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 ao14C 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 Earths 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 Earths 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 ao14C 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 d13CDIC 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 (e13CDIC-CO2 » 9 @ 25°C, Fig. 5-5). As the pH increases, the strong 13C enrichment between CO2(soil) and HCO3 becomes increasingly important and the d13CDIC goes up. However, it is still controlled by the d13CCO2(soil) and a14C is still 100 pmC.
Under fully closed conditions, the increase in d13CDIC 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 d13CDIC is more dramatic because here the influence of calcite dissolution is felt. We can calculate 14C dilution by the additional enrichment in d13CDIC 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:
d13Ccarb = d13C of the calcite being dissolved (usually close to 0)
However, Fig.5-5 shows that at higher pH values (pH 7.5 to 10) the DIC in equilibrium with the CO2(soil) is enriched in 13C. This enrichment with respect to the original CO2(soil) varies between 7 and 10 depending on temperature (Table 5-3). The d13Csoil is therefore replaced by a initial d13C value for DIC in the infiltrating groundwaters (d13Crech) defined as:
d13Crech = d13Csoil + e13CDIC-CO2(soil)
Here, e13CDIC-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 e13CDIC-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. Lets look at an example by varying the pH of the recharge waters. Remember that:
e13CDIC-CO2(soil) = mCO2(aq) · (e13CCO2(aq)-CO2(g)) + mHCO3 · (e13CHCO3-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
|Input:||Case A||Case B||Case C|
|Ages (yr B.P.):|
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 d13CDIC 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 d13Ccarb. 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 (ao14CFA)
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 a14CFA 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, SO42 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 (ao14CFA)
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:
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/Rair for crustal fluids = 0.007 to 0.022 (Andrews, 1985). Rocks rich in U, Th and K can have 3He/4He < 1010 with complementary increases in total He (Clarke and Kugler, 1973).
Table 8-9 Helium abundances and isotope ratios in different reservoirs
(R = 3He/4He)
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):
where: [ He] is the groundwater helium content in cm3 STP g1 water
f is the fractional porosity of the rock
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 · 105 cm3 STP g1 H2O were measured in thermal waters with modern 14C activities and measurable 3H. The low 3He/4He ratio of 7.8 · 10-8 (R/Rair = 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
(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.
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:
= 0.31 (23 1.1) + 0.69 (23 + 9.6)
We can now use the 13C mass balance equation using enrichment
factors for e13CHCO3CO2(g)
that are calculated from the equations in the Table on the front cover,
or found in Table 5-3:
1.5 = 0.71 (d13CCO2(g) + 9.0) + 0.29 (d13CCO2(g) 1.1)
and using mole fractions (mf):
mfCO2(aq) + mfHCO3 = 1
Thus, mfCO2(aq) =
= 0.027 and mHCO3 = 0.973
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
The dilution factor is then calculated from the 13C mass balance equation:
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-PCO2
= 0.96 + 1.21
mDICcarb = mCa2+ + mMg2+ mSO42 + ½(mNa+ + mK+ mCl)
This model then calculates how much of this carbonate has exchanged with the soil CO2 under open system conditions, using a 13C mass balance:
A summary of the model ages is useful for comparision:
A final and important note: the interpretation of groundwater age according
to model results such as this must be done in conjunction with as much
additional information as possible. This includes a good understanding
of the hydrogeological setting in the recharge area and along the groundwater
flow paths. It also includes an understanding of the groundwaters geochemical
evolution. Simple carbonate dissolution is often accompanied by some of
the secondary processes discussed above in this chapter, such as sulphate
reduction and dolomite dissolution. This is particularly so in deep aquifers
in arid regions where paleo-groundwaters are often found, and their exploitation
of critical economic importance.
= -23 1.1
mDICcarb = mCa2+ + mMg2+ mSO42 + ½(mNa+ + mK+ mCl)
2CH2O + SO42 ® H2S + 2HCO3
The correction for sulphate reduction can then be approximated by:
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 (d13CDIC-rech).
The 13C content of the organic substrate must be measured or
assumed. A value for fixed organic carbon of d13Corg
= 26 ± 2 is reasonable.
d13CDIC-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:
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: