Matrix diffusion coefficients in volcanic rocks at the Nevada test site: Influence of matrix porosity, matrix permeability, and fracture coating minerals

Journal of Contaminant Hydrology 93 (2007) 85 – 95 www.elsevier.com/locate/jconhyd

Matrix diffusion coefficients in volcanic rocks at the Nevada test site: Influence of matrix porosity, matrix permeability, and fracture coating minerals Paul W. Reimus a,⁎, Timothy J. Callahan b,1 , S. Doug Ware a , Marc J. Haga a , Dale A. Counce c a

b

Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States Department of Geology and Environmental Geosciences, College of Charleston, 66 George Street, Charleston, SC 29424, United States c Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States Received 9 February 2006; received in revised form 29 January 2007; accepted 30 January 2007 Available online 8 February 2007

Abstract Diffusion cell experiments were conducted to measure nonsorbing solute matrix diffusion coefficients in forty-seven different volcanic rock matrix samples from eight different locations (with multiple depth intervals represented at several locations) at the Nevada Test Site. The solutes used in the experiments included bromide, iodide, pentafluorobenzoate (PFBA), and tritiated water (3HHO). The porosity and saturated permeability of most of the diffusion cell samples were measured to evaluate the correlation of these two variables with tracer matrix diffusion coefficients divided by the free-water diffusion coefficient (Dm/D⁎). To investigate the influence of fracture coating minerals on matrix diffusion, ten of the diffusion cells represented paired samples from the same depth interval in which one sample contained a fracture surface with mineral coatings and the other sample consisted of only pure matrix. The log of (Dm/D⁎) was found to be positively correlated with both the matrix porosity and the log of matrix permeability. A multiple linear regression analysis indicated that both parameters contributed significantly to the regression at the 95% confidence level. However, the log of the matrix diffusion coefficient was more highly-correlated with the log of matrix permeability than with matrix porosity, which suggests that matrix diffusion coefficients, like matrix permeabilities, have a greater dependence on the interconnectedness of matrix porosity than on the matrix porosity itself. The regression equation for the volcanic rocks was found to provide satisfactory predictions of log(Dm/D⁎) for other types of rocks with similar ranges of matrix porosity and permeability as the volcanic rocks, but it did a poorer job predicting log(Dm/D⁎) for rocks with lower porosities and/or permeabilities. The presence of mineral coatings on fracture walls did not appear to have a significant effect on matrix diffusion in the ten paired diffusion cell experiments. © 2007 Elsevier B.V. All rights reserved. Keywords: Matrix diffusion; Tracers; Matrix tortuosity; Matrix porosity; Matrix permeability

1. Introduction ⁎ Correspoding author. Tel.: +1 505 665 2537; fax: +1 505 665 4955. E-mail addresses: [email protected] (P.W. Reimus), [email protected] (T.J. Callahan). 1 Fax: +1 843 953 5446. 0169-7722/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jconhyd.2007.01.017

It is well known that in fractured rock groundwater systems, the diffusive mass transfer of solutes between flowing water in fractures and relatively stagnant water

86

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

Fig. 1. Locations where core samples were obtained for diffusion cell experiments (solid gray corresponds to mountain ranges or mesas, textured gray corresponds to major basins). It is ~60 miles (~100 km) from the southeast corner of the test site to downtown Las Vegas.

in the surrounding rock matrix (matrix diffusion) can significantly retard the movement of solutes through the flow system (Neretnieks, 1980; Grisak and Pickens, 1980; Tang et al., 1981; Maloszewski and Zuber, 1984; Robinson, 1994). Therefore, accounting for matrix diffusion is critical in assessing contaminant migration in fractured rock groundwater systems. In this paper, we examine the dependence of matrix diffusion coefficients, Dm, on matrix porosity and

matrix permeability in volcanic rocks from the Nevada Test Site (NTS). Matrix diffusion coefficients are inherently difficult and expensive to measure, although doing so is critical to assess matrix diffusion mass transfer rates in fractured rocks for risk assessment calculations. Our goal here is to show that matrix diffusion coefficients can be predicted to a sufficient degree of accuracy from matrix porosity and permeability, both of which are relatively easy to measure. The

Fig. 2. Schematic illustration of diffusion cell apparatus.

