New dating method : Groundwater residence time estimated from the 4 He accumulation rate calibrated by using cosmogenic and subsurface-produced 36 Cl

Groundwater contains dissolved He, and its concentration increases with the residence time of the groundwater. Thus, if the He accumulation rate is constant, the dissolved He concentration in groundwater is equivalent to the residence time. Since accumulation mechanisms are not easily separated in the field, we estimate the total He accumulation rate during the half-life of Cl (3.01 × 10 years). We estimated the He accumulation rate, calibrated using both cosmogenic and subsurface-produced Cl, in the Great Artesian Basin (GAB), Australia, and the subsurface-produced Cl increase at the Äspö Hard Rock Laboratory, Sweden. He accumulation rates range from (1.9±0.3)×10−11 to (15±6)×10−11 ccSTP·cm−3·y−1 in GAB and ∗E-mail: mahara@rri.kyoto-u.ac.jp EPJ Web of Conferences DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences , 2012 , epjconf 20122 / 24 03002 (2012) 403002 SIF This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20122403002 (1.8 ± 0.7) × 10−8 ccSTP·cm−3·y−1 at Äspö. We confirmed a groundwater flow with a residence time of 0.7–1.06 Ma in GAB and stagnant groundwater with the long residence time of 4.5 Ma at Äspö. Therefore, the groundwater residence time can be deduced from the dissolved He concentration and the He accumulation rate calibrated by Cl, provided that He accumulation, groundwater flow, and other geoenvironmental conditions have remained unchanged for the required amount of geological time.


Introduction
Long-term isolation of high-level radioactive wastes in deep, stable geological formations has been proposed as an effective way to protect human life and the human genetic effects from radiation, and sequestration of large amounts of CO 2 in such formations has been proposed for counteracting anthropogenic carbon dioxide emissions to reduce global warming.The key requirements for long-term subsurface storage of both high-level radioactive wastes and CO 2 are geochemical and hydrological stability and groundwater stagnancy.
In this paper, we discuss the estimation of groundwater stagnancy by measuring the groundwater residence time.We propose the use of dissolved chlorine-36 ( 36 Cl) and helium-4 ( 4 He) as environmental tracers for estimating groundwater residence times longer than 2 million years, a period long enough for all cosmogenic 36 Cl in groundwater to decay or to reach secular equilibrium with subsurface production of 36 Cl.
The sources of 36 Cl in groundwater are cosmogenic and subsurface production.The latter occurs by activation of 35 Cl by weak neutrons released in (α, n) reactions via α particles released from the decay of U and Th series radionuclides contained in the rock.Dissolved 4 He in groundwater has three different sources: atmospheric radiogenic and mantle helium.The concentration of 4 He of atmospheric origin in groundwater is almost constant and is determined by salinity and temperature of the recharge water.The 4 He concentration in groundwater is not constant but increases as the residence time increases, owing to the addition of radiogenic 4 He and accumulation due to the degassing crustal He flux, which includes a mantle component.The amount of radiogenic 4 He added to groundwater depends on the intensity of α radionuclide decay of U and Th, which depends on their contents in the rock, the He release rate (usually assumed to be 1.0, which is a factor of the relative number helium released into groundwater to the helium produced in situ) from rock, and the rock's porosity [1][2][3].On the other hand, the accumulation rate from crustal He components depends on the diffusion rates of ancient He left in crustal rock and of the mantle component as well as advection by groundwater flow, which cannot be easily estimated in the field individually.However, the total He accumulation rate during the half-life of 36 Cl (3.01 × 10 5 years) can be estimated, provided that the 4 He accumulation mechanisms, groundwater flow conditions, and other geo-environmental conditions have not changed over the required amount of geological time.In addition, long residence times of groundwater on the order of millions of years can be estimated from the excess 4 He concentration and the 4 He accumulation rate.We can thus evaluate groundwater stagnancy at a candidate site for disposal of high-level radioactive waste or injection of CO 2 from the estimated groundwater residence time in combination with the results of other geo-hydrological investigations.
In this paper, we summarize a new, practical 4 He-36 Cl dating method developed as part of our research activities in the Great Artesian Basin (GAB), Australia [4,5] and at the Äspö Hard Rock Laboratory (HRL), Sweden [6,7].

