Groundwater moving through the geosphere appears to be a simple enough process, yet a groundwater realm of cryptic underground rivers and channels has remained in our culture since early historic times, sustained by water diviners and rural myths. Surface waters seem easier to understand, their intricacies more apparent because we can see them flow and follow them to their source. But to quench your thirst, they must first be flocculated, sedimented, filtered, limed, chlorinated and often chilled, provided industrial effluents have not already damaged the supply. For groundwaters, the geosphere provides these treatments naturally. Groundwater represents more than 50 times the freshwater resource that surface waters do, yet in North America groundwater is used for less than half of freshwater needs; in Central Europe, groundwater is the dominant source for drinking water.

The dawn of hydrogeology as a science began with Darcy’s early experimenting with the plumbing for the fountains of Dijon. Today, the over-exploitation and contamination of this resource has moved groundwater research to the forefront of the geosciences. Nonetheless, like the diviners of historic times, hydrogeologists still wrestle with the questions of groundwater provenance, its renewability and the subsurface processes affecting its quality. These questions become increasingly relevant as we continue to test the limits of groundwater resource sustainability.

Environmental Isotopes in Hydrogeology

Environmental isotopes now routinely contribute to such investigations, complementing geochemistry and physical hydrogeology. Meteoric processes, for instance, modify the stable isotopic composition of water, and so the recharge waters in a particular environment will have a characteristic isotopic signature. This signature then serves as a natural tracer for the provenance of groundwater. On the other hand, radioisotopes decay, providing us with a measure of circulation time, and thus groundwater renewability. Environmental isotopes provide, however, much more than indications of groundwater provenance and age. Looking at isotopes in water, solutes and solids tells us about groundwater quality, geochemical evolution, recharge processes, rock-water interaction, the origin of salinity and contaminant processes. Let’s start with the basics.
 

Elements, nuclides, and isotopes

The nuclear structure of a nuclide (an isotope-specific atom) is classically defined by its number of protons (Z) which defines the element, and the number of neutrons (N) which defines the isotope of that element. For a given nuclide, the sum of protons and neutrons gives the atomic weight (A), expressed by the notation . For example, most oxygen has 8 protons and 8 neutrons, giving a nuclide with 16 atomic mass units () while about 0.2% of oxygen has 10 neutrons (). In reality, the mass of a nuclide is slightly less than the combined mass of its neutrons and protons. The "missing" mass is expressed as the nuclear binding energy (according to Einstein’s mass-energy relationship E = mc²), which represents the amount of energy required to break the nucleus into its constituent nucleons. Conventional notation for a nuclide uses only the elemental symbol and atomic weight (e.g. ¹⁸O or ³⁴S).

Whereas the number of neutrons in the nucleus can vary, the range is limited by the degree of instability created by having too many or too few neutrons. Unstable isotopes or radioactive nuclides have a certain probability of decay. Stable isotopes, on the other hand, do not spontaneously disintegrate by any known mode of decay. To date, some 270 stable nuclides and over 1700 radionuclides have been identified. For the light elements (Z up to 20) the greatest stability occurs with a Z:N ratio close to 1, and increases towards 1.5 for heavy elements. In a chart arranged according to Z and N (Fig. 1-1), the stable isotopes of the elements form a stable valley from hydrogen to uranium. Departures from this stable valley produce radionuclides of decreasing stability (shorter half-lifes). Oxygen, for example, has eleven isotopes (¹²O to ²²O) although only the median isotopes, ¹⁶O, ¹⁷O and ¹⁸O, are stable (Fig 1-2). The others are radioactive with half-lives varying from 122 seconds to less than a femtosecond (10^-15 s).
 

Fig. 1-1 Plot of Z vs. N for nuclides up to tin (Z=50) showing the "stable" valley of the nuclides. The Z : N ratio is 1 for the light nuclides and increases towards 1.5 for the heavier nuclides. Increases or decreases in N for given element produces increasingly unstable isotopes (decreasing T½).

The distribution of stable isotopes reflects the structure of the nucleus. Like electron orbits, the most stable nuclei have filled neutron and/or proton shells. Those nuclides with a "magic number" (2, 8, 20, 28, 50, 82 and 126) of neutrons and/or protons are the most common (e.g. = 99.99986% of all helium; = 99.76% of all oxygen; or = 96.9% of all calcium) whereas others have lower abundances (e.g. = 19.9% of all boron). As the nuclear binding energy occurs between nucleon pairs (protons or neutrons), stable nuclides with even numbers for N and Z, dominate. Thus, 161 of the known stable nuclides have an even N and Z while only 4 have an odd values for N and Z. There are 105 with either an odd N or Z.

Why "environmental" isotopes?

