0 100 200 300 400 500 Time (years)
0 0.2 0.4 0.6 0.8 1
Probability of Excedence of Recovery Time
0 100 200 300 400 500
Time (years) 0
0.2 0.4 0.6 0.8 1
Cumulative Probablity of Recovery Time
0 100 200 300 400 500
Time (years) 0
0.02 0.04 0.06
Frequency
Figure 3.7. Results of the analysis of the recovery of Lake Pontchartrain from PCB load with the source rate fixed at 0.1%
0 100 200 300 400
Time (years) 0
0.2 0.4 0.6 0.8 1
Probability of Excedence of Recovery time
0 100 200 300 400
Time (years) 0
0.2 0.4 0.6 0.8 1
Cumulative Probability of Recovery Time
0 100 200 300 400
Time (years) 0
0.02 0.04 0.06
Frequency
Figure 3.8. Results of the analysis of the recovery of Lake Pontchartrain from PCB load with an uncertain source rate
Pontchartrain has a 0.1 probability of cleaning itself in more than a year from the atrazine load calculated in this model.
Since atrazine is the most soluble chemical in water among the three representative contaminants selected in this study, decay within the relatively larger volume of water compartment and outflow with the tributaries enables the more rapid removal of this chemical.
In the second case, in which the source rate is also randomly selected, atrazine has an average recovery time of 0.9 years. In the application of the second case, the source value can take the lower or the higher values with equal probability. The probability of exceeding one year for self-cleansing has a higher value of 0.3 for this case. The cumulative probability plot shows that atrazine will reach MCL values within three years (see Figure 3.4).
In the first case, Figure 3.5 shows that the average time to recover from benzene load is 1.12 years. The same figure also shows that, despite a 50% probability of exceeding one year recovery time, benzene concentrations will reach MCL values within two years.
When the source rate is also randomly sampled, the average time of recovery is 0.8 years for benzene as shown in Figure 3.6. The probability that benzene concentrations will still be higher than MCL values after the first year is 0.25. As benzene is the most volatile of the three contaminants, it can be rapidly removed from the Lake Pontchartrain system.
Lake Pontchartrain would recover from a benzene loading of the magnitude calculated in this study within at most two years.
PCBs, the most hydrophobic, are expected to stay the longest in the system. Figures 3.7 and 3.8 show that PCBs are indeed very persistent in nature. In the first case with the fixed source rate, Lake Pontchartrain requires about a century to clean itself from PCB contamination. The recovery time ranges from 15 to 400 years. Figure 3.7 shows that the probability is 0.4 for a recovery time longer than a century. The probability of exceeding the allowable values after 200 years is 0.03. In the second case, the average time of recovery drops to 65 years. However, the probability of recovery in more than 100 years, with a value of 0.2, is still high.
This chapter presented an unsteady state fugacity model to examine the effects of contaminant loads with various physicochemical characteristics. The model provides the fugacities in the water, air, and sediment phases as a function of time, which can be converted to concentrations. This study further includes a Monte Carlo analysis, which serves as a method of determining uncertainties in the parameters used for the solution of the model.
The model developed in this study provides a tool that can be used to explain the behavior of Lake Pontchartrain after Hurricane Katrina. The model can also be used to study the effect of any contaminant load on any shallow lake system. As expected, the
more volatile it is, the shorter time it will remain. The amount of contaminant load introduced into the system is a crucial parameter that determines the time of recovery.
Therefore, to evaluate the uncertain terms, Monte Carlo Simulation is an effective tool.
The model developed in this study offers a very simple yet effective procedure to assess the environmental response of surface water systems. Thus, in simulated or real emergency response scenarios in the environment, the model represents a powerful design tool. As it can be generalized, the model can be used for any chemical compound, so decision makers who are forced to find solutions within a short time will find it useful during emergencies such as that which followed Hurricane Katrina.
The time requirements for computation are not long, with single runs taking only a few minutes. Monte Carlo analysis requires more computation time, the longest simulation taking no more than three days. The computations were performed on IBM PC compatible computational platforms. Such an analysis, in turn, could be very effective for decision making and preventing decisions that may lead to long-term pollution of surface water resources. If policymakers had been aware of the results of this study when Hurricane Katrina took place, they would have had alternative solutions at their disposal.
For example, they may have applied a primary treatment to flood waters, prior to discharging them into Lake Pontchartrain, using large-scale portable treatment devices that would have significantly reduced the level of pollution rather than leaving the clean- up to natural attenuation alone.
CHAPTER 4
RIVER HYDRODYNAMICS
Rivers and streams are natural open channels with a free surface as a streamline along which the pressure is constant and equal to atmospheric pressure (Sturm 2001). The existence of a free surface means that the flow boundaries are no longer fixed by the channel geometry but adjust themselves to accommodate the flow conditions. Another aspect of open channel flow is the wide variability of the cross-sectional shape and roughness of the channel. Due to the free surface, gravity, instead of pressure, is the driving force, as in closed conduits (Sturm 2001).
The flow of water in natural channels is almost always unsteady (Mahmood and Yevjevich 1975). The unsteady nature of open channel flow causes the complexity of its analysis. The procedure one follows to predict the temporal and spatial variations of a flood wave as it traverses a river reach or reservoir is known as flood routing (Baltas 1988).
Advanced mathematical treatment of unsteady flow in open channels began with the
French Academy of Sciences, Volume 73, July-December 1871, presented by Barre de Saint-Venant. The English title of this document was “Theory of unsteady water flow, with application to river floods and to the propagation of tides in river channels.” The second part of this document, titled “Theory and general equations of unsteady flow in open channels,” contained two partial differential equations currently known as the Saint- Venant partial differential equations of unsteady flow. These two equations have remained unchanged in their general form since they were first published, during which time many scientists and researchers attempted to modify or improve them. Although these attempts result in more complete and sophisticated versions of the equations, they reduce to the basic Saint-Venant equations upon simplification for practical use (Mahmood and Yevjevich 1975).
Saint-Venant, an engineer as well as a mathematician-physicist, realized that the properties of fluid phenomena, as discovered by observations in nature as well as obtained by experiments, should be the guiding factors in postulating basic hydraulic equations. The fundamental assumptions in the development of Saint-Venant equations can be listed as: (i) hydrostatic pressure distribution along the depth of the flow; (ii) friction losses in the unsteady flow are similar to those in steady flow (so that the Manning or Chezy equations can still be used to calculate the mean shear boundary stress (Sturm, 2001); (iii) velocity distribution does not affect wave propagation; (iv) the flow can be represented in one dimension with negligible transverse velocity and average boundary shear stress applicable to the whole cross-section; and, (v) the bed slope is
small enough so that the sinus of the slope angle can be replaced by the tangent of the angle (Mahmood and Yevjevich 1975; Sturm 2001).