Interphase Mass Transfer 2

[jproj]

I am looking for some guidance in calculating the mass transfer of non-condensable gases from liquid (water) to steam. I have Perry's (7th ed.), but am not real sure how to even approach this situation (I've been looking in chapter 5 in Perry's, but I'm not having much luck). All we were taught in college was how to calculate mass transfer in distillation columns with solutions that have clear (easily found) equilibrium relationships (benzene & toluene etc...), and it's been years since I've even done those calculations.

The liquid flows in a thin hollow cone countercurrent to stripping steam (in a degasifier). Liquid is initially cold and is heated to saturation temperature thereby releasing the dissolved gases by Henry's law. The non-condensable concentration in the liquid is low (from 3 - 15 ppm) and I would assume that the concentration in the gas would be negligible.

Can someone please point me in the right direction (books, websites, equations, examples)? Everything I've read so far is geared toward distillation columns. I'm inclined to think that the geometry (surface area / thickness) of the film has an effect on the mass transfer, but I can't find anything even mentioning geometry.

Thanks a million in advance!!!

jproj

 

[PHP78]

Hi
Your problem is stripping problem. I think you got different geometry for your case and thats why you are not able to make decision about using distillation kind of approach.
I will suggest following way:
If you got a small stripping unit then treat it as one seperating stage. Now you can do it two ways:
1. Either treat it as equilibrium stage
2. or treat it as non-equilibrium stage

As you know the henry's constant, you can find the equlibrium relation easily. For non-equilibrium apporach, either use efficieny type of approach with equilibrium or rate based models. Both considers geometry etc but rate based approach (e.g with two-film theory ) is more rigorous and more difficult to solve.

My above explaination is anologous to equilibrium stage seperation. If you got quite different case like conical shaped equipment and can't make assumptions like equilibrium then you have to consider hydrodynamics for that geometry and apply first principles (momentum, enery balance) to solve rigorous equations.

But as you said you got very low conc (in ppm) i will suggest that don't get caught in more rigorous cases. Even if you try to find more sophisticated models, you will find it diificult to judge with experimental case.

Whats your primary goal? do you want to find the concentration in outlet streams? heat effects? Apply simple anologies.

If you are interested in seperation stage based models then refer
"Separation Process Principles", Seader j D and Henley E J, John Wiley and Sons New York.

I hope you will find something interesting from above if i have understood your problem correctly.

Prashant

 

[jproj]

PHP78:

I guess what I am trying to do (to clarify my problem) is to come up with the amount of gas (dissolved non-condensables) transfered from the cold water flowing into the vessel to the steam, which is heating the inlet water (and later condensing). One problem I have is that the Henry's constants I have are nowhere near the saturation temperature (I guess I could extrapolate?). Another problem is the geometry (conical shaped thin walled falling film). Most of the mass transfer relations deal with a wetted wall column (w/ mass transfer on one side), not a turbulent spray in mid air. On top of that, I don't have a clue as to how I'm supposed to calculate the mass transfer coefficients (zero experimental data).

Am I spinning my wheels because of a lack of information (e.g. experimental data) or am I just missing something (e.g. equation to calculate the mass transfer coefficients).

By the way, I have the reference you mentioned (Separation Process Principles) and have looked through it for most of the day. Any particular section / pages I sould be looking at?

Thanks for the help.... sorry I'm not very good at mass transfer.... it's been WAY to long.

Best Regards,
jproj

 

[mirchee]

For a given solute in a given solvent, Henry's constants are generally a strong function of temperature and also a function of concentration. The liquid phase is not required to be boiling (i.e., stripping from a cold solution is feasible and the Henry's constants for the solutes still apply and are mainly a function of temperature, T, and the liquid phase concentrations, x).

For solutes with a substantial heat of solution, you must also model the heat transfer aspects since the liquid film temperature will change as the material is stripped. Also, any heat transfer against the vapor phase must be considered.

For a thorough discussion of mass transfer, see:
(1) Sherwood, Pigford and Wilke, "Mass Transfer" (McGraw-Hill, 1975)
(2) Treybal, "Mass Transfer Operations", 2nd edition(McGraw-Hill, 1968)
(3) For a more advanced text dealing extensively with the multicomponent case, see Taylor and Krishna, "Multicomponent Mass Tansfer (Wiley-Interscience, 1993)
(4) For how to proceed with computations in odd geometries (cylindrical or spherical coordinates) and for much additional discussion re. simultaneous momentum, heat and mass transfer, see Bird, Stewart and Lightfoot, "Transport Phenomena", 2nd edition (Wiley, 2002). This second edition is the last word on the general subject of transport phenomena.

Your problem would appear to require consideration of a conical surface, so cylindrical coordinates seem most appropriate. In this geometry, it is certain that the liquid film thickness and velocity will vary sharply as you go down the cone. Remember also that if you have turbulent flow, the eddy diffusivities also come into play.

If you are dealing with the transient case, start with the appropriate equations of change for momentum, heat and mass transfer and solve the resulting coupled partial differential equations using a suitable PDE solver (do you have access to FEMLAB?). For the steady-state case, the PDEs will lose the terms containing the transients, but you will still have PDEs since the film thickness and velocity remain strong functions of how far down the cone you are.

As you might imagine, obtaining a rigorous solution is by no means a trivial task. Generally, in industry, such problems are handled by specialists. Asking university faculty for assistance is also not unheard of.

 

[jproj]

mirchee:

Thank you for the references, I'll definately look into them. After looking into this problem, I've realized why I haven't progressed very far towards a solution! Problem is, I work for a (very) small company with a tight budget, which means that things like this are done "in house". "We" also work under the common mentality that "it has worked this way for X years..."

I hope you can understand my frustration! I really appreciate the help though!

Best regards,

jproj