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

concept of matrix diffusion coefficients being correlated with matrix porosity and permeability follows logically from work originally conducted by Archie (1942), who showed that resistivity (a measure of interconnectedness of porosity) has a power law relationship with porosity. We also provide a cursory evaluation of the influence of fracture coating minerals on matrix diffusion coefficients. We use data obtained from laboratory diffusion cell experiments conducted over the past ten years to characterize solute transport processes in saturated, fractured volcanic rock at the NTS (Callahan et al., 2000; Reimus et al., 2002a,b, Bechtel-SAIC, 2004). Thirty-seven core samples were obtained from eight locations at the NTS, with most of them coming from Pahute Mesa where underground nuclear tests were conducted for several years, and the potential for legacy radionuclide transport from detonation cavities is being evaluated. Fig. 1 shows the locations where cores samples were collected. The hydrogeology at all these locations is dominated by fracture flow within a rock matrix that ranges in total porosity from about 0.06 to 0.37. Many of the rock units are comprised of ash fall and ash flow tuffs of varying degrees of welding, and the matrix permeability is usually smaller in units with higher degrees of welding. One location, the UE-25 C wells complex, was used for field-scale tracer testing in layered ash flow tuffs just southeast of the proposed high-level nuclear waste repository at Yucca Mountain, where the goal is to study solute transport processes to support risk assessments for the proposed Yucca Mountain nuclear waste repository (Reimus et al., 2003). A second location, the ER-20-6 well complex, was used for field tracer testing in a fractured lava flow aquifer on Pahute Mesa (Reimus and Haga, 1999). The tracers used in the C wells and ER-20-6 diffusion cell experiments were bromide, iodide, and pentafluorobenzoate (PFBA) — the same tracers that were used in field testing. For all other locations, the tracer used in the diffusion cell experiments was tritiated water (3HHO). 2. Materials and methods Details of the experimental methods are provided in Callahan et al. (2000) and Bechtel-SAIC (2004) for the C wells diffusion cell experiments, in Reimus et al. (2002a) for the ER-20-6#1 diffusion cell experiments, and in Reimus et al. (2002b) for the experiments associated with all other locations. We provide a brief summary here. Fig. 2 is a schematic illustration of a typical diffusion cell apparatus, which consisted of two solution reservoirs separated by a cylindrical-shaped

87

(usually) piece of core (with parallel cuts on the upper and lower surfaces to ensure a constant sample thickness in the direction of diffusion) that was embedded within an epoxy or RTV silicon “frame” that served to force all hydraulic and diffusive communication between the two reservoirs to be through the rock matrix pores. Samples with mineral-coated fractures had only one cut that was approximately parallel to the fracture surface; the fracture surface formed one side of the diffusion cell sample. The “framed” samples were saturated with groundwater or synthetic groundwater prior to assembling the cell by placing the samples under water in a beaker, setting the beaker in a vacuum chamber, and drawing a vacuum of − 2.9 to − 3.5 kPa. The mass of each sample was checked until it no longer increased, whereupon it was assumed the pores were saturated with water. After assembling the saturated sample into a diffusion cell apparatus, a groundwater solution containing tracers was loaded into the larger reservoir, and the smaller reservoir was filled with tracer-free ground water to initiate the diffusion experiment. The latter reservoir was kept well mixed with a magnetic stir bar to eliminate concentration gradients, and it was also continuously flushed so that water samples can be collected in a fraction collector and subsequently analyzed for tracers. The resulting tracer “breakthrough curves” were analyzed to estimate matrix diffusion coefficients (see below). Most of the diffusion cells were oriented horizontally as shown in Fig. 2 (i.e., diffusion in the horizontal direction through the rock sample) to Table 1 Chemical composition of waters used in diffusion experiments Constituent Ca++ Cl− F− K+ Mg++ Na+ NO−3 Si SO2− 4 HCO−3 pH

a

Well J-13 water

b

NaHCO3 water

12 7.1 5 2.1 42 22 17 124 d 7.2

c Synthetic WW-20 water

12 2.6 1.3 54

141 7.8–8.0

68 1.5 22 32 110 8.0–8.5

Water was passed through a 0.2 μm filter prior to use. Concentrations in mg L− 1. a Used for samples from UE-25C#2 553 m and UE-25C#1 573 m (A and B). b Used for samples from UE-25C#2 533 m, UE-25C#1 715 m and UE-25C#1 795 m. c Used for all samples not from UE-25 C wells. d Initial pH; pH probably drifted to ∼ 8 during the experiments.

88

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

coefficient of ∼7.6 × 10− 10 m2s− 1 (Bowman, 1984; Farnham et al., 1997). Thus, the ratio of the free-water diffusion coefficients of the paired tracers was between 2.5:1 and 3:1. The diffusion cell experiments associated with the other locations involved the simultaneous diffusion of 3HHO, 99TcO4− and H14CO3− , although we only present the 3HHO data here because the 99TcO4− and H14CO3− reacted with several of the rock matrices. The free-water diffusion coefficient of 3 HHO is 2.4 × 10− 9 m2s− 1 (Kozaki et al., 1999). A limited number of batch sorption experiments were conducted to confirm that the anionic tracers did not sorb to the C wells rocks (Bechtel-SAIC, 2004), and tracer experiments in fractured cores confirmed that there was no evidence of tracer sorption to any of the rocks (as indicated by complete mass recoveries of the tracers) (Reimus et al., 2002a,b; Bechtel-SAIC, 2004). The major ion chemistry of the waters used in all experiments is listed in Table 1. The waters were all similar in composition and had relatively low ionic strengths (∼0.003 M), so diffusion coefficient comparisons between

avoid density-driven flow through the rock that might be induced by the density contrast between the tracer solution and the tracer-free groundwater on either side of the rock sample. The maximum density contrast in any of the experiments was less than 0.2%, which, though small, was considered enough to potentially induce a small amount of density-driven flow. However, none of the experiments had tracer responses indicating significant density-driven flow (i.e., very small or no separation of breakthrough curves of tracers with different diffusion coefficients). All of the C wells and ER-20-6#1 diffusion cell experiments involved the simultaneous diffusion of a pair of nonsorbing tracers with different diffusion coefficients. In each case, the tracer with the larger diffusion coefficient was either bromide ion or iodide ion, and the tracer with the smaller diffusion coefficient was pentafluorobenzoate (PFBA). Bromide and iodide have free-water diffusion coefficients, D⁎, equal to 2.08 × 10− 9 m2s− 1 and 2.04 × 10− 9 m2s− 1, respectively (Newman, 1973); and PFBA has a free-water diffusion

