Multiple-Point Statistics for Modeling Facies Heterogeneities in a Porous Medium: The Komadugu-Yobe Alluvium, Lake Chad Basin

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 x 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.