Constraining the age of groundwaters that are clearly sub-modern or older can be important in establishing the long-term potential for aquifer recharge. For groundwater development and management policy, the question of renewability is most important. However, the exploitation of a nonrenewable resource can have serious political and sociological implications, as documented for the Mexico City (where the City centre has sunk by several meters), Northern Chile (where the fossil water resources of the Pampa del Tamuragal have been critically depleted by the City of Iquique) and in Libya where the exploitation of the Nubian sandstone aquifer to grow wheat in the northern Sahara desert have drawn water levels down several hundreds of meters. Determining whether a groundwater is 2,000 or 20,000 or even 200,000 years old is thus relevant to more than paleohydrologic and paleoclimatic studies.

Terminology for groundwaters that are older than "modern" as identified by the methods discussed above is important because of the implications for recharge. Fossil groundwaters have been recharged in the past by meteorological processes that no longer prevail (pluvial paleoclimates). However, paleogroundwaters in many regional flow systems may be old due simply to their low velocities and long flow paths, and may actually receive modern inputs in the recharge environment. None of these terms addresses the aspect of induced recharge under the stress of exploitation. While most paleogroundwaters are not part of active flow systems, heavy pumping can potentially induce flow from adjacent aquitards, poorly connected aquifers or from surface water sources.

Age dating old groundwaters begins with a determination that they are tritium-free, and so have no modern component (Chapter 7). Tritium-free groundwater can be considered sub-modern (recharged >50 years ago) or older, and have not incorporated any significant amount of modern water during discharge. The only absolute, albeit indirect, dating techniques for groundwater involve the decay (or in-growth) of long-lived radionuclides. By far the most routinely applied is ¹⁴C, which is transported as dissolved inorganic carbon (DIC) or dissolved organic carbon (DOC).

Geochemical techniques for dating, such as the extent of water-rock interaction, or the degree of salinization are also important, but not quantitative. The d¹⁸O-d²H signature of a paleogroundwater may also indicate age, by showing a change in climate controls on precipitation. The hydrodynamic characteristics of the groundwater flow system itself are important in estimating subsurface mean residence times. It is important to note that one technique alone can be misleading if applied without an understanding of the geochemical and hydrodynamic processes in the aquifer. A collaboration of methodologies is the best approach.

Stable Isotopes and Paleogroundwaters

Changes in temperature and precipitation patterns are the basis of climate change. Given the good correlation we see between isotopes in precipitation and groundwater, climate change should be recorded in fossil or paleogroundwaters. Temperate latitude climates have experienced significant changes in temperature since late Pleistocene time, whereas precipitation variability has dominated low latitude paleoclimate change. Such climate changes are manifested by a shift in the stable isotope content of precipitation, and in deuterium excess. This "paleoclimatic effect" is one of the most important tools in identifying paleogroundwaters.

In temperate regions, the dominant effect of climate change is in the position of precipitation on the local meteoric water line. Late Pleistocene paleogroundwaters from temperate regions (e.g. North America or Europe) will be isotopically depleted with respect to modern waters and shifted along the GMWL towards negative values. Fig. 8-1 shows the depletion in ²H for paleogroundwaters as compared with modern groundwaters for various regions of Europe. The recharge of such groundwaters can be affected by the distribution of ice sheets and permafrost. Canada was ice covered until about 10 to 15 ka B.P., and so paleogroundwaters generally post-date glaciation. Often they contain a component of isotopically-depleted glacial meltwater as remnant pore water (e.g. glacio-lacustrine clays studied by Desaulniers et al., 1981, and Remenda et al., 1994) or glacial meltwaters that have infiltrated Shield terrain during deglaciation (Douglas, 1997). Less commonly, they may have been recharged at an earlier interstadial or interglacial when the land was ice-free and could then be isotopically enriched (e.g. the Milk River aquifer; Hendry and Schwartz, 1988).

(Fig. to come)

Fig. 8-1 The d ¹⁸O and d ²H composition of Pleistocene groundwaters in Europe compared with the average of modern local precipitation and the GMWL. From regional data compiled by Rozanski (1985).

Unlike a depletion in ¹⁸O and ²H as observed for temperate region paleogroundwaters, the paleoclimatic effect in arid regions is manifested by a displacement of the meteoric water line. Recall that variations in humidity during primary evaporation affect the deuterium excess value, d. In arid regions like the Eastern Mediterranean and North Africa, the modern MWL is characterized by a deuterium excess value of 15 to 30‰. However, pluvial (humid) climates have characterized these regions in the past, e.g. the early Holocene pluvial which has been observed by high lake stands in North and East Africa (Street and Grove, 1979) and by lacustrine sediments found in the sand dunes of the Empty Quarter of Oman and Saudi Arabia (McClure, 1976).

Under such conditions, the meteoric water line is closer to the global line. So, pluvial-climate groundwaters tend to plot on or even below the GMWL. This has been observed in many deep artesian groundwaters from such regions that have been identified by other means (¹⁴C) to be paleogroundwaters (Fig. 8-2). Such paleogroundwaters are also characterized by a depletion in ¹⁸O and ²H with respect to modern waters. The significance of an observed paleoclimatic shift in groundwaters is that it shows them to be fossil, and not part of actively recharged flow systems. These resources are finite and their exploitation is mining.

