Groundwater ages in fractured rock aquifers

Journal of Hydrology 308 (2005) 284–301 www.elsevier.com/locate/jhydrol

Groundwater ages in fractured rock aquifers P.G. Cooka,*, A.J. Loveb, N.I. Robinsonc,1, C.T. Simmonsd a

CSIRO Land and Water, Adelaide Laboratory, Private Mail Bag 2, Glen Osmond, SA 5064, Australia b Department of Water, Land and Biodiversity Conservation, Adelaide, SA, Australia c CSIRO Mathematical and Information Sciences, Glen Osmond, SA, Australia d Flinders University of South Australia, Bedford Park, SA, Australia Received 2 September 2003; revised 9 November 2004; accepted 12 November 2004

Abstract In fractured porous media, matrix diffusion processes mean that groundwater ages obtained with environmental tracers usually do not reflect the hydraulic age of the water. The distribution of groundwater ages within these heterogeneous systems will be related to the groundwater velocity within the fractures, but also to the size of the fractures and the geometry of the fracture network, and to the hydraulic properties of the aquifer matrix. In this paper, we present analytical and numerical simulations of environmental tracer concentrations in fractured rock aquifers to examine the effect of changes in aquifer parameters on the tracer distributions. In particular, we show that where horizontal fractures are strongly vertically connected, then it may be reasonable to use one-dimensional models of flow and transport through vertical fractures to represent flow through aquifers containing both horizontal and vertical fractures. The presence of large numbers of horizontal fractures will not cause flow to depart significantly from the one-dimensional approximation. Where a smaller number of horizontal fractures are present, then abrupt decreases in the vertical water velocity can occur, as water is intercepted and diverted laterally. Measurements of 14C, 3H, 36Cl, and chlorofluorocarbons within nested piezometers from the Clare Valley, South Australia, display a number of the features apparent in the generic simulations. The use of a number of different tracers appears to allow some fracture and matrix parameters to be constrained more tightly than might previously have been thought possible. q 2004 Elsevier B.V. All rights reserved. Keywords: Groundwater; Tracers; Fractured rock; Residence time

1. Introduction There have been many studies in porous media aquifers in which groundwater ages estimated using

* Corresponding author. Tel.: C61 8 8303 8744. E-mail address: [email protected] (P.G. Cook). 1 Present address: Flinders University of South Australia, Bedford Park, SA, Australia. 0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2004.11.005

environmental tracers have been used to determine groundwater flow velocities (e.g. Pearson and White, 1967; Solomon et al., 1995). Environmental tracers that can be used to estimate groundwater ages include 14C, 3 H, 36Cl and chloroflourocarbons (Cook and Herczeg, 2000; Fig. 1). Because hydrodynamic dispersion is small in many aquifers, groundwater ages determined using these tracers closely approximate hydraulic ages (subsurface residence times) of the water (Ekwurzel et al.,

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Fig. 1. Tracer concentrations versus time. 3H are for Adelaide, South Australia, from the IAEA database (http://www.iaea.or.at/ programs/ri/gnip/gnipmain.htm). 36Cl fallout is from Phillips (2000), scaled for measured total fallout in South Australia (Cook and Robinson, 2002). Atmospheric CFC concentrations are as measured at Cape Grimm, Australia (Cunnold et al., 1994). Concentrations of 14C in atmospheric CO2 are based on Levin et al. (1992).

1994). In unconfined, porous media aquifers, the rate of increase of groundwater age with depth can be used to determine the aquifer recharge rate. In fractured porous media, however, solute transport is characterised by rapid advection through the fractures, with diffusive exchange between solute in the fractures and that in the relatively immobile water in the matrix. Over the past two decades, analytical and numerical models have been developed that are capable of simulating groundwater flow and solute transport through fractured media (e.g. Sudicky and Frind, 1982; Therrien and Sudicky, 1996). The implications of matrix diffusion processes for the migration of groundwater contaminants is reasonably well understood, and the application of these models in contaminant studies is increasing (e.g. Toran et al., 1995). However, the implications of matrix diffusion processes for apparent groundwater ages measured with environmental tracers are less well understood. It is clear that groundwater flow through vertical fractures can result in rapid water movement, and very young apparent groundwater ages at considerable depth. For example, Bradbury and Muldoon (1992) observed above-background 3H concentrations at 70 m depth in fractured dolomite in Wisconsin, and Sheldon and Solomon (2001) measured CFCs and 3H at 60 m depth in fractured dolostone from Smithville, Ontario. Busenberg and Plummer (1996) (see also

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Shapiro, 2001) measured CFCs and 3H to over 100 m depth in schists in New Hampshire. A number of studies have also observed discrepancies between apparent groundwater ages obtained with different tracers in fractured rock aquifers. Weaver et al. (1999) describe groundwater samples containing measurable 3 H despite apparent 14C ages in excess of 1000 years in fractured rock aquifers of the Table Mountain Group, South Africa. Plummer et al. (2001) and Burton et al. (2002) measured CFC-113 ages that were significantly younger than CFC-12 ages in fractured rocks aquifers in Virginia and Pennsylvania, respectively. However, only a very small number of studies have sought to quantitatively interpret groundwater data from fractured rock aquifers using matrix diffusion models (e.g. Shapiro, 2001; Cook and Robinson, 2002). Theoretical studies have clearly shown that apparent groundwater ages in fractured rock systems will be much greater than hydraulic ages of the water, and will be influenced by the geometry and size of the fractures and by the properties of the unfractured rock matrix (Grisak and Pickens, 1980; Neretnieks, 1981). Groundwater flow rates based on increases in apparent water ages along groundwater flow paths will therefore greatly underestimate the groundwater velocity through the fractures, but will overestimate the mean water velocity (total flow rate divided by total mobile and immobile water content). Groundwater sampling in fractured rocks creates additional difficulties. Because of the heterogeneous distribution of fractures in most natural systems, groundwater flowpaths can be highly irregular. Collection of samples representing water evolution along a flowpath may therefore be difficult. Intuitively, one might expect large differences in water residence time over relatively short distances, depending on the aperture of fractures that are sampled, or whether water samples are obtained from the unfractured aquifer matrix. The tracer concentration measured on a pumped groundwater sample will be a flux-averaged concentration of water in fractures intercepting the well, with concentrations weighted by the fracture (and matrix) transmissivities (Shapiro, 2002). Also, because vertical wells are more likely to intercept horizontal or sub-horizontal fractures than vertical or steeplyinclined fractures, groundwater samples are more likely to reflect water within horizontal fractures than within vertical fractures.

