Contribution 6
Submitted by: Krishna R. Reddy, University of Illinois Chicago, USA
Contaminant transport through a low permeability vertical barrier due to advective-diffusion transport mechanisms and effect of sorption
Sample Description
(1) Course Name/Type: Geoenvironmental Engineering/Elective course during junior or senior year for undergraduate students (4-year curriculum) and graduate students
(2) Course Emphasis: Geochemistry, Groundwater flow, Contaminant transport and fate, Contaminated site remediation, Waste containment and landfill engineering, Sustainability considerations
(3) Descriptive Title of Sample: Contaminant transport through a low permeability vertical barrier due to advective-diffusion transport mechanisms and effect of sorption
(4) Brief Teaching Note: The example helps us understand the following: (1) Importance of diffusion in contaminant transport despite resisting hydraulic gradient; (2) Downside of being too conservative, if diffusion is considered as the only mode of transport, as evident from the example; (3) A high Kd value has been chosen to demonstrate the significance of having an efficient sorbent, as a barrier material, in preventing contaminant transport, and (4) the use of only the first term of Ogata and Banks’ solution as an approximate method can be inappropriate in certain cases.
The concentration results on the slide were obtained for the following parameters:
x=3ft (x=0.914m), hydraulic conductivity k=1×10-7 cm/s, seepage velocity vs=-8.25 x 10-8 cm/s (vs=-0.026m/y), effective diffusion coefficient D = 1×10-5 cm²/s (D=0.0315 m²/y), ne=0.4, Κd=3cm³/g, ρd=1.2g/cm³
(5) References: Sharma, H.D. and Reddy, K.R. (2004). Geoenvironmental Engineering: Site Remediation, Waste Containment, and Emerging Waste Management Technologies, John Wiley, Hoboken, New Jersey (The example on the slide is Example 8.7 on page 205, see also solution for finite flow domain, Eq. 8.53, page 201).
This work is licensed under a Creative Commons Attribution 4.0 International License.
This example of contaminant transport through a low-permeability vertical barrier is very instructive. Under the assigned boundary conditions, the advective flux, driven by the hydraulic head gradient, occurs in the opposite direction of the diffusion flux, driven by the concentration gradient.
An engaging question may arise. Under similar boundary conditions, is it physically meaningful to model mechanical dispersion using Fick’s law, just like diffusion?
Adopting Fick’s law in this specific scenario, the mechanical dispersion flux would take place in the opposite direction of the advection flux.
However, we commonly consider mechanical dispersion a macroscopic effect related to local variations in water seepage velocity. The local velocities are expected to differ from the average macroscopic velocity in value but not in direction, as the direction is controlled by the hydraulic gradient. As a result, the dispersion flux could not occur against the water flow direction.
When the concentration and hydraulic gradients are in opposite directions, the consequent dispersive flux against the direction of flow appears to be an artefact caused by using Fick’s law to model the mechanical dispersion flux.
Under such conditions, the use of a different modelling approach to represent mechanical dispersion may be taken into account. A possible alternative to using Fick’s law is to model the hydraulic conductivity as a random field. In this way, the macroscopic dispersion becomes the effect produced by the local random variations in hydraulic conductivity without introducing a specific flux term in the macroscopic mass balance of the contaminant.
Suggested readings:
Carrera, J. (1993). An overview of uncertainties in modelling groundwater solute transport. Journal of Contaminant Hydrology, 13, 23-48.
Hassanizadeh, S.M. (1996). On the Transient Non-Fickian Dispersion Theory. Transport in Porous Media, 23, 107-124.
Irvine, D.J., Werner, A.D., Ye, Y., and Jazayeri, A. (2021). Upstream Dispersion in Solute Transport Models: A Simple Evaluation and Reduction Methodology. Groundwater, 59(2), 287-291.
Konikow, L.F. (2011). The secret to successful solute-transport modeling. Groundwater, 49(2), 144–159.