(Fig. to come)

Fig. 8-2 Stable isotope signature of various paleogroundwaters from the Middle East and North Africa. Continental Intercalaire — Gonfiantini et al., 1974; Kufra and Sirte Basins — Edmunds and Wright, 1979; Sonntag et al., 1979; Negev — Gat and Dansgaard, 1972; Disi Sandstone — Lloyd, 1980; Umm er Radhuma, Saudi Arabia — Moser et al., 1978; Wadi Dawasir — Hötzl et al., 1980, Umm er Radhuma, Oman — Clark et al., 1987; Tibesti — Sonntag et al., 1979; Southern Sahara — Dray et al., 1983.

Natural variations in atmospheric ¹⁴C

A constant production and stable concentration of atmospheric ¹⁴C would require that the secondary neutron flux from cosmic radiation has been constant. In fact, it has not. Dendrochronology studies show strong variations in the ¹⁴C activity of atmospheric CO₂ during the Holocene. Counting rings provides a firm chronology (t in the dating equation). Measurement of a¹⁴C in tree rings by AMS, then provides a measure of a_o¹⁴C through time. Fig. 8-6 shows that ¹⁴C activity in the atmosphere has varied by over 10% during the Holocene. This record has been extended into the late Pleistocene by measuring the ¹⁴C content of corals (Bard et al., 1990). A reliable chronology of the corals was provided by U/Th disequilibrium dating by TIMS (thermal ionization mass spectrometry). This work shows that atmospheric ¹⁴C was a whopping 40% higher during the last glacial maximum. In addition to this systematic decrease since ca. 30,000 years ago are second-order excursions, the so-called "Suess wiggles" with ca. 200-year period (Suess, 1980). There is even an 11-year cycle to ¹⁴C production that matches the sunspot cycles.

Fig. 8-6 Composite of atmospheric ¹⁴C activity from tree rings, determined using their dendrochronological age (from Pearson et al., 1986), and from shallow marine corals, based on their U/Th age (from Bard et al., 1993). Holocene data show the ca 200-year period Seuss variations that are related to changes in solar output. The strong decrease from ca. 30,000 years BP to present are related to changes in the Earth’s geomagnetic field.

Why the variations? The short-term cycles have been related to variations in solar output (Stuiver and Quay, 1980; Damon et al., 1989). Satellite measurements of solar output since 1979 document variations that follow the 11-year sunspot cycle (Hoyt et al., 1992). Historical records of sunspot activity also show strong correlation with atmospheric ¹⁴C. However, they are weak compared to the long-term evolution in atmospheric ¹⁴C. This is due to the changing structure of the Earth’s geomagnetic field (Damon et al., 1989), which shields the Earth from much of the incoming flux of charged particles. This field is internally generated by the dynamo of the rotating/convecting Fe-Ni liquid outer core. Subtle variations in its dipole affect the flux of solar rays into the atmosphere and by consequence the production of ¹⁴C. These huge variations in a_o¹⁴C will affect the calculated age of a radiocarbon-dated sample. If the standard 100 pmC is categorically used, one expresses the age in radiocarbon years rather than calendar years.

Correction for Carbonate Dissolution

The approaches to correct apparent ¹⁴C water ages have evolved over the past 30 years from "statistical models" and "mixing models," to "process-oriented models." The following discussion presents a few of the published models. These are followed by the development of algorithms useful for correcting the various dilution processes. Calculations require some familiarity with alkalinity and aqueous geochemistry. A brief review was given in Chapter 5. References for further reading include such texts as Garrels and Christ (1965), Freeze and Cherry (1979), Stumm and Morgan (1996) and Drever (1997).

In the approaches presented here, the diluting source of carbon is presumed to be ¹⁴C-free. This is certainly the case with marine limestone, which is generally millions of years old. On the other hand, some soil carbonates may have measurable ¹⁴C activities. Conversely, the oxidation of old carbon in soils can generate soil CO₂ with a¹⁴C that is slightly less than modern. In such cases, the correction factor must be modified accordingly.

Recall from Chapter 5, that the carbonate evolution of many groundwaters involves the dissolution of soil CO₂ with the subsequent dissolution of carbonate:

Under closed system conditions, the stoichiometry of calcite dissolution by carbonic acid imparts about a 50% dilution to the initial ¹⁴C:

Fig. 5-6 shows the evolution of d¹³C_DIC towards enriched values as carbonate is dissolved. Under open system conditions, this is due to the increase in fractionation of ¹³C between soil gas and DIC as the pH rises (e¹³C_DIC-CO2 » 9‰ @ 25°C, Fig. 5-5). As the pH increases, the strong ¹³C enrichment between CO_2(soil) and HCO₃^– becomes increasingly important and the d¹³C_DIC goes up. However, it is still controlled by the d¹³C_CO2(soil) and a¹⁴C is still 100 pmC.

Under fully closed conditions, the increase in d¹³C_DIC is due solely to mixing between DIC from soil (d¹³C » –12 to –20‰) and marine carbonate (d¹³C » 0‰; Fig. 5-12). The closed system evolution of d¹³C_DIC is more dramatic because here the influence of calcite dissolution is felt. We can calculate ¹⁴C dilution by the additional enrichment in d¹³C_DIC from this dilution.

d¹³C mixing (d¹³C model)

Carbon-13 can be a good tracer of open and closed system evolution of DIC in groundwaters (Chapter 5). The large difference in d¹³C between the soil-derived DIC and carbonate minerals in the aquifer can provide a reliable measure of ¹⁴C dilution by carbonate dissolution. The d¹³C mixing model allows for incorporation of ¹⁴C-active DIC during carbonate dissolution under open system conditions, and subsequent ¹⁴C dilution under closed system conditions.