Although all elements present in hydrogeological systems have a number of isotopes, only a few are of practical importance to us. The environmental isotopes are the naturally occurring isotopes of elements found in abundance in our environment: H, C, N, O and S. These are principal elements of hydrological, geological and biological systems. The stable isotopes of these element serve as tracers of water, carbon, nutrient and solute cycling. They are also light elements. As a consequence, the relative mass differences between their isotopes are large, imparting measurable fractionations during physical and chemical reactions. For example, ²H has 100% more mass than its sister isotope ¹H, whereas the two stable isotopes of bromine (⁸¹Br and ⁷⁹Br) have a mass difference of only 2.5%. Radioactive environmental isotopes are also important in hydrogeology. From their decay we have a measure of time and so environmental radionuclides such as ¹⁴C and ³H can be used to estimate the age or circulation of groundwater.

The family of environmental isotopes is growing as new methods allow the routine analysis of additional isotopes. Accelerator mass spectrometry (AMS) analysis has brought ³⁶Cl into mainstream isotope hydrogeology. Refinements in solid source mass spectrometry and inductively coupled plasma mass spectrometry (ICP-MS) allows high precision measurement of the isotopes of trace elements such as U, Th, Li and B. The major stable environmental isotopes used in hydrogeology are presented in Table 1-1.

Environmental isotopes are now used to trace not only groundwater provenance, but also recharge processes, subsurface processes, geochemical reactions and reaction rates. Their importance in studies of biogeochemical cycles and soil-water-atmosphere processes is increasingly being recognized, and new applications in contaminant hydrogeology are being made.

 
Table 1-1 The stable environmental isotopes
 

The variations in numbers of neutrons in an element provides for the different masses (atomic weights) of the element and the molecules of which they may be a part. For example, heavy water, ²H₂¹⁶O, has a mass of 20 compared to normal water, ¹H₂¹⁶O, which has a mass of 18. Molecules with differences in mass have different reaction rates. This leads to the isotope partitioning or fractionation described by Urey (1947).
 

Stable environmental isotopes are measured as the ratio of the two most abundant isotopes of a given element. For oxygen it is the ratio of ¹⁸O, with a terrestrial abundance of 0.204%, to common ¹⁶O which represents 99.796 of terrestrial oxygen. Thus the ¹⁸O/¹⁶O ratio is about 0.00204. Fractionation processes will of course modify this ratio slightly for any given compound containing oxygen, but these variations are seen only at the fifth or sixth decimal place.
 

Measuring an absolute isotope ratio or abundance is not easily done and requires some rather sophisticated mass spectrometric equipment. Further, measuring this ratio on a routine basis would lead to tremendous problems in comparing data sets from different laboratories. However, we are mainly interested in comparing the variations in stable isotope concentrations rather than actual abundance, and so a simpler approach is used. Rather than measuring a true ratio, an apparent ratio can easily be measured by gas source mass spectrometry. The apparent ratio differs from the true ratio due to operational variations (machine error, or m) and will not be constant between machines or laboratories or even different days for the same machine. However, by measuring a known reference on the same machine at the same time, we can compare our sample to the reference. Isotopic concentrations are then expressed as the difference between the measured ratios of the sample and reference over the measured ratio of the reference. Mathematically, the error (m) between the apparent and true ratios is cancelled. This is expressed using the delta (d) notation:
 

 

   ‰ VSMOW
 

Carbonate, organic carbon and hydrocarbon

The range of oxidation states of carbon makes it a fundamental element of the biosphere and hydrosphere. Carbon-13 traces carbon sources and reactions for a multitude of inter-reacting organic and inorganic species. The paleotemperature scale developed in the early 1950s using the ¹⁸O/¹⁶O ratio in marine carbonates adopted PDB as the international reference material (Urey et al., 1951). PDB was the internal calcite structure (rostrum) from a fossil Belemnitella americana from the Cretaceous Pee Dee Formation in South Carolina. In 1957, Craig formally introduced PDB as the standard for both ¹³C and ¹⁸O in carbonate minerals. It has subsequently been adopted as the ¹³C standard for all carbon compounds, including CO₂, dissolved inorganic carbon species (DIC), dissolved organic carbon (DOC), cellulose and other fixed-C solids (CH₂O), organic liquids, methane and other hydrocarbons. However, VSMOW is the standard for measurements of ²H or ¹⁸O in organic molecules (e.g. CH₄, CH₂O etc.).

