Zero Order Source with Partitioning
This post introduces the new zero-order source with partitioning command, added to HGS in revision 2291 (August 2021 update). This command enables more realistic modeling of gaseous species production in the unsaturated zone (USZ), considering the partitioning between the aqueous and gas phases based on solubility and water saturation. The new command improves upon the previous zero-order feature by scaling production smoothly, using a partition coefficient and water saturation, instead of a simple on/off function. We find this command especially useful for modeling species like 222Rn, where equilibrium between gas and aqueous phases is critical for accuracy in simulations.
The objective of this new command is to consider the production of gaseous species within the unsaturated zone (USZ) in a more realistic manner than is currently achievable with HGS. Gaseous species produced within the USZ (e.g. 37Ar or 222Rn) will partition between the aqueous and gas as a function of their solubility in water and water saturation. The native HGS zero-order feature leads to high concentrations in the USZ, as produced species are dissolved in a comparatively smaller volume of water; in reality, the concentrations will sometimes be lower, due to the partitioning in the gas phase described above.
A saturation threshold command was added last year (Oct. 2020), which switches off zero-order production when water saturation falls below a user-specified value. This feature is particularly well-suited to species with low solubilities, and those which are in close contact with the atmosphere (shallow subsurface). However, for species which are more soluble (e.g. 222Rn) and/or produced in the USZ at depths of more than a couple of meters, it is more realistic to assume an equilibrium between the gas and aqueous phases, as a function of both the partition (or Henry) coefficient and the water saturation.
Figure 1: Effective production rate
Based on a simple instant-equilibration mass-balance model, the new ‘zero order source with partitioning’ command scales production according to the following relationship
Figure 2: Command description for “zero-order source with partitioning”
The partition coefficient (Hcc) is defined by the user and can be considered a constant (although it does vary with temperature in reality). This equation assumes that every produced atom in the USZ will partition immediately into both gas and aqueous phases according to this coefficient.
The result is that the zero-order source is produced more smoothly as a function of saturation, rather than use a simple on/off function. It remains quite simplistic, as it assumes completely static conditions in the gas phase, and also assumes a constant partition coefficient, which is synonymous with isothermal conditions.
Let’s take a closer look at the new command in action. To use this command in your *.grok file you must specify a number of panels for a time-value table, and for each panel you will specify the time on, time off, the mass production rate under fully saturated conditions, and the partition coefficient. Note that production rate and partition coefficients must be specified for all species in your simulation. A detailed description of the command is included in section 2.7.7.6 of the reference manual, and is reproduced in Figure 2 for your convenience:
Figure 3 illustrates the impact that the zero-order source with partitioning command has when compared to the original zero-order source and zero-order source with saturation threshold commands. The figure below shows the 222Rn activity as a function of distance from the top of the column when all three variations of the command are applied:
Figure 3: Results from three different versions of the “zero order source” commands
You can reproduce these results yourself using the example project below, which includes all three versions of the ‘zero order source’ commands (although only one should be active at a time).
This simple simulation applies steady-state infiltration from top of a 1-D column, with zero-order source and first order decay corresponding to 222Rn production and disintegration. The column is 5 meters in length, and discretized into 100 elements. A constant rain flux of 0.05 m/d is applied to the upper boundary, and a constant head of 2 m is applied to nodes at the bottom (z = 0) of the column. The column flows under unsaturated conditions until approximately 2.8m from the inlet. van Genuchten parameters are given in .mprops file. Figure 4 illustrates the correct application of the zero-order source with partitioning command.