Pearson (1965) and Pearson and Hanshaw (1970) first introduced a d¹³C correction based on variations in ¹³C abundances. Any process that adds, removes or exchanges carbon from the DIC pool and which thereby alters the ¹⁴C concentrations will also affect the ¹³C concentrations. The q-factor was obtained from a carbon isotope-mass balance where:

However, Fig.5-5 shows that at higher pH values (pH 7.5 to 10) the DIC in equilibrium with the CO_2(soil) is enriched in ¹³C. This enrichment with respect to the original CO_2(soil) varies between 7 and 10‰ depending on temperature (Table 5-3). The d¹³C_soil is therefore replaced by a initial d¹³C value for DIC in the infiltrating groundwaters (d¹³C_rech) defined as:

d¹³C_rech = d¹³C_soil + e¹³C_{DIC-CO2(soil)}

Here, e¹³C_{DIC-CO2(soil)} is the pH-dependent enrichment between soil CO₂ and the aqueous carbon. An approximate value can be read from Fig. 5-5 or calculated from the distribution of DIC species and their respective enrichment factors (problem 3). The effect of this parameter is to control the amount of correction by the model according to the pH conditions during infiltration. The modified dilution model is then:

The main problem with this approach is that the enrichment factor that you choose for e¹³C_{DIC-CO2(soil)} can affect groundwater ages enormously. This enrichment factor is based on the pH of the groundwater during recharge, which a diligent hydrogeologist may measure in situ. However, this may not be an accurate representation of conditions in the past if the groundwaters are old and recharge conditions have changed. Let’s look at an example by varying the pH of the recharge waters. Remember that:

e¹³C_{DIC-CO2(soil)} = mCO_2(aq) · (e¹³C_{CO2(aq)-CO2(g)}) + mHCO₃ · (e¹³C_HCO3-CO2(g))

where m is the mole fraction of the two carbonate species and the enrichment factors, e¹³C, are from the fractionation equations in Chapter 5 (Table 5-2). The mole fraction of these DIC species is a function of pH (see Fig. 5-2 and equations on page 116). From Table 8-2, we see that the variations in corrected ages will vary by almost 50%.

Table 8-2 Example of the influence of initial pH on ¹³C and ¹⁴C ages in the ¹³C mixing model.
 

Input:	Case A	Case B	Case C
PH	6.0	6.4	7.0
mCO2(aq)/mHCO3–	2.5	1	0.25
d13CDIC (measured)	–12.5‰	–12.5‰	–12.5‰
d13Csoil (estimated)	–23‰	–23‰	–23‰
d13Ccarb (estimated)	0‰	0‰	0‰
a14C pmC	35	35	35
Calculated:
e13CDIC-CO2(g)	1.5	3.4	5.7
d13Cinf	–21.5	–19.6	–17.3
q	0.58	0.64	0.72
Ages (yr B.P.):
Uncorrected	8700	8700	8700
Corrected	4175	4990	5960

Thus, by varying the pH assumed for the infiltrating groundwaters by 1 pH unit, the age will vary considerably. However, this is only over the range from pH 6 to 7. If we find that in the recharge area groundwater pH values are neutral or higher there is little variation because the soil CO₂ exchanges mainly with HCO₃^–.

Case study of the Triassic sandstone aquifer, U.K.

Groundwaters of the Triassic age Bunter sandstone in the English East Midlands were studied by Bath et al. (1979) and provide a good example to study radiocarbon dating with relatively few geochemical complications. The Bunter aquifer is a non-marine quartzose sandstone confined above and below by marls and mudstones, and dips eastward under the North Sea from outcrops in the East Midlands (Fig. 8-9). The highlands of the outcrop region are situated just beyond the limit of glacier ice during the last glacial maximum, which is a consideration for the recharge of paleogroundwaters.

Fig. 8-9 Geological setting of the Triassic Bunter sandstone, eastern England (modified from Andrews et al., 1994).

The carbonate evolution of the groundwaters in a down-gradient direction is characterized by increases in mHCO₃^– and d¹³C_DIC due to interaction with minor carbonate in the fluvial sediments. Radiocarbon activities decrease from 40 to 60 pmC in the unconfined aquifer region to less than 2 pmC in the deep groundwaters. Fig. 8-10 shows the inversely proportional evolution of ¹⁴C and ¹³C. Shifts in ¹⁴C along the down-gradient trend are matched by an opposite shift in d¹³C, demonstrating that much of the loss of ¹⁴C is through geochemical reaction with carbonate in the sandstone matrix. The low a¹⁴C values in the recharge area are evidence that the carbonate system evolves under closed system conditions, and the ¹³C mixing model presented above is appropriate for age corrections.

Fig. 8-10 Down-gradient evolution of a¹⁴C and d¹³C in groundwaters from the Bunter sandstone. The inverse correlation of a¹⁴C with d¹³C demonstrates the loss of ¹⁴C by reaction with matrix rather than decay (Bath et al., 1979).

From these data, three groups of groundwaters can be identified: (i) tritium-bearing groundwaters with highly variable ¹⁴C and ¹³C contents (sites 1 to 12), (ii) tritium-free groundwaters with intermediary ¹⁴C contents (18 to 42 pmC), and (iii) tritium-free groundwaters with very low a¹⁴C (<5 pmC).