Before the limited PDB supply was exhausted, Friedman et al. (1982) used it to calibrate a crushed slab of white marble of unknown origin, designated as NBS-19:
 

The measurement of isotopes in carbonate minerals is done on CO₂ gas that is normally produced by acidification, a method developed by McCrea (1950). Carbon dioxide is produced from carbonate minerals by reaction with 100% phosphoric acid (H₃PO₄) at 25°C (Urey et al., 1951). The conversion of calcite to CO₂ follows the reaction:
 

CaCO₃ + 2H⁺ CO₂ + H₂O + Ca²⁺
 

Both VPDB and VSMOW are recognized international standards for ¹⁸O. While waters are exclusively referenced to VSMOW, carbonates can refer to either. VPDB was originally introduced for paleoclimatic studies, where the ¹⁸O content of carbonate was used as a paleotemperature scale. However, the use of carbonate isotopes has gone far beyond this field, and in water-carbonate studies it is common to express d¹⁸O data for carbonate against the VSMOW scale. Conversion is also necessary when deriving information about the d¹⁸O content of the water in which a carbonate has formed. The conversion chart in Fig. 1-3 or the following equations can be used (Coplen et al., 1983):
 

Fig. 1-3 Conversion chart for ¹⁸O between VSMOW and VPDB, with fractionation factors for 25°C. The bold line equates values on the VPDB scale to values on the VSMOW scale according to the two reciprocal equations: d ¹⁸O_VSMOW=1.03091 · d ¹⁸O_VPDB + 30.91 ‰, and d ¹⁸O_VPDB=0.97002 · d ¹⁸O_VSMOW –29.98 ‰.

Gas source mass spectrometry

In 1947, Alfred Nier developed the first dual-inlet, double-collector gas-source mass spectrometer. The double collector allowed the simultaneous measurement of two isotopes and the dual inlet allowed ratio measurement on both a sample and a standard by alternating between inlets. Gas source mass spectrometry has since become the measurement technique of preference for isotope ratios of most of the light elements (e.g. H, C, N, O and S) because of its relative simplicity and because the use of international standards allows comparison of data bases from different laboratories. A host of preparation methods have been developed and improved to convert different sample compounds to an appropriate gas including CO₂, SO₂, H₂ and N₂.

A heated tungsten-coated iridium (thoria) filament inside the source block cavity ionizes a laminar stream of gas entering the ultra-high vacuum source (Fig. 1-4). The gas molecules are stripped of one electron, producing positive ions (e.g. CO₂⁺) which are then accelerated through a voltage gradient and focused into the flight tube upon exiting the source. The ionization efficiency varies between 0.01 and 0.1% for different instruments. The ion beam bends as it passes through the field of a magnet installed over the flight tube. Here, the beam separates into a spectrum of masses according to the isotopes present. Each mass beam continues to the ion detectors where preset faraday cup collectors measure each ion current. By collecting two or three ion beams simultaneously, the ion currents can be expressed as mass ratios. For example, CO₂ would contribute three principal peaks at mass 44 (¹²C¹⁶O₂), mass 45 (¹³C¹⁶O₂ or ¹²C¹⁷O¹⁶O) and mass 46 (¹²C¹⁶O¹⁸O). A dual-inlet system allows the mass spectrometer to alternately measure ratios in the sample and a working or laboratory standard. Thus, the extreme fractionation imparted during ionization in the source is resolved. The early mass spectrometers suffered from drifting electronics, which precluded accurate abundance measurements. These instabilities have since been overcome with solid-state and fibre optic signal transfer systems.

Fig. 1-4 Schematic of a gas source isotope ratio mass spectrometer (IRMS), showing both continuous flow and dual inlets. The continuous flow inlet here is shown with a sample combustion and gas chromatograph configuration. Capillary tubes ensure laminar, non-fractionating gas flow. Example shows mass range of CO₂ gas, and includes the short radius flight tube for H₂ found on many designs. Other mass ranges (for SO₂ and N₂) are attained by either additional fixed-position faraday collectors or by adjusting the beam. For manufacturers details, see <http://beluga.uvm.edu/geowww/isogeochem.htm>.

Quadrupole mass spectrometers employ a method of isotope separation and measurement that offers economies in size and cost, but lack the precision of a Nier-type instrument. However, the portability of quadrupole mass spectrometry allowed the Viking mission to perform isotope analyses of Martian soil and atmosphere.

The direction of gas source mass spectrometry is now towards continuous flow systems where the sample and standard gases are carried into the mass spectrometer source in a stream of helium gas (Fig. 1-4). In this way, pulse injections of sample gas can be analysed, reducing volume constraints and sample size. Measurement in the nano-mole (10^–9 moles of gas) size range is now possible, opening a host of research possibilities. These systems also greatly increase sample through-put when configured with automated sample preparation systems. In particular, an elemental analyzer on the front end of a continuous flow mass spectrometer allows the analysis of solid, liquid, and mixed matrix samples which can be combusted and the gases separated on a chromatographic column. Helium carries the sample through the column and into the mass spectrometer. Continuous flow mass spectrometers configured with a laser ablation sampling system provide researchers with a tool for micro-analysis of sulphides and carbonates, with a spatial resolution in the order of 10 to 50 mm.