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In this paper, we examine the distribution of groundwater ages in fractured rock aquifers where there is strong vertical connection of fractures. The objectives are (i) to quantify the effect of matrix diffusion on groundwater ages measured using environmental tracers; (ii) to determine whether it is possible to estimate aquifer parameters (e.g. fracture aperture, fracture spacing, matrix porosity, matrix diffusion coefficient, water velocity within the fractures, aquifer recharge rate) using measurements of apparent groundwater age obtained with environmental tracers. In Section 2, we examine these issues using analytical models of one-dimensional flow through parallel vertical fractures. Next in Section 3 we extend this analysis using numerical simulations of tracer concentrations in aquifers containing both vertical and horizontal fractures and subject to flow in two- and three-dimensions. In Section 4 of the paper, field measurements of apparent groundwater ages obtained from fractured rock aquifers from the Clare Valley, South Australia, are presented. The distributions of apparent groundwater age measured at this site are compared with age distributions produced in the numerical simulations. The purpose is not to calibrate the model to the field data, but to determine whether key features of the observed field data are consistent with environmental tracer distributions produced from model simulations.

2. One-dimensional flow through vertical fractures 2.1. Theory An analytical solution for the transport of radioactive tracers through a system of evenly-spaced, identical, planar, parallel vertical fractures in an impermeable matrix has been presented by Sudicky and Frind (1982). The model simulates one-dimensional flow through a single fracture, and uses no-flow boundary conditions at a specified distance (B) from the fracture to represent flow through evenly-spaced parallel fractures. Matrix diffusion occurs in the direction perpendicular to the fracture. Thus, although flow is one-dimensional, solute transport occurs in two dimensions. The model assumes that transverse diffusion and dispersion result in complete mixing

across the fracture width at all times, and that transport along each fracture is much faster than transport within the matrix (which occurs only by diffusion). The model calculates solute concentrations within the fracture and in the matrix as a function of time, for constant input concentration (at time tO0). (Initial concentrations are zero everywhere.) Tracer concentrations within the fracture become a function of the vertical water velocity (Vw) and dispersivity (a) within the fractures, matrix porosity (qm), diffusion coefficient within the matrix (D), radioactive decay constant (l), fracture aperture (2b), fracture spacing (2B), depth (z) and time. The diffusion coefficient within the matrix is related to the matrix porosity by D Z D0 qm t

(1)

where D0 is the free solution diffusion coefficient and t is the tortuosity. The aquifer recharge rate (R) represents the total flux of water into the system, and is equal to the vertical water velocity within the fracture (Vw) multiplied by the fraction of the aquifer that conducts water: R Z Vw

b B

(2)

Solutions for variable input concentrations are calculated by representing the input concentrations as a summation of adjacent rectangular pulses, as described by Cook and Robinson (2002). Although the simulations that follow use the analytical solution described above, it is also possible to develop a number of approximate analytical solutions by applying simplifying assumptions to either the general transient solution or the steady state solutions of Sudicky and Frind (1982). These simplified solutions can often be very useful for gaining an understanding of how fracture and matrix properties affect the distribution of groundwater ages. Several authors (e.g. Neretnieks, 1981; Sudicky and Frind, 1982; Maloszewski and Zuber, 1985; Sanford, 1997) have shown that the steady-state solution for constant tracer input and zero dispersion reduces to a simple algebraic expression that can be used to describe the distribution of apparent 14C ages within fractures. Thus
 1=2 ta q1=2 m D K1 1=2 K1=2 1=2 Z Vw 1 C tanhðBqm D l Þ (3) z bl1=2

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where ta is the apparent groundwater age and l is the radioactive decay constant for 14C. Cook and Simmons (2000) suggested that (3) could also be used to approximate CFC ages within fractures, if the chlorofluorocarbon input function could be approximated by an exponential growth curve (aeKkt). In this case, the decay constant, l, is replaced by the exponential growth rate, k. For large fracture spacings, defined by Maloszewski and Zuber (1985) K1=2 1=2 K1=2 1=2 as Bq1=2 l R 2, tanhðBq1=2 l Þ approaches m D m D 1, and so (3) can be approximated by: pffiffiffiffiffiffiffiffiffi ta qm D Z (4) z Vw bl1=2 K1=2 1=2 For small fracture spacings ðBq1=2 l ! 0:25Þ, m D 1=2 K1=2 1=2 1=2 K1=2 1=2 tanhðBqm D l Þ approaches Bqm D l , and so (3) reduces to:

ta Bq q Z mZ m z Vw b R

(5)

Cook and Simmons (2000) also argued that an analytical solution for the transport of a short rectangular pulse of solute through a system of planar, parallel fractures could be used to approximate the transport of 3H and 36Cl. Where the fracture spacing is large (no interaction between adjacent fractures) and dispersion within fractures is negligible, the concentration within the fracture as a function of depth can be approximated by


 cðx; tÞ TD1=2 q1=2 KDqm z2 K tl m z Z exp c0 2bVw p1=2 t3=2 4tb2 Vw2

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(6)

where c0 is the concentration of tracer during the pulse input, T is the length of the pulse and t is the time which has elapsed since the commencement of the pulse (Lever and Bradbury, 1985). It is relatively straightforward to show that the maximum 3H or 36Cl concentration will occur at a depth given by: pffiffiffiffi Vw b zmax Z 2t pffiffiffiffiffiffiffiffiffi (7) qm D 2.2. Simulations Simulations of 3H, 36Cl, 14C, CFC-11, CFC-12 and CFC-113 transport were obtained by numerically evaluating the analytical solution presented by Sudicky and Frind (1982) using the method outlined by Cook and Robinson (2002). Results are presented in Figs. 2–5. All of these results depict concentrations within the fractures, as would have been measured in 2002, based on input distributions shown in Fig. 1. The input files are in fact a series of rectangular pulses of 1year width, representing mean annual values. For 36Cl, fallout values (atoms/m2/yr) are converted to concentrations (atoms/L) by dividing by the recharge rate (mm/yr). (36Cl thus differs from the other tracers because the solute is concentrated by evaporation and so input concentrations are a function of the recharge

Fig. 2. Simulations of 3H, 36Cl, 14C and CFC concentrations in an aquifer comprising planar, parallel, vertical fractures in an impermeable matrix. Profiles depict concentrations within the fracture, as would have been measured in 2002. The simulations are for aquifer parameters qmZ0.02, tZ0.03, bZ40 mm, BZ4 m, VwZ50 m yrK1 and RZ0.5 mm yrK1. (Run 15 in Table 1.) Input concentrations of all tracers are depicted in Fig. 1.