The ¹⁴C modelling results match nicely with d¹⁸O data which show a paleo-recharge effect (Fig. 8-12). The tritium-bearing waters have 760-year-old to "future" ages, which reflect the degree of uncertainty in the correction model. The intermediate (ii) groundwaters fall in an age bracket of 1300 to 8000 years B.P., and the deeper (down-gradient) groundwaters of group (iii) have modelled ages in the 19- to 35-ka range.

Fig. 8-12 Correlation of corrected ¹⁴C ages with d¹⁸O. Confidence limits on the ¹⁴C ages are ± 50%, and for d¹⁸O are ± 0.1‰. The strong shift in d¹⁸O to higher values signifies warmer climatic conditions at the beginning of the Holocene (after Bath et al., 1979). Paleotemperatures determined by Ar-Kr concentration relationships (recall Fig. 7-10) given in the inset diagram also document this paleoclimatic shift (after Andrews and Lee, 1979).

Comparison with d¹⁸O data substantiate the radiocarbon ages (Fig. 8-12). The Holocene groundwaters have d¹⁸O values similar to or enriched over modern groundwaters. Paleotemperatures established by Andrews and Lee (1979) from the relative concentrations of argon and krypton in these groundwaters (inset in Fig. 8-12) show that the Holocene was as warm as today or warmer (in the early Holocene hypsithermal). By contrast, the deeper groundwaters with very low ¹⁴C activities were recharged under the cooler climatic conditions of the late Pleistocene.

The tremendous amount of geochemical reaction in the Pleistocene samples has unlikely been fully accounted for by the d¹³C correction model. In question is the value selected for d¹³C_carb. In calculating the ages in Fig. 8-12 this parameter was assigned the typical marine value of 0‰, although the authors measured values averaging –7‰ in the carbonate cement of the sandstone aquifer. Using this value shifts the age of the group (iii) groundwaters to between 12 and 30 ka (although the ³H groundwaters jump to future ages of a few thousand years). A more accurate assessment likely falls somewhere in between, and for this reason errors of ±  50% are indicated in Fig. 8-12. This would account for the apparent hiatus in groundwater recharge during the period of deglaciation between 10 and 20 ka.

¹⁴C Dating with Dissolved Organic Carbon (DOC)

The development of AMS (accelerator mass spectrometry) for the precise measurement of very small amounts of carbon (<5 mg C) now allows measurement of ¹⁴C in DOC. Like DIC, ¹⁴C-active DOC is derived from the groundwater in the soil zone. Unlike DIC, however, it is unaffected by dilution during the host of carbonate reactions experienced by groundwater, and so provides an independent method to date groundwater.

From the discussion of DOC in Chapter 5, soil-derived organics are dominantly humic and fulvic acids. However, subsurface sources of humic substances, such as buried peat or brown coal, are not uncommon (e.g. Aravena, 1993; Geyer et al., 1993), and it is essential to establish a pedogenic rather than geogenic origin. The initial ¹⁴C activity of the soil DOC may also be less than 100 pmC. As soils develop over thousands of years, a component of their organic carbon (some of the humic compounds) can be sub-modern. For this reason, it is the fulvic acid fraction which is generally derived from the most recently decomposed vegetation, that is used for dating.

Dating groundwaters with DOC is not without methodological difficulties. Its concentration in groundwater is typically below 1 mg-C/L, which makes sampling difficult. DOC is usually stripped from 100 L or more of groundwater, using ion exchange resins, and then eluted in the laboratory and fractionated into humic (HA) and fulvic acid (FA) components. The FA is then analysed by AMS.

 
The initial ¹⁴C activity in fulvic acid (a_o¹⁴C_FA)

The FA fraction of DOC is more labile than HA, but can also be derived from older sources of organic carbon in the subsurface. Like DIC, an initial ¹⁴C activity that is less than 100 pmC must be used in the decay equation. Data are presented in Fig. 8-19 from five German sites (Geyer, 1993) and three Canadian sites (Wassenaar et al., 1991), where FA was collected from shallow, tritium-bearing groundwaters. The a¹⁴C_FA measurements range between 100 pmC to as low as 38 pmC, with most in the 75 to 100 pmC range. Recall that if groundwaters contain tritium, any atmospherically-derived carbon fractions should have 100 to ~130 pmC from "bomb" ¹⁴C, although a lag of several years to decades for the formation of humic substances from dead vegetation can be expected.

Fig. 8-19 The ¹⁴C activity of FA in modern, tritium-bearing groundwater from Quaternary sediments. Sedimentary organic carbon (SOC) in some aquifers is a source of at least part of the FA. The aquifer derived FA has lower ¹⁴C activities (data from Wassenaar et al., 1991; Geyer et al., 1993)

Clearly, FA is a mixture of variable-aged organic carbon sources in the soil. Some is also derived from sedimentary organic carbon (SOC) in the aquifer. Where redox conditions evolve through NO₃^– reduction, SO₄^2– reduction and fermentation, bacteria may preferentially use the younger (labile) FA — a process that would reduce the ¹⁴C content of the residual FA sampled in the groundwater. Just as we do for ¹⁴C dating with DIC, this less-than-modern initial ¹⁴C activity in the FA (a_o¹⁴C_FA) must be taken into account in the decay equation.
 

