Movement of Pollutants in Lakes

Transcription

1 Movement of Pollutants in Lakes Simplest pattern of water movement in a lake: win-riven currents: Moule 2: Surface Waters, Lecture Chemical Fate an Transport in the Environment, 2 n eition. H.F. Hemon an E.J. Fechner-Levy. Acaemic Press. Lonon Principles of Surface Water Quality Moeling an Control. R.V. Thomann an J.A. Mueller. Harper & Row, New York Hemon an Fechner-Levy 2000 Fickian Mixing in Lakes A mass of tracer injecte into a lake will move by avection with the water currents, but will also sprea out into an ever-larger volume of water. Given enough time, it will ten to become completely mixe. This mixing is primarily ue to turbulence, carrying chemicals away from regions of higher concentrations to areas of lower concentrations. Hemon an Fechner-Levy

2 Concentrations for an instantaneous ischarge into a twoimensional boy of water (vertically mixe): Hemon an Fechner-Levy 2000 C( x, y, t) = 4πt M D D x y e 2 2 (( x Vxt) /(4Dx t) + ( y V yt ) / 4Dyt) kt e M is the mass of the chemical ischarge, per epth of water [M/L] x an y are the istances from the injection location [L] t is the time lapse since injection [T] V x an V y are the average velocity in the x an y irections [L/T] D x an D y are the Fickian transport coefficients in the x an y irections [L 2 /T] K is the first-orer ecay rate constant [T -1 ] The epth is the total epth for a vertically well-mixe lake, or the thickness of a layer in a stratifie lake. What woul lake temperatures look like in winter (very col area)? Hemon an Fechner-Levy

3 W = QeSe + QrSr + QT ST + PAsSp + SDV W= mass input [M/T] QeSe = waste effluent ischarge to lake QrSr = mass from main river QtSt = mass from tributary PAsSp = mass input from precipitation SV= seiment release Qe= effluent ischarge Qr = river flow Qt = tributary flow P = precipitation amount As = lake surface area V = lake volume Se = effluent concentration Sr = river concentration St = tributary concentration Sp = rain concentration S = seiment concentration

4 Concentration increases with time, since the start of the ischarge: Concentration Decrease after Discharge Stops Vs = W ( t) Qs kvs Change of mass with time = input mass (gain) mass outflow (loss) ecay (loss) K = Q+kV Assuming a constant Q an k over time Expaning the erivative: Vs = V s + s V V If V is temporarily constant: = 0 Then: Vs = V s Re-arranging results in: s W ( t) = V + Qs + kvs Concentration ecreases from initial conitions (at en of input) by a combination of flushing an ecay: Can simplify if efine: k ' = Q + kv Then: Resulting in: s W ( t) = V + k ' s 1 s = s 0 exp + k t t Where the lake etention time, t is efine as: V t = Q 4

5 Response ue to step loa = sum of initial conition (from previous loa), plus step loa effect: W Q Q s = + k t + s + k t Q + kv 1 exp V exp o V Total response an transitions can be etermine by calculating iniviual responses an summing the effect. Response ue to varying loa: (a) Step input an subsequent reuction to zero (b) Step input with reuction to new loa level Example Problem: A Lake (with initial s = 0), receives a loa of a slowing reacti ng pesticie (triallate) of 1080 /b/ay for 1.5 years an is then terminate. 1. Determine the equilibrium concentration 2. The maximum concentration. The time until a level of 100 µg/l is reache 5

6 (1) Determine the equilibrium concentration W W / Q s = = Q + kv 1+ kt 9 t V.15x10 ft ay year = = x x = 1. year Q 100 ft / sec 86,400sec 65ays 0 W / Q s = 1 + kt 1080lb / ay 100 ft / sec x86,400sec/ ay = = lb / ft ( 1.0year ) ay lb ft gal 454,000mg s = x x x = 1.6mg/ L = 160µ g / L ft 7.48gal.78L lb (2) Determine the maximum concentration (the max. concentration will occur at the en of the ischarge time, at t=1.5 years) s = s 1 exp 1 ( + kt ) t t yr s = 160 µ g / L 1 exp yr = 170 µ g / L yr 1.0 yr Never reaches the equilibrium concentration before it starts to ecrease. () Determine the time until a level of 100 µg/l is reache s = s 0 exp ( 1+ Kt ) t' t Where: t' = t 1. 5years 0.2 t' 100 µ g / L = 170µ g / Lexp yr yr 1.0yr t'= 2. 1 years 6

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