Abstract
Based on a three-dimensional heterogeneous aquifer model exhibiting non-stationary, statistically anisotropic correlation, three hydrostratigraphic models (HSMs) are created within a sedimentary hierarchy. A geostatistical analysis of natural log conductivity (lnK) is conducted for the units of the HSMs. Hydraulic conductivity is then upscaled using numerical and analytical methods. Increasing lnK variances are evaluated. Results suggest that for the aquifer model tested: (1) the numerical method is capable of upscaling irregular domains with reasonable accuracy for a lnK variance up to 7.0. (2) Accuracy of the upscaled equivalent conductivities (K*) and associated performance of the HSMs are sensitive to homogenization level, heterogeneity variance, and boundary condition. Variance is found to be the most significant factor impacting the accuracy of the HSMs. (3) Diagonal tensor appears a good approximation for the full-tensor K*. (4) For the HSM units, when the variance is low (less than 1.0), all analytical methods are nearly equally accurate; however, when variance becomes higher, analytical methods generally are less accurate.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ababou, R.: Identification of effective conductivity tensor in randomly heterogeneous and stratified aquifers. In: Proceedings of the 5th Canadian/American Conference on Hydrogeology: Parameter Idenfitication and Estimation for Aquifer and Reservoir Characterization, pp. 155–157 (1991)
Ababou R.: Random porous media flow on large 3-D grids: numerics, performance and application to homogenization. In: Wheeler, M.F. (eds) Mathematics and its Applications: Environmental Studies—Math, Comput and Statistical Analysis, IMA vol 79, Chapter 1, pp. 1–25. Springer, New York (1996)
Desbarats A.J.: Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media. Math. Geol. 24(3), 249–267 (1992)
Desbarats A.J., Srivastava R.M.: Geostatistical analysis of groundwater flow parameters in a simulated aquifer. Water Resour. Res. 27(5), 687–698 (1991)
Deutsch C.V.: Geostatistical Reservoir Modeling, pp. 376. Oxford University Press, NY, USA (2002)
Durlofsky, L.J.: Upscaling and gridding of fine scale geological models for flow simulation. In: Proceedings of the 8th International Forum on Reservoir Simulation. Stresa, Italy, 20–25 June 2005
Gelhar L.W.: Stochastic Subsurface Hydrology. Prentice Hall, Englewood Cliffs, NJ, USA (1993)
Gelhar L.W., Axness C.L.: Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19(1), 161–180 (1983)
Journel, A.G., Deutsch, C., Desbarats, A.J.: Power averaging for block effective permeability. SPE Paper 15128 (1986)
Knudby C., Carrera J.: On the relationship between indicators of geostatistical, flow and transport connectivity. Adv. Water Resour. 28(4), 405–421 (2005)
Knudby C., Carrera J.: On the use of apparent hydrauilc diffusivity as an indicator of connectivity. J. Hydrol. 329(3–4), 377–389 (2006)
Milliken, W., Levy, M., Strebelle, S., Zhang, Y.: The effect of geologic parameters and uncertainties on subsurface flow: deepwater depositional systems. SPE Paper 109950 (2007)
Noetinger B., Haas A.: Permeability averaging for well tests in 3D stochastic reservoir models. SPE J. 36653, 919–925 (1996)
Renard P., de Marsily G.: Calculating equivalent permeability: a review. Adv. Water Resour. 20(5-6), 253–278 (1997)
Ritzi, R.W., Allen-King, R.M.: Why did Sudicky (1986) find an exponential-like spatial correlation structure for hydraulic conductivity at the Borden research site? Water Resour. Res. (2007). doi:10.1029/2006WR004935
Sanchez-Vila X., Girardi J.P., Carrera J.: A synthesis of approaches to upscaling of hydraulic conductivities. Water Resour. Res 31(4), 867–882 (1995)
Sanchez-Vila X., Carrera J., Girardi J.P.: Scale effects in transimissivity. J. Hydrol. 183(1-2), 1–22 (1996)
Sanchez-Vila, X., Guadagnini, A., Carrera, J.: Representative hydraulic conductivities in saturated groundwater flow. Rev. Geophys. (2006). doi:10.1029/2005RG000169
Schlumberger: ECLIPSE, Technical Description 2009.2. Schlumberger (2009)
Wen, X.-H., Gómez-Hernández, J.: Upscaling hydraulic conductivities in heterogeneous media: an overview. J. Hydrol. (1996). doi:10.1016/S0022-1694(96)80030-8
Wen X.H., Durlofsky L.J., Edwards M.G.: Use of border regions for improved permeability upscaling. Math. Geol. 35(5), 521–547 (2003)
Zhang D.: Stochastic methods for flow in porous media, coping with uncertainties. Academic Press, San Diego, CA (2002)
Zhang, Y.: Hierarchical geostatistical analysis of an experimental stratigraphy. Math. Geosci. (2008). doi:10.1007/s11004-008-9180-6
Zhang, Y., Gable, C.W., Person, M.: Equivalent hydraulic conductivity of an experimental stratigraphy—implications for basin-scale flow simulations. Water Resour. Res. (2006). doi:10.1029/2005WR004720
Zhang Y., Gable C.W., Sheets B.: Equivalent hydraulic conductivity of three-dimensional heterogeneous porous media: an upscaling study based on an experimental stratigraphy. J. Hydrol. 388, 304–320 (2010). doi:10.1016/j.jhydrol.2010.05.009
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, Y., Liu, B. & Gable, C.W. Homogenization of Hydraulic Conductivity for Hierarchical Sedimentary Deposits at Multiple Scales. Transp Porous Med 87, 717–737 (2011). https://doi.org/10.1007/s11242-010-9711-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-010-9711-8