⁴He and old groundwater

The ingrowth of helium from radioactive decay in crustal waters offers a qualitative measure of time. The uranium decay series is dominated by a (plus b^–) decay (Fig. 8-26). During the decay of ²³⁸U to ²⁰⁶Pb, 32 atomic mass units are lost, which is accounted for by 8 a particles. These are 2n, 2p, nuclei that pick up two electrons and become ⁴He atoms. The ²³²Th decay series also produces a particles. Another source of crustal helium is through the fission of ⁶Li by neutrons in high U and Th rocks:
 

⁶Li +n ® a + ³H ® ⁴He + ³He + b^–

The concentration and ³He/⁴He ratio of atmospheric helium (Table 8-9) represents a dynamic steady-state of He diffusion from the mantle through spreading ridges plus crustal ⁴He, and loss through planetary helium escape (Nicolet, 1957). Mantle helium is primordial, incorporated during planetary accretion, and is the largest reservoir of ³He (Kurtz and Jenkins, 1981).

By contrast, crustal helium is highly enriched in ⁴He and greatly exceeds the He concentration in air-saturated water. The ³He/⁴He ratio is often expressed as a fraction of that in air; and thus, R/R_air for crustal fluids = 0.007 to 0.022 (Andrews, 1985). Rocks rich in U, Th and K can have ³He/⁴He < 10^–10 with complementary increases in total He (Clarke and Kugler, 1973).

Table 8-9 Helium abundances and isotope ratios in different reservoirs (R = ³He/⁴He)
 

Source	He concentration	3He/4He	R/Rair
Atmosphere	5.24 ppmv	1.38 · 10–6	1
Surface water	4.5 · 10–8 cm3 STP g–1	~1 · 10–6	~1
Crustal fluids	10–7 to 10–4 cm3 STP g-1	~10–8 to <10–10	0.007 to 0.022
Mantle He	up to 2.7 · 10–5 cm3 STP g-1	1 to 3 · 10-5	7 to 21

 

Dating groundwaters by He in-growth requires that some details of the host aquifer be known. Corrected for atmospheric helium gained during recharge (Table 7-10), measured ⁴He should then reflect the groundwater residence time. The helium production after time t can be described by (Andrews et al., 1982):
 

[ He] = r f ^–1 t (1.19 · 10^–13 [ U] + 2.88 · 10^–14 [ Th]

where: [ He] is the groundwater helium content in cm³ STP g^–1 water

r is the rock density in g cm^–3

f is the fractional porosity of the rock

[ U] and [ Th] are the uranium and thorium contents of the rock matrix in ppm

No ³He measurements were made in these studies, although such data would have most likely documented that indeed radiogenic helium was added to the groundwater. Recall that the ³He/⁴He ratio is strongly dependent on the lithium contents of the aquifer rocks and, therefore, can potentially indicate where the helium was produced, if different rock types are present (Andrews, 1985; 1987). As these two aquifers show, diffusion of He from other strata must be taken into account. Nevertheless, the systematic increase in He along the flow gradient, whether from decay within the aquifer or diffusion from adjacent strata, provides a useful tool to estimate groundwater age. Empirical or semi-quantitative corrections for diffusion can extend the He-dating range well beyond that of ¹⁴C.

Fig. 8-26 He contents in two confined aquifers (Blumau fluvial sand in southeastern Austria and Bunter sandstone in the East Midlands, England) correlated with their corrected radiocarbon ages. Arrows indicate "greater than" ages (data from Andrews et al., 1983).

A cautionary note should be made with respect to helium accumulation in regions of tectonic activity. Active faults and other crustal discontinuities can act as conduits for migration of helium, which is a highly diffusive gas. In geothermal groundwaters from the Cordillera of western Canada, He concentrations up to 1.760 · 10^–5 cm³ STP g^–1 H₂O were measured in thermal waters with modern ¹⁴C activities and measurable ³H. The low ³He/⁴He ratio of 7.8 · 10^-8 (R/R_air = 0.06) signifies also a strong radiogenic He source. These strong inputs of crustal ⁴He to a young groundwater implicated mixing with He migrating along a regional thrust fault underlying the flow system (Phillips, 1994).

Problems and Solutions

There are three ways to constrain groundwater ages with these data:

(i) Tritium to distinguish between modern and submodern groundwater. The first group of data all contain tritium and so are modern, whereas the second set is submodern.

(ii) The stable isotope data can be plotted, and show that the modern waters plot on or close to the LMWL. However, the ³H-free data all show a paleoclimatic effect, as they plot below the modern meteoric water line, but not on an evaporation slope. These submodern groundwaters were recharged under a cooler paleoclimate. With some background in the Quaternary climates in this region, you would be able to say that prior to about 9 ka, this region experienced a cooler and wetter climate. This accounts for the lower deuterium excess and more depleted isotope values.

(iii) The radiocarbon data provide the third line of evidence for constraining groundwater ages. The ³H-bearing groundwaters have ¹⁴C activities that average 44.8 pmC. A ¹⁴C dilution factor can be determined from the relationship:
  For the nuclear era (modern tritium levels) the activity of atmospheric CO₂ (a¹⁴C) can be estimated at about 120 pmC. Thus, the carbonate dilution factor would be 44.8/120 = 0.37. The ¹⁴C ages calculated using a¹⁴C_atm = 100 pmC give groundwater ages varying between 8.0 and 14.4 ka, which fit with the stable isotope and paleoclimate data.

