Raoult's Law / Psychrometric Charts / Humidity 1

[BenjaminM]

I've got what I would have thought would be a fairly simple problem, and I am trying not to over complicate it.

I've got a tank half full of water at 80*C. I've got an air line blowing through the reactor at some flow rate, and I am trying to make an estimate of how much water is evaporating. I am assuming the air flow is fully saturated with water. I haven't located any psychrometric charts at higher temperatures.

Is Raoult's Law all I need for this estimate?

At 80*C the vapor pressure would be 6.85 PSIA.

(yi)(P)=(xi)(Psat)

yi = (1.0)(6.85)/(14.7) = 0.465

So the head space of the vessel is 46.5 mole % water?

Thermodynamics has been too long ago.

 

[Latexman]

Your logic seems sound to me.

Good Luck,
Latexman

 

[TiCl4]

If you have a very small air flow rate, this might be correct. If you have any significant flow rate of air, then the headspace will not be "well-mixed" and you will have a concentration gradient within the tank. You would need to analyze the evaporation based on diffusion of water in air.

At what flow rate/headspace turnover it starts requiring diffusion calcs, I'm not sure.

 

[BenjaminM]

TiCl4,

I may be somewhere in the middle. I am estimating 20 ft3/min air flow and around 350 ft3 headspace to start with. I have not yet had the opportunity to measure the air flow, so it may be significantly more.

For the diffusion coefficient for water into air at 80*C, I am looking at 1.47 ft2/hr.

I am scratching my head for the values of z2 and pA2, especially if it headspace is not considered well mixed.

 

[BenjaminM]

Latexman,

Thank you for the quick followup!

 

[MortenA]

In many such estimates you may not be interested in the actual value but just that it dosnt exceed a certain value. In these cases i usually do a rough estimate (same as you did initially) and then see if im happy. Only if the results causes me "problems" then i will sharpen my pencil and do a more detailed calculation (and only if i think it will matter).

I cant see that you have told us what z2 and pA2 is?

With regards to the water content in the air: Since the vapour pressure you calculated in 6.85 psia and the total pressure is 14.5 psia (atm pressure) then molar % vol would be 6.85/14.5=47% as you calculated. But you have to consider that a volume of air at 80ºC has les moles than at say 0ºC

You could have a look at this calculator from checalc:

https://checalc.com/calc/wetBulb.html

With this i calculate that for each 1m³ air you replace (assuming perfect mixing) then you loose 0.3 kg water (i would check this myself ) Then you just need the energy to evaporate the water or your water will become colder and colder. If this (either the water loss or the energy loss is acceptable then i would go no further.

Best regards, Morten



--- Best regards, Morten Andersen

 

[BenjaminM]

MortenA,

Roughly speaking I'm looking at an 8,000 gallon vessel which is half full being slowly heated to maintain 80*C.

I am considering z1 to be 0ft at the surface of the liquid. I'm trying to determine how well mixed the headspace will be. If it is well mixed, I would think z2 would be inches above the surface. If not, it could be several feet up into the head space. With roughly a 12ft straight side, I'd have 5 ft to the top dish.

If the head space is relatively well mixed, and I have about 350 ft3 head space initially, and I am flowing in 20 ft3/min. I believe pA2 would be proportional to that ratio.

But also as I stated, I have not yet taken measurement of the air flow. If my assumption of 20 ft3/min is way off, pA2 may be significantly different.

Also thank you for the link that is an excellent resource!

 

[pierreick]

Hi,
Another resource to support your work
Pierre

 

[MortenA]

@OP, OK, but what im trying to say is dont overcomplicate it if you can live with the result. It more or less can only get better if your assumptions are conservative. And if its for sizing then at least you wont have under designed your heating system.

--- Best regards, Morten Andersen

 

[pierreick]

Hi,
Consider the PPT attached about molecular diffusion which is doing echo to Ticl4's comments .
Hope this is helping you.
Pierre

 

[chicopee]

Here is a thought, do some research into the principle of hot tubs particularly about those used indoors. Hot tubs have air bubble equipment which cause significant moisture in the air which has to be exhausted.