Environ. Sci. Technol. 2009, 43, 6730–6736
A Comparision of Laboratory and Field Based Determinations of Molecular Diffusion Coefficients in a Low Permeability Geologic Medium M . J I M H E N D R Y , * ,† S . L E E B A R B O U R , ‡ BRIGITTE E. J. BOLDT-LEPPIN,† LAURA J. REIFFERSCHEID,† AND L E O N A R D I . W A S S E N A A R †,§ Department of Geological Sciences and Department of Civil Engineering, University of Saskatchewan, Saskatoon, SK, Canada, and Environment Canada, Saskatoon, SK, Canada
ne′
Received April 7, 2009. Revised manuscript received July 23, 2009. Accepted July 27, 2009.
Molecular diffusion is the dominant transport mechanism for contaminants in many saturated clay-rich aquitards. The effective coefficient of diffusion (De) is traditionally determined by conducting laboratory tests on cm-scale core samples that may not be representative of the bulk geologic formation. Here we conducted the first long-term field based in situ diffusion experiment to compare the effect of experimental scale (5 × 10-5 m3 in the diffusion cells and (5-20) × 10-2 m3 in the in situ experiments) on De values for clay-rich aquitards. Using a conservative tracer (deuterium), our testing shows De values estimated from in situ testing ((2.5-3.5) × 10-10 m2 s-1) are similar but lower than the average De values measured in the laboratory (4 × 10-10 m2 s-1). The difference was attributed to greater porosity values in the laboratory samples resulting from core barrel extrusion and sample swelling. With representative core sampling and care, laboratory-based diffusion testing remains a viable method to assess solute transport mechanisms in clay aquitards.
Introduction Diffusion is a crucial mass transport mechanism in low permeability clay-rich aquitards (c.f. 1, 2) and in engineered clay barriers (c.f. 3, 4). Accurate and representative quantification of the diffusive transport mechanism is critical to our understanding and prediction of the long-term movement of contaminants contained in clay media. In low permeability geologic formations where solute transport is dominated by molecular diffusion, the onedimensional, total solute flux in a saturated media can be represented by Fick’s first law: Jd ) -neDe
∂C ∂x
(1)
where Jd is the diffusive mass flux rate [M L-2 T-1], De is the effective coefficient of diffusion of the solute [L2 T-1], ne is * Corresponding author phone: (306) 966-5720; fax: (306) 9668593; e-mail:
[email protected]. † Department of Geological Sciences, University of Saskatchewan. ‡ Department of Civil Engineering, University of Saskatchewan. § Environment Canada. 6730
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the effective porosity, and ∂C/∂x represents the concentration gradient in x-direction [M L-3 L-1]. The definition of De is not consistent within the literature (5). In some cases, ne is incorporated within De. Here we define De according to eq 1 and designate the alternate form of De as De′ (i.e., De′ ) De ne). Under transient flow conditions, diffusive mass transport can be expressed using Fick’s second law:
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 43, NO. 17, 2009
∂C ∂2C ) neDe 2 ∂t ∂x
(2)
where ∂C/∂ t represents the change in concentration with time. Implicit in this form of Fick’s second law is the assumption that the area of pore space available for diffusive transport (ne on the right-hand side) is the same as the volume of pore space accessible by the species of interest (ne′ on the left-hand side). Pearson (6) provides a discussion of the definition of ne as it relates to diffusive transport. Hendry and Wassenaar (2) and van der Kamp et al. (7) demonstrate that ne is equivalent to the total porosity, n, for the conservative tracer deuterium in the clay tills described in this paper. The De and ne of dissolved solutes are traditionally measured in the laboratory using a range of testing procedures (5, 7, 8) and then applied to field scales of tens to hundreds of meters. Although laboratory parameters are assessed under controlled environments (e.g., isothermal, short time scales, small sample size, 1-D flow) and employ well-defined boundary conditions, their direct applicability to field conditions may be questioned because the transport distance in small core samples are often