 

 

2. What would be the isotopic composition of a groundwater that has recharged under open system conditions with respect to the soil CO₂ with pH 6.8 and at temperature 10°C.
  This question follows the same solution path as problem 5 in Chapter 5. However, calculations of this type are important in ¹⁴C dating, as establishing the DIC-d¹³C conditions in the recharge area are critical for some of the correction models. The solution requires establishing the distribution of DIC species to weight the CO_2(g) - DIC fractionation factors. Because the pH is acidic, CO₃^2– is not important, and so only the distribution of bicarbonate and carbonic acid are determined. Using data from Tables 5-2 and 5-3:
 
  At pH = 6.8, the DIC species ratio is:
 
  Assume that molality m is equal to activity [ ] for at low salinity, and that H₂CO₃ is essentially CO_2(aq). As only the relative concentration of DIC species are needed, we can assume that mDIC = mCO_2(aq) + mHCO₃^– = 1. The relative concentrations of HCO₃^– and CO_2(aq) are then:
  mHCO₃^– = 1 – mCO_2(aq)

 

Thus the fraction of: and the fraction of HCO₃^– = 0.69

Accordingly, the d¹³C of the DIC for this water is then determined from the isotope mass balance equation using e¹³C values from Table 5-3:
 

d¹³C_DIC = 0.31 (d¹³C_CO2(g) + e¹³C_{CO2(aq)–CO2(g)}) + 0.69 (d¹³C_CO2(g) + e¹³C_{HCO3–CO2(g)})

= 0.31 (–23 – 1.1) + 0.69 (–23 + 9.6)

= –16.7‰
 

This value is important in the d¹³C mixing model, as it represents the d¹³C of the DIC before any closed system dissolution of carbonate (d¹³C_rech). The difference between this value and the measured d¹³C_DIC for the sample is a measure of closed system ¹⁴C dilution.
 
  3. Calculate the d¹³C of the CO_2(g) in equilibrium with a water whose DIC (2.1 ppm) has a d¹³C = –1.5‰ and a pH of 6.8 at 15°C. Determine the appropriate enrichment factors from equations in Table 1-5. What is a likely source of this CO₂?
  The d¹³C_CO2 is a theoretical value for the CO_2(g) that would be in equilibrium with this water. Whether it exists or not depends on the hydrogeological setting. The calculation is the reverse of the problem above, and depends on the relative proportions of the three principal DIC species, CO_2(aq), HCO₃^– and CO₃^2–, which is pH dependent. We can take a short-cut and discount any contribution from CO₃^2– because the pH is well below 8.4 where carbonate becomes important.

We can now use the ¹³C mass balance equation using enrichment factors for e¹³C_{HCO3–CO2(g)} and e¹³C_{CO2(aq)–CO2(g)} that are calculated from the equations in the Table on the front cover, or found in Table 5-3:
 

d¹³C_DIC = 0.71(d¹³C_CO2(g) + e¹³C_{HCO3–CO2(g)}) + 0.29(d¹³C_CO2(g) + e¹³C_{CO2(aq)–CO2(g)})

–1.5 = 0.71 (d¹³C_CO2(g) + 9.0) + 0.29 (d¹³C_CO2(g) – 1.1)

d¹³C_CO2(g) = –7.57‰
 

A source of CO₂ with this d¹³C value and such low concentration is most likely to be atmospheric.

 

4. Results of analyses for tritium and a¹⁴C_DIC in a groundwater sample submitted to you for interpretation are 10.8 TU and 18.5 pmC. How would you proceed and what additional data or observations would you request for a meaningful interpretation?
  Discounting unreliable analyses, there are only two possibilities for the age of this groundwater sample. It is either (1) a mixture of a modern meteoric water with an old groundwater that has low ¹⁴C_DIC activity or (2) it is a modern water that has had its ¹⁴C_DIC significantly diluted by reaction in the aquifer. Your interpretation should be made only with these additional information:

• A good description of the sampling location and aquifer configurations to determine whether there is the possibility of mixing between modern and paleo-groundwaters.
• Stable isotope data for the water to see whether there is a paleo-signal to indicate old water.
• Carbonate dissolution (calcite and dolomite) is unlikely to impart much more than a 40 to 60% dilution on the initial ¹⁴C activity, and so other geochemical processes must occur (e.g. sulphate reduction or methanogenesis) if the tritium data are valid and the groundwater is indeed young.

(i) Calculate the uncorrected age of this groundwater, and the corrected age using the ALK and STAT models, and compare the results.
  The uncorrected age uses only the decay equation, the measured a¹⁴C, and a value of 100 pmC for the ¹⁴C activity of atmospheric CO₂ at the time of recharge. This gives:

 

The statistical correction model applies a dilution factor of 0.65 to 0.75 for karst or carbonate systems. Using a median value of 0.7, we get:
 

 

The alkalinity model ALK calculates a dilution factor based on the pH and DIC speciation:
 
  From the pH and HCO₃^– content, we can calculate the distribution of DIC species:
  mHCO₃^– = 119/61000 = 0.00195

 

The dilution factor is then:
 

 

The uncorrected model gives the greatest groundwater age, as it assumes that the difference between the measured a¹⁴C and a¹⁴C_atm is due exclusively to decay. The uncorrected age represents a open system conditions where the dissolved carbonate has fully exchanged with ¹⁴C-active soil CO₂. The statistical model is based on average dilution found for this type of terrain, and so may have some validity if this is a typical groundwater. The alkalinity correction model provides the greatest correction, and actually overcorrects to produce "future" ages. This model assumes closed system conditions where the correction is proportional to the amount of carbonic acid consumed to dissolve carbonate. Clearly, carbonate dissolution for this sample has not taken place under completely closed system conditions.
 
