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 Print version Updated: 23 October 2017 Lecture #15 Gas Transfer (Chapra, L20) David Reckhow CEE 577 #15 1 The two film theory p g p i Interface c i c l David Reckhow CEE 577 #15 2 1

CEE 577 Lecture #15 10/23/2017 n  Two film model P Universal Gas Law V RT a Molar concentration  Flux from the bulk liquid to the interface   ( ) J K c c l l i l  Flux from the interface to the bulk gas K Mass transfer  g  ( ) J p p g g i velocities (m/d) RT a  And the K’s are related to the molecular diffusion coefficients by: D D  l  g K K l g z z l g David Reckhow CEE 577 #15 3 Two film theory (cont.)  We want to be able to relate flux to bulk air and water concentrations  interface concentrations cannot be directly measured   p     g J v c   v l   H e  to do this we must substitute expressions for the interface concentrations David Reckhow CEE 577 #15 4 2

CEE 577 Lecture #15 10/23/2017 Whitman’s 2 film model (cont.)  p H c  According to Henry’s law: i e i  And relating this back to the bulk concentration   ( ) J K c c Recall:   l l i l J     l J p H c     l i e l c c K So: i l l K l  now solving and equating the fluxes, we get (pg. 371 in text): 1 1 RT   a v K H K The net transfer v l e g velocity across the air- water interface (m/d) David Reckhow CEE 577 #15 5 correction (atm m 3 gmol -1 ) Figure 20.4, page 373 in text. David Reckhow CEE 577 #15 6 3

CEE 577 Lecture #15 10/23/2017 Two film theory and reaeration  The reaeration coefficient  represented by k a or k 2 or sometimes k L a  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 Units of L/T v a  v k Units of 1/T H David Reckhow CEE 577 #15 7 Reaeration Constant  Reaeration Constant, k a , depends on:  temperature  internal mixing  wind induced mixing  waterfalls, dams, rapids  surface films David Reckhow CEE 577 #15 8 4

CEE 577 Lecture #15 10/23/2017 DO Deficit D = DO - DO sat act where = oxygen deficit, [mg/L] D DO sat = saturation value of dissolved oxygen, [mg/L] DO act = actual dissolved oxygen value for the stream, [mg/L] David Reckhow CEE 577 #15 9 DO Deficit Mass Balance  Let us assume that the rate of oxygen entering the stream through the atmosphere is proportional to the dissolved oxygen 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 BOD u (ultimate BOD). dD   k L k D d a dt Where: = time, [days] t = ultimate stream BOD, [mg/L] L = deoxygenation constant, [day -1 ] k d = reaeration constant, [day -1 ] k a David Reckhow CEE 577 #15 10 5

CEE 577 Lecture #15 10/23/2017 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 David Reckhow CEE 577 #15 11  To next lecture David Reckhow CEE 577 #15 12 6