krokhicheva, I.V., Danilov, V.V., and Zubkov, A.A., Effect of schematization of sediment heterogeneity to forecasts of pollutant migration, Vestn. Mosk. Univ., Ser. 4: Geol., 2012, no. 1, pp. 40–48.Google Scholar
  9. 9.
    Shvidler, M.I., Statisticheskaya gidrodinamika poristykh sred (Statistical Hydrodynamics of Porous Media), Moscow: Nedra, 1985.Google Scholar
  10. 10.
    Shestakov, V.M., To take into account the geological heterogeneity is the key problem of hydrogeodynamics, Vestn. Mosk. Univ., Ser. 4: Geol., 2003, no. 1, pp. 25–28.Google Scholar
  11. 11.
    Carle, S.F., and Fogg, G.E., Modeling spatial variability with oneand multi-dimensional Markov chains, Math. Geol., 1997, vol. 29, no. 7, pp. 891–918.CrossRefGoogle Scholar
  12. 12.
    Carle, S.F., and Fogg, G.E., Transition probabilitybased indicator geostatistics, Math. Geol., 1996, vol. 28, no. 4, pp. 453–476.CrossRefGoogle Scholar
  13. 13.
    Carrera, J., Alcolea, A., Medina, A., et al., Inverse problem in hydrogeology, Hydrogeology J., 2005, vol. 13, pp. 206–222.CrossRefGoogle Scholar
  14. 14.
    De Marsily, G., Delay, F., Goncalves, J., et al., Dealing with spatial heterogeneity, Hydrogeology J., 2005, vol. 13, pp. 161–183.CrossRefGoogle Scholar
  15. 15.
    De Marsily G., Delay F., Teles V. et. al., Some current methods to represent the heterogeneity of natural media in hydrogeology, Hydrogeology, J., 1998, vol. 6, pp. 115–130.CrossRefGoogle Scholar
  16. 16.
    Deutsch, C., Journel, A., GSLIB: Geostatistical Software Library, New York, Oxford University Press, 1992.Google Scholar
  17. 17.
    Di Federico, V., Neuman, S.P., Transport in multiscale log conductivity fields with truncated power variograms, Water Resour. Res., 1998, vol. 34, no. 5, pp. 963–973.CrossRefGoogle Scholar
  18. 18.
    Elfeki, A., and Dekking, M., A Markov chain model for subsurface characterization: theory and applications, Math. Geol., 2001, vol. 33, no. 5, pp. 569–589.CrossRefGoogle Scholar
  19. 19.
    Falivene, O., Cabrera, L., Munoz, J.A., Arbues, P., Fernandez, O., and Saez, A., Statistical grid-based facies reconstruction and modelling for sedimentary bodies. Alluvial-palustrine and turbiditic examples, Geol. Acta, 2007, vol. 5, no. 3, pp. 199–230.Google Scholar
  20. 20.
    Gelhar, L., Stochastic subsurface hydrology, PrenticeHall, 1993.Google Scholar
  21. 21.
    Gelhar, L.W., Welty, C., and Rehfeldt, K.R., A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 1992, vol. 28, no. 7, pp. 1955–1974.CrossRefGoogle Scholar
  22. 22.
    Harp, D.R., and Vesselinov, V.V., Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations, Stochast. Environ. Res. Risk Assessment, 2010, vol. 24, no. 7, pp. 1023–1042.CrossRefGoogle Scholar
  23. 23.
    Huggenberger, P., and Regli, C., A sedimentological model to characterize braided river deposits for hydrogeological applications, in Braided rivers: process, deposits, ecology and management, SambrookSmith, G.H., Best, J.L., Bristow, Ch.S., and Petts, G.E., Eds., Blackwell Publishing, 2006, no. 36, pp. 51–74.CrossRefGoogle Scholar
  24. 24.
    Huysmans, M., and Dassargues, A., Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium), Hydrogeol. J., 2009, vol. 17, pp. 1901–1911.CrossRefGoogle Scholar
  25. 25.
    Journel, A.G., and Deutsch, C.V., Entropy and spatial disorder, Math Geol., 1993, vol. 25, no. 3, pp. 329–355.CrossRefGoogle Scholar
  26. 26.
    Koltermann, C.E., and Gorelick, S.M., Heterogeneity in sedimentary deposits: A review of structure-imitating, process-imitating, and descriptive approaches, Water Resour. Res., 1996, vol. 32, no. 9, pp. 2617–2658.CrossRefGoogle Scholar
  27. 27.