Radioisotopes

The radioisotopes routinely employed in hydrogeology include tritium and carbon-14. Measurement of chlorine-36 is becoming increasingly available to non-specialists, while the use of other radioisotopes like argon-39 and the krypton (⁸⁵Kr and ⁸¹Kr) is restricted to a limited number of research laboratories due to complications in sampling, analysis and interpretation. For the noble gases, huge volumes of water must be vacuum extracted in the field for analysis in low-level counters. Details on these radionuclides are given in Table 1-4. Sampling methods are covered in detail in Chapter 10.

Table 1-4 The environmental radioisotopes

Tritium, ³H, is a short-lived isotope of hydrogen with a half-life of 12.43 years. It attracted considerable interest during the era of thermonuclear bomb testing. Dr. R. Brown with Atomic Energy of Canada Limited (AECL) was the first to begin monitoring ³H fallout from atmospheric weapons tests. His data for Ottawa precipitation begins in 1952 and documents the dramatic increases in atmospheric ³H produced during the ensuing two decades of hydrogen bomb testing.

Small but measurable amounts of tritium are also produced naturally in the stratosphere by cosmic radiation on ¹⁴N. Both natural and anthropogenic tritium enter the hydrological cycle via precipitation. Its presence in groundwater provides evidence for active recharge. As it is part of the water molecule, it is the only direct water dating method available.

Tritium has also gained importance in the medical field to tag compounds in biological reactions, although the concentrations used here exceed environmental concentrations by several orders of magnitude. Environmental concerns limit the use of artificial ³H as a tracer in hydrological studies.

Tritium concentrations are expressed as absolute concentrations, using tritium units (TU) and so no reference standard is required. One TU corresponds to one ³H atom per 10¹⁸ atoms of hydrogen. For 1 litre of water, its radioactivity is equivalent to 0.12 Bq (1 Becquerel = 1 disintegration/second), or 3.2 pCi/l (1 pCi is 10^–12 Curies and a Curie is the radioactivity of 1 gram of ²²⁶Ra; 1 Curie = 3.7·10¹⁰ Bq). Groundwaters today seldom have more than 50 TU and are typically in the <1 to 10 TU range.

Tritium is measured by counting b^– decay events in a liquid scintillation counter (LSC). A 10 mL sample aliquot is mixed with the scintillation compound that releases a photon when struck by a b^– particle. Photomultiplier tubes in the counter convert the photons to electrical pulses that are counted over a several-hour period. Results are calculated by comparing the count to those of calibrated standards and blanks. Increased precision is gained through concentration by electrolytic enrichment of ³H in the water before counting, or by conversion to propane (C₃H₈) for gas proportional counting. Direct liquid-scintillation counting carries a precision of ±7 TU, whereas with enrichment and LSC this is improved to better than ±0.8 TU. With propane synthesis, a precision of ±0.1 TU can be obtained.

Isotope Fractionation

Although it was shown early this century that stable isotopes of oxygen and hydrogen existed, it was not until much later that their abundance and variation in the hydrosphere were investigated. Friedman, in 1953, first noted that in precipitation a change in concentration of H₂¹⁸O was accompanied by a change in ²HHO. In 1961, Craig published his landmark finding that these two isotopes are partitioned by meteorological processes in a rather predictable fashion. Subsequent work has shown how isotopes are partitioned through other systems, such as ¹³C in the carbon cycle.

How are environmental isotopes partitioned? Thermodynamic fractionation is a fundamental process. Here we will explore the details of isotope fractionation, using ¹⁸O and ²H in the hydrological cycle as an example. Fractionation of ¹³C, ³⁴S, ¹⁵N and other isotopes will be discussed in other chapters.

Isotope fractionation occurs in any thermodynamic reaction due to differences in the rates of reaction for different molecular species. The result is a disproportionate concentration of one isotope over the other on one side of the reaction. It is expressed by the fractionation factor a which is the ratio of the isotope ratios for the reactant and product:
 

 

Problems and Solutions

1. What is the relative enrichment or depletion of VSMOW, in d–‰ notation, relative to the average terrestrial abundance of ¹⁸O given in Table 1-1? What about VPDB?
 

 

= –17.1‰ vs. terrestrial abundance

Calculating R_VPDB: determine VPDB on the VSMOW scale

d¹⁸O = 1.03091 · d¹⁸O_VPDB + 30.91 = 30.91‰ VSMOW (for 0‰ VPDB)

= 13.3‰ enriched over the terrestrial abundance.

 

 

SLAP = –55.5‰ VSMOW, therefore:

 

 

8. Isotope fractionation effects are expressed as a-values and isotope abundances are given as permil differences from a reference (d-value). Establish the relationship between a and d in the form of a simple equation.
 
 

 

d²H_H2 = –754‰ VSMOW

 

, , 

  This equation can be made only when the ratios are equal to 1 (i.e. no fractionation).