  (ii) Could these results be explained as an open system for CO₂ uptake and calcite dissolution, and if so, what is the "age" of the water?
  The open system condition can be tested by calculating the d¹³C_DIC value for the given pH and d¹³C of the soil. Recall that during open system carbonate dissolution, exchange with the soil CO₂ dominates and so the isotopic composition of the carbonate does not influence the DIC. First, use pH to determine the distribution of carbonate species that exchange with the CO₂. The pH is less than 8.4 and so only CO_2(aq) and HCO₃^– are important. Using data from Tables 5-2 and 5-3 we get:

and using mole fractions (m_f):

m_fCO_2(aq) + m_fHCO₃ = 1

Thus, m_fCO_2(aq) =  = 0.027 and mHCO₃^– = 0.973
 

d¹³C_DIC-calc = 0.027(d¹³C_CO2(g) + e¹³C_{CO2(aq)–CO2(g)}) + 0.973 (d¹³C_CO2(g) + e¹³C_{HCO3–CO2(g)})
  = 0.027 (-21 – 1.1) + 0.973 (-21 + 7.9)
  d¹³C_DIC-calc = –13.34‰
  This value is essentially the same as the measured value (–13.5‰), and so yes, this can be explained by open system conditions. However, one must be careful because this assumes that the measured pH and the carbonate system has not evolved during the residence time of this groundwater in the saturated zone of the aquifer. If the pH was lower in the recharge area, then this calculated d¹³C_DIC would be lower than the measured value. The difference would reflect reaction in the aquifer (dolomite dissolution, matrix exchange etc.).

If recharge has taken place under fully open system conditions, then the ¹⁴C of the DIC was fully exchanged with the ¹⁴C in soil CO₂ and was 100 percent modern at the time of recharge. In this case, q = 1 and direct application of the decay equation is valid:
 

= 4942 years
 

  (iii) Assume that a pH of 6.25 and DIC of 0.96 mmoles (at P_CO2 = 10^–1.8) were measured for the infiltrating groundwaters in the recharge area, prior to closed system dissolution of calcite. Calculate the age of these groundwaters using the d¹³C mixing model.
  The distribution of DIC species is calculated in the same way as in (ii) only using pH 6.25 instead of the measured pH. This gives a HCO₃^–/CO_2(aq) ratio of 0.79, and so the relative fractions of DIC are 0.44 as HCO₃^– and 0.56 as CO_2(aq). From the isotope mass balance equation, this gives a value for d¹³C_rech of: d¹³C_rech = 0.56 (d¹³C_CO2(g) + e¹³C_{CO2(aq)–CO2(g)}) + 0.44(d¹³C_CO2(g) + e¹³C_{HCO3–CO2(g)}) = 0.56 (-21 – 1.1) + 0.44 (–21 + 7.9)

= –18.14‰

The dilution factor is then calculated from the ¹³C mass balance equation:

Using this dilution factor, we get a corrected age of:

This corrected age is much younger than the open system (uncorrected) groundwater age, and reflects the uncertainty in the assumption of recharge conditions (open vs. closed system, and the open system pH-P_CO2 conditions).
 

(iv) What is the corrected age using the chemical mass balance models (CMB-Chem and CMB-Alk) again presuming that carbonate dissolution took place under closed system conditions?
  Recall the formulation of the chemical mass balance correction:
 
  mDIC_rech is calculated from pH and P_CO2 in the recharge area during CO₂ uptake, although the value for DIC is given ( 0.96 mmoles). The final DIC is then:
  mDIC_final = mDIC_rech + [mCa²⁺ + mMg²⁺ – mSO₄^2– + ½(mNa⁺ + mK⁺ – mCl^–)] = 0.96 + [0.62 + 0.11 – 0.0125 + ½(0.74 + 0 – 0.25)

= 0.96 + 1.21

= 2.17
 

and:   The CMB-Chem modelled age is then:
 
  Dilution using the CMB-Alk model is calculated using mDIC_final = mDIC_meas:
 

 

These models give future ages, which means that they are over-correcting. Either we have underestimated amount of DIC gained in the recharge area (mDIC_rech) or carbonate dissolution did not take place exclusively under closed system conditions. Increasing the P_CO2 or the pH would increase mDIC_rech to a level where these models no longer give future ages. On the other hand, the assumption of closed system conditions is not consistent with the d¹³C data, as was shown above.
 
  (v) Test the age correction for this groundwater sample using the Fontes-Garnier model of carbonate dissolution and matrix exchange.
  The F-G model calculates the contribution from carbonate from geochemical data, as we did above for the CMB-Chem model:

mDIC_carb = mCa²⁺ + mMg²⁺ – mSO₄^2– + ½(mNa⁺ + mK⁺ – mCl^–)

= 0.972

This model then calculates how much of this carbonate has exchanged with the soil CO₂ under open system conditions, using a ¹³C mass balance:

 

  The dilution factor is then calculated from these various proportions of DIC:
 
    This gives an corrected age of:
 
  The Fontes-Garnier model is often the most representative as it does not require any estimates of the pH and P_CO2 conditions in the open-system recharge environment. It uses only the measured pH and DIC values and the model of carbonate dissolution to calculate a dilution factor. Thus, it accounts for both open system and closed system carbonate dissolution.

