Lesson 7 – Representing the Boundary Conditions for an Aquifer Element
In this Lesson we are going to discuss two input fields for the Aquifer that we skipped in Lesson 4 (highlighted below):
These inputs determine how the boundary conditions of the Aquifer element are represented.
Let’s first consider the Source Zone Length, which impacts the boundary condition at the upstream end of the pathway. This input allows you to control where mass enters an Aquifer. It represents a length along the flow direction in the pathway. Hence, if your pathway had a length of 100 m, and you specified a Source Zone Length of 40 m, mass would enter the pathway uniformly over the first 40 m (rather than at the beginning of the pathway):
This is useful, for example, if your Aquifer represents a pathway that is being loaded from above with mass from source which is of such an areal extent (e.g., a landfill) that it extends over a significant portion of the pathway and therefore cannot be treated as entering at the beginning of the pathway.
By default, the Source Zone Length for an Aquifer is zero. In this case, any mass entering the Aquifer is applied at the beginning of the Aquifer (the first “temporary” Cell). If the Source Zone Length for an Aquifer is greater than zero, the mass is distributed uniformly over the specified length.
A number of points regarding the use of the Source Zone Length are worth noting:
- The Source Zone Length must be static (it cannot change with time).
- If a non-zero Source Zone Length is defined, the Aquifer Length and Area cannot change with time (doing so will generate a fatal error).
- The Source Zone Length is applied to all forms of mass that enter the Aquifer: mass that enters as an initial or boundary condition, mass that enters the Aquifer from other pathways via a mass flux link, and mass that enters the Aquifer as a specified discrete change via the Discrete Changes field (which we will discuss in Unit 12).
- If the Source Zone Length is larger than the Aquifer Length, the Source Zone Length is assumed to be equal to the Aquifer Length (and a warning message is written to the Run Log).
The Source Zone Length should only be used if the total flow in the Aquifer is substantially larger than the flow associated with the incoming mass. This is because the Source Zone Length does not change the flow rate along the Aquifer (all of the pathway’s inflows are assumed to enter at the beginning of the pathway); it only impacts where the mass is input. Hence, it is equivalent to assuming that the amount of flow associated with the mass entering the pathway is negligible relative to the total flow in the pathway (e.g., associated with “clean” upgradient water).
We will work on an Exercise in the next Lesson that uses the Source Zone Length.
In addition to specifying the input boundary condition for an Aquifer, you can also control the output boundary condition. In particular, the checkbox Enable dispersive and diffusive outfluxes to downstream pathway(s) changes the boundary condition on the downstream end of the pathway.
If this box is cleared (the default), only advective transport out of the pathway is allowed. If the box is checked, a zero concentration in the receiving pathway is assumed, and dispersive and diffusive transport into downstream pathways is allowed.
These two boundary condition options represent two possible extremes for the behavior of the system. The actual behavior of most real-world systems would be somewhere between these two extremes (although in most real-world systems, it will be typically be very close to either one or the other). The default boundary condition (no dispersive and diffusive fluxes) is most appropriate if the downstream concentration is similar to the concentration leaving the pathway. In this case, the concentration gradient is small (and hence the dispersive and diffusive fluxes would be small). If the box is checked, dispersive and diffusive transport into downstream pathways is allowed (assuming a zero concentration in those pathways). This might be appropriate, for example, if the downstream pathway represents a rapidly-flowing, “clean” pathway.
In the previous Exercise, we did not discuss this setting (and hence you probably left it at its default setting). However, due to the low concentration in the stream (relative to the groundwater pathway), checking the box (allowing dispersive/diffusive fluxes and assuming a zero downstream concentration) would probably be more appropriate. To see the impact, you can rerun the model from that Exercise with the box checked. The plot below shows the concentration in the stream for species X (which sorbs onto the sand) with and without the box checked (i.e., with and without dispersive fluxes allowed):
As can be seen, allowing dispersive/diffusive outfluxes results in a (slightly) faster breakthrough.