Mechanisms of the 36 Cl-4 He dating method
Chloride ions contain a radioactive 36 Cl "clock", which has a half-life of approximately 3.0×10 5 years.Radioactive decay and subsurface production control the number of 36 Cl atoms in groundwater during its residence time in the aquifer, which begin when it enters the aquifer as recharge.The number of 36 Cl atoms in groundwater can be deduced from the residence time as follows [8]: where 36 Cl is the number of 36 Cl atoms per liter of groundwater; Cl (t) is the number of stable chlorine atoms per liter of water at time t; t is the residence time; λ is the decay constant of 36 Cl (2.31 × 10 −6 y −1 ); Cl 0 is the initial number of stable chlorine atoms in the recharged groundwater; R 0 is the initial cosmogenic 36 Cl/Cl ratio, measured by accelerator mass spectrometry, in the recharged groundwater; and R eq is the 36 Cl/Cl ratio at secular equilibrium within the rock matrix.
The first and second terms on the right-hand side of eq. ( 1) express the radioactive decay of the initial cosmogenic 36 Cl and the subsurface-produced 36 Cl of the initial stable chlorine in the recharged water, respectively.The third term expresses the addition of 36 Cl by dissolution from the rock matrix.As shown by eq. ( 1), the number of 36 Cl atoms in groundwater reaches a constant value after a period of at least five times the 36 Cl half-life if no chlorine is added from the rock matrix.On the other hand, the number of helium atoms dissolved in groundwater increases over time if the accumulation rate is constant and mixing, dilution, diffusion, and degassing from groundwater do not occur.The excess 4 He concentration is thus proportional to the residence time.In other words, the ratio (t = 4 He (ex) /α) of the dissolved excess 4 He concentration ( 4 He (ex) ) to the 4 He accumulation rate (α) can replace the residence time of the groundwater in eq. ( 1).Using the following equations ( 2) to (4), we can therefore rewrite equation (1) as eq.( 5) to estimate the relationship between 4 He (ex) /α and the 36 Cl/Cl ratio (R): where Cl m is the measured Cl ion concentration in groundwater, and R m is the measured 36 Cl/Cl ratio in groundwater.We can estimate the He accumulation rate α from the slope of the correlation straight line drawn by plotting 4 He (ex

Groundwater with mainly cosmogenic 36 Cl: The Coonamble Embayment in the GAB, Australia
The Coonamble Embayment is a small basin located at the south-eastern edge of the GAB.The confined aquifer consists of Pilliga Sandstone, a porous quartzose sandstone formation with 20%-30% porosity and high groundwater conductivity (i.e., 10 −5 m•s −1 ).Since the variation of the chloride ion concentration in the groundwater from the upstream to the downstream end of the surveyed flow line was very small, we can assume that the chloride ion concentration is almost constant.Since the ( 36 Cl/Cl) eq ratio, estimated as (8 ± 0.7) × 10 −15 from the average U (1.5 ± 0.2 μg•g −1 ) and Th (6 ± 2 μg•g −1 ) contents of the Pilliga Sandstone, is negligibly small compared to the initial cosmogenic ratio, the number of 36 Cl atoms in the recharge area is controlled by the cosmogenic source.We fitted equation ( 5) to the data (fig.1) and estimated the 4 He accumulation rate to be 6.9 × 10 −11 ccSTP g −1 water •y −1 (r 2 = 0.75) from the slope of the linear correlation line, using 24 mg•L −1 as the constant chloride concentration in the recharge area 241 × 10 −15 as the initial cosmogenic 36 Cl/Cl ratio and neglecting the secular equilibrium 36 Cl/Cl ratio in the Pilliga Sandstone.We thus estimated the longest residence time, at the downstream end of the survey line, to be 1.12 Ma.