Table 2 Properties and dimensions of core samples used in diffusion cell experiments involving halides and PFBA, and the matrix diffusion coefficients measured in these experiments Diffusion cell sample a well, depth (m bgs)

Matrix porosity

Matrix permeability (m2)

Sample thickness (m)

Sample cross-sectional area (×10− 4 m2)

Halide bDm PFBA Dm Ratio of halide (×10− 10 m2s− 1) (×10− 10 m2s− 1) to PFBA Dm

ER-20-6#1, 682 A ER-20-6#1, 682 B ER-20-6#1, 682 C ER-20-6#1, 733 A ER-20-6#1, 733 B ER-20-6#1, 733 C ER-20-6#1, 733 D ER-20-6#1, 793 A ER-20-6#1, 793 B ER-20-6#1, 793 C ER-20-6#1, 857 A ER-20-6#1, 857 B c ER-20-6#1, 857 C ER-20-6#1, 864 A d ER-20-6#1, 864 B ER-20-6#1, 864 C ER-20-6#1, 869 A ER-20-6#1, 869 B UE-25C#2, 533 UE-25C#2, 553 UE-25C#1, 573 A UE-25C#1, 573 B UE-25C#1, 715 UE-25C#1, 795

0.297 0.297 0.297 0.369 0.369 0.369 0.369 0.259 0.259 0.259 0.303 0.303 0.303 0.179 0.179 0.179 0.111 0.111 0.272 0.138 0.288 0.288 0.094 0.298

3.95E-18 4.94E-18 1.97E-18 3.36E-17 3.06E-17 2.76E-17 3.06E-17 8.49E-16 2.66E-16 2.40E-16 7.04E-15 3.25E-15 8.26E-15 5.92E-18 1.74E-16 8.83E-15 2.37E-17 3.95E-18 4.66E-15 7.76E-19 4.49E-16 4.49E-16 1.06E-18 9.37E-17

0.0219 0.0214 0.0106 0.0150 0.0152 0.0233 0.0232 0.0198 0.0177 0.0162 0.0234 0.0320 0.0270 0.0211 0.0278 0.0250 0.0127 10.014 0.0098 0.0123 0.0227 0.0182 0.0112 0.0079

44.89 44.89 40.45 20.27 20.27 137.9 137.9 44.18 20.27 19.75 42.89 44.5 19.91 19.75 44.65 44.65 20.27 19.75 79.4 79.7 79.4 20.08 79.4 75.9

0.40 0.45 0.55 2.55 2.55 3.15 3.15 2.4 1.78 1.6 4.3 2.8 3.9 0.2 0.9 2.9 0.33 0.09 6.2 0.38 3.0 2.8 0.42 1.0

a b c d

0.175 0.2 0.2 0.85 0.88 1.15 1.15 0.9 0.65 0.5 1.6 1.1 1.45 0.1 0.45 1.2 0.08 0.018 2.0 0.13 1.1 1.0 0.12 0.35

Letters indicate multiple diffusion cell samples from the same interval. Depths are rounded to the nearest meter. Bromide was used in C wells diffusion cells (lower set), and iodide was used in ER-20-6#1 diffusion cells. Diffusion in this sample was perpendicular to depositional flow bands. Diffusion in this sample was through a densely-filled fracture within the matrix.

2.3 2.3 2.8 3.0 2.9 2.7 2.7 2.7 2.7 3.2 2.7 2.5 2.7 2.0 2.0 2.4 4.1 5.0 3.1 2.9 2.7 2.8 3.5 2.9

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

the experiments should be valid without making corrections to account for multicomponent diffusion effects or activity coefficients. 3 HHO was analyzed by liquid scintillation counting (Packard Tri-Carb 2500) and the anions were analyzed by liquid chromatography (Dionex model 4500) with a conductivity (bromide, iodide) or UV absorbance (PFBA) detector. Detection limits were ≤0.04 mg L− 1 for bromide and iodide, ≤ 0.02 mg L− 1 for PFBA, and ∼5 × 10− 13 M for 3HHO. The interpretive method used to obtain matrix diffusion coefficient estimates from the tracer breakthrough curves involved solution of the one-dimensional diffusion equation with appropriate boundary conditions representing the reservoirs. The equations

89

and procedure are described by Callahan et al. (2000). Independently of the diffusion cell experiments, matrix porosity, Ф, was measured on several representative pieces of core from each diffusion cell sample by subtracting dry weights from water-saturated weights to determine pore volume and then dividing by the total volume of the sample measured by water displacement. A single average porosity was reported for each interval (variability within an interval was generally very small). Matrix permeabilities for most of the diffusion cell samples were measured by imposing either a constant or a falling head across the sample and measuring the resulting flow rate through the sample (Callahan et al., 2000). Many of the samples were also characterized for

Table 3 Properties and dimensions of core samples used in diffusion cell experiments involving 3HHO, and the matrix diffusion coefficients measured in these experiments Diffusion cell sample a well, depth Matrix (m bgs) porosity

Matrix permeability Sample (m2) thickness(m)

