2.8  Dissolved Gas Tracers and Liquid‑Vapor Partitioning

Peter Cook

2.8 Dissolved Gas Tracers and Liquid‑Vapor Partitioning

Several of the commonly used environmental tracers are gases at natural atmospheric temperatures and pressures. However, all gases will dissolve in water, so they can provide information on groundwater processes. Under equilibrium conditions, the relationship between the concentration of gas in air and its concentration in water is given by Henry’s Law. This can be expressed as shown in Equation 6.

$\displaystyle C_w=K_HC_a\left(P-p_{H_{2}O}\right)$

(6)

where:

C_w	=	concentration dissolved in water
C_a	=	concentration in dry air
K_H	=	Henry’s Law constant (solubility of the gas in water)
P	=	total atmospheric pressure
$\displaystyle p_{H_{2}O}$	=	water vapor pressure

The solubility of a gas in water will be a function of the water temperature and salinity, and the resultant equilibrium concentration in water will also be a function of the atmospheric pressure. The water vapor pressure is also a function of temperature and salinity. In general, concentrations of dissolved gases will be higher in colder water and in water with lower salinity. Gas solubility as a function of temperature and salinity is well known for most gases of interest in hydrology. Data on gas solubility have been compiled by Cook and Herczeg (2000).

The relationship between a gas’s concentration in air and its equilibrium concentration in water can also be expressed in terms of a partition coefficient. The partition coefficient reflects the relative mass of tracer in equivalent volumes of water and air and will be one when equal mass occurs in each phase. Partition coefficients at 10°C and 1 atm pressure for commonly used tracers range from approximately 0.01 for helium and SF₆ to 0.5 for CFC-11 and ²²²Rn (Figure 10). This means that great care needs to be taken when sampling for helium and SF₆, as contact with the atmosphere can rapidly change concentrations. It also means that transport of helium and SF₆ through the unsaturated zone predominantly occur within the gas phase, whereas transport of CFC-11 and ²²²Rn occur in both liquid and gas phases. In contrast, dissolved ions such as chloride move exclusively in the liquid phase. Analysis of ¹⁴C in inorganic carbon that is dissolved in the water includes dissolved CO₂ and carbonate and bicarbonate ions, so the partition coefficient for total inorganic carbon will be greater than that of CO₂ alone. In areas with thick unsaturated zones, groundwater ages estimated with CFCs, SF₆ and ⁸⁵Kr may include a component that reflects the travel time through the unsaturated zone (Engesgaard et al., 2004). The effect will be more pronounced for tracers with large partition coefficients, and this can sometimes cause differences between water ages obtained with these tracers (Cook and Solomon, 1997).

Figure showing partition coefficients for some commonly used environmental tracers. — **Figure 10** – Partition coefficients (moles per cm³ of water divided by moles per cm³ of air under equilibrium conditions) at 1 atm pressure for some commonly used environmental tracers. Low values of the partition coefficient indicate that the tracer occurs predominantly in the gas phase within the unsaturated zone (Cook, 2020).

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