5 replies to this topic

[Ahmdoon]

Dear members..
At the begining, I'd like to thank you for this amazing forum that supports sharing knowldge, and I wish you all the best guys. I have a multicomponent distillation column with a feed composed of Dimethyl ether (DME), Water, and Methanol.

my column is designed to separate the DME from the water and methanol. The light component is DME, and the heaviest is water.

The flow rates are:

The feed is: 682.2 Kmol/hr at (Pressure = 10 atm; Temp = 125 C) with fractions of:
DME = 0.4
Water = 0.4
Methanol = 0.2

And the flow of Distillate is 272.19 kmol/hr, at Pressure = 9.35 atm, Temp = 46 C, with fractions:
DME = 0.995
Water = 0.003
Methanol = 0.002
_____________

Bottom flow is 410.01 kmol/hr, at Pressure = 10 atm, Temp = 150 C, with fractions:
DME = 0.005
water = 0.665
Methanol = 0.33
_____________

I excuted most of the overhead calculations by myself, and I found the vapour presures to be:
DME = 8.79 atm
Water = 0.0996 atm
Methanol = 0.4592
_____________

My problem is the relative volatility. I tried to calculate it many times, but the numbers are big! Would you please guys be kind enough to help me in this one, and I will carry on the rest of the design calculations? Just show me how much the "relative volatility of the heavy key" and the "relative of the light key" are, and their average in my case.

[MrShorty]

My problem is the relative volatility , i tried many times to calculate but the numbers are big !

What do you mean by "big?" What makes you think that the large values you are calculating are wrong?

The next question would be, how are you calculating relative volatility? We could assume Raoult's law -- which makes the relative volatility equal to the ratio of the vapor pressures. Raoult's law is likely an oversimplification, though. If you have some activity coefficient information, we could use that to get a better value for the relative volatility. You could even use UNIFAC to estimate the activity coefficients if you don't have measured activity coefficient data to go on.

Edited by MrShorty, 30 December 2010 - 10:00 AM.

[Ahmdoon]

Thanks Mr Shorty for the reply,,
well i used raults law which states : Ka= (VP)a/P ( vapour pressure of component a / total pressure )

for example for the DME, Whater and Methanol K values , i did :

DME = 8.79/9.35 = 0.94
Water= 0.0996/9.35=0.0106
Methanol = 0.4592/9.35=0.0491

from raoult's law again aab= Ka/Kb
and in my case i did aab= 0.94/0.0106 = 88.679 !!
is such calculation right ? If not plese help me out in this one and show me the exact way of carrying these calculations out.

I apperciate your help

[Eng-G]

Hi Ahmdoon !

You have a multicomponent system .. and the relative volatility of a&b = Ka/Kb .. but this law is only for a binary system not for multicomponent !!!

So, to apply it in your system you have to combined two of the three components you have..

If you assume Ka to be for DME .. you have to assume Kb to be for both Methanol and Water..

aab= Ka/Kb

where Ka=ya/xa (for DME) ..
and Kb=(yb/xb)/(yc/xc)

where yb and xb are for methanol because it's more voltile than water .. yc and xc are for water

good luck

Edited by Eng-G, 31 December 2010 - 03:57 AM.

[Eng-G]

Hi !

try also this law.. but in this case you have to calculate the vapor pressure of DME at the temperature of distillation column.. do the same thing to calculate VP for Methanol and Water
aa,b= VPa/VPb

where VPa is vapor pressure of DME
and VPb=VP of Methanol/VP of Water

try the two relation I gave to you and choose the more easier and logical value of the relative volatility !

Edited by Eng-G, 31 December 2010 - 04:56 AM.

[MrShorty]

Ahmdoon: That is correct for Raoult's law. A couple of additional notes:

1) As EngG suggested, with multicomponent systems, it is important to know which compound is the "reference" compound for relative volatility. In your case, if "relative volatility of light key" means "relative volatility of DME relative to water," then you have the answer (assuming Raoult's law).

Part of this is knowing what the software means by "relative volatility of the light key." All of our ramblings here are meaningless if the software has a different idea of what these quantities represent. You might spend some time with your software documentation to determine what the software is doing.

2) It depends on how important this is to the simulator (I'm not familiar with commercial simulators), but I would probably challenge the assumption that Raoult's law applies. I would expect a nonpolar compound (like DME) with a very polar compound (like water) to have a substantial activity coefficient. The only point in the system where the relative volatility of DME over water is 90 would be at the point where the activity coefficients of water and DME are equal.

Introducing the activity coefficient makes the relative volatility dependant on composition as well as temperature. As you go up in the column, the activity coefficient of DME approaches 1, I would expect the activity coefficient of water to increase, which lowers the relative volatility of DME over water as you go higher in the column (maybe this is why you thought 90 was too large). Approaching the bottom of the column, I would expect the relative volatility of DME over water to increase.

Hopefully that didn't make the problem worse.