Sample cross-sectional area (×10− 4 m2)

3

UE20c, 871 A UE20c, 871 B UE20c, 871 C UE20c, 871 C UE20c, 871 C UE20c, 872 UE20c, 872 UE20c, 856 A UE20c, 856 B⁎ UE20c, 839 A UE20c, 839 B⁎ UE20c, 886 A UE20c, 886 B⁎ UE20f, 866 UE18t, 306 A UE18t, 306 B⁎ UE18t, 423 A UE18t, 423 A UE18t, 423 B UE18t, 423 B UE18t, 424 UE18t, 424 UE18r, 679 A UE18r, 679 A UE18r, 679 B PM1, 1470 A PM1, 1470 B⁎ PM2, 1273 A PM2, 1273 A PM2, 1273 B PM2, 1273 B PM2, 1273 C⁎ PM2, 1273 C⁎

5.6E-17 3.0E-17 2.4E-17 2.4E-17 2.4E-17 9.6E-18 9.6E-18 NM b NM b 2.8E-17 3.8E-17 NM b NM b 4.1E-18 NM b NM b 6.00E-18 6.00E-18 2.40E-17 2.40E-17 6.40E-18 6.40E-18 NM b NM b 3.30E-18 3.00E-17 4.20E-17 1.2E-18 1.2E-18 1.1E-18 1.1E-18 2.1E-18 2.1E-18

20.1 20.1 20.0 20.0 20.0 62.1 62.1 20.1 20.0 20.2 19.9 61.0 20.0 60.8 20.2 20.5 28.6 28.6 28.6 28.6 28.6 28.6 62.1 62.1 55.4 59.5 20.2 61.5 61.5 61.5 61.5 20.2 20.2

1.1 0.85 0.9 2.3 1.2 1.2 1.0 0.75 1.4 1.4 1.3 3.0 2.4 0.55 1.3 0.7 0.85 0.85 0.8 0.95 0.9 0.75 0.44 0.43 0.35 3.5 3.5 2.1 0.8 2.3 0.9 2.0 1.0

0.21 0.21 0.21 0.21 0.21 0.17 0.17 0.16 0.16 0.2 0.2 0.31 0.31 0.3 0.10 0.10 0.26 0.26 0.26 0.26 0.26 0.26 0.057 0.057 0.057 0.24 0.24 0.17 0.17 0.17 0.17 0.17 0.17

0.0122 0.0099 0.0192 0.0192 0.0192 0.0170 0.0170 0.0095 0.0100 0.0164 0.0182 0.0169 0.0200 0.0105 0.0110 0.0060 0.0238 0.0238 0.0254 0.0254 0.0159 0.0159 0.0167 0.0167 0.0170 0.0200 0.0162 0.0152 0.0152 0.0174 0.0174 0.0155 0.0155

HHO Dm(×10− 10 m2s− 1)

a Letters indicate multiple diffusion cell samples from the same interval. Repeated entries indicate repeat experiments using the same diffusion cell sample. Samples denoted with an asterisk (⁎) contained a fracture surface with mineral coatings. Depths are rounded to the nearest meter. b NM = not measured.

90

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

mineralogy by quantitative X-ray diffraction (Reimus et al., 2002a,b; Bechtel-SAIC, 2004). We do not provide mineralogic details here other than to say that all rocks were dominated by silicate phases (mostly quartz and feldspars) with varying amounts of alteration minerals such as zeolites and clays. The dry weights of the samples used for porosity measurements divided by their volumes confirmed that the bulk densities of all the rocks were approximately 2.65(1 − Ф) g cm− 3 (grain densities of volcanic rocks at the NTS are known to be ∼ 2.65 g cm− 3). 3. Results The measured matrix porosities and permeabilities of the C wells and ER-20-6#1 diffusion cell samples and the dimensions of the cut samples used in the diffusion cell experiments are listed in Table 2. The diffusion coefficient estimates obtained from these diffusion cell experiments are also listed in Table 2. Table 3 contains the same information as Table 2 for the diffusion cell experiments that involved 3HHO as the tracer. All of the tracer breakthrough curves and model fits to obtain estimates of diffusion coefficients can be found in Bechtel-SAIC (2004) for the C wells diffusion cells, Reimus et al. (2002a) for the ER-20-6#1 diffusion cells, and Reimus et al. (2002b) for the remaining diffusion cells. Fig. 3 is a tracer breakthrough plot for one of the C wells samples (Callahan et al., 2000). For several of the core intervals, diffusion cell experiments were conducted on “replicate” samples to assess the variability in the diffusion coefficient due to variability in matrix properties. However, some of the

samples from the same interval had obvious differences that were expected to result in different measured diffusion coefficients; e.g., filled fractures within the matrix, depositional flow bands perpendicular to the diffusion direction, or fracture surfaces coated with alteration minerals (see Tables 2 and 3). Some of the experiments involving 3HHO were repeated a second time to assess experimental reproducibility. To examine the relationship of matrix diffusion coefficients to matrix porosity and permeability, we normalized the matrix diffusion coefficients by dividing them by the free-water diffusion coefficients for each tracer (i.e., Dm/D⁎). This ratio is often referred to as the tortuosity factor for the porous medium. Fig. 4 shows the correlation of log(Dm/D⁎) with matrix porosity, and Fig. 5 shows the correlation with log permeability. Note that Dm/D⁎ and matrix permeability were transformed to log space because the ranges of these variables were approximately 2 and 4 orders of magnitude, respectively, which would have resulted in excessive weighting of the high ends of these ranges in regression analyses unless weighting factors were introduced. Transformation was not necessary for matrix porosity because the range in untransformed values was about the same (approximately a factor of 6) as the range in transformed values. Figs. 4 and 5 indicate that there is a positive correlation of the log of Dm/D⁎ with both matrix porosity and log permeability. For these rock samples, porosity and log permeability are weakly correlated (Fig. 6), so we also regressed the log of the matrix diffusion coefficients with both porosity and log permeability in a stepwise fashion to determine whether

