Transcript Air / Water Gas Exchange

Air / Water Gas Exchange
The distribution of a chemical across the air-water interface
between the atmospheric gas phase and the water dissolved phase
•Equilibrium transfer of organic chemical between Air and Water
KH = Pa / gw Cw
Appropriate for:
Exchange between air and falling raindrop (over ~10 m fall)
Low MW organic gases exchanging between peat water and bubbles
(in wetlands and marshes)
Confined headspace over a solution
Sheltered systems with more or less constant water and atmospheric
conditions
Inappropriate for :
Large Lakes
Flowing rivers
Spills in both rivers and lakes
Oceans ( sometimes ! )
In these you must consider Mass Transport (absolute and net fluzes)
Processes of Air / Water Exchange
Depiction of the physical processes responsible for the movement of chemicals
through four zones spanning an intact “air-water” interface (i.e. no bubbles or
aerosols).
Figure from Schwarzenbach, Gschwend and Imboden, 1993
Processes of Air / Water Exchange
“Little” Mixing: Stagnant, 2-film model
“More” Mixing: surface renewal model
Wave Breaking: intense gas transfer ( breaking bubbles)
Figure from Schwarzenbach, Gschwend and Imboden, 1993
Stagnant Boundary Layer Model
of Air / Water Exchange –
Whitman Two Film Model
Figure from Schwarzenbach, Gschwend and Imboden, 1993
Two Film Model
Net Flux =
Kol
*
(Cw – Ca/H*)
resistance to transport * Concentration gradient
relative to equilibrium
H* is “dimesnionless” Henry’s Law Constant at ambient temperature
1/ Kol
= ( 1/ Kw + 1/ (Ka H*) )
= (1 / Dw / zw) + (1/ Da/ za H*)
where
Dw = diffusivity in water
zw = water film thickness
Da = diffusivity in air
za = air film thickness
un-measurable parameters: zw, za
Figure from Schwarzenbach, Gschwend and Imboden, 1993
Two Film Model- Continued
Fw = - Dw ( Cw/a – Cw ) / zw
So, at steady state:
Fw = - Dw ( Cw/a – Cw ) / zw = -Da (Ca – Ca/w) / za = Fa
Fluxtotal= Fw = Fa
since: KH’ = Ca/w / Cw/a
then:
( mol / Lair / mol / Lwater)
Dw (Cw-Cw/a) / zw = Da (KH’ Cw/a- Ca) za
Cw/a = ( ( Dw / zw) + ( Da / za) Ca ) / ( ( Dw / zw) + ( Da KH’ / za ) )
Foverall = 1 / ( zw / Dw ) + (za / Da KH’) * ( Cw- Ca / KH’)
mass transfer coefficient (cm/hr) * Conc. gradient
Fnet= (+) then water ====> air b/c (Cw > Ca / KH’)
Fnet = (-) then air ====> water b/c (Cw < Ca / KH’)
Two Film Model- “Velocities”
Fluxtotal= vtot * ( Cw – Ca/ KH’)
mol m-2 sec-1 = m sec-1 * mol m-3
Defining “Partial Transfer Velocities:
vw = Dw / zw
&
va = Da / za
1 / vtot = 1 / vw + 1 / va KH’
Resistance analogy:
1 / Rtot = 1 / Rw + 1 / Ra
Transfer dominated by layers:
vw << va KH’ ==> vtot ~= vw
vw >> va KH’ ==> vtot ~= va KH’
1 / vw ~=~ 1 / va KH’ ==> Both phases important
Steady State Flux
Figure from Schwarzenbach, Gschwend and Imboden, 1993
Two Film Model- Important Factors
za & zw
: higher turbulence (wind, flow ===> decreasing thickness)
H
: Temperature, Ionic Strength ( x 2-3 for every 10oC)
Surface films (surfactants) additional barrier & additional resistance.
