Statistical analysis of head and transmissivity in natural aquifers: Application to structure identification and transport prediction

Flow and transport in natural aquifers depend on the spatially variable transmissivity T, usually modeled as a space random function. As a consequence, all the derived quantites, like piezometric head H, are random functions, and their statistical moments depend on those of T. The present work introduces a methodology for identification of logtransmissivity statistics that use the measured piezometric heads. In particular, second order moments like the head-logtransmissivity cross-covariance C_HY and the head variogram Γ_H can be conveniently used for parameter inference. The logtransmissivity statistics is characterized by three parameters: the variance σ_Yc and the integral scale I_Y of correlated residuals, and a nugget σ²_Yn that represents variability over small support. Unlike previous studies that pursue the same objective through a first order approximation in the logtransmissivity variance, the emphasis here is on highly heterogeneous formations, characterized by large values of σ²_Yc. Under the proposed methodology, indentifications is achieved by fitting the experimental head variograms with the theoretical ones; the latter are derived by the means of the effective medium approximation and are validated through accurate numerical simulations, based on analytic element method. The methodology is applied to the Eagle Valley basin in the west-central Nevada for which numerous transmissivity and head measurements are available. The values of σ²_Yc and σ²_Yn computed directly, from logtransmissivity data, agreed well with the values computed by fitting head variograms. A disparity prevails for the integral scale I_Y. A prediction of the solute transport behavior of the aquifer is then made from the inferred data and the theoretical results of -xbDagan et al. [4]. Comparison is also made with results based on the first-order analysis of flow and transport.