Fig. 3. Plot of bromide and pentafluorobenzoate (PFBA) concentrations relative to injection concentration in diffusion cell experiment for sample UE25C#2 533. The model results are obtained using Eqs. (11) and (12) of Callahan et al. (2000). The discontinuities in concentration are due to flow rate changes through the outlet reservoir (Fig. 1), which are accounted for by the model equations.

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

91

one value for each diffusion cell sample), Eq. (1) becomes: logDm =D⁎ ¼ ð1:42F1:60Þ þ ð1:91F1:29ÞU þ ð0:19F0:089ÞðlogPerm:Þ;

ð2Þ

R2 ¼ 0:542:

Fig. 4. log(Dm/D⁎) from the diffusion cell experiments as a function of matrix porosity. The triangles correspond to halide values, the squares to PFBA values, and the black circles to 3HHO values.

the use of both parameters together yielded a significantly better predictive capability for log(Dm/D⁎) than either variable alone. That is, sequential F tests (Draper and Smith, 1981) were conducted to determine if it was statistically justified to add a second predictor variable to a regression that already had one predictor variable. The resulting multiple linear regression equation with both independent variables is log Dm =D⁎ ¼ ð1:51F1:05Þ þ ð2:16F0:88ÞU þ ð0:20F0:058ÞðlogPerm:Þ; R ¼ 0:617

ð1Þ

2

where the values in parentheses indicate the upper and lower 95% confidence intervals of the regression coefficients. The standard error (estimated standard deviation) of log Dm/D⁎ in the regression is 0.27. The F tests indicated that both porosity and log permeability contributed significantly to the multiple linear regression at the 95% confidence level (F = 24.1 for adding porosity to a regression that already contains log permeability, and F = 40.4 for adding log permeability to a regression that already contains porosity; compared with F(95%) = 3.98 as a significance measure). We note that these regression results may be somewhat misleading because there are two highlycorrelated values of (Dm/D⁎) associated with many of the diffusion cells: a halide ion and and PFBA for each of the C wells and ER-20-6#1 experiments, and repeat 3 HHO measurements for many of the other diffusion cell experiments. If only the halide data from the C wells and ER-20-6#1 diffusion cells and the 3 HHO data from the first of any repeat experiments in the remaining diffusion cells are considered (that is, only

While this equation has very similar regression coefficients to Eq. (1), the correlation coefficient (R2) is slightly smaller and the 95% confidence intervals are significantly wider than for Eq. (1) because the number of degrees of freedom is approximately half that for Eq. (1). The standard error of log Dm/D⁎ in the regression of Eq. (2) is 0.29. The sequential F test values at the 95% confidence level for Eq. (2) are F =9.0 for adding porosity to a regression that already contains log permeability, and F = 14.4 for adding log permeability to a regression that already contains porosity; compared with F(95%)= 4.1 as a significance measure. Regardless of whether all the diffusion coefficient data or only the reduced data set (one value for each diffusion cell) are considered, the regressions indicate that both matrix porosity and log matrix permeability provide a significantly better predictive capability than either variable by itself. However, the F values (and the R2 values of Figs. 4 and 5) indicate that log permeability is a better predictor variable than matrix porosity. This result can probably be attributed to the fact that diffusion through rock matrices must occur via interconnected porosity, which may not necessarily be highly-correlated with total porosity if there are dead-end pores, but will be correlated to permeability because flow requires interconnected pores. Permeability is clearly the determining factor in samples from the same interval that nominally have the same porosity but have internal

Fig. 5. log(Dm/D⁎) from the diffusion cell experiments as a function of log matrix permeability. The triangles correspond to halide values, the squares to PFBA values, and the black circles to 3HHO values.

92

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

Fig. 6. Correlation of log matrix permeability with matrix porosity for diffusion cell samples.

