Optimal estimation of residual non–aqueous phase liquid saturations using partitioning tracer concentration data

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 cpvariances 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.