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Fig. 3. Comparison of apparent groundwater ages within fractures, based on numerical simulations shown in Fig. 2. (a) Linear scale; (b) logarithmic scale. Apparent 14C ages have been calculated assuming a constant input concentration of 100 pmc.

rate.) The treatment of 14C input is slightly different, and uses the steady-state distribution of 14C within the fracture and matrix under the prescribed parameters (and input concentration of 100 pmC) as initial values. The elevated 14C values (O100 pmC) that have occurred since the 1950 s are then used as input

Fig. 4. Simulations of CFC-12 and 3H concentrations in an aquifer comprising planar, parallel, vertical fractures in an impermeable matrix. Numerals refer to run numbers shown in Table 1. Similar profiles of CFC-12 arise despite different aquifer parameters, although inclusion of an additional tracer (3H) reduces the problem of non-uniqueness.

Fig. 5. Relationship between 3H, CFC-12 and CFC-113 concentrations in fractures based on numerical simulations, and compared with atmospheric input concentrations. Parameters for simulations are given in Table 1. (Numerals in parentheses denote run numbers.) Squares denote measured mean 3H, CFC-12 and CFC-113 input concentrations each year between 1950 and 2002, as per Fig. 1, and hence denote the relationships between the tracers that would occur in a purely advective flow field (no dispersion or matrix diffusion).

concentrations. The simulations shown in Fig. 2 are for parameters aZ0.1 m, qmZ0.02, tZ0.03, bZ40 mm, BZ4 m, Vw Z50 m yrK1 and RZ0.5 mm yr K1. (These values are chosen for illustrative purposes only, and are not intended to be representative of any particular situation. However, they might represent a low porosity, crystalline rock that is relatively poorly fractured, with very low recharge characteristic of an arid environment.) Free solution diffusion coefficients D0Z0.03, 0.035, 0.035, 0.04, 0.05 and 0.07 m2 yrK1 have been used for CFC-113, CFC-11, CFC-12, 14C (as 36 3 HCOK 3 ), Cl and H, respectively (Cook and Herczeg, 2000). Radioactive decay constants of 0.0558 and 0.000121 yrK1 were used for 3H and 14C, respectively. Although the recharge rate used in the simulations shown in Fig. 2 is very low (RZ0.5 mm yrK1), 3H,

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CFC-11 and CFC-12 are present in fractures to approximately 60 m depth. Cook and Robinson (2002) used numerical modelling to show that reducing matrix porosity and matrix diffusion coefficient and increasing fracture spacing would all increase the depth of the 3H peak. (The increase in fracture spacing caused an increase in depth of the 3H peak because the recharge rate, R, was held constant, and thus the water velocity, Vw, was increased proportionally.) Similarly, for any particular depth, higher CFC and 14C concentrations will result from greater water velocity and fracture aperture, and lower matrix porosity and diffusion coefficient. Fig. 3 depicts apparent 14C and CFC ages as a function of depth, calculated from the concentration data shown in Fig. 2. The apparent tracer ages are much greater than the hydraulic age of the water (z/Vw), which increases from zero at the land surface to 2 years at 100 m depth. Fig. 2 also shows that the groundwater ages obtained with the various tracers is different. (14C activities are greater than 100 pmc above 32 m, and so 14C ages cannot be determined.) This is due to differences in diffusion coefficients of the different tracers, and also differences in concentration gradients that arise from differences in the input distributions. In particular, apparent CFC-11 and CFC-12 ages are greater than CFC-113 ages at all depths. Between 40 and 70 m depth, CFCs are present despite 14C ages greater than 100 years. Fig. 4 compares CFC-12 and 3H profiles produced using three different sets of aquifer parameters (Runs 10, 22 and 23 in Table 1). In these simulations, dispersivity, matrix porosity and tortuosity have been held constant, but water velocity, fracture aperture and fracture spacing have been varied by at least an order of magnitude.

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The CFC-12 profiles produced by these simulations are very similar, and might not be able to be distinguished in field studies. This illustrates the problem of non-uniqueness that arises due to the large number of aquifer parameters that determine solute transport through fractured rocks. However, these same simulations produce markedly different 3 H profiles. Thus the use of multiple tracers may reduce problems of non-uniqueness and help constrain aquifer parameters. Fig. 5 depicts the relationship between CFC-113, 3 H and CFC-12 concentrations within fractures from simulations using a range of aquifer parameters, as given in Table 1. At low values of the dispersivity (all simulations are for aZ0.1 m), the relationship between the different tracer concentrations is largely a function of the value of the ratio B2qm/D. This parameter measures the extent to which matrix and fracture concentrations are able to equilibrate due to the diffusion process. For B2qm/D!0.6 yr, the relationship between the different tracer concentrations within the fractures approaches the relationship between the input concentrations of these tracers. For B2qm/DO350 yr, the relationship between the tracer concentrations is also independent of aquifer parameters. In this case, the scale length for matrix diffusion is small relative to the fracture spacing, so that there is no interaction between solutes diffusing from adjacent fractures. At intermediate values of B2qm/D, the relationship between the two tracers is dependent on the value of B2qm/D. Increasing the value of the dispersion coefficient has a similar effect to decreasing the value of B2qm/D, but the effect is negligible for all reasonable values of this parameter (a!100 m). (Simulations were performed with values of a between 0.1 and 10,000 m and other

Table 1 Parameters used in one-dimensional numerical modelling Run

1

4

5

6

8

10

12

15

22

23

a (m) Vw (m/yr) qm b (m) B (m) t B2qm/D

0.1 300 0.1 0.00005 0.5 0.3 24

0.1 300 0.1 0.00005 2 0.3 380

0.1 300 0.1 0.00005 5 0.3 2380

0.1 300 0.025 0.00005 0.5 0.12 60

0.1 30 0.025 0.00005 0.05 0.12 0.6

0.1 300 0.1 0.00005 0.3 0.3 8.6

0.1 30 0.1 0.0005 0.3 0.3 8.6

0.1 50 0.02 0.00004 4 0.03 15 240

0.1 30 0.1 0.00085 1 0.3 95

0.1 60 0.1 0.00005 0.05 0.3 0.24

The value of B2qm/D listed is based on the free solution diffusion coefficient for CFC-12 (D0Z0.035 m2 yrK1).

