13 replies to this topic

[Fardu]

Hi,

May be either I have forgotten how to do it or I am not getting the point.

The attached is a quote from Treybal's and how he's drawing the Enthalpy-Composition diagram.

I am unable to get the straight lines for constant heat capacities and neglecting heat of solution of a binary solution noting that the bubble points and the dew points will be changed as the concentration of "A" (the more volatile component) changes.

Please help me out.

Regards,

Attached Files

•  Mass-Transfer-Operations-Robert-Treybal.jpg   60.43KB   16 downloads
•  Mass-Transfer-Operations-Robert-Treybal1.jpg   226.07KB   16 downloads

Edited by Fardu, 10 February 2013 - 08:11 AM.

[thorium90]

I think the straight lines are the tie lines in figure 9.11?

 

Attached Files

•  enthalpy conc diagrams.pdf   196.2KB   22 downloads

[Fardu]

I think the straight lines are the tie lines in figure 9.11?
 

Thanks thorium90, Sorry my question was not clear earlier. I wanted to have straight and parallel lines for saturated liquid and vapor in the H-x-y diagram so that Mc-Cabe thiele method assumptions of constant L and V can be met. The problem is that I am unable to find the conditions when these lines are straight and parallel. The conditions that Treybal specifies are of constant molal heat capacities and constant and equal molal latent heat of vaporization of A and B. But the enthalpy of the liquid as well as vapors also depend on the bubble and dew points as well which vary with composition, so how can these lines be straight and parallel as per Treybal.

[thorium90]

In the following link, benzene and toluene system. You can observe that Hgy and Hlx lines are parallel which means equal molal latent heat and constant heat capacities. (Middle picture)

 

http://faculty.ksu.e.../CHE411/CH3.pdf

 

There can be different cases no doubt, (left picture) In fact at the azeotropic composition, the line is vertical and so when drawn onto the xy diagram, the curve touches the diagonal line

 

But you can still draw parallel lines for your mccabe thiele diagram (Right picture)

Attached Files

•  different.jpg   201.62KB   9 downloads
•  pix1.jpg   29.38KB   8 downloads
•  mccabe_thiele.jpg   58.75KB   7 downloads

Edited by thorium90, 11 February 2013 - 02:21 AM.

[Fardu]

Dear thorium90,

 

Thanks for your reply, but the paper attached with your last post depcits the H-x and H-y lines straight but they indeed are not completly straight as you can observe by the very formula using which the liquid and vapor enthalpies were calculated. Let's focus the attention to the liquid enthalpy first. The formula is as given below:

 

h_x = x_A * C_pA * (T-T₀) + (1-x_A) * C_pB * (T-T₀) + del H_s

 

Neglecting the heat of solution, the enthalpy of the liquid (h_x) depends on x_A as well as T (the boiling point of the mixture). The T varies with x_A as rightly done in the calculation that followed. So my question is that the H-x line can't be a pure straight line although it can be very close to the straight line as shown in the H-x-y diagram drawn in the calculation.

 

Whether I am correct or missing something. If I am correct then the very assumption of the Mc-Cabe Thiele method of constant molal overflow and constant molal vaporisation would be an approximation rather than a fact. But certainly I am not very sure. Also the very statement written by Treybal's (the attached diagram in the very first post) will not hold true.

 

Attached here is the chart drawn for the same values used in the calculation used in the paper. Also shown are the straight trend lines (in black).

Attached Files

•  Book1.jpg   57.5KB   2 downloads

Edited by Fardu, 11 February 2013 - 03:03 AM.

[thorium90]

Yes its an approximation for the molal heat of vaporization part. The enthalpy line doesnt have to be straight but the gap (latent heat) is approximately constant, thats the approximation. This website has a nice description too. It also clarifies that constant molal vaporisation can be used unless it is reactive distillation.

http://www.chemicalf...p?topic=17538.0

 

From the picture, you can see that even if the Hxy lines are not straight, the lines on the xy diagram are still straight and mccabe thiele diagrams can easily be built. The thing is that the method is graphical thats why it can still make straight lines. But if the assumptions dont hold, then one cant use the graphical method and need to resort to the equations.

