Multiple-Point Statistics for Modeling Facies Heterogeneities in a Porous Medium: The Komadugu-Yobe Alluvium, Lake Chad
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Multiple-Point Statistics for Modeling Facies Heterogeneities in a Porous Medium: The Komadugu-Yobe Alluvium, Lake Chad Basin Mathieu Le Coz · Pierre Genthon · Pierre M. Adler
Received: 26 December 2009 / Accepted: 4 May 2011 / Published online: 13 July 2011 © International Association for Mathematical Geosciences 2011
Abstract Multiple-point statistics are used to model facies heterogeneities in the vadose zone of the Komadugu-Yobe River valley (southeastern Niger) which is presently submitted to an undergoing intensive agricultural development; therefore, increasing quantitative and qualitative pressures are exerted on groundwater resources. The sand–clay heterogeneities are analyzed by means of a Landsat image acquired during a high flow period over a 160 km stretch in the downstream part of the valley and a set of 50 boreholes drilled near the town of Diffa (4 km × 4 km area). The horizontal variograms of heterogeneities are characterized by a noticeably constant length scale of 380 m and clayey objects are shown to be randomly distributed in space according to a Poisson process. A set of two-dimensional vertical images is built based on a Boolean procedure and the Snesim algorithm is used to simulate synthetic three-dimensional media. When the vertical correlation length is fitted, the three-dimensional model satisfactorily reproduces the second order statistics of heterogeneities and the specific facies patterns. Keywords Multiple-point statistics · Facies modeling · Variographic analysis · Komadugu–Yobe River · Fluvial deposits
M. Le Coz · P. Genthon IRD, UMR HydroSciences Montpellier, Avenue de Maradi, BP 11416, Niamey, Niger M. Le Coz () UM2, UMR HydroSciences Montpellier, Place Eugène Bataillon, 34095 Montpellier, France e-mail: [email protected] P.M. Adler UPMC-Sisyphe, 4 Place Jussieu, 75005 Paris, France
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Math Geosci (2011) 43:861–878
1 Introduction Heterogeneities of hydraulic conductivity K are crucial for modeling flow and solute transport in natural porous media. Within a single sedimentary facies, K is commonly represented as a continuous variable with a log-normal probability density function (pdf) (Fogg et al. 1998). However, in heterogeneous sedimentary media, the bounding surface between two facies corresponds to a discontinuity in the K pdf and the spatial arrangement of discrete geologic structures often constitutes the most significant heterogeneity for hydrological processes (Feyen and Caers 2006; Ye and Khaleel 2008). Various techniques are available to model the spatial distribution of stratigraphic material from scarce data. Koltermann and Gorelick (1996) and de Marsily et al. (2005) summarized the stochastic methods dealing with heterogeneities in hydrogeological applications. One of the main advantages of the stochastic approach is that a set of realistic realizations can be generated and this may contribute to shed some light on geological uncertainties (Haldorsen and Damsleth 1990). Numerous stochastic simulation procedures are based on twopoint spatial statistic cr
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