features such as filled fractures or flow bands that affect directional permeability and hence diffusion coefficients (e.g., ER-20-6#1, 864 m bgs; and ER-20-6#1, 857 m bgs — see Table 2). Nevertheless, we are not advocating that matrix porosity measurements, which are relatively easy and inexpensive, not be conducted. They are ultimately very important for assessing the effects of matrix diffusion in fractured rocks because the porosity determines the storage capacity of the matrix for contaminants. Also, matrix diffusion mass transfer coefficients are linearly dependent on matrix porosity, while they have only a square-root dependence on matrix diffusion coefficients (Reimus et al., 2003). Fig. 7 shows the 3HHO matrix diffusion coefficients for pairs of samples in which one sample had a mineralcoated fracture surface on one face of the rock wafer and the other sample consisted of pure matrix material. The presence of these secondary minerals did not affect solute matrix diffusion in any consistent way, as there are 2 pairs with greater diffusion coefficients in the fracture samples, 4 pairs with greater diffusion coefficients in the matrix samples, and 1 pair with equal diffusion coefficients (Fig. 7). Also, the differences between paired samples was never more than about a factor of two, which is comparable to or even less than differences in some of the pure matrix samples from the same core interval (see Tables 2 and 3). The fracture coatings were not quantitatively characterized, but most of them had the appearance of being rich in manganese oxides, with perhaps some clay and iron oxides also present. Permeability was not measured in the paired samples with and without fracture surfaces. 4. Discussion Although we did not conduct a formal error analysis for the experiments, we feel confident in stating that

tracer analytical errors and errors in experimental technique are relatively minor contributors to the scatter about the regression equations and to the 95% confidence intervals presented for the regression coefficients. In general, we believe that the accuracy of the diffusion coefficient measurements was better for the diffusion cells that exhibited larger diffusion coefficients because tracer breakthrough curves tended to be less scattered in these experiments (probably because they were substantially higher than background concentrations of the tracers) and there were generally more data points to fit because of earlier tracer breakthroughs. The greater scatter in Fig. 4 at lower permeabilities (corresponding to smaller diffusion coefficients) may be reflecting this. The reproducibility of repeat experiments involving 3 HHO was generally quite good (within a factor of two for the matrix diffusion coefficients), although there was tendency toward decreased matrix diffusion coefficients the second (or third) time an experiment was conducted using the same sample (Fig. 8). We attribute this result to possible microbial growth on the sample surfaces. Although not directly observed, such growth was certainly possible given that no special precautions were taken to prevent it. For this reason, we used the first 3HHO measurement associated with any of the samples for which multiple measurements were obtained to develop Eqs. (1) and (2). In cases where diffusion coefficients increased in repeat measurements, it is possible that the rock samples were still increasing in saturation (and hence the interconnected wetted porosity was increasing), or minor dissolution of mineral phases could have occurred, which would have opened up additional pore spaces. There were several potential experimental errors or biases that could not be readily assessed but may have affected the results. One of these was the potential influence of microfractures in the relatively thin matrix samples that could have been induced (or propagated) during cutting and handling. Even a few microfractures might significantly bias matrix diffusion coefficients to higher values than would be observed in an otherwise uncompromised matrix sample. Another potential error is that the rock cutting process could have effectively polished some of the matrix surfaces, filling small pores with rock dust and other debris during cutting. If this occurred, it would be expected to introduce a downward bias in the measured matrix diffusion coefficients. Finally, we cannot discount the possibility that a small amount of advective transport may have occurred through some of the diffusion cell samples — most likely as a result of barometric pressure cycling.

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

Fig. 7. Comparison of 3HHO matrix diffusion coefficients in paired samples from the same depth interval with one sample having a fracture surface coated with alteration minerals. A repeat comparison was conducted for PM2, 1273 m bgs.

However, if advection had been significant, it should have resulted in ratios of halide and PFBA diffusion coefficients quite different from their free-water diffusion coefficient ratio. The measured ratios of halide to PFBA matrix diffusion coefficients in most of the diffusion cell experiments involving these tracers ranged from about 2.5:1 to 3:1, which is the approximate ratio of the free-water diffusion coefficients. The observed ratios are listed in the last column of Table 1. The poorest agreement with the free-water diffusion coefficient ratio is generally associated with the diffusion cell samples that had smaller matrix diffusion coefficients. We conclude that the effects of all these potential errors and biases were probably not significant

93

for most of the samples, but they may have contributed to some of the observed scatter in the data and in the regressions. Eq. (2) predicts matrix diffusion coefficients of halides in volcanic rock matrices at the NTS if matrix porosity and permeability estimates are available but diffusion coefficients estimates are not. These properties are generally easier to measure than matrix diffusion coefficients. We recommend Eq. (2) over Eq. (1) because Eq. (2) reflects truly independent measurements (one measurement for each diffusion cell sample), whereas Eq. (1) reflects several highly-correlated measurements and repeat measurements. Because Eq. (2) predicts log(Dm/D⁎), it should be valid for any nonsorbing solute for which a free-water diffusion coefficient is known. We caution that Eq. (2) was developed from measurements on saturated volcanic rocks from the NTS, so it may not necessarily be applicable to other types of rocks. To test Eq. (2) for other rock types, we searched the literature for studies in which porosity, permeability and diffusion coefficients were measured on the same samples, and we found very few. Polak et al. (2003) reported all three variables for a single chalk sample (porosity of 0.3, permeability of 4.1 × 10− 16 m2) in which they obtained iodide matrix diffusion coefficients by X-ray computed tomography, and Vilks et al. (2003) reported iodide diffusion coefficients in four granite samples in which porosity and permeability were measured. Kelley and Saulnier (1990) reported measurements of porosity, permeability, and formation factor (based on electrical resistivity) on dolomite core

Fig. 8. Comparison of 3HHO matrix diffusion coefficients in repeat experiments using the same diffusion cell sample. Note that for UE20c 871C, the first experiment was conducted over a year before the second experiment, and the sample was completely dried out during most of the time between experiments. In all other cases, the samples remained in water between experiments, and the time interval between experiments was much shorter.

