LPG blend in a closed vessel

[Roberttt]

Hi all!

First of all, sorry if my English isn't that good. I'm a Dutch Chemical Engineering trainee so still learning things.

After a day of 2 doing some research to the problem described below, I don't know what to do next. I hope someone here can help me to find a solution for this problem.
This is the situation:

In a Chemical factory is an closed vessel filled with (liquid) LPG. This (liquid) LPG consists of 18.886 mol% propane & 89.114 mol% butane. The vapour pressure from this blend at 24 degrees Celcius is around 310264 Pa. The closed vessel has a total volume of 60 m3. The LPG level is mostly 52.8 m3, 24.8m3 or 6m3.

My job is to calculate the composition of the blend, as the LPG level in the tank becomes lower. I think that the ratio propane:butane becomes lower in the liquid phase as the level gets lower, because propane got a higher vapour pressure, so there will evapourate more propane than butane. This will make the fraction propane lower in the liquid phase and makes the blend have a different composition.

This thread (

https://www.eng-tips.com/viewthread.cfm?qid=121516)

helped me already calculate the composition from the vapour at a LPG level of 52.8m3, but I don't know how to go further now as the level lowers. Someone who can help me?

If there are any questions left, then I'd like to hear that!

Thanks,

Robert

 

[georgeverghese]

The maths for this is quite involved for a forum type environment if you were to run this calc manually. Fortunately, you can use the depressure utility routine on a process simulator (Pro/ II or Hysis) to model this batch operation to see how the liquid phase changes composition as level drops.

 

[Roberttt]

Hmm, allrighty. Is there maybe a way then how to calculate the number of moles that evapourates? I used the pV=nRT for that to calculate n/V (the concentration) and than multiply that answer by the volume above the liquid (in case of 52.8m3 it will be 7.2m3 (60-52.8) to get the number of moles in the vapour. But I don't think that it's correct, is it?

 

[rense]

you know initial composition and, from mass balance, you can calculate compositions (vapor and liquid at equilibria) at different time steps,
a simple model could be based on ideal gas law and vapor pressure of different components but if you need accurate results consider a EOS,
with simple models maybe you can solve analytically (look in textbooks for details), working with Excel and Prode I prefer direct integration procedures which provide accurate results without too much efforts, see for example this old paper

http://files.engineering.com/getfile.aspx?file=Chemputers1994.pdf

 

[Roberttt]

Hmm. A simple model is enough in this case so via Excel should be enough.

So in a mass balance way it should go:

Accumulation = STREAM IN - STREAM OUT

STREAM IN is in this case 0 and STREAM OUT should be the flow that the pump produces. This is an overall mass balance over the whole vessel. I'm only stuck when I have to add the vapour process in this formula.

The old paper example does not open for me, could you maybe upload it on something else?

 

[georgeverghese]

For the theory and expressions related to this exercise if you have to do this manually, you will have to:
a) Refer to vapor liquid phase equilibrium narratives in your Uni thermo text book. There may even be a section on how batch mixes behave.
b) K value nomograph for C3 and C4
c) Decide whether this level reduction operation is slow enough to be considered as isothermal or if it is adiabatic. Adiabatic calcs could turn out to be more painful.
In most oil/ gas engineering or operating companies, trainees would not be expected to run this calc manually, though I agree it may help you appreciate how multicomponent 2phase mixes behave in real life.

 

[rense]

you know the initial conditions (compositions and volume of vessel),
at each time step you subtract a predefined amount (vapor and/or liquid phase) ,
from mass balance calculate and define the new composition (remember you have fixed volume for vessel and different specific volumes for vapor / liquid fractions) , with Excel VBA and Prode you can redefine composition with setZ() macro ,
calculate new conditions for example solving a V,P (volume and pressure) or isothermal T,P (temperature and pressure) flash specifications, with these tools you have access to a full set of flash operations... ,
again, subtract vapor/liquid, solve mass balance, redefine compositions and go on...

I think it is not much different from the procedure discussed for the last case in the paper...

 

[Compositepro]

Obviously the composition of the vapor and liquid will change slightly as the vessel empties, but it should not be a very significant change, or else LPG would not be a very useful fuel mixture. And also remember that the vessel will go though many empty and fill cycles so, on average, there should be no composition change.

 

[Roberttt]

@rens The link from the old paper does not work for me. Is there another way how I can see it?

 

[rense]

http://www.google.com/search?q=chemputers1994.pdf

as alternative you may wish to consider simplified models, with these you can try to compute the integral analytically (solving differential mass balances at specified conditions), an example is the Rayleigh equation but several other cases are discussed in textbooks..

 

[Roberttt]

Thanks @rense!

Just a quick question;

If I want to calculate the number of moles in the headspace with n = pV/RT, is p the vapour pressure from the pure component, or (like in this case with propane) the fraction 0.18886 times the vapour pressure of the pure component? And is the volume the volume of space in the tank above the liquid?

 

[MarcTroy]

as said by others, with simplified models you can combine Raoult's law (partial vapor pressure of each component is equal to the vapour pressure of the pure component multiplied by its mole fraction in the mixture) or p1 = Vp1*x1 ; p2 = Vp2*x2 ... and so on, with Dalton's law (total pressure is the sum of partial pressures of different components or P = p1*x1+p2*x2...),
I do not know if these simplifications (ideal laws) are applicable in your case,
also you do not give us details about the process (isothermal, isobaric, isochoric, adiabatic ?)
with Prode Properties (applying rigorous simulation models) you can solve different flash operation and (of course) obtain different results...