    Mariethoz, G., Renard, P., Cornaton, F., and Jaquet, O., Truncated plurigaussian simulations to characterize aquifer heterogeneity, Ground Water, 2009, vol. 47, no. 1, pp. 13–24.CrossRefGoogle Scholar
  28. 28.
    Neuman, S.P., Universal scaling of hydraulic conductivities and dispersivities in geologic media, Water Resour. Res., 1990, vol. 26, no. 8, pp. 1749–1758.CrossRefGoogle Scholar
  29. 29.
    Neuman, S.P., and Di Federico, V., Multifaceted nature of hydrogeologic scaling and its interpretation, Rev. Geoph., 2003, vol. 41, no. 3, pp. 1014–1045.CrossRefGoogle Scholar
  30. 30.
    Newman, S.P., Comments on “Longitudinal” Dispersivity Data and Implications for Scaling Behavior,” by Dirk Schulze-Makuch, May–June 2005, Ground Water, vol. 43, no. 3: 443–456, Ground Water, 2006, vol. 44, no. 2, pp. 139–141.Google Scholar
  31. 31.
    Park, E., Elfeki, A.M., Song, Y., and Kim, K., Generalized coupled Markov chain model for characterizing categorical variables in soil mapping, Soil Sci. Soc. Am. J., 2007, vol. 71, no. 3, pp. 909–917.CrossRefGoogle Scholar
  32. 32.
    Pozdniakov, S.P., and Tsang, C.F., A self-consistent approach for calculating the effective hydraulic conductivity of a binary, heterogeneous medium, Water Resour. Res., 2004, vol. 40, W05105, doi: 10.1029/2003WR002617.CrossRefGoogle Scholar
  33. 33.
    Pozdniakov, S.P., and Tsang, C.F., A semianalytical approach to spatial averaging of hydraulic conductivity in heterogeneous aquifers, J. Hydrol., 1999, vol. 216, nos. 1–2, pp. 78–98.CrossRefGoogle Scholar
  34. 34.
    Renard, Ph., Stochastic hydrogeology: What professionals really need?, Ground Water, 2007, vol. 45, no. 5, pp. 531–541.CrossRefGoogle Scholar
  35. 35.
    Schulze-Makuch, D., Longitudinal dispersivity data and implication for scaling behavior, Ground Water, 2005, vol. 43, no. 3, pp. 443–456.CrossRefGoogle Scholar
  36. 36.
    Sivakumar, B., Harter, T., and Zhang, H., A fractal investigation of solute travel time in a heterogeneous aquifer: transition probability/Markov chain representation, Ecolog. Model., 2005, vol. 182, nos. 3–4, pp. 355–370.CrossRefGoogle Scholar
  37. 37.
    Teles, V., Delay, F., and de Marsily, G., Comparison of transport simulations and equivalent dispersion coefficients in heterogeneous media generated by different numerical methods: A genesis model and a simple geostatistical sequential Gaussian simulator, Geosphere, 2006, vol. 2, no. 5, pp. 275–286.CrossRefGoogle Scholar
  38. 38.
    Weissmann, G.S., Carle, S.F., and Fogg, G.E., Threedimensional hydrofacies modeling based on soil surveys and transition probability geostatistics, Water Resour. Res., 1999, vol. 35, no. 6, pp. 1761–1770.CrossRefGoogle Scholar
  39. 39.
    Weissmann, G.S., and Fogg, G.E., Multi-scale alluvial fan heterogeneity modeled with transition probability geostatistics in a sequence stratigraphic framework, J. Hydrol., 1999, vol. 226, pp. 48–65.CrossRefGoogle Scholar
  40. 40.
    Yong, Z., and Fogg, G.E., Simulation of multi-scale heterogeneity of porous media and parameter sensitivity analysis, Sci. China, 2003, Ser. E, vol. 46, no. 5, pp. 459–474.Google Scholar
  41. 41.
    Zhang, H., Harter, T., and Sivakumar, B., Nonpoint source solute transport normal to aquifer bedding in heterogeneous, Markov chain random fields, Water Resour. Res., vol. 42, p. W06403, doi: 10.1029/2004WR003808, 2006.Google Scholar
  42. 42.
    Zimmermann, D.A., de Marsily, G., Gotway, C.A., et al., A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow, Water Resour. Res., 1998, vol. 34, no. 6, pp. 1373–1413.CrossRefGoogle Scholar
  43. 43.
    Zinn, B., and Harvey, C.F., When good statistical models of aquifer heterogeneity go bad: A comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields, Water Resour. Res., 2003, vol. 39, no. 3, pp. 1051–1068.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Water Problems InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia

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