94

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

samples from the Waste Isolation Pilot Plant site near Carlsbad, NM. Even though diffusion coefficients were not measured directly by Kelley and Saulnier (1990), the inverse of the product of formation factor and porosity (1/FFФ, where FF is formation factor) provides an estimate of Dm/D⁎ (Walter, 1982). The data of Kelley and Saulnier (1990) are of interest for this study because the dolomite samples had ranges of matrix porosity (0.07 to 0.25) and permeability (3 × 10− 17 to 6 × 10− 14 m2) that were similar to the volcanic rock samples reported here (Tables 2 and 3). Fig. 9 is a plot of measured log(Dm/D⁎) values or measured log(1/FFФ) values from this study and the studies mentioned above vs. predicted log(Dm/D⁎) values from Eq. (2). The solid line has a slope of 1 and an intercept of zero, so it corresponds to perfect agreement between the data and Eq. (2). The dashed lines represent the approximate 90% confidence interval associated with Eq. (2) calculated using the methods of Draper and Smith (1981). It is apparent that while Eq. (2) slightly underpredicts values of log(1/FFФ) for the dolomite samples and log(Dm/D⁎) for the chalk sample, most of the data points fall within the 90% confidence interval for Eq. (1). Walter (1982) measured both (1/ FFФ) and Dm/D⁎ in six volcanic tuff samples taken from the NTS, and (1/FFФ) was found to be larger than Dm/D⁎ in 5 of these 6 samples. These data suggest that the prediction of log(1/FFФ) as a proxy for log(Dm/ D⁎) of the dolomite samples would likely be improved if

the tendency for (1/FFφ) to be larger than Dm/D⁎ were accounted for (we considered the Walter (1982) data to be too sparse and scattered to attempt a quantitative correction). The granite samples of Vilks et al. (2003) all had matrix porosities less than 0.01, which was well below the lowest porosity of any of the volcanic rock samples (∼ 0.06), so it is perhaps not surprising that the log(Dm/D⁎) for these samples were significantly overpredicted by Eq. (2). Fig. 9 shows a tendency for greater scatter in the volcanic rock data at lower predicted values of log(Dm/D⁎), which also corresponds to lower matrix porosity and permeability values, so it appears that the predictive capability of Eq. (2) becomes degraded as matrix porosities and permeabilities decrease. We consider our evaluation of the effects of fracture coating minerals on matrix diffusion coefficients to be rather inconclusive. The sample population was small, and the potential for sample-specific biases was probably greater than for the diffusion samples without fracture surfaces. Variability in microfracturing within fracture samples and in thickness and spatial distribution of fracture coating minerals (neither of which were quantified) could have influenced the results. Nevertheless, in the absence of any other data, one would have to conclude that the effects of NTS fracture mineral coatings on matrix diffusion coefficients appear to be minimal Our work suggests that the effects of fracture coating minerals in any type of rock will probably be dictated by the extent to which the coatings have a permeability contrast with the underlying matrix material, and there will be a significant effect of the coating only if its permeability is significantly less than that of the matrix. 5. Conclusions

Fig. 9. Measured values of log(Dm/D⁎) or log(1/FFФ) vs. log(Dm/D⁎) values predicted using Eq. (2). Squares are log(Dm/D⁎) for the volcanic rocks of this study, triangles are log(1/FFФ) for dolomite samples (Kelley and Saulnier, 1990), “×” is log(Dm/D⁎) for a chalk sample (Polak et al., 2003), and dashes are log(Dm/D⁎) for granite samples (Vilks et al., 2003). The solid line corresponds to perfect prediction of Eq. (2), and the dashed lines represent the 90% confidence interval of Eq. (2).

The diffusion cell results indicate that matrix diffusion coefficients of iodide, bromide, pentafluorobenzoate (PFBA), and tritiated water (3 HHO) in fractured volcanic media at the NTS are dependent on both matrix porosity and matrix permeability, although (log of) permeability is the better predictor variable. This result is not surprising given that both matrix diffusion coefficients and matrix permeabilities are expected to depend most strongly on the interconnectedness of porosity within the matrix, not on the matrix porosity itself. A large value of porosity, while tending to be positively correlated with permeability, will yield a large diffusion coefficient only if the porosity is reasonably well interconnected (which also yields a high permeability).

