An example of solute spreading in nonstationary, bounded geological formations

Abstract

We analyze the impact of a linear trend in the mean log-conductivity on the transport of a conservative tracer in a bounded domain. The effects of such a linear trend on solute transport were analyzed in depth for unbounded domains (Rubin and Seong, Water Resour Res 30(11):2901–2911, 1994; Indelman and Rubin, Water Resour Res 31(5):1257–1265, 1995; Water Resour Res 32(5):1257–1265, 1996), whereas studies concerning this special case of medium nonstationarity in finite domains usually focus on head or flow statistics (Guadagnini et al., Stoch Environ Res Risk Assess, 17:394–407, 2003). In this study both ensemble and effective plume moments are provided for an instantaneous release of a solute through a linear source normal to the mean flow direction, by taking into account different sizes of the source. The analysis involving a steady velocity field spatially nonstationary is developed by using the stochastic finite element method. Results show that ensemble moments are affected by increasing trends both parallel and normal to the mean flow direction, but the impact on effective plume moments is very different. A parallel trend does not seem to influence the effective second moments; while a normal trend, although modifies the transverse effective moment only weakly, strongly increases the longitudinal one, especially for large initial sizes of the source. Furthermore, the increase of the particle displacement variance produced by a parallel trend in the finite domain disagrees with the results obtained in an unbounded domain, due to the boundary conditions here considered making both head and velocity moments nonstationary and nonsymmetric.