Spatial characterization of a hydrogeochemically heterogeneous aquifer using partitioning tracers: Optimal estimation of aquifer parameters

Abstract

In this paper a distributed‐parameter extended Kalman filter is developed to estimate spatially distributed residual saturation of nonaqueous phase liquids (NAPL) and Darcy flux and to predict site‐specific movement of a partitioning tracer plume in a three‐ dimensional heterogeneous aquifer. The NAPL and Darcy flux fields are assumed to be time‐invariant spatial random fields with known spatial correlation structures. The extended Kalman filter consists of two components: (1) a moment propagation algorithm that uses a set of coupled stochastic partial differential equations derived from the advection‐dispersion‐retardation equation to predict how the moments propagate through space between measurement times [Zhang and Graham, this issue] and (2] a moment update algorithm, which updates the moments at measurement times. Because the optimal Kalman filtering algorithm is computationally intensive for three‐dimensional problems, a simplified sequential conditioning algorithm is developed that first conditions the Darcy flux field using only nonpartitioning tracer measurements and then conditions the NAPL field using only partitioning tracer measurements. The extended Kalman filter is applied to a three‐dimensional domain patterned after the interwell partitioning tracer tests conducted at Hill Air Force Base by Annable et al. [1998]. Two different cross‐correlation scenarios and two different sampling networks are investigated.