Abstract. Stochastic methods are applied to the analysis of partitioning and nonpartitioning tracer breakthrough data to obtain optimal estimates of the spatial distribution of subsurface residual non-aqueous phase liquid (NAPL). Uncertainty in the transport of the partitioning tracer is assumed to result from small-scale spatial variations in a steady state velocity field as well as spatial variations in NAPL saturation. In contrast, uncertainty in the transport of the nonpartitioning tracer is assumed to be due solely to the velocity variations. Partial differential equations for the covariances and cross covariances between the partitioning tracer temporal moments, nonpartitioning tracer temporal moments, residual NAPL saturation, pore water velocity, and hydraulic conductivity fields are derived assuming steady flow in an infinite domain [Gelhar, 1993] and the advection-dispersion equation for temporal moment transport [Harvey and Gorelick, 1995]. These equations are solved using a finite difference technique. The resulting covariance matrices are incorporated into a conditioning algorithm which provides optimal estimates of the tracer temporal moments, residual NAPL saturation, pore water velocity, and hydraulic conductivity fields given available measurements of any of these random fields. The algorithm was tested on a synthetically generated data set, patterned after the partitioning tracer test conducted at Hill AFB by Annable et al. [1997]. Results show that the algorithm successfully estimates major features of the random NAPL distribution. The performance of the algorithm, as indicated by analysis of the "true" estimation errors, is consistent with the theoretical estimation errors predicted by the conditioning algorithm.

Abstract. Estimates of spatially variable residual NAPL saturations S•v are obtained in heterogeneous porous media using first temporal moments of breakthrough curves (BTCs) obtained from multilevel samplers during in situ partitioning tracer tests. An approach is adopted in which the distribution of the log NAPL/water volumetric ratio (Y = In [SN/(1 --SN)]) and log hydraulic conductivity (F = In K) are treated as spatially correlated random fields. A nonlinear Gauss-Newton search technique is used to identify the spatial distribution of Y that minimizes the weighted sum of the deviation of the temporal moment predictions from their measured values and the deviation of the estimate of Y from its prior estimate obtained from the temporal moments of extraction well BTCs. Sensitivities required for the algorithm are obtained using a coupled flow and transport adjoint sensitivity method. In addition to obtaining optimal estimates for the spatial distribution of Y, the method also provides the estimation error covariance. The estimation error covariance can be used to evaluate the information that may be obtained from alternate pumping and monitoring configurations for tracer tests designed to detect NAPL in the subsurface. To this end, we tested the method using two different NAPL distributions (one with a random spatially correlated field and a second that was a block of NAPL) and three different pumping configurations (a double five-spot pattern, an inverted double five-spot pattern, and a line-drive pattern). The results show that measured temporal moments are more sensitive to Y in the double five-spot and inverted double five-spot patterns, and estimates produced in these configurations are slightly superior to those produced in the line-drive pattern.

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