Attached Files

•  mccabe_thiele.jpg   63.31KB   4 downloads

Edited by thorium90, 11 February 2013 - 03:48 AM.

[Fardu]

Dear thorium90,

 

Thanks for your efforts. The link you provided gave how to use Mc-Cabe Thiele method when all the conditions are not fulfilled. Again, I am very sorry that I am still not getting my point explained. I want the H-x line to be straight on an H-x-y diagram, can it be possible at least theoritically. Yes or No.

 

If the answer is yes, then how (using what equation for definition of entalpy).

 

If no, then how can one derive the constant molal overflow and constant molal vaporisation condition from the enthalpy composition diagram. Please see attached pics in which Badger and Banchero (Introduction to Chemical Engineering by W L Badger and J T Banchero) tries to explain and deduced by similar triangle method the concept of constant molal overflow and constant molal vaporisation-a basic foundation of Mc-Cabe Thiele method.

Attached Files

•  scan0008.jpg   167.6KB   8 downloads
•  scan0009.jpg   108.79KB   9 downloads
•  scan0009 - Copy.jpg   38.72KB   6 downloads

[thorium90]

Hi, as your pictures explain," this relationship... is more nearly true if quantities are measure in moles, compositions in pound moles...". This sentence implies that the straightness of the Hxy lines and its parallelism is assumed when they are expressed in moles and pound moles. ie: it is an assumption that they are approximately straight and parallel. The truth is that not all mixtures combination can satisfy this assumption, thats why McCabe Thiele is really an approximate way of calculating no of trays and is not a rigorous method. Nevertheless, as in my previous post, its still possible to do this method and get results (even if it is questionable). The condition of the lines being straight is a physical property, you cant change it with maths. The method only states that one can assume they are straight and parallel if the units of moles and pound moles are used. If the assumptions cant be applied, then one really has to do a tedious (on paper) tray by tray heat and mass balance.

Edited by thorium90, 11 February 2013 - 07:44 AM.

[Fardu]

Dear thorium90,

 

I was thinking the same way as you stated in your last post. But when I see the statement made by Treybal (see the figure attached) it made me think otherwise. Anyways If the statement could be rewritten as follows, do you think it would be more appropriate. By the way it's sort of challenging the intellect of Treybal.

 

"If the HGy and HLx curves are straight parallel lines (which are more nearly so if the molar latent heats of A and B are equal, if the heat capacities are constant over the prevailing temperature range, and if there is no heat of solution)."
 

Attached Files

•  Mass-Transfer-Operations-Robert-Treybal.jpg   60.43KB   7 downloads

[thorium90]

It can be interpreted as, if the molar latent heats are equal, the gap between the two lines are equal and if the heat capacities are constant, the lines are straight.

Therefore if both molar latent heats and heat capacities are not equal then it will look like Figure 9.12

[Fardu]

Thanks thorium90.

 

Thanks, but I am not satisfied.

"and if the heat capacities are constant, the lines are straight."

 

The lines may be nearly straight, i.e., the curvature is less for the condition stated above, but the lines are never straight even for constant specific heats. Are they?

 

Please forgive me, that's not arogancy but needed to get this right.

[breizh]

http://ihome.ust.hk/...3210/221-05.pdf

 

Take a look ! It might answer your question.

Breizh

[thorium90]

Perhaps one can try thinking of it this way. The equation for a straight line is y=mx+c. Using the link from breizh, one can see some semblance to a straight line. However, you will note that Cp is a function of temperature too, but since the mixture is boiling over a presumably small enough range to not change too much, the enthalpy line can be assumed to straight enough

Attached Files

•  straight line.jpg   16.28KB   3 downloads

[Fardu]

Thanks thorium90 and breizh,

 

I think I have got my point cleared. Thanks again for showing interest.