2.4 Total Dissolved Gas Pressure
Henry’s Law gives the relationship between the dissolved concentration of a gas and the partial pressure of the gas in contact with the liquid phase. By knowing the dissolved concentration of the dominant gas species, it is possible to compute the partial pressure of each gas. The sum of these partial pressures is known as the total dissolved gas pressure (TDGP) as shown in Equation (7).
| [latex]TDGP = \sum_{i = 1}^{n}{p_{i} = \sum_{i = 1}^{n}{K_{w,i}c_{i} \cong K_{{w,N}_{2}}c_{N_{2}}}}{+ \ K}_{{w,O}_{2}}c_{O_{2}} + K_{w,Ar}c_{Ar}[/latex] | (7) |
|---|
where:
| TDGP | = | total dissolved gas pressure (ML-1T-2, typically in atm) |
|---|---|---|
| [latex]K_{w,N_{2}}[/latex] | = | dimensioned Henry Coefficient for [latex]N_{2}[/latex] (M2L-4T-2, typically in g‑atm/ccSTP) |
| [latex]c_{N_{2}}[/latex] | = | concentration of [latex]N_{2}[/latex] in water (L3M-1, typically in ccSTP/g) |
| [latex]K_{w,O_{2}}[/latex] | = | dimensioned Henry Coefficient for [latex]O_{2}[/latex](M2L-4T-2, typically in g‑atm/ccSTP) |
| [latex]c_{O_{2}}[/latex] | = | concentration of [latex]O_{2}[/latex] in water (L3M-1, typically in ccSTP/g) |
| [latex]K_{w,Ar}[/latex] | = | dimensioned Henry Coefficient for [latex]Ar[/latex] (M2L-4T-2, typically in g‑atm/ccSTP) |
| [latex]c_{Ar}[/latex] | = | concentration of [latex]Ar[/latex] in water (L3M-1, typically in ccSTP/g) |
For groundwater that equilibrated with the atmosphere, the TDGP is essentially the sum of the [latex]N_{2}[/latex], [latex]O_{2}[/latex] and [latex]Ar[/latex] pressures. Because the Henry Coefficient is a function of temperature and salinity, the TDGP will change if the water temperature or salinity changes, even if the dissolved concentration stays constant.
The TDGP is a useful quantity for predicting the formation of bubbles (i.e., the exsolution of dissolved gases). If the TDGP is less than the fluid pressure, dissolved gases will remain in solution. If the TDGP exceeds the fluid pressure, bubbles can theoretically form; however, bubble nucleation is a complex process that can require activation energy. This is particularly important during sampling as a lowering of the fluid pressure via a pump and delivery at the land surface can result in effervescence if the in‑situ pressure is not maintained.
When groundwater that has equilibrated at the water table warms and/or becomes saltier, the TDGP increases because the Henry Coefficient changes, even though the gas concentration does not change. While the increase in fluid pressure is typically much greater than the increase in TDGP in recharge areas—areas of downward flowing groundwater—in discharge areas where warmed groundwater approaches the surface, the TDGP can exceed the fluid pressure, potentially leading to gas exsolution. When bubbles do form, the concentrations of both the major and minor components in the dissolved phase can be strongly affected. Low solubility gases such as [latex]He[/latex] and [latex]{SF}_{6}[/latex] will preferentially partition into the gas phase, leaving the water depleted relative to its original concentration.
The TDGP can be measured directly using a probe. A TDGP probe consists of a length of tubing that is permeable to gases—including water vapor—but not permeable to liquid water (Manning et al., 2003). One end of the tube is connected to a pressure sensor and the other end is plugged. When the tube is placed in water, the gas inside the tube can equilibrate with dissolved gases in the water; the pressure inside the tube will eventually reach the TDGP. A TDGP probe is particularly useful when collecting samples for dissolved gas analysis. If the fluid pressure is greater than the TDGP, the probability of bubble formation is minimal. As described in subsequent sections, the use of sampling containers such as copper tubing that allow the groundwater to be sealed under pressure can effectively eliminate degassing that might otherwise occur. Box 1⮧ provides more details and examples of using a TDGP probe for groundwater studies.