2 What Causes Groundwater Density Variations?

Fluid density varies as the concentration, temperature and, to a much lesser extent fluid pressure, vary. Figure 3 shows the dependence of the density of water as a function of salt mass fraction (the mass of solutes divided by the total mass of the solution) and temperature at atmospheric pressure. At low solute concentrations, the water density (ρ) is around 1000 kg m⁻³, although this depends somewhat on the temperature. Typically, seawater has a salt mass fraction of around 35 g kg⁻¹ with a density of approximately ρ = 1025 kg m⁻³.

Figure 3 – Contour lines of the density (ρ in kg m⁻³) of mixtures of seawater and fresh water as a function of temperature and salt mass fraction according to the international thermodynamic equation of seawater (IOC, 2010).

The values shown in Figure 3 are based on the international thermodynamic equation of seawater (TEOS-10) which was developed to determine the density of the world’s oceans (IOC, 2010). As it turns out, it can also be used to approximate the density of groundwater in coastal aquifers (Post, 2012). Figure 4 shows the relationship between the specific conductance (SC₂₀, the electrical conductivity of water at a specific temperature, 20 °C in this case) and the density (ρ₂₀, also at 20 °C). The black line is the relationship according to the TEOS-10 and the data points are for samples from different groundwater systems. The samples from Portugal are from a sandy coastal aquifer in which mixing is the main process that determines the water composition, without significant changes in the chemistry by chemical reactions. These samples closely follow the theoretical relationship. Seawater has a specific conductance of approximately SC₂₀= 47 mS cm⁻¹. The samples from Portugal with higher specific conductance values represent evaporated seawater (from evaporation ponds for salt production) and they too follow the TEOS-10 relationship, as long as salinity does not get too high. Samples with SC₂₀ > 125 mS cm⁻¹ deviate significantly from the theoretical values because the TEOS-10 loses its validity at these salinity values. One reason is that the TEOS-10 relationship simply cannot be extrapolated too far outside the salinity range for which it was developed (the oceans). The other is that at these salinity levels, minerals like calcite and gypsum start to precipitate, changing the relative proportions of the solutes, thus rendering the TEOS-10 fitting parameters invalid (Pawlowicz, 2012).

Figure 4 – The density (ρ₂₀) plotted against the specific conductance (SC₂₀) of water samples from different groundwater systems. The solid line is the theoretical relationship according to the TEOS-10. Deviations from theoretical values occur because TEOS-10 loses its validity at salinity values above those of seawater for which the relationship was developed and because at these salinity levels minerals such as calcite and gypsum start to precipitate, changing the relative proportions of the solutes, thus rendering the TEOS-10 fitting parameters invalid. Inland Australia samples are courtesy of Margaret Shanafield.

The latter holds for the data points from the Australian south coast, which plot just below the TEOS-10 line. In this case, the relative proportions of the ions deviate significantly from seawater due to chemical reactions in the aquifer, which caused the groundwater to be depleted in magnesium and sulphate. The data points for the Ti Tree Basin in inland Australia on the other hand, plot above the TEOS-10 line. Their chemical composition differs from seawater-freshwater mixtures in that they contain a lot more sulphate.

The above examples show that some care must be exercised when selecting a relationship for a particular area as the chemical characteristics of the water can have an important influence. There are various relationships between salinity and density, and a useful overview has been presented by Adams and Bachu (2002). The TEOS-10 is a complex algorithm and special software is required to perform the density calculation as indicated by Figure 3 and Figure 4. More information can be found at TEOS-10 software website.