C = W/a a = Q + v s A + kv C=C o e -λt. 7. Lakes (reactors) in series (SS)

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1 What have we done to date? 1. Regulations 2. Hydrology (ΔS = Rivers + Precip. + Groundwater disch. Outflow Evap. GW out ) 3. Kinetics 4. Eutrophication description, model 5. Limnology (field trips) 6. Mass Balance Model SS, NSS gen l Precipitation River inflow C River outflow C = W/a a = Q + v s A + kv C=C o e -λt Burial (v s CA) 7. Lakes (reactors) in series (SS) River, groundwater Inflows Reactions Biological uptake Precipitation/dissolution Biological decay Radioactive decay Hydrolysis Oidti Oxidation/Reduction /Rd Photolysis Diffusion Precipitation Air-water Exchange (gas transfer) River, Ground water outflows Mixing (Dispersion) Settling Burial 1

2 SS Example: Greifensee Lake Characteristics: Greifensee Parameters Value Volume (m 3 ) 1.51x10 8 Surface Area (m 2 ) 8.49x10 6 Mean Depth (m) 17.8 Q in (m 3 /d) 3.7x10 5 Q out (m 3 /d) 3.7x10 5 Temperature ( o C) 20 Residence Time (yr) 1.12 Suspended Solids (mg/l) 5 f OC 0.4 Particle settling velocity (m/d)

3 Chemical Properties Henry s Law Constant K ow, K OC or K D Diffusion coefficient Reaction rate constants (biodegradation, photolysis, hydrolysis, gas transfer, settling) Chemicals: General properties ATRAZINE: pesticide, low volatility, high solubility, low tendency towards sorption, slow biodegradation in water TETRACHLORO- ETHYLENE: highly volatile, low solubility, low tendency towards sorption, slow biodegradation 3

4 Chemicals: General properties PCBs: moderately volatile, low solubility, high tendency to sorb, very slow biodegration PHOSPHATE: nonvolatile, high solubility, moderate tendency to sorb, highly bioreactive SULFATE: nonvolatile, high solubility, no tendency to sorb, moderately bioreactive Mass Balance Model dc V = W Q C V C k dt rxn 4

5 GREIFENSEE Chemical fate comparison. Atrazine PCE PCB PO 4 SO 4 K h unitless 1.0E K ow unitless ,200, K oc unitless ,200, K d L/kg ,260, k sed 1/d 5.6x x x x x10-5 k gas 1/d 2.8x x x k chem 1/d 2.8x x10-5 k photo 1/d 8.4x x A m3/d 5.5x x x x x10 5 β C/Cin τ r d River, groundwater Inflows Reactions Biological uptake Precipitation/dissolution Biological decay Radioactive decay Hydrolysis Oidti Oxidation/Reduction /Rd Photolysis Diffusion Precipitation Dissolved Mixing (Dispersion) Air-water Exchange (gas transfer) Particulate Settling River, Ground water outflows Burial 5

6 Equilibrium Processes Inputs Outflow PCB Total Settling ONLY SORBED PCBs SETTLE Equilibrium Processes Inputs Gas Exchange (only dissolved phase) Outflow PCB Dissolved PCB Particulate Outflow Settling ONLY SORBED PCBs SETTLE C Total = C dissolved + C particulate = f particulate C Total + f dissolved C Total K K f D ow OC [ C particulate] [ C ] dissolved 6

7 Fraction in each phase f f f sorbed sorbed dissolved M sorbed Csorbed SS Csorbed SS = = = M C Total Csorbed SS + Cdissolved Csorbed SS+ K KD SS = K SS + 1 D = 1 1 f = sorbed 1 + K SS D sorbed D SETTLING FLUX = v s C Total f PARTICULATE A Equilibrium partitioning Air-water exchange = (PCB * -PCB Total f dissolved )v aw A Inputs Outflow PCB Total Settling = f part PCB Total v s A 7

8 Diffusion & Dispersion Diffusive or dispersive transport is one common form of feedback. Examples include: Diffusion from pore waters (x); Reversible reaction such as Air-water exchange; Vertical and horizontal mixing in lakes; Sediment mixing (e.g, bioturbation); Hypolimnetic exchange; Plume dispersion in air or water; Mixing of embayments (estuaries) with lakes or oceans. 8

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10 Movement from high to low concentration t = 1 Depth Flux Conc. Distance t = 2 t = 3 g Flux( J ) 2 m d Mathematical formulation: D m d = F H G I K J F I HG K J dc g m dx( m) 2 3 D = E = K x,y,z dc D V = ΔC A= vxyz,, A Δ C = Kx' Δ C = k ΔC V dt Δx So K x Kx' = vx A= A= k A Δx Δx Units: D or E or K x = m 2 /yr or cm 2 /s v x = m/yr or cm/s K x = m 3 /yr or cm 3 /s k = 1/yr 10

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12 Depth Profile of [Cu] in L. S. (FR) Concentration (ug/l) Depth (m) FR1 (F) FR2 (F) FR1 (UF) FR2 (UF) What is the rate of crossmargin exchange? V dc dt C dv Δ + = QC QC W J A K C dt x A v Cf A in + river + dissolution Stampsand x int erface s sorbed Δ 12

13 100 Kx = cm2/s 0.1 cm2/s Conc. difference (μ μg/l) cm2/sr 1000 cm2/s 1 1e5 cm2/s 1.0E E+10 1e7 cm2/s 1.0E Q (m 3 /yr) Gradients depend on: 1. Different rates of production/consumption 2. Dispersion and flow slower than difference in #1 200 Nearsh hore/offshore (%) TDP Cu (aq) Cu (part) TSP-May TSP-July Cl- NO3- SO42- Na K Mg Ca Analyte 13

14 Height above sediment (m) Dispersion/Diffusion Coefficients in Lakes Log Dispersion Coefficient (cm 2 s -1 ) Epilimnion Hypolimnion vertical Horizontal 0 Comparison of Environmental Exchange Velocities Velocity (m yr -1 ) icle settling Parti P settling Molecular diffusion Ho orizontal mixing Gas Excha ange 0.1 Process 14

15 Points to remember: Approach for equilibrium processes (partitioning); Three common parameterizations for dispersive/diffusive fluxes; What processes are modeled as dispersive; Approximate velocities of dispersive processes. 15