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parameters as shown for Run 1 in Table 1, although these are not shown here.)

3. Two- and three-dimensional flow through networks of horizontal and vertical fractures Aquifers are not comprised simply of vertical fractures of uniform aperture and spacing, and so it is not clear that the above one-dimensional analytical models are appropriate for understanding field conditions. For systems comprising fractures with more than one orientation, we need to move from analytical to numerical models. Even so, computational requirements limit available numerical models to simulation of flow through a small numbers of fractures. 3.1. Numerical model FRAC3DVS (Therrien and Sudicky, 1996) is a discrete fracture, saturated–unsaturated numerical model where the porous matrix is represented in three dimensions and fractures are represented by two-dimensional planes. Flow can occur both within the matrix and within the fractures, and exchange of water between fractures and matrix can occur in response to head gradients. Matrix diffusion between the fractures and the matrix occurs in response to concentration gradients. Here, we use FRAC3DVS to examine how the presence of horizontal fractures modifies the groundwater age profiles obtained using the one-dimensional analytical model. The matrix hydraulic conductivity was set to be very low, to simulate flow through fractures only, but with diffusion into the matrix. The model dimensions are 1!100!100 m (x, y, z dimensions) as shown in Fig. 6. In all cases, a single vertical fracture with aperture 100 mm ran the length of the model (the fracture plane is defined by xZ 0.5 m) with no flow boundaries parallel to this fracture to simulate flow through identical parallel fractures with a spacing of 1 m. The plane defined by zZ0 is specified flux, and planes defined by xZ0, 1 and yZ0 are no flow in all simulations. Initially, a simulation was carried out to simulate vertical flow only, by using no flow boundary conditions at yZ0 and 100 m and a constant head

Fig. 6. Model dimensions for FRAC3DVS simulations (xZ0–1 m, yZ0–100 m, zZ0–100 m). In most simulations (Figs. 7–10), a single vertical fracture with aperture 100 mm runs the length of the model. (The fracture plane is defined by xZ0.5 m.) The plane defined by zZ0 is specified flux, and planes defined by xZ0, 1 and yZ0 are no flow in all simulations. For one-dimensional flow, a no flow boundary is used at yZ100 m, and a specified head boundary at zZ100 m. For two-dimensional flow, a no flow boundary is used at zZ100 m, and a specified head boundary at yZ100 m. The circle shows the location of the vertical profile through the fracture (xZ 0.5 m, yZ50 m) depicted in Figs. 7–11.

boundary condition at zZ100 m. Where no horizontal fractures are present, this simulates one-dimensional, vertical flow (z direction), with matrix diffusion occurring transverse to the fracture (x direction). Two-dimensional flow through the vertical fracture was simulated by using a no flow boundary at zZ 100 m, and a constant head boundary at yZ100 m. The addition of horizontal fractures then creates a three-dimensional flow field. In all simulations the matrix porosity was set to qmZ0.02, and tortuosity was tZ0.03. A specified flux of 15 mm/yr on the upper boundary was used to simulate aquifer recharge. 3.2. Simulations Figs. 7–10 depict concentrations within the vertical fracture (at yZ50 m, xZ0.5 m), as would have been measured in 2002, based on input distributions shown in Fig. 1. The concentration profile simulated by FRAC3DVS using boundary conditions for one-dimensional, vertical flow is depicted in Fig. 7. The profile is indistinguishable

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Fig. 7. Simulations of CFC-12 concentrations in vertical fracture in year 2002. The circles depict results of the analytical solution. The solid line represents simulation results using FRAC3DVS for a onedimensional flow field. The broken line represents FRAC3DVS simulations for a two-dimensional flow field.

Fig. 8. Simulations of CFC-12 concentrations in 2002, for a twodimensional flow field comprising identical planar parallel vertical fractures, with and without horizontal fractures at 30 m depth.

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Fig. 9. Simulations of CFC-12 concentrations in 2002, for a twodimensional flow field comprising identical planar parallel vertical fractures, with different numbers of horizontal 500 mm fractures.

Fig. 10. Simulations of CFC-12 concentrations in vertical fracture, for a two-dimensional flow field comprising identical planar parallel vertical fractures and a single discontinuous horizontal 500 mm fracture (0!x!1 m, 50!y!100 m, zZ30 m).

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from that obtained using the analytical solution of Sudicky and Frind (1982). Two-dimensional flow through the vertical fractures was then simulated by making the zZ100 m boundary no flow, and the yZ 100 m boundary constant head. Fig. 7 shows that CFC-12 concentrations at all depths within the vertical fracture in the two-dimensional flow field are less than in the vertical flow simulation, although in the upper part of the aquifer the difference is relatively small. This results from the curvature of the flow lines in a two-dimensional flow field, with the vertical component of the groundwater velocity decreasing linearly with depth. (In porous media, groundwater ages increase linearly with depth in a vertical flow field, and exponentially with depth in a two-dimensional flow field. In the two-dimensional flow field, ages are greater at all depths.) All of the simulations that follow are for the two-dimensional flow field. Fig. 8 shows the effect on CFC concentrations of a continuous horizontal fracture extending throughout the model domain, located at zZ30 m depth. Where the horizontal fracture aperture is 200 mm or less, it has minimal effect on CFC-12 concentrations. Increasing the fracture aperture has two noticeable effects. Firstly, concentrations above the fracture increase slightly. This occurs because water is drawn down vertically towards the high conductivity horizontal fracture (i.e. it reduces the curvature of the flowlines above the fracture). More importantly, increasing the horizontal fracture aperture decreases concentrations below the fracture, as the vertical flow velocity is reduced by water draining laterally through the fracture. Fig. 9 shows the effect of increasing the number of horizontal fractures. In all these simulations, the horizontal fracture aperture is 500 mm. The addition of a further horizontal fracture at zZ60 m depth causes an increase in concentration at depth, as water is drawn deeper into the aquifer to flow through the deeper flow path. As the number of horizontal fractures increases further, the influence of each fracture decreases, so that ultimately the concentration profile resembles that for the single vertical fracture, with no horizontal fractures. Where horizontal fractures are discontinuous, more complex flow fields can be created. For example, near the upstream end of a discontinuous

