4.5 Contaminant mass discharges

As alluded to in previous sections, real-world aquifers are to some degree heterogeneous. This means that they are composed of geologic materials and structures of different properties that influence flow and chemical constituents. A great concern to hydrogeologists is that the heterogeneity may manifest itself as continuous layers, channels, faults, or other conduits that are highly conductive to flow. When this occurs, flow through these units can be focused and fast enough that mass losses to surrounding less permeable units, via diffusion for example, may be too slow to meaningfully retard a plume front. The delivery of pollutants to down-stream receptors may therefore occur much faster than predicted from conventional Darcy-based characterization methods. Moreover, if the pollutant source is a long-term one, the rate at which mass accumulates at the receptor will also be higher than expected. The combined concerns of time-to-arrival (from knowledge of v and q) and rate of mass delivery are captured in the concept of mass flux. Mass flux has dimensions of mass per time per unit cross-sectional area of aquifer (Figure 24).

Figure showing relationship between mass flux and mass discharge
Figure 24 Relationship between mass flux and mass discharge. Mass flux is the mass of a contaminant that crosses a unit cross-sectional area of an aquifer per unit of time, and it may vary within a plume, as it does between the two example areas shown by the differing colors (dark red and light red). Mass discharge is simply the sum of fluxes over the entire plume

The mass per time portion of a mass flux can be determined by multiplying the observed concentration of contaminant considered representative of a unit area by the Darcy flux (see the introduction of this book). Within a plume, flow rates and concentrations of a pollutant may vary, so the mass flux may also vary from location to location. The total plume mass per time passing through a transect consisting of many unit area sections is calculated simply by adding up the mass fluxes for each unit area in the transect. This value is called the mass discharge (dimensions of mass/time).

While mass flux is a number that can be compared across sites, and within sites, because it always references the same amount of area, mass discharge provides a site-specific value that can facilitate risk assessment analysis. A mass flux number can be high but if the total plume area is small, the total mass reaching a boundary or receptor may not pose much risk. On the other hand, large mass discharge is unambiguously problematic in most cases of contaminated sites.

In heterogeneous media, the determination of mass discharge depends on the discovery and characterization of all zones where groundwater velocities are high. A well-instrumented transect, i.e., one with many monitoring points on it, such as the one illustrated in Figure 24, can provide the detail necessary to determine the mass fluxes across the plume — including large fluxes associated with preferential flow pathways — and from them the mass discharge crossing the transect (Einarson and Mackay, 2001).

To illustrate another use of mass discharge for practical purposes, imagine a water supply well that is pumped at a rate Q that happens to capture the entire plume of a contaminant known for causing health problems. The people in charge of the water supply might ask if the concentrations that develop in the well will remain dilute enough that the contamination can be ignored, or if there is a possibility that the concentration of pollutant rise to a level that requires action. Prior knowledge of the mass discharge in the plume, together with the pumping rate of the well, permits the needed in-well concentration to be estimated in advance (Figure 25), assuming complete mixing of polluted and unpolluted water in the well.

Figure showing a plume being captured by a water-supply well
Figure 25 A plume is captured by a water-supply well. If the mass discharge of a contaminant in the aquifer is known, the concentration that will appear in the well, Cwell, can be anticipated for any rate of pumping, Q, that captures all of the plume. The simple relationship shows that Cwell is proportional to MD, e.g., doubling MD will double Cwell.


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