Estimation of local scale dispersion from local breakthrough curves during a tracer test in a heterogeneous aquifer: the Lagrangian approach

The local scale dispersion tensor, Dd, is a controlling parameter for the dilution of concentrations in a solute plume that is displaced by groundwater flow in a heterogeneous aquifer. In this paper, we estimate the local scale dispersion from time series or breakthrough curves, BTCs, of Br− concentrations that were measured at several points in a fluvial aquifer during a natural gradient tracer test at Krauthausen. Locally measured BTCs were characterized by equivalent convection dispersion parameters: equivalent velocity, veq(x) and expected equivalent dispersivity, λeq(x) . A Lagrangian framework was used to approximately predict these equivalent parameters in terms of the spatial covariance of loge transformed conductivity and the local scale dispersion coefficient. The approximate Lagrangian theory illustrates that λeq(x) increases with increasing travel distance and is much larger than the local scale dispersivity, λd. A sensitivity analysis indicates that λeq(x) is predominantly determined by the transverse component of the local scale dispersion and by the correlation scale of the hydraulic conductivity in the transverse to flow direction whereas it is relatively insensitive to the longitudinal component of the local scale dispersion. By comparing predicted λeq(x) for a range of Dd values with λeq(x) obtained from locally measured BTCs, the transverse component of Dd, DdT, was estimated. The estimated transverse local scale dispersivity, λdT=DdT/U1 (U1=mean advection velocity) is in the order of 101–102 mm, which is relatively large but realistic for the fluvial gravel sediments at Krauthausen.