fracture, convergence of flowlines occurs as water is drawn towards the fracture from both shallow and deeper depths. Fig. 10 shows the CFC profile that is produced near the upstream end of a 500 mm horizontal fracture that extends throughout only half of the model domain. (The fracture is defined by zZ30 m, 0!x!1 m, 50 m!y!100 m, and the profile is located at xZ0.5 m, yZ50 m.) Convergence of flowlines causes an abrupt decrease in concentration (increase in apparent groundwater age) at 30 m depth. Fig. 11 depicts the vertical CFC profile generated by flow through a more complex network of vertical and horizontal fractures. The profile shown is for xZ 0.5 m, yZ50 m, and intersects six horizontal fractures, but does not intersect any vertical fractures. Nevertheless, the CFC concentration profile within the fractures at this location (solid circles) is similar to that for two-dimensional flow through parallel vertical fractures, with the same aquifer properties. Concentrations within the matrix are lower, but these would not be sampled by piezometers, owing to the low matrix hydraulic conductivity. Thus even complex fracture networks may result in environmental tracer profiles that can be simulated using models of parallel

Fig. 11. Simulations of vertical profile of CFC-12 concentrations in horizontal fractures (closed circles) and within the aquifer matrix (open circles) for a two-dimensional flow field comprising three 100 mm vertical fractures (xZ0.25 m, 0!y!100 m, 0!z!30 m; xZ0.75 m, 0!y!100 m, 20!z!80 m; xZ0.25 m, 0!y!100 m, 70!z!100 m) and seven 500 mm horizontal fractures (0!x!1 m, 45!y!75 m, zZ10 m; 0!x!1 m, 50!y!100 m, zZ20 m; 0! x!1 m, 0!y!45 m, zZ30 m; 0!x!1 m, 25!y!75 m, zZ 40 m; 0!x!1 m, 25!y!100 m, zZ50 m; 0!x!1 m, 0!y! 75 m, zZ60 m; 0!x!1 m, 45!y!100 m, zZ80 m).

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vertical fractures, and the parameters derived from these simulations may be reasonable estimates of the matrix and vertical fracture properties at the field site. They may yield little information, however, on horizontal fracturing. 4. Field example 4.1. Background The Clare Valley is located approximately 100 km north of Adelaide, South Australia, within the Northern Mount Lofty Ranges, and forms part of the Adelaide Geosyncline. The geology consists of low-grade metamorphic, folded and faulted rocks of Proterozoic age, mostly shales, siltstones, sandstones, dolomites and quartzites (Morton et al., 1998). The field sites described in this paper are all located on the west limb of the Hill River Syncline, where strata dip at high angles to the east, with the majority of fractures and bedding planes oriented vertically. Nested piezometers were installed between 1996 and 1998 at three sites within the Clare Valley, allowing the vertical distribution of water quality to be determined within the upper 100 m of aquifer. Each nest contains ten 50 mm PVC piezometers, with screen lengths ranging from 0.5 to 6 m, being longer in the deeper piezometers. Rather than using inflatable packers for sampling in open boreholes, we specifically chose to install nested peizometers with relatively short screens (and with cement plugs to seal the borehole between the piezometer screens) to minimise the likelihood of flow between sampling zones. At Pearce Road the watertable depth varies between approximately 4 and 7 m, and groundwater occurs with the Mintaro Shale. At Wendouree the watertable depth varies between approximately 3 and 7 m, and groundwater occurs within the Auburn Dolomite. At Neagles Rock Road the watertable depth varies between approximately 22 and 23 m, and groundwater occurs within sandstone and dolomitic marble of the Skillogalee Dolomite. 4.2. Methods At least two well volumes were purged from most piezometers prior to sampling. In some cases, however, very low hydraulic conductivities made

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purging difficult, and these were sampled after only one volume of the well casing and gravel pack had been removed. 14C and 13C were measured after first precipitating the dissolved inorganic carbon as BaCO3. 14C was analysed using a liquid scintillation counter and the direct absorption method. 3H concentrations were measured either by liquid scintillation counting after electrolytic enrichment, or by helium ingrowth. 36Cl/Cl ratios were determined by accelerator mass spectrometry. Above-background 36Cl concentrations (atoms LK1) were determined by subtracting the assumed background 36Cl/Cl ratio of 25!10K15 from the measured values, and then multiplying by the measured Cl concentration (Cook and Robinson, 2002). CFC-11 and CFC-12 concentrations were measured by gas chromatography. Measured concentrations of CFCs in groundwater have been converted to equivalent atmospheric concentrations using a recharge temperature of 16 8C. All samples described in this paper were collected between August 1996 and May 1998, except for CFC and 3 H samples from Neagles Rock Road that were collected in August 2003. Mean hydraulic conductivities of the aquifer were determined from single-well pumping tests carried out in each of the piezometers. At each site, the matrix hydraulic conductivity is much less than aquifer hydraulic conductivities, so that groundwater samples represent water from within the fractures. For further details of well construction, sample collection and analysis, and hydraulic properties of the aquifer the reader is referred to Cook and Simmons (2000) and Love et al. (1999). 4.3. Field results Fig. 12 depicts profiles of hydraulic conductivity, C, 36Cl, 3H and CFC-12. At each site, environmental tracers show a general decrease in concentration with depth. At Pearce Road, 14C activities above 30 m depth range between 92 and 101 pmC, decreasing to 20–30 pmc in the deepest two piezometers. d13C values (Table 2) range between K12 and K15‰, and show no significant variation with depth. The values are consistent with a d13C value for soil CO2 of K22‰, and a C8‰ fractionation between gaseous CO2 and dissolved bicarbonate. Thus, no corrections