A summary of the model ages is useful for comparision:

• The first process which imparts a dilution on the ¹⁴C_DIC is the dissolution of carbonate.
• The Mg²⁺ suggests that this was followed by dolomite dissolution.
• The dissolved sulphide (HS^–) and low sulphate indicates that sulphate reduction is an active process and adds a third dilution to the ¹⁴C content of the DIC.
• The d¹³C_DIC value is very depleted, which is consistent with sulphate reduction via an organic substrate. Calcite is super-saturated in this groundwater because sulphate reduction is an alkaline reaction that adds to the DIC pool.
• The strong enrichment in d³⁴S also signals sulphate reduction.
• A correction model for this water would rely on data from the recharge area to determine the dilution from carbonate dissolution that occurred under closed system conditions. Alternatively, this could be estimated from a ¹³C mass balance, provided the dilutions from dolomite dissolution and sulphate reduction can be reliably quantified.
• Dolomite dissolution can be calculated from the Mg concentration, providing there is no geological evidence for other sources of Mg.
• The ¹⁴C dilution from sulphate reduction can be calculated from the amount of HS^– produced, assuming that none was lost from solution. The redox state of the DOC (usually 0) is required (i.e. usually 2 moles of DOC produce 1 mole HS^–).

(i) Determine a corrected age for this water using the d¹³C model and the Fontes Garnier model and compare your results with the uncorrected age.
  Using the d¹³C model requires an estimate of the recharge pH, which determines the DIC_rech and d¹³C_rech. As this model ignores the influence of sulphate reduction (which is a source of ¹³C-depleted DIC) the low d¹³C_DIC would then suggest that recharge occurred under low pH conditions where mHCO₃^– was low: Let’s assume that carbonic acid (CO_2(aq)) dominates in the recharge waters and is derived from a soil CO₂ with d¹³C = -23‰ at 15°C: d¹³C_rech = d¹³C_CO2(g) + e¹³C_{CO2(aq)–CO2(g)}

= -23 – 1.1

= -24.1

 

 

Using the Fontes-Garnier model, we get:

mDIC_carb = mCa²⁺ + mMg²⁺ – mSO₄^2– + ½(mNa⁺ + mK⁺ – mCl^–)

= 3.00
 
 
  The dilution factor is then calculated from these various proportions of DIC:
 
  This gives a corrected age of:
 
  which is greater than the uncorrected age:
 
  Clearly our two process models do not represent the true geochemical system. The d¹³C model, we know, is incorrect because sulphate reduction has diluted the DIC pool with DIC derived from oxidation of organics, which is why the measured d¹³C_DIC is so low. The correction it gives is minimal and so the groundwater age is overestimated. The Fontes-Garnier model gives a highly over-estimated age because it uses parameters that are influenced by sulphate reduction (i.e. d¹³C_DIC, mSO₄^2–, and mDIC).
 
  (ii) Apply a correction for sulphate reduction, assuming that the DOC in the sample has a redox state of 0 (i.e. DOC of the form CH₂O) and is ¹⁴C-free.
  A correction for dilution by DIC contributed through sulphate reduction can be derived from the amount of sulphide produced, providing none has been lost from solution. Sulphate reduction can be represented by the general reaction:

2CH₂O + SO₄^2– ® H₂S + 2HCO₃^–

The correction for sulphate reduction can then be approximated by:
 

  This algorithm assumes that bicarbonate has remained unchanged during sulphate reduction, which is valid if calcite precipitation has maintained DIC relatively constant.

A correction for carbonate dissolution prior to sulphate reduction must now be made. Using 2mHS^– as a measure of the amount of organic carbon added to the DIC pool by sulphate reduction, the d¹³C value produced by carbonate dissolution prior to sulphate reduction can be estimated (d¹³C_DIC-rech). The ¹³C content of the organic substrate must be measured or assumed. A value for fixed organic carbon of d¹³C_org = –26 ± 2‰ is reasonable.
 

 

and so the d¹³C value for the DIC after carbonate dissolution, but prior to sulphate reduction would be:

d¹³C_DIC-rech = –10.86‰

We can now use this value to estimate ¹⁴C dilution by carbonate dissolution prior to sulphate reduction, using either the Fontes-Garnier model or the d¹³C mixing model.

The Fontes-Garnier model requires a modification to the amount of sulphate used to correct mCa²⁺ and mMg²⁺. The value used in the model must be corrected to the sulphate content prior to sulphate reduction, by adding in the amount of HS^–. Thus:
 

mDIC_carb = mCa²⁺ + mMg²⁺ – (mSO₄^2– + mHS^–) + ½(mNa⁺ + mK⁺ – mCl^–)
  = 1.03 Now calculating mDIC_CO2exch prior to the influence of sulphate reduction:

 

  This value is close to 0, suggesting that there has been little CO₂ exchange, i.e. recharge under relatively closed system conditions. The dilution factor for carbonate dissolution is then close to 0.5:
 

and 
 

A corrected age for this groundwater sample, within the limits of the assumptions we have included in these calculations, is determined using a combined correction factor:
 

q_t = q_H2S ´ q_F-G = 0.51 ´ 0.44 = 0.22
  which gives an age of:
 
  Considering that most geochemical processes in the subsurface conspire to dilute ¹⁴C and artificially "age" groundwaters, a strong correction such as we have calculated here is warranted. The process can be refined by varying certain parameters within their range of error (e.g. the measurement of mHS^–). However, modelled ages must be evaluated in the context of other hydrogeological and paleoclimatic data (such as d¹⁸O and d²H) before being considered reliable estimates of subsurface residence time.