6246lect14_S10

6246lect14_S10 - Advanced Environmental Geochemistry, GLY...

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Advanced Environmental Geochemistry, GLY 6246, ©David Warburton, 2010 1 LECTURE 14 - Lakes - II The Chemistry of Lakes Models The physics of lakes was discussed in Lecture 13. We saw that lakes may stratify by formation of an epilimnion and hypolimnion with a thermocline in between, or may become isothermal with turnover and complete mixing eliminating any stratification. In principle, this makes it easy to construct a model for a lake. If no stratification is present, a one box model may be used (Berner and Berner, 1987). This model assumes complete mixing of the entire lake. To maintain homogeneity, the rates of addition and removal must be slow compared with mixing. If these rates were not slow, concentrations would build up or decrease in part of the lake. The assumption of homogeneity would not be met. To construct a one-box model we need to define certain parameters: F i = Rate of flow into the lake F o = Rate of flow out of the lake M = Total mass of dissolved substance in lake R p = Removal rate of substance via precipitation and sedimentation to the bottom of the lake R d = Rate of addition of substance via dissolution of solids R s = Rate of burial of sediments C i = Concentration of dissolved substance in stream(s) flowing into the lake C l = Concentration of dissolved substance in the lake t = time V = volume of lake NOTE: For the parameters M through Cl, we may need to add subscripts to differentiate several different dissolved substances. Lect14, slide 2 here
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Advanced Environmental Geochemistry, GLY 6246, ©David Warburton, 2010 2 14-1 14-2 14-3 14-4 If dV/dt = 0 (constant volume lake) then: If the lake is in a steady state with respect to the substance (dM/dt = 0) then: Lect14, slide 3 here If the dissolution of the substance represents only dissolution of the substance previously precipitated then: Lect14, slide 4 here If the above-mentioned conditions are met, we can use equation 14-2 to calculate the maximum allowable concentration of a pollutant element in an influent stream if we are to keep the concentration of the element in the lake at or below the permissible limit. Lect14, slide 5 here For a given substance we also can write equations for the replacement time for the substance.
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Advanced Environmental Geochemistry, GLY 6246, ©David Warburton, 2010 3 14-5 14-6 14-7 14-8 Lect14, slide 6 here Here J r is the residence time of the substance in question. M can be computed: Lect14, slide 7 here Combining equations 14-5 and 14-6 gives: Lect14, slide 8 here However, Lect14, slide 9 here Lect14, slide 10 here
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Advanced Environmental Geochemistry, GLY 6246, ©David Warburton, 2010 4 14-9 14-10 Therefore, As we saw with the replacement time for water, if the lake is in a steady state with respect to the substance of interest (as well as water), then J r represents a residence time. The residence time represents the average time spent by the dissolved species before removal. If we are attempting to reduce the concentration of the dissolved species in the lake, steady state will clearly not be maintained. Equation 14-9 then shows that lakes with low values of J w will
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6246lect14_S10 - Advanced Environmental Geochemistry, GLY...

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