Lesson 9 - Modeling Mixing (Dilution) in the Stream
Note: In this Lesson, we continue to explore the example file named Example1_ContaminatedPond.gsm. It can be found in the “Examples” subfolder of the “Contaminant Transport Course” folder you should have downloaded and unzipped to your Desktop.
The pathway network for this model can be seen inside the Contaminant_Transport container. In the previous Lesson, we looked at the Saturated_Zone element (which represented the groundwater flowing toward the stream). In this Lesson, we are going to focus on the Stream element (which is represented using a Cell pathway).
Recall that we assume that the entire plume discharges to a stream and quickly mixes throughout the stream. Our objective is to predict the peak concentration of the contaminant at some point downstream of where the groundwater plume discharges (at the point that it is well-mixed). As a result of this assumption, we do not need to model the geometry of the stream itself. All we need to do is calculate the dilution the stream provides at that point (downstream of where the groundwater plume discharges).
The dialog for the Stream pathway looks like this:
Note that the amount of Water is specified as the Stream_Reach_Volume. This simply represents the volume of water in the reach downstream of where the groundwater plume discharges (and the mass becomes well-mixed). We assume that in this volume any incoming contaminant mass is instantaneously mixed throughout the Cell as the plume discharges into it. But how do we select the volume? Actually, it is simply an arbitrarily small number. Physically, we can think of it as being on the order of the river length over which we can assume complete mixing (we’ll assume 3 widths of the plume) multiplied by the width of the stream multiplied by the depth of the stream. Recalling that the plume width is 100 m, and assuming a stream width of 5 m and a stream depth of 1 m produces a value of 1500 m3. We say this is an arbitrarily small value because it is small compared to the volume of water passing through it in a timestep (1 day). That is, the stream flow rate averages about 300,000 m3/day (though it varies seasonally). This means that the compartment represented by the Stream Cell has a flushing time of ten minutes or so. As a result, given the time scales of how things change in this model (days to months) and the timestep (1 day), it essentially responds to the incoming plume mass instantaneously. This is consistent with our assumption that the plume is quickly well-mixed in the stream.
Note: As long as the flushing time is small (relative to the timestep), the computed concentration in the Cell is quite insensitive to Cell volume. In fact, the concentration we calculate in this Cell would not change appreciably until we made the volume on the order of 1000 times larger. At this point the flushing time would be on the order of 7 days or so, and the peak concentration would be lowered by perhaps 10%. Physically, a larger volume has more “inertia” and hence takes longer to respond to the incoming mass (and as a result, peaks are spread out).
The Inflows tab indicates that there is an inflow from the Aquifer pathway (with a Flow Rate equal to Plume_Flow_Rate):
The Outflows tab indicates that there is an outflow from the Stream pathway (with a Flow Rate equal to the Stream_Flow_Rate) to a pathway named Sink:
What is the Sink? This is the downstream boundary of the model. Once mass is transported there, we are no longer interested in tracking it. As such, it does not really represent a physical location (and as a result, the amount of Water it is specified to contain is arbitrary). Concentrations in the Sink have no meaning. We could use it, however, to track the total amount of mass that has “left the system”.
Note that the Flow Rate in the Inflows and Outflows tabs for Stream do not balance (just as they did not balance for the Saturated_Zone). This simply indicates that the mass is being diluted in the stream (i.e., in addition to any contaminated inflow from the aquifer listed in the Inflows tab, “clean” stream water is assumed to also be entering the pathway). Hence, contaminant mass entering from the plume is being diluted with clean water.