OPTIMAL ESTIMATION OF RESIDUAL NONAQUEOUS PHASE LIQUID SATURATIONS USING PARTITIONING TRACER CONCENTRATION DATA

Stochastic methods are applied to the analysis of partitioning and non partitioning tracer breakthrough data to obtain optimal estimates of t he spatial distribution of subsurface residual non-aqueous phase liqui d (NAPL). Uncertainty in the transport of the partitioning tracer is a ssumed to result from small-scale spatial variations in a steady state velocity field as well as spatial variations in NAPL saturation. In c ontrast, uncertainty in the transport of the nonpartitioning tracer is assumed to be due solely to the velocity variations. Partial differen tial equations for the covariances and cross covariances between the p artitioning tracer temporal moments, nonpartitioning tracer temporal m oments, residual NAPL saturation, pore water velocity, and hydraulic c onductivity fields are derived assuming steady flow in an infinite dom ain [Gelhar, 1993] and the advection-dispersion equation for temporal moment transport [Harvey and Gorelick, 1995]. These equations are solv ed using a finite difference technique. The resulting covariance matri ces are incorporated into a conditioning algorithm which provides opti mal estimates of the tracer temporal moments, residual NAPL saturation , pore water velocity, and hydraulic conductivity fields given availab le measurements of any of these random fields. The algorithm was teste d on a synthetically generated data set, patterned after the partition ing tracer test conducted at Hill AFB by Annable et al. [1997]. Result s show that the algorithm successfully estimates major features of the random NAPL distribution. The performance of the algorithm, as indica ted by analysis of the ''true'' estimation errors, is consistent with the theoretical estimation errors predicted by the conditioning algori thm.