P.W. Reimus et al. / Journal of Contaminant Hydrology 93 (2007) 85–95

We found that the regression model provided satisfactory predictions of Dm/D⁎ for other types of rocks with similar ranges of matrix porosity and permeability as the volcanic rocks we tested (0.06 to 0.37 for porosity and ∼ 10− 18 to ∼ 10− 14 m2 for permeability), but it did a poorer job of predicting Dm/ D⁎ for rocks with lower porosities and/or permeabilities (e.g., granite). Our work suggests that relatively inexpensive matrix porosity and permeability measurements coupled with the application of Eq. (2) offers a cost-effective method of estimating matrix diffusion coefficients in saturated volcanic rocks at the NTS and potentially in other rocks with similar ranges of matrix porosity and permeability. Acknowledgments This work was supported in part by the U.S. Department of Energy Underground Test Area Program, managed out of the National Nuclear Security Administration's Nevada Area Office. This work was also supported in part by the U.S. Department of Energy Office of Civilian Radioactive Waste Management. We thank the editor, E.O. Frind, and two anonymous reviewers for their suggestions, which improved the quality of the manuscript. References Archie, G.E., 1942. The electrical resistivity log as an aid in determining some Reservoir characteristics. Transactions of the American Institute of Mining and Metallurgical Engineers, Vol. 146, pp. 54–62. Bechtel-SAIC Corporation, 2004. Saturated zone in-situ testing. ANLNBS-HS-000039, Rev. 01. Yucca Mountain Project Analysis ReportBechtel-SAIC, Las Vegas, NV. (available for viewing at http://www.lsnnet.gov/ ). Bowman, R.S., 1984. Evaluation of some new tracers for soil water studies. Soil Science Society of America Journal 48 (5), 987–993. Callahan, T.J., Reimus, P.W., Bowman, R.S., Haga, M.J., 2000. Using multiple experimental methods to determine fracture/matrix interactions and dispersion in saturated fractured volcanic tuff. Water Resources Research 36 (12), 3547–3558. Draper, N.R., Smith, H., 1981. Applied Regression Analysis, 2nd edn. John Wiley and Sons, New York, NY. Farnham, I.M., Meigs, L.C., Dominguez, M.E., Lindley, K., Daniels, J.M., Stetzenbach, K.J., 1997. Evaluation of tracers used for the WIPP tracer tests. In: Meigs, L.C., Beauheim, R.L., Jones, T.L. (Eds.), Interpretations of Tracer Tests Performed in the Culebra Dolomite at the Waste Isolation Pilot Plant Site. SAND97–3109. Sandia National Laboratories, Albuquerque, NM. Appendix H. Grisak, G.E., Pickens, J.F., 1980. Solute transport through fractured media, 1. The effect of matrix diffusion. Water Resources Research 16, 719–730.

95

Kelley, V.A., Saulnier Jr., G.J., 1990. Core analyses for selected samples from the Culebra dolomite at the Waste Isolation Pilot Plant Site. SAND-90–7011. Sandia National Laboratories, Albuquerque, NM. Kozaki, T., Sato, Y., Nakajima, M., Kato, H., Sato, S., Ohashi, H., 1999. Effect of particle size on the diffusion behavior of some radionuclides in compacted bentonite. Journal of Nuclear Materials 270, 265–272. Maloszewski, P., Zuber, A., 1984. Interpretation of artificial and environmental tracers in fissured rocks with a porous matrix. In Isotope Hydrology 1983, proceedings of an International Symposium on Isotope Hydrology in Water Resources Development. International Atomic Energy Agency (IAEA), Vienna, Austria, pp. 635–651. Neretnieks, I., 1980. Diffusion in the rock matrix: an important factor in radionuclide retardation? Journal of Geophysical Research 85, 4379–4397. Newman, J., 1973. Electrochemical Systems. Prentice-Hall, Englewood Cliffs, New Jersey. Polak, A., Grader, A.S., Wallach, R., Nativ, R., 2003. Chemical diffusion between a fracture and the surrounding matrix: measurement by computed tomography and modeling. Water Resources Research 39 (4), 1106. doi:10.1029/2001WR000813. Reimus, P.W., Haga, M.J., 1999. Analysis of tracer responses in the BULLION forced-gradient experiment at Pahute Mesa, Nevada. LA-13615-MS. Los Alamos National Laboratory, Los Alamos, NM. Reimus, P.W., Haga, M.J., Humphrey, A.R., Counce, D.A., Callahan, T.J., Ware, S.D., 2002a. Diffusion cell and fracture transport experiments to support interpretations of the BULLION forced-gradient experiment. LA-UR-02–6884. Los Alamos National Laboratory, Los Alamos, NM. Reimus, P.W., Ware, S.D., Benedict, F.C., Warren, R.G., Humphrey, A.J., Adams, A.I., Wilson, B., Gonzales, D., 2002b. Diffusive and advective transport of 3H, 14C, and 99Tc in saturated, fractured volcanic rocks from Pahute Mesa, Nevada. LA-13891-MS. Los Alamos National Laboratory, Los Alamos, NM. Reimus, P.W., Haga, M.J., Adams, A.I., Callahan, T.J., Turin, H.J., Counce, D.A., 2003. Testing and parameterizing a conceptual solute transport model in saturated fractured tuff using sorbing and nonsorbing tracers in cross-hole tracer tests. Journal of Contaminant Hydrology 62–63, 613–626. Robinson, B.A., 1994. A strategy for validating a conceptual model for radionuclide migration in the saturated zone beneath Yucca Mountain. Radiation Waste Management and Environmental Restoration 19, 73–96. Tang, D.H., Frind, E.O., Sudicky, E.A., 1981. Contaminant transport in fractured porous media: analytical solution for a single fracture. Water Resources Research 17, 555–564. Vilks, P., Cramer, J.J., Jansen, M., Miller, N.H., Miller, H.G., Stanchell, F.W., 2003. In situ diffusion experiment in granite: phase I. Journal of Contaminant Hydrology 61, 191–202. Walter, G.R., 1982. Theoretical and experimental determination of matrix diffuion and related solute transport properties of fractured tuffs from the Nevada Test Site. LA-9471-MS. Los Alamos National Laboratory, Los Alamos, NM.