Laboratory Estimation of Dispersivity Coefficients

The dispersion phenomena in aquifers through experimental activities have been extensively studied in the past; recently the availability of digital images of the transport process made possible the development of new techniques for the evaluation of the dispersivity coefficients (Sànchez et al., 2008, 2011). This work shows the application of an innovative procedure that allows a detailed estimation of longitudinal and transverse dispersivities in an experimental plume devised in a laboratory sandbox. The dataset was provided processing the results of a sandbox developed at the hydraulic laboratory of the University of Parma (DICATeA). The equipment represents a 2-D unconfined aquifer controlled through two constant head levels (upstream and downstream); it consists of a PMMA tank filled of 1 mm glass beads as porous medium. An injector was placed inside the porous medium and sodium fluorescein salt was used as tracer. The tests consist of injecting a known solution discharge for a specific time duration and then observing the plume through the collection of side wall images obtained by means of a digital camera (see Citarella et al. (2010) and Cupola et al. (2014) for more details). The study case presented in this work considers a homogeneous porous media and a uniform flow in the vertical plane; the plume develops according to 2-D plane advection-dispersion equation. The pictures were collected with time interval equal to 5 s. Using the collected frames, it is possible to estimate the concentration in each point of the domain at different times and also the partial derivatives of the concentration in space and time. This information allows easily to estimate the two dispersivity coefficients using the Advection-Dispersion equation. This analysis was carried out for each picture collected during the test (about 650). The results showed, as expected, that the longitudinal dispersivity presents the same order of magnitude of the pore dimension and the ratio between longitudinal and transverse dispersivity is constant through the whole domain, although higher than that reported in literature. Even though the dispersivities are estimated for each pixel of the figures, only a few of them provide reliable information; in fact, only on the plume boundaries a significant variation in concentration could be detected. For this reason a selection criterion for the credibility of the results was developed. Future developments will estimate the apparent dispersivities considering a heterogeneous media.