Experimental Determination of Effective Diffusion Parameters in the Matrix of Fractured Till

Abstract

a solute diffuses may cause the observed, or effective diffusion coefficient (D e ) to be lower than the diffusion Diffusion is often the dominant mode of solute transport in soils coefficient of a compound in water (D 0 ) (Rao et al., when advection is minimal. This paper describes the application of a radial diffusion cell method to estimate the effective diffusion coeffi-1980). Moreover, exclusion of a solute from some pore cient (D e ) and effective diffusive porosity ( De ) for use in solute trans-classes may reduce the effective diffusive porosity ( De ), port models for fractured-porous media. Twenty-four experiments or that portion of a porous medium that is accessible were conducted for 28 d using three conservative solutes (Br, PFBA, to diffusing molecules (van der Kamp et al., 1996). These and PIPES) on eight late Wisconsinan and Pre-Illinoian till samples effective parameters are likely to be specific to each from Iowa. The mean value of the total porosity ( T ) of the till samples soil-solute combination, and therefore require direct was 30.0%. Concentrations of the three tracers in the reservoir demeasurement for the solute and material of interest.creased with time and eventually approached equilibrium concentra-Mathematical solutions to the diffusion problem are tions. A model simulated the observed concentration data and the well established (Crank, 1975). In addition, models are modified goodness-of-fit (d 1 ) values ranged from 0.878 to 0.950. Mean now capable of simulating solute diffusion coupled with values of De from the model were 28.3 (Br Ϫ ), 26.5 (PFBA), and 21.6% (PIPES) and there were significant differences in De among advection through macroporous soil and fractured till the three tracers (p ϭ 0.05). Mean values of D e were 5.6 ϫ 10 Ϫ10 m 2 (Therrien and Sudicky, 1996; Toride et al., 1999). These s Ϫ1 (Br Ϫ ), 2.9 ϫ 10 Ϫ10 m 2 s Ϫ1 (PFBA), and 1.3 ϫ 10 Ϫ10 m 2 s Ϫ1 (PIPES). models require that effective diffusion parameters be Values of D e differed significantly by compound and were significantly provided as input. Laboratory methods, including the different (p ϭ 0.05) from the aqueous diffusion coefficient (D 0 ). Calcuhalf-cell, the reservoir-cell, and radial diffusion cell, lated mean values of the first-order mass exchange coefficient (␣) have been proposed for determination of D e . The most were 8.4 ϫ 10 Ϫ7 (Br Ϫ ), 4.1 ϫ 10 Ϫ7 (PFBA), and 1.6 ϫ 10 Ϫ7 s Ϫ1 (PIPES); widely used is the half-cell method, where two cells, they differed by compound (p ϭ 0.05) and generally decreased with one spiked with a solute, are pressed together, allowing increasing molecular weight of the tracer. This study confirmed that diffusion to take place (Li and Gregory, 1974; Robin et the radial diffusion cell method is an efficient method to estimate al., 1987). Work by van Rees et al. (1991), however, effective diffusion parameters necessary to accurately model solute transport in fractured till and soil.

Fracture‐Controlled Nitrate and Atrazine Transport in Four Iowa Till Units

“…These values of α should be considered approximate, however, because they were determined by the inverse method, which has been shown to produce nonunique and/or insensitive estimates of α (Parker and van Genuchten, 1984). Independent estimates of α for Br − , PFBA, and PIPES determined by the radial diffusion method in these tills (Helmke et al, 2004) resulted in values that were one to two orders of magnitude less than those estimated by fitting the MIM to BTCs. In addition, not all of the MIM‐estimated values of α increase as a function of D 0 (i.e., PIPES should have the smallest α, followed by PFBA, then Br − ), which indicates that the accuracy of using the inverse method is suspect.…”

“…Conservative compounds of differing aqueous diffusion coefficients ( D 0 ) (Br − , PFBA, and PIPES) were selected because differences in the morphology of their breakthrough curves (BTCs) would indicate matrix diffusion and provide evidence of fracture flow and fracture–matrix interaction. The D 0 values of Br − , PFBA, PIPES, NO − 3 , and atrazine are 1.8 × 10 −9 , 7.6 × 10 −10 , 4.1 × 10 −10 , 1.6 × 10 −9 , and 6.6 × 10 −10 m 2 s −1 , respectively (National Research Council, 1929; Scott and Phillips, 1973; Bowman and Gibbens, 1992; Helmke et al, 2004). The use of conservative tracers with unique diffusion coefficients has been used to demonstrate matrix diffusion in soil with macropores (Mayes et al, 2003) and fractured saprolite (Moline et al, 1997), but has not previously been applied to studies of fractured till.…”

On the flow field about an electrophoretic particle

“…The electrophoretic mobility μ ⊥ , as provided by Eq. (21), which is identical to that of a spherical particle of same radius, is always different from the along-axis mobility μ // = μ 0 . That has some notable consequences as discussed here below.…”

“…However, a value of 4.1 × 10 −10 m 2 s −1 in water had been calculated, based on the Stokes-Einstein equation. 21 As the involved electrolyte is not a binary and symmetric one, Eq. (A14) should be applied to calculate β.…”

Simulating Conservative Tracers in Fractured Till under Realistic Timescales

“…The diffusion coefficients in pure aqueous solution of Br and PFBA at 25°C are 1.8 × 10 −9 and 7.6 × 10 −10 m 2 /s, respectively (Bowman and Gibbens 1992). The D 0 of PIPES has not been determined experimentally; however, the calculated D 0 using the Stokes‐Einstein equation is 4.1 × 10 −10 m 2 /s (Helmke et al 2004).…”