Groundwater with mainly subsurface-produced 36 Cl:
The Äspö HRL, Sweden The HRL was constructed as the in situ testing site for disposal of high-level radioactive waste in the Äspö Island.The Äspö Island consists of 1.8-billionyear-old granite.Although tunnel excavation has caused severe groundwater disturbance, which is gradually extending deeper into the tunnel as modern Baltic seawater intrudes through fractures connecting to the surface, palaeohydrogeochemical conditions are partially preserved in deep, highly saline waters of seawater origin that remain unmixed.At Äspö, the dissolved 4 He concentration is positively correlated with the 36 Cl/Cl ratio, which have been measured every two years from 1995 to 2001, just like an activation curve observed in a nuclear reactor.Subsurface production is responsible for the majority of the 36 Cl and excess dissolved 4 He in interstitial groundwater in fractures.The secular equilibrium ratio of 36 Cl/Cl in rock was theoretically estimated to be (5.1 ± 0.8) × 10 −14 from the neutron flux intensity, a value comparable to the measured 36 Cl/Cl ratio in rock and groundwater.The degassing crustal 4 He flux was estimated to be 1.3 × 10 −6 (ccSTP cm −2 •y −1 ), which is only one-third the value (3.6 × 10 −6 ccSTP cm −2 •y −1 ) estimated in the GAB, Australia.The estimated 4 He accumulation rate therefore ranges from 6.8 × 10 −10 (the in situ accumulation rate) to 7.0 × 10 −9 (ccSTP g −1 water •y −1 ) (considering both in situ 4 He production and the degassing flux), if a constant accumulation rate of 4 He in groundwater is assumed.Thus, by comparing the subsurface 36 Cl increase with the 4 He concentration in groundwater, the 4 He accumulation rate can be determined for groundwater in which 36 Cl/Cl has reached its secular equilibrium value.In this way, an 4 He accumulation rate of (1.8 ± 0.7) × 10 −8 ccSTP g −1 water • y −1 could be es-timated from the relationship between the dissolved 4 He concentration and the 36 Cl/Cl secular ratio in rock without determining the magnitude of the degassing 4 He flux (fig.2).The longest residence time of the groundwater was then estimated to be 1.2-4.5 Ma in the area isolated from intrusion of modern Baltic seawater.

3.3
Groundwater with both cosmogenic and subsurface-produced 36 Cl: The central GAB, Australia We tested the validity of the method for dating groundwater that cannot be reliably measured by 36 Cl dating alone, based on 4 He accumulation rates calibrated with 36 Cl.We sampled groundwater from confined aquifers along six inferred regional groundwater flow paths in the GAB, and then selected three groundwater paths along which the decrease in 36 Cl was mainly controlled by cosmogenic 36 Cl radioactive decay without any significant increase in the chloride concentration, taking account for the condition of the secular 36 Cl/Cl ratio.The selected three paths have neither strong evaporation nor strong effects of mixing with chloride ion having a low 36 Cl/Cl ratio supplied from dissolution from aquifer rock and diffusion from adjoining aquitards.Along these paths, the 4 He concentration can therefore be approximated by eq. ( 5) in the semi logarithmic diagram with a constant accumulation rate.
The estimated 4 He accumulation rate ranged from (1.9 ± 0.3) × 10 −11 ccSTP cm −3 • y in the central GAB to (1.5 ± 0.6) × 10 −10 ccSTP cm −3 • y −1 in the western GAB (fig.3).These rates are from one-half to 1/15 the previously reported rates [9].However, our estimated rate of 1.51 × 10 −10 ccSTP cm −3 • y −1 in the western GAB is compatible with previous estimates of (0.2-1.9) × 10 −10 ccSTP cm −3 • y −1 based on 81 Kr ages [10].The residence time was estimated to be approximately 7×10 5 y, based on the 4 He accumulation rate near Lake Eyre.Finally, we can extend this method to estimate residence times after secular equilibrium of 36 Cl has been reached if the groundwater velocity and the 4 He accumulation rate are constant.

Conclusion
We can deduce groundwater residence times from the dissolved 4 He concentration and the 4 He accumulation rate calibrated by 36 Cl provided that 4 He accumulation mechanisms, groundwater flow, and other geo-environmental conditions have remained unchanged for the required amount of geological time.Furthermore, this proposed 4 He-36 Cl dating method can probably be used to estimate very long groundwater residence times of more than 2 Ma, which cannot be estimated by using 36 Cl alone, from the dissolved excess 4 He concentration, even after cosmogenic 36 Cl has decayed or subsurfaceproduced 36 Cl has reached secular equilibrium.

Figure 1 :
Figure 1: Groundwater with mainly cosmogenic 36 Cl (subsurface production of 36 Cl was neglected): correlation between the 36 Cl/Cl ratio and the excess 4 He concentration dissolved in groundwater of the Coonamble Embayment Basin in the GAB, Australia.

Figure 2 :
Figure 2: Groundwater with mainly subsurface-produced 36 Cl: correlation between the 36 Cl/Cl ratio and the 4 He concentration dissolved in groundwater.The theoretical growth curve of 36 Cl/Cl and the secular equilibrium range for the granites of Äspö are shown (after Mahara et al. [7]).

Figure 3 :
Figure 3: Groundwater with both cosmogenic and subsurface-produced 36 Cl: correlation between the excess 4 He concentration and the transformed function of the 36 Cl/Cl ratio along selected flow paths A, C, and D in the GAB, Australia (after Mahara et al. [5]).