14

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Fig. 12. Hydraulic conductivity determined from pumping tests, and 14C, 36Cl, 3H, CFC concentrations measured in piezometer nests at (a) Pearce Road, (b) Wendouree, and (c) Neagles Rock Road. Arrows indicate hydraulic conductivities that are outside the range shown on the figures. (36Cl was not measured at Neagles Rock Road.)

to the 14C values for chemical reactions appear necessary at this site. CFC-12 concentrations decrease gradually from approximately 370 pptv at 10 m to 300 pptv at 36 m. CFC-12 concentrations measured in

the two deepest piezometers are greater than zero, but this is believed to be due to contamination. It is possible that water with high concentrations of CFCs was introduced to the formation by drilling fluids used

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Table 2 Environmental tracer concentrations measured in nested piezometers in the Clare Valley, South Australia Piezometer

Screen depth (m)

14

C (pmC)

Pearce Road 36393-6 8–8.5 92.1G1.1 36393-5 10.85–11.35 92.9G1.1 36393-4 12.8–13.8 92.5G1.1 36393-3 15.2–16.3 97.3G1.1 36393-2 19.6–20.6 100.3G2.4 36393-1 25–26 94.5G1.2 36392-4 35–38 65.3G0.9 36392-2 75–80 22.0G4.8 36392-1 94.25–99.25 29.1 Wendouree 41497-6 9–12 88.3G2.1 41497-5 18–21 85.2G2.1 41497-4 27–30 78.2G1.6 41497-3 35–38 71.4G1.9 41497-2 44–47 28.2G0.9 41497-1 51.5–53.5 30.9G0.9 36385-4 63–66 2.6G0.8 36385-3 71–74 3.5G0.8 36385-2 80–86 6.6G0.8 36385-1 95–98 2.7G0.8 Neagles Rock Road 36387-6 26–26.5 85.6G1.4 36387-5 29–29.5 80.5G1.3 36387-4 34–34.5 79.5G1.4 36387-3 38.75–39.75 69.7G1.1 36387-2 44–45 69.4G1.3 36387-1 54–56 68.8G1.3 36388-4 63.2–66.2 52.8G1.1 36388-3 81.5–84.5 47G1.1 36388-2 95–100 49.3G1.1 a b c

13

C (‰)

K14.7 K14.4 K14.9 K14.7 K13.8 K14.0 K12.9 K13.0

K14.1 K13.9 K13.2 K12.8 K6.8 K6.7 K2.6 K2.7 K3.9 K3.0 K9.9 K11.0 K11.4 K11.5 K10.7 K10.7 K10.2 K10.0 K9.7

CFC-12 a (pptv)

CFC-11 a (pptv)

36

Cl (106 at/L) b

365 379 359 341 363 331 300 122 160

184 186 165 200 169 172 55 0 13

213 245 182

18 12 10

14 0 0 0 0 8

0 0 0 0 0 0

219 207

56 55

0.55G0.02

148

16

0.35G0.02

169

16

0.13G0.02

176G13 c 201G8 228G10 220G9 235G10 239G18 225G11 2G9 44G9c

3

H (TU)

2.2G0.2 2.4G0.2 2.7G0.2 c 3.7G0.2 1.85G0.2 c 0.5G0.03

111G18

1.6G0.05

93G19 157G26 76G21 76G21

1.3G0.04 0.9G0.03 0.3G0.02

K32G16

0.025G0.015

25G38

0.0G0.02

Assumes a recharge temperature of 16 8C. Estimated above-background 36Cl concentrations, based on a background 36Cl/Cl ratio of 25!10K15 (Cook and Robinson, 2002). Mean of two measurements reported in Cook and Robinson (2002).

during well construction or that air contaminated with CFCs was introduced by air blast methods used to remove these fluids during well development. (Noble gas samples collected shortly after drilling contained very large quantities of excess air.) Contamination of these deeper zones may also have resulted from borehole flow that occurred after drilling but before the installation of the piezometers (Shapiro, 2002). Such flows could move younger water into fractures at depth if the hydraulic head in the shallow fractures is greater than that in the deeper fractures. In the case of CFCs, contamination of water within the well

casing could also occur due to exchange with the atmosphere. Thus the relatively high values at depth are believed to be largely the result of incomplete purging of these low hydraulic conductivity zones both after drilling and prior to sample collection. 36Cl and 3H concentrations decrease below 40 m depth. Although concentrations of both isotopes in the deepest piezometer are significantly above analytical detection limit, this may also be due to contamination. Temperature and density logs and hydraulic conductivity testing indicate the presence of a large fracture at approximately 37 m (Cook and Simmons, 2000).

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The decrease in concentrations of all tracers beneath 30–40 m depth at this site may thus be due to the presence of this fracture. At Wendouree, 14C concentrations decrease gradually between 5 and 35 m depth, and then decrease abruptly between 35 and 40 m and between 50 and 55 m depth. These sudden decreases in concentration (and hence increases in apparent age) resemble those shown in Fig. 10, and appear to indicate the location of large horizontal or sub-horizontal fractures. The presence of fractures at these locations has been supported by electrical conductivity and temperature logs obtained at the site (Love et al., 1999). They are not apparent from the hydraulic conductivity data, presumably because the screen intervals of the piezometers (Table 2) did not intersect the fractures. d13C values range between K12 and K15‰ above 35 m depth, but decrease to between K2 and K4‰ below 50 m. The decrease in 14C concentration with depth at the Wendouree site thus appears to be in part due to chemical interaction with the aquifer materials, but also partly due to radioactive decay. CFC-12 concentrations are between 180 and 250 pptv above 30 m depth, but approach background below 40 m. 3H and 36Cl concentrations approach background below 60 m.