The time needed for average molecule to cross film / boundary layer:
tw ~= zw2 / Dw = zw / vw
ta ~= za2 / Da = za / va
if:
zw ~ 5x10-3 cm
za ~ 5 x 10-2 cm
Dw ~10-5 cm s-1
Da ~ 0.1 cm s-1
then, diffusion times ~ seconds
 a-w exchange is rapid ( & increased with greater turbulence)
Film Resistance in Whitman Model
Flux = vtot (Cw – C*)
where C* = Ca / KH
1/ vtot = 1 / vw + RT / H va
( kol )
( kw )
( ka )
Compounds exhibiting liquid phase resistance:
O2, CO2
kw = 2-10 cm hr -1
Compounds exhibiting gas phase resistance:
H20
ka = 200 to 2000 cm hr-1
Dominant phases for resistance to transfer:
Resistance = ( RT kw ) / ( KH ka ) = 0.024 * 0.005 / KH
so
Resistance = 0.00012 / KH @ 25 oC
KH >~ 10-3 atm m3 mol-1 ===> resistance is 95 % in water phase
KH <~ 5 x 10-6 atm m3 mol-1 ===> resistance is primarily in air phase
Air – Water Exchange Mechanisms
4 layers of resistance to transfer in series:
Vertical Transport in turbulent air and water is fast (& generally not limiting to gas exchange).
Transport is diffusion limited in stagnant films (layers) on both air and water side of the interface
Exchange is instantaneous at the air-water interface.
In cases where effectively no mixing occurs in boundary layers,
Whitman 2 layer (film) model applies
In cases of high turbulence on air and water sides, “new” and and water parcels displace “old” air
and water parcels,
Surface Renewal Model applies.
In both models, mixing forces dissipate rapidly below 1mm on air side and 0.1 mm on water side
So, Boundary Layer thicknesses are:
~1000 mm – air
~100-200 mm – water
In both models, gas penetration is rapid (high injection velocities) at interface and equilibrium is
achieved and assumed (thus we can use KH)
Overall: Limitations to transfer are provided by both boundary layers
Influence of KH on Dominant Process
Large Compounds
Polar Compounds
Small compounds
Non-Polar Compounds
Figure from Schwarzenbach, Gschwend and Imboden, 1993
Surface Renewal Model
Figure from Schwarzenbach, Gschwend and Imboden, 1993
Surface Renewal Model
Renewed Surface
Non-renewed Surface
Eddies
Parcels of Air and water are mixed to interface where exchange occurs (instantaneously).
Surface Renewal Model
F = ( 1 / (1/ ( r * Dw )1/2 ) + (1 / (KH’ (r * Da)1/2) ) * ( Cw – Ca / KH’ )
Mass transfer coefficient
(or, water parcel renewal rate)
where r = water parcel renewal rate (t-1)
Dw, Da = molecular diffusion coefficents
vtot = [ ( 1 / ( rw Dw )1/2 ) + 1 / (KH’ (ra Da)1/2) ]-1
vw = ( rw Dw )1/2
va = ( ra Da )1/2
Conc. gradient
Surface Renewal Model: Continued
Conceptually, describes turnover of parcels of air and water at interface
Dominant exchange process is renewal or exchange of parcels
no diffusive exchange in boundary layers ( diffusive exchange at
interface)
size of boundary layer is not important
Account for time varying diffusion
vw = ( rw Dw )1/2
where
va = ( ra Da )1/2
rw = renewal rate for water parcels (sec-1)
ra = renewal rate for air parcels (sec-1)
Conceptually ==> when r, then z  and thus F .
Surface Renewal Model: Continued
F = Kol * ( Cw – Ca H*)
resistance to mass transfer * conc. gradient
1 / Kol = ( 1 / ( rw Dw )1/2) + ( 1 / H* ( ra Da )1/2)
1 / Kol = 1 / kw + 1/ (H* ka)
un-measurable parameters: rw, ra
Where do these two models leave us?
F = Kol * ( Cw – Ca / H)
Whitman two film model un-measurable parameters: zw & za
Surface renewal model un-measurable parameters: rw, & ra