Non-Fickian Solute Transport in a Single Fracture of Marble Parallel Plate

Abstract

Accurate prediction of solute transport processes in a fracture aquifer is an important task not only for proper management of the groundwater but also for pollution control. A key issue of this task is how to accurately obtain the experimental data and to analyze the solute transport in fracture in subsurface hydrology, which would greatly help us to understand the releasing mechanism and transport of the solute in a fracture. In this study, a fracture experiment is conducted in a laboratory based on previous studies. The fracture used with a length of 60 cm and a width of 10 cm is sealed with glass glue to avoid leakage of tracer due to uneven fracture walls. The sodium chloride (NaCl) solute is injected from the left of the fracture. And an electrical conductivity monitoring system is installed on the right of the fracture. Then breakthrough curves (BTCs) of solute transport are fitted using the classical advectiondispersion equation (ADE) and the truncation power-law function (TPL) model in the package of the continuous time random walk (CTRW). The results show that the flow satisfies non-Darcian law in the experimental conditions, which can be better fitted using the Forchheimer equation and Izbash equation. The solute transport presents non-Fickian phenomena and shows a long tailing. The fitting results of the TPL model are far better than ADE in fitting the long tailing at three different flow velocities. Furthermore, electrical conductivity monitoring method not only is effective but also has an advantage of no disturbance to water and concentration fields in a fracture.

Comparison of Surface Roughness and Transport Processes of Sawed, Split and Natural Sandstone Fractures

“…However, the fitting parameter β of the TPL in the CTRW was previously used as an indicator for non-Fickian transport processes [24] and linked to contact area and Hurst exponent. However, the obtained parameters by [24] and [25] for β were smaller than 2, which is also given as a limit by [56] for Fickian transport. Our study shows, that for values of β larger than 4, the ADE is a suitable description and differences between fitting parameters of CTRW and ADE are within the range of fitting accuracy.…”

“…However, through the usually strong non-Fickian transport behavior indicated through multiple peaks and the long tailing of the BTC, the ADE often results in an insufficient match of the transport parameters [38]. Previous studies showed that the continuous time random walk (CTRW) method is able to reproduce those non-Fickian features superior to a fit of the ADE (e.g., [25,26]). The CTRW is based on a Laplace transformation of the ADE using a memory function M [54].…”

“…A higher proportion of nonlinear flow also effects the solute transport with a higher degree of non-Fickian transport [3]. Non-Fickian transport often results in early arrivals, multiple peaks and a long tailing of breakthrough curves (BTCs) [24][25][26][27][28].…”

“…However, as in the BTCs, non-Fickian transport becomes obvious through a long tailing, multiple peaks and early arrivals, the ADE often falls short of a suitable description of the experimental observations. The continuous time random walk model (CTRW) with a truncated power law has been shown to much more accurately reproduce the experimentally obtained BTC than the conventional ADE approach [3,17,24,25].…”

“…Within a single fracture generated by a cut through a block of marble, ref. [25] studied the effect of various flow velocities on the tracer transport, observing strong non-Fickian transport processes. In the BTCs, the peak concentration was found to increase with increasing velocity, naturally also shortening the time of the first arrival.…”