At Neagles Rock Road, 14C activities decrease from 85 pmc at 26 m depth to less than 50 pmc below 80 m, and follow a step-like pattern, similar to that observed at Wendouree (although the decrease in concentration at each step is less). d13C values range between K9.5 and K11.5‰. CFC-12 concentrations range between 150 and 220 pptv. CFC-12 concentrations measured in the deepest piezometer at Neagles Rock Road are similar to those measured in the deepest piezometers at Pearce Road, and both may be due to contamination. 3H concentrations decrease with depth, although all values are above analytical detection limit. 4.4. Simulations Fig. 13 compares the tracer profiles measured at Pearce Road with results of numerical modelling. Input concentrations of all tracers are as shown in Fig. 1, except that 14C activities have been multiplied by 0.78 to account for exchange with dead organic CO2 within the unsaturated zone. The value of 0.78 is calculated from the ratio of the 14C activity of CO2 in the modern atmosphere (115 pmC, Fig. 1), with the measured activity of 90 pmC in the soil atmosphere in South Australia (Leaney and Allison, 1986).

Fig. 13. Comparison of measured tracer concentrations at Pearce Road with results of FRAC3DVS numerical modeling. The model dimensions are 100!100!0.2 m, representing a vertical fracture spacing of 0.2 m. The vertical fracture aperture is 2bZ70 mm. An aquifer recharge rate of RZ70 mm yrK1 has been used, which is consistent with a vertical water velocity into the vertical fracture of VwZ200 m yrK1. The aquifer matrix is represented by two layers: an upper weathered layer of 6 m thickness (qmZ0.12, tZ0.35) overlying an unweathered layer (qmZ0.02, tZ0.035). A horizontal fracture with aperture of 3 mm occurs at 37 m depth. Field samples were collected between 1996 and 1998, and numerical modeling represents concentration profiles in 1997.

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The simulations use boundary conditions for the twodimensional flow field described in Fig. 6, with a model dimension of 0.2!100!100 m, representing a vertical fracture spacing of 0.2 m. The vertical fracture aperture is 2bZ70 mm. An aquifer recharge rate of RZ70 mm yrK1 has been used, which is consistent with a vertical water velocity into the vertical fracture of VwZ200 m yrK1. A horizontal fracture with aperture of 3 mm occurs at 37 m depth. The aquifer matrix is represented by two layers: an upper weathered layer of 6 m thickness (qmZ0.12, tZ0.35) overlying an unweathered layer (qmZ0.02, tZ0.035). These model parameters were selected to provide the best fit to the field data in a trial-and-error process. All of the parameters appear reasonable, and are consistent with measured fracture and matrix parameters at the site (Cook and Simmons, 2000). Identical model simulations for all tracers can be produced by reducing the vertical water velocity, and increasing the aperture of both fractures proportionally. Very similar model simulations for 3H, CFC-12 and 14C can also be produced with a vertical fracture spacing of 2BZ0.1 m, recharge rate RZ 140 mm yrK1, matrix porosities of qmZ0.24 and 0.04 and tortuosities of tZ0.09 and 0.009 for the unweathered and weathered zones, respectively. However, increasing the recharge rate will reduce the simulated 36Cl concentrations because the 36Cl fallout is diluted by the greater volume of water. (Presumably other satisfactory fits to 3H, CFC-12 and 14 C could also be produced by increasing R and qm and decreasing D and 2B by the same ratio.) It should be emphasised, however, that our intention is not to calibrate the model using the field data, but simply to demonstrate the reasonableness of the model in reproducing the observed tracer distribution. While if any particular tracer is considered alone it is possible to obtain significantly better fits than those shown in Fig. 13, it is more difficult to provide close fits to all of the tracers simultaneously. If only a single tracer is used, then aquifer parameters are not so well constrained. Of course, additional piezometers between 30 and 75 m depth would be required to properly evaluate the model. Nevertheless, the available data for 3H, CFC-12 and 14C is reasonably well reproduced by the model simulation. This is encouraging in view of the complex, heterogeneous nature of the aquifer

297

system. The poor fit for 36Cl is more interesting, with the measured concentrations greatly exceeding simulated concentrations at shallow depths. In a previous paper we were able to provide reasonable fits to the 36Cl and 3H data from Pearce Road (Cook and Robinson, 2002), but when these same model parameters are used to simulate CFC-12 concentrations, the fit to the field data is very poor. One explanation is that 36Cl is not behaving as a conservative tracer at this site, but is retarded by vegetation uptake and subsequent redeposition, or other mixing processes that occur within the unsaturated zone (Cook et al., 1992). (A similar observation has been made for 36Cl profiles obtained from Sturgeon Falls, Ontario; Milton et al., 2003.)

5. Discussion and conclusions In this paper, we have explicitly examined the effect of matrix diffusion on concentrations of environmental tracers (and hence on apparent groundwater ages determined with the tracers) as a first step towards providing a sound basis for quantitative interpretation of groundwater ages in fractured rock aquifers. In particular, we have used numerical simulations to show that one-dimensional models of flow and transport through vertical fractures may sometimes be used to represent flow through aquifers containing both horizontal and vertical fractures. In a previous paper (Cook and Robinson, 2002), we examined 3H and 36Cl profiles obtained in the Clare valley using models of parallel vertical fractures, and argued that vertical age gradients can be used to estimate vertical water fluxes even though fractures may be inclined. In this case, Vw simply becomes the vertical component of the water velocity. Vertical tracer profiles within the fractures are thus unchanged when plotted versus depth (rather than distance along the fracture). Thus, simple models of parallel, planar, evenly-spaced vertical fractures may be used to represent flow through more complex fractures geometries. If horizontal fractures are vertically well-connected, then apparent groundwater ages within the horizontal fractures will increase with depth, and

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the rate of increase will be related to the vertical water velocity. This is important, because samples from vertical fractures are unlikely to be obtained from vertical wells. If horizontal fractures are closely spaced, then groundwater samples will represent mixtures of water from the different fractures that intercept the well. However, because tracer concentrations decrease monotonically with depth, while this mixing may result in some smoothing of the tracer profiles, it will not seriously distort their shape. Vertical profiles showing increasing age with depth, however, may only be apparent if a sufficiently good connection between the horizontal fractures occurs throughout the flow system. In our simulations, we have used closely spaced vertical fractures with their axis aligned parallel with the flow direction to provide this connection. If the fractures are not wellconnected vertically, then groundwater ages may show no systematic variation with depth, and the age in each horizontal fracture will reflect its degree of connection to the shallow system. This appears to be the situation in the fractured carbonate aquifer of the Lockport Formation, southern Ontario (Zanini et al., 2000), for example. Due to the complexity of fractured systems, only a very small number of studies have used models that incorporated matrix diffusion processes to explain observed distributions of groundwater ages (Cook and Simmons, 2000; Shapiro, 2001; Cook and Robinson, 2002). Rather, most previous studies have used porous media models (e.g. AeschbachHertig et al., 1998). A number of these studies have invoked mixing between water of different ages to explain apparent discrepancies between groundwater ages obtained using different tracers (Talma et al., 2000; Plummer et al., 2001; Burton et al., 2002), but a porous media model is used to calculate the age of each end-member. Certainly, the relationships between concentrations of different environmental tracers produced by matrix diffusion processes (e.g. Fig. 5) are similar to those that might be produced by end-member mixing processes. The problem with such mixing models is that they fail to explain the processes by which the mixing takes place, and the calculated ages of the end-members have little physical meaning. Although requiring a greater number of parameters, matrix diffusion models are preferable because they seek to model physical

