Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers

The evolution of concentration variance sigma(c)(2) for conservative solutes in aquifers is presented by accounting for advection heterogeneity, local dispersion, and sampling volume. The concentration variance distribution is obtained by scaling the zero local dispersion form of sigma(c)(2). The scaling function results from the local dispersion and it is derived in a closed integral form such that it satisfies the measure of total concentration variance, obtained from the Eulerian mass balance using spatially integrated concentration moments. The use of spatially integrated concentration moments avoids the need to apply closing hypothesis on joint moments between velocity and concentration held. This study finds that sampling volume and local dispersion act as a smoothing mechanism on the concentration fluctuations. Contrary to the sampling volume, the smoothing due to the local dispersion is a slow occurring process compared to the advection and increases with transport time. At early stage of transport, the source size, its orientation with respect to the mean flow, and size of the sampling volume are key factors in determining the magnitude of concentration variance. The local dispersion becomes a dominant factor at the later stage and its influence on collected samples is significantly reduced by the presence of sampling volume. The local dispersion dimensionless number is introduced as an indicator for local dispersion importance in modeling the evolution of concentration fluctuations in the subsurface tin the absence of sampling volume). The presented model for concentration variance compares favorably with field data and numerical simulations.