Dating of ground water

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Candice Nicholson
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1 PART 16 Dating of ground water Introduction Why date? - to determine when recharge occurred - to determine groundwater velocities - to reconstruct regional flow patterns How to do this? - decay of radioactive isotopes - buildup of daughter isotopes - peak matching of certain tracers Radioisotopes commonly used for groundwater dating: - tritium, 3 H, t ½ =12.3 y, bomb produced - radiocarbon, 14 C, t ½ =5730 y, bomb + natural - chlorine-36, 36 Cl, t ½ = y, bomb + natural Can also use 3 He- 3 H system, where 3 He is from radioactive decay of 3 H.

2 Dating of ground water 130 Principles of radioisotope dating Assume that at time t=0 we have N 0 atoms of a radioactive isotope. The isotope decays at a constant rate λ (=ln2/t ½ ). N changes with time according to: dn = λn linear, first order ODE dt Integrate to get: ln( N) = λt + C From the initial condition N = N t = 0, integration constant C = ln(n 0 ), and the solution is: N = N 0 e λt And the solution for time is: t = λ N ln N 0 Plot solution for N (black line). Concentration N decreases by one-half every one half-life (t 1/2 ). If the initial concentration is N 0, after one t 1/2 it will be reduced to N 0 /2 (see figure).

3 Dating of ground water 131 Real-world dating Calculated age represents average age of many water molecules in the sample. Each of these molecules might have had a different history in the aquifer. Individually, they would give different ages. COllectivey, they give an average age of the water parcel. These differences are due to different flow paths for individual molecules, and these different flow paths are the result of heterogeneities and dispersion.

4 Dating of ground water 132 Tritium method Tritium, 3 H: half-life t 1/2 =12.3 y, decay constant λ=0.056 y -1. Natural tritium is produced in the atmosphere by cosmic rays. Its concentration is below ca. 20 tritium units, TU (1 TU = H/H, or one atom of 3 H in atoms of H). In the 1950s-1960s, nuclear explosions introduced artificial 3 H into the atmosphere; this is called the bomb tritium. Concentrations were at several thousand TU, then they started coming back to the pre-bomb levels. We can trace the bomb peak and date the water directly by looking at the peak. Alternatively, if we do not have a profile in which the peak could be found, we can use radioactive decay to calculate the age of water. Problem - the initial condition is unknown because the concentrations of atmospheric 3 H changed in time (see figure below). Solution - look at the parent ( 3 H) and the daughter ( 3 He) together to eliminate the need to know the initial condition. This is the 3 H- 3 He method (see next page).

5 Dating of ground water H- 3 He (tritium-helium) method (1) In 3 H dating, we need to know N H0 (N H at time t=0) to compute N H at any time (see figure): N H = N H0 e λt (2) Add daughter 3 He (red line in figure): N He = N H0 ( 1 e λt ) Solve for N H0 : N H0 = N He e λt (3) Combine N He with N H : N H = N He e e λt λt N He N H Solve for t: 1 e λt = = e λt e λt e λt N = He N H N He N H 1 t = λ -- ln Result: by measuring two isotopes, the parent and its daughter, the need to know the initial condition is eliminated. Measurement technique: noble-gas mass spectrometry for both 3 He (standard measurement) and 3 H (in-growth method).

6 Dating of ground water C dating of ground water Radiocarbon, 14 C: half-life t 1/2 =5730 y, decay constant λ=1.21*10-4 y -1. Measurements reported as percent of modern carbon (pmc). Production: natural, in upper atmosphere, by cosmic-ray interactions with N; anthropogenic, byproduct of nuclear bomb tests (bomb produced 14 C). In ground water: dissolution of CO 2 in water; CO 2(gas) has 100 pmc; CO 2(aqueous) has slightly more than100 pmc. After that: decay with half-life of 5730 y. N = N 0 e λt Solution for time t: N 0 1 t = λ ln N Problems: carbonate system - exchange reactions: Dissolution of carbonate minerals and introduction of dead carbon (0 pmc - old carbon that has no 14 C). Dissolution and precipitation of carbonates. Addition of dead carbon from organic mtter, methane, etc. Isotopic exchange - usually negligible. Many models exist to account for these reactions and to estimate N 0 : (1) The Vogel model: N 0 = 85 pmc (±5 pmc) Vogel equation Good for temperate climates (e.g., Europe). (2) The Tamers model: weighted contribution of CO 2 and CaCO 3 (calcite):

7 Dating of ground water 135 (a+b)a0 = (a+0.5b)n CO2 +0.5bN CaCO3 N CO2 = activity of CO2 (usually 100 pmc) N CaCO3 = activity of CaCO 3 (usually 0 pmc) a+b = C T = total moles of C in water N 0 is computed using the following equation: ( a + 0.5b) N N CO2 0 = a + b or, in terms of total carbon C T = a+b ( C N T 0.5b) N CO = Tamers equation C T (3) The Mook model: a + 0.5b a + b δ 13 C T δ 13 C c δ 13 C CO2 δ 13 C c = Mook equation where δ 13 C measures the extent of carbonate reactions. (4) Other, more complicated models account for many other reactions that could affect C composition in ground water. Some are so complex that they require numerical codes to do the calculations.

8 Dating of ground water 136 Chlorofluorocarbons (CFCs, freons) Used since the 1930s. CCl2F2 (freon-12) CCl3F (freon-11) - makes up 77% of freons C2Cl3F3 C2ClF5 - makes up almost the entire remaining 23% Present input to atmosphere: 10 9 kg/y Input functions are smooth (see figure):

9 Dating of ground water 137 Krypton-85 ( 85 Kr)

10 Dating of ground water 138

Physics of Aquatic Systems II

Physics of Aquatic Systems II 10. C-Dating Werner Aeschbach-Hertig Institute of Environmental Physics University of Heidelberg 1 Contents of Session 10 General principles of C dating Conventional C age,