Evidence of non-Darcy flow and non-Fickian transport in fractured media at laboratory scale

Abstract

Abstract.During a risk assessment procedure as well as when dealing with cleanup and monitoring strategies, accurate predictions of solute propagation in fractured rocks are of particular importance when assessing exposure pathways through which contaminants reach receptors.Experimental data obtained under controlled conditions such as in a laboratory allow to increase the understanding of the fundamental physics of fluid flow and solute transport in fractures.In this study, laboratory hydraulic and tracer tests have been carried out on an artificially created fractured rock sample. The tests regard the analysis of the hydraulic loss and the measurement of breakthrough curves for saline tracer pulse inside a rock sample of parallelepiped shape (0.60 × 0.40 × 0.08 m). The convolution theory has been applied in order to remove the effect of the acquisition apparatus on tracer experiments.The experimental results have shown evidence of a nonDarcy relationship between flow rate and hydraulic loss that is best described by Forchheimer's law. Furthermore, in the flow experiments both inertial and viscous flow terms are not negligible.The observed experimental breakthrough curves of solute transport have been modeled by the classical onedimensional analytical solution for the advection-dispersion equation (ADE) and the single rate mobile-immobile model (MIM). The former model does not properly fit the first arrival and the tail while the latter, which recognizes the existence of mobile and immobile domains for transport, provides a very decent fit.The carried out experiments show that there exists a pronounced mobile-immobile zone interaction that cannot be neglected and that leads to a non-equilibrium behavior of solute transport. The existence of a non-Darcian flow regime has showed to influence the velocity field in that it gives rise to a delay in solute migration with respect to the predicted value assuming linear flow. Furthermore, the presence of inertial effects enhance non-equilibrium behavior. Instead, the presence of a transitional flow regime seems not to exert influence on the behavior of dispersion. The linear-type relationship found between velocity and dispersion demonstrates that for the range of imposed flow rates and for the selected path the geometrical dispersion dominates the mixing processes along the fracture network.

On the reliability of analytical models to predict solute transport in a fracture network

“…Inertial forces dominate viscous ones at the critical Forchheimer number (Fo = 1) corresponding in our case to a flow rate equal to Q crit = 6.30×10 −6 m 3 s −1 , which is coherent with the results obtained in the previous study (Cherubini et al, 2013a). The term in square brackets in Eq.…”

“…Travel time decreases more slowly for high flow rates. In particular, a change of slope is evident in correspondence of the injection flow rate equal to 4 × 10 −6 m 3 s −1 (Cherubini et al, 2013a), which means the setting up of a transitional flow regime; the diagram of velocity profile is flattened because of inertial forces prevailing on the viscous one, as already shown by Cherubini et al (2013a). The presence of a transitional flow regime leads to a delay on solute transport with respect to the values that can be obtained under the assumption of a linear flow field.…”

“…The experimental setup has been already extensively discussed in Cherubini et al (2013a), however, for the completeness in this section a summary is reported. The analysis of flow dynamics through the selected path (Fig.…”

“…Herein, in order to give a more physical interpretation of the flow and transport behavior, we build on the work by Cherubini et al (2013a) by interpreting the obtained experimental results of flow and transport tests by means of the comparison of two conceptual models: the 1-D single rate MIM and the 2-D explicit network model (ENM). Unlike the former, the latter expressly takes the fracture network geometry into account.…”

“…In previous studies by Cherubini et al (2012Cherubini et al ( , 2013a) the presence of nonlinear flow and non-Fickian transport in a fractured rock formation was analyzed at bench scale in laboratory tests. The effects of nonlinearity in flow have been investigated by analyzing hydraulic tests on an artificially created fractured limestone block of parallelepiped (0.6 × 0.4 × 0.8 m 3 ) shape.…”