Points to Learn. τ C. τ R. conservative substance reactive substance. τ W V Q. out. out
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1 Pots to Learn Steady State: defition Assimilation capacity - Concept - Mathematical defition: Transfer Coefficient, β =C /C Residence time: hydraulic conservative substance reactive substance τ R = a = τ W τ C W Q+ va+ kv = = V Q V Q out V Q + v A+ k V out
2 Mass Balance Change mass = Inputs - Outputs + ternal changes Rate of change of mass = Rate of put - Rate of output + rate of ternal change Inputs Reaction Outputs
3 dmass ( ) puts outputs transformations = ± Δt Δt Δt b dv C g = W Q C± k C V Constant volume = W Q C± kcv River puts domant Changg volume + C dv = W Q C± kcv River, atmospheric, groundwater puts = Q C Q C ± kcv = Q C + PC A ± Q C QC ± kcv ra GW GW First-order reaction = Q C Q C± kcv First-order transformation, settlg = Q C Q C± kcv v CA s
4 dmass ( ) puts outputs transformations = ± Δt Δt Δt b dv C g = W Q C± k C V Constant volume = W Q C± kcv River puts domant Changg volume + C dv = W Q C± kcv River, atmospheric, groundwater puts = Q C Q C ± kcv = Q C + PC A ± Q C QC ± kcv ra GW GW First-order reaction = Q C Q C± kcv First-order transformation, settlg = Q C Q C± kcv v CA s
5 dmass ( ) puts outputs transformations = ± Δt Δt Δt b dv C g = W Q C± k C V Constant volume = W Q C± kcv River puts domant Changg volume + C dv = W Q C± kcv River, atmospheric, groundwater puts = Q C Q C ± kcv = Q C + PC A ± Q C QC ± kcv ra GW GW First-order reaction = Q C Q C± kcv First-order transformation, settlg = Q C Q C± kcv v CA s
6 dmass ( ) puts outputs transformations = ± Δt Δt Δt b dv C g = W Q C± k C V Constant volume = W Q C± kcv River puts domant Changg volume + C dv = W Q C± kcv River, atmospheric, groundwater puts = Q C Q C ± kcv = Q C + PC A ± Q C QC ± kcv ra GW GW First-order reaction = Q C Q C± kcv First-order transformation, settlg = Q C Q C± kcv v CA s
7 River puts domant = Q C Q C kcv vsca
8 Changg gvolume with atmospheric,,groundwater puts + C dv = PCra A ± QGWCGW QGWC kcv vsca
9 C = STEADY STATE MODEL (or SOLUTION) = W QC kcv = 0 W Q+ kv Assumptions? W a = a = Assimilation il i capacity Can compare different compounds or sgle compound different lakes.
10 Lake Superior Assimilation Capacity Cl - 7x10 10 m 3 /yr NO 3-3x10 14 m 3 /yr P 1x m 3 /yr
11 Transfer Coefficient or (1- Removal Efficiency) C = QC Q + kv + v A C Q β = = C Q+ kv + v A s s Assumptions?
12 Residence Time Water Residence Time: V τ = Q Hydrologic or Conservative Chemical: V τ = V Q out Chemical Residence Time V Mass system τ = = Q + kv + v A effluxes out s
13 Lake Superior Residence Times Water Residence Time Hydrologic Residence Time TN Residence Time TP Residence Time 75 yr 175 yr yr yr 10 yr 50 d Longer chemical residence times ignore ternal recyclg.
14 Role of ketics dmass ( ) puts outputs transformations = ± Δt Δt Δt Possible transformations: Burial l adsorption, settlg Biological uptake growth ketics Biodegradation growth or enzyme ketics Volatilization mass transfer Photolysis Adsorption mass transfer Hydrolysis Dissolution/Precipitation
15 KINETICS: Pots to Learn Rate Laws: Zero Order: First Order: dc dc Second Order: Monod: dc/ dc dc = V Max C = k = kc = kc 2 C ln(c) 1/C C K + C Differential Analysis of Rates: FdC log log( k ) n log( C ) M I HG K J = + Reversible: Zero order: dc First order: dc Vmax = K C C k C app + = M t t t =V Max R = kcc * Ch Temperature Corrections: k = A k Q F H E RT K A exp H G I K J = k Θ T T 1 2 kt + = Θ = k k T
16 Reversible Reactions - Slow mass * Flux = J = v C C area time ( ) aw w w mass dc * Rate = = k ( C w C w ) vol time v = mass transfer coefficient (units of velocity, length/t) aw k = rate constant t (units of 1/time) * C = concentration at equilibrium Example processes: Air-water exchange (volatilization) Dissolution/precipitation
17 Reversible Reaction Example Air-water exchange: Henry s Law Constant - K = H C air C water C C * = air w K H
18 Reversible Reaction fast (equilibrium) Fast reactions: Acid-base Sorption HA H + A K a f HA + + { H }{ A } = { HA} 1 1 [ HA ] [ A ] Ka = = 1+ = 1+ + [ HA] + [ A ] [ HA] [ H ]
19 Equilibrium Processes Inputs Gas Exchange (only dissolved phase) Outflow PCB Dissol ved PCB Particul ate Settlg Outflow 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
20 Fraction each phase f f f sorbed sorbed dissolved M sorbed Csorbed SS Csorbed SS = = = M C Total Csorbed SS + Cdissolved C sorbed SS + K = KD SS K SS + 1 D 1 = 1 fsorbed = 1 + K SS D sorbed D SETTLING FLUX = v s C Total f PARTICULATE A
21 Equilibrium partitiong Air-water exchange = (PCB * -PCB Total f dissolved )v aw A Inputs PCB Total Outflow Settlg = f partpcb Totalv sa
22 SS Example: Greifensee
23 Lake Characteristics: Greifensee Parameters Value Volume (m 3 ) 1.51x10 8 Surface Area (m 2 ) 8.49x10 6 Mean Depth (m) 17.8 Q 3 (m /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 settlg velocity (m/d)
24 Chemical Properties Henry s Law Constant K ow, K OC or K D Diffusion coefficient Reaction rate constants (biodegradation, photolysis, hydrolysis, gas transfer, settlg)
25 Chemical Properties Henry s Law Constant K ow, K OC or K D Diffusion coefficient Reaction rate constants (biodegradation, photolysis, hydrolysis, gas transfer, settlg)
26 Chemicals: General properties PCBs: moderately volatile, low solubility, high tendency to sorb, very slow biodegration PHOSPHATE: nonvolatile, high solubility, moderate tendency to sorb, highly bioreactivee SULFATE: nonvolatile, high solubility, no tendency to sorb, moderately bioreactive
27 Chemicals: General properties ATRAZINE: pesticide, low volatility, high solubility, low tendency towards sorption, slow biodegradation water TETRACHLORO- ETHYLENE: highly volatile, low solubility, low tendency towards sorption, slow biodegradation
28 Mass Balance Model dc V = W Q C V C k rxn
29 GREIFENSEE Chemical fate comparison. Atraze 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 84x10 8.4x x10 5.6x A m3/d 5.5x x x x x10 5 β C/C τ r d
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