The two film theory p g p i Interface c i c l David Reckhow CEE - - PDF document

CEE 577 Lecture #15 10/23/2017 1

Lecture #15 Gas Transfer

(Chapra, L20)

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Updated: 23 October 2017

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The two film theory

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Interface pi pg cl ci

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Two film model

 Flux from the bulk liquid to the interface  Flux from the interface to the bulk gas

 And the K’s are related to the molecular diffusion

coefficients by:

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J K c c

l l i l

  ( )

J K RT p p

g g a g i

  ( ) Mass transfer velocities (m/d)

K D z

l l l



K D z

g g g



a

RT P V n 

Universal Gas Law Molar concentration

Two film theory (cont.)

 We want to be able to relate flux to bulk air and

water concentrations

 interface concentrations cannot be directly measured

 to do this we must substitute expressions for the

interface concentrations

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         

l e g v

c H p v J

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Whitman’s 2 film model (cont.)

 According to Henry’s law:  And relating this back to the bulk concentration  now solving and equating the fluxes, we get (pg. 371 in

text):

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p H c

i e i



p H J K c

i e l l l

       

1 1 v K RT H K

v l a e g

 

The net transfer velocity across the air- water interface (m/d) J K c c

l l i l

  ( )

l l l i

c K J c  

Recall: So:

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Figure 20.4, page 373 in text. (atm m3 gmol-1) correction

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Two film theory and reaeration

 The reaeration coefficient

 represented by ka or k2 or sometimes kLa  is the first order rate constant for the loss of D.O. deficit

in a water body

 it is equal to the net transfer velocity divided by the

water depth

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H v k

v a 

Units of L/T Units of 1/T

Reaeration Constant

 Reaeration Constant, ka, depends on:

 temperature  internal mixing  wind induced mixing  waterfalls, dams, rapids  surface films

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DO Deficit

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D = DO

• DO

sat act

where D =

• xygen deficit, [mg/L]

DOsat= saturation value of dissolved oxygen, [mg/L] DOact= actual dissolved oxygen value for the stream, [mg/L]

DO Deficit Mass Balance

 Let us assume that the rate of oxygen entering the stream

through the atmosphere is proportional to the dissolved

• xygen deficit in the stream. Similarly, let us assume that

the rate of oxygen consumed or leaving the stream is proportional to the amount of organic matter in the stream, expressed as BODu (ultimate BOD).

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Where: t = time, [days] L = ultimate stream BOD, [mg/L] kd = deoxygenation constant, [day-1] ka = reaeration constant, [day-1]

D k L k dt dD

a d

 

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D.O.: sources & sinks

 Sources

 reaeration from atmosphere  photosynthesis  loading from aqueous inflow

 point: tributaries  non‐point: runoff

 Sinks

 CBOD oxidation  NBOD oxidation  SOD  Plant Respiration

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 To next lecture

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