processes, and so the derived model parameters have some physical meaning. Representing a complex fractured aquifer as a system of coplanar, evenly-spaced, vertical fractures is perhaps akin to representing a heterogeneous sedimentary aquifer with a single value of hydraulic conductivity. It greatly reduces the number of parameters that need to be specified to describe the system. However, because of the large number of fracture and matrix parameters that control solute transport, measurements of apparent groundwater age made using a single groundwater tracer are still unable to uniquely constrain the system. Only when additional information is used are aquifer parameters able to be tightly constrained. For example, Cook and Simmons (2000) solved the simplified analytical solution describing transport of a tracer with exponentially increasing input concentration (3) simultaneously with the cubic law and Darcy’s Law, in an attempt to constrain fracture and matrix parameters. They found that the CFC-12 age gradient above 40 m at Pearce Road (0.1 yr/m) was consistent with the measured fracture spacing BZ0.08 m, and measured hydraulic conductivity of KZ0.1 m/day, together with a fracture aperture of 2bZ64 mm, matrix porosity qmZ0.02, effective diffusion coefficient DZ2!10K6 m2/yr, vertical water velocity within the fractures VwZ256 m/yr, and aquifer recharge rate of RZ102 mm/yr. However, they also observed that the estimated recharge rate was highly sensitive to the assumed values for the matrix porosity and matrix diffusion coefficient, and the measured fracture spacing. In this paper we have shown that aquifer parameters can be more tightly constrained when a number of different environmental tracers are considered. Because of the different patterns of temporal variation in their input functions, the use of both CFC-12 and 3H, for example, allows most aquifer parameters to be much more tightly constrained than is the case for CFC-12 alone. The relationships between CFC-12 and CFC-113 concentrations and between 3H and CFC-12 concentrations are most sensitive to the parameter B2qm/D. In a previous study, Shapiro (2001) attempted to reproduce the relationship between 3H and CFC-12 concentrations that had been observed by Busenberg and Plummer (1996) at Mirror Lake, New Hampshire.

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The author’s model considered a porous media overlying fractured rock, although the fractured rock component did not allow interaction between adjacent fractures (BZN). Thus, the author observed relatively low sensitivity of the relationship to model parameters. When the spatial distribution of the tracer concentrations is also considered (rather than just the relationship between concentrations of different tracers), then additional parameters can be constrained. The effect of changes in fracture and matrix parameters on the vertical distribution of apparent groundwater ages can be readily determined from simplified analytical solutions for one-dimensional flow through parallel fractures. Fig. 14 shows how the parameters that can be constrained using CFC-12 and 3 H profiles will vary with the value of the parameter B2qm/D. When the value of this parameter is between approximately 1 and 100 years, then both B2qm/D and pffiffiffiffiffiffiffiffiffi be constrained. When B2qm/D is large, qm D=Vw bpcan ffiffiffiffiffiffiffiffiffi then only qm D=Vw b can be constrained, and when B2qm/D is small, then the parameter Bqm/Vwb is constrained. (When B2qm/D is either small or large, then the relationship between CFC-12 and 3H will be determined only by the input functions of these tracers, and so the second tracer does not provide additional information and only a single parameter can be constrained.) However, in more complex, three-dimensional fracture networks, the value of the parameter B2qm/D is likely to vary spatially. In this case, determining the relationship between different model parameters is more complex. Inpsome ffiffiffiffiffiffiffiffiffi cases, it may be possible to constrain B2qm/D, qm D=Vw b and

299

Bqm/Vwb. This is equivalent to contraining Vwb, Bqm and D/B. Thus if the fracture aperture and spacing could be estimated using other means, 3H and CFC-12 profiles could conceivably constrain qm, D and Vw, and hence also R. Alternatively, if R can be constrained using 36Cl, as proposed by Cook and Robinson (2002), then 3H, 36Cl and CFC-12 may allow estimation of Vwb, B, qm, D and R. Field observations of groundwater age profiles obtained from nested piezometers in the Clare Valley show some of the features produced in the generic modelling. Observed tracer distributions show large intervals where concentrations vary relatively smoothly with depth, and short intervals where concentrations decrease rapidly with depth. The latter are believed to indicate the locations of major horizontal or sub-horizontal fractures. Numerical modelling of observed tracer distributions were attempted at one site, and reasonable fits to 14C, CFC-12 and 3H profiles were obtained using a model with identical, parallel vertical fractures intersected by a single horizontal fracture. We would not expect to precisely simulate the observed tracer distributions applying such a simple model to a highly heterogeneous environment. However, our ability to do so with reasonable success is encouraging, and provides some confidence that such simple models using idealised fracture distributions may have field application.

Acknowledgements The authors would like to thank Glenn Harrington, Sebastien Lamontagne, Niel Plummer and an anonymous reviewer for constructive criticisms of this manuscript. The work was funded by the Department of Water, Land and Biodiversity Conservation, CSIRO Land and Water, and Land and Water Australia (Project MAE1).

References Fig. 14. Parameters that can be constrained by vertical profiles of CFC-12 and 3H. When B2qm/D is between approximately 1 and 100 pffiffiffiffiffiffiffiffiffi years, then both B2qm/D and qm D=Vw b can be constrained. When pffiffiffiffiffiffiffiffiffi 2 B qm/D is large, then only qm D=Vw b can be constrained, and when B2qm/D is small, then the parameter Bqm/Vwb is constrained.

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