Ponchon-Savarit Method: Isolating Stages for Separations

[gfd43tg]

Hello,

I am wondering what the purpose of the Ponchon Savarit method is for determining the theoretical number of stages using an enthalpy-concentration diagram. From what I am seeing, the method requires using a xy diagram with the equilibrium curve. Isn't it superfluous to use the H-x diagram when it needs the xy diagram which is already finding the number of stages with the McCabe-Thiele method?

The crux of my question is if the H-x diagram can be used in isolation to find the number of stages for a separation?

Edit:
Or rather it seems, at least if you are not given the tie line for the H-x diagram, then you would need the x-y diagram to find the tie line. So I guess I should rephrase my questiion, "In the absence of a tie line on a H-x diagram, is it superfluous to use the Ponchon-Savarit method to find the number of stages for a separation, when the McCabe-Thiele diagram is necessary to even construct the diagram?" and "Can a H-x diagram be used in isolation to find then number of stages for a separation in the absence of a tie line?"

Thanks

 

[Chestermiller]

My understanding is that the McCabe Thiele method assumes that the liquid and vapor molar flow rates are constant in each section of the column. The Ponchon Savarit method does not make this simplifying assumption, so it is more accurate. The Ponchon Savarit method can be implemented independently of the McCabe Thiele method.

Chet

 

[gfd43tg]

Yes, that is true. However, it is possible to make a McCabe-Thiele diagram with non-constant stripping/rectifying operating lines, and then just make the triangles to determine the stages. To make the operating lines, you go through a long process of iterations using the material and enthalpy balance and using the H-x-y diagram. So they are sort of interconnected.

The problem I'm having is how it is possible to solely use a H-x-y diagram to find the number of stages. It seems like you would need to know what the mole fraction is at the next stage $x_{n+1}$ in order to draw a tie line from the previous stage position ($y_{n}$,$H_{y,n}$). Otherwise the tie line must be given.

So from this, something seems off. You either need the tie line (which implies the stage is known from the x-y diagram), or you need the x-y diagram to get that position ($x_{n+1},H_{x,n+1}$). Either way you look at it, you need an x-y diagram. Hence it appears superfluous to me.

 

[maistral]

Hello,

I've worked for quite some time with Ponchon-Savarit (at least, for binary distillation). I personally understand it this way: M-T would provide me with a basic approximation on the number of stages, assuming enthalpy concentration data is not available. Assuming that the data are available, the P-S would provide an even more accurate calculation. I don't know of any method on how would you calculate for the next stage x_i+1 without having the equilibrium data when using P-S.

I'm not really sure, but with the way I'm understanding it I think you would really have to have the equilibrium data as well, I think having an enthalpy-concentration data set would just improve your accuracy.

Eitherway you could actually compute for the number of stages using M-T while incorporating the enthalpy balances (I think you know that as well), but personally I find P-S method faster than M-T incorporating such balances because at least with P-S you just have to continually draw straight lines without having to worry about recomputing the operating and stripping lines every single time, lol. With M-T I think you would have to recompute the operating/stripping lines every time it would bounce off the equilibrium curve.

 

[gfd43tg]

I hope this graphic will help elucidate my problem

So to use the Ponchon-Savarit method, it is clear that I need the x-y data in order to know where to draw lines from the points. Otherwise, How will I know where my maroon dot will connect to my dark blue dot? I have to have that x-y data and the operating line. And in doing so, I am already figuring out the number of stages using the McCabe-Thiele method.

Yes, I know this is a constant molal overflow situation, and one where the rectifying and stripper operating lines are the same as the 45 degree line, but nonetheless even for other situations, it seems like I would already need the x-y diagram with proper operating lines in order to even begin to use the H-x-y plot. So it seems superfluous to me to use an H-x-y diagram.

Now the Ponchon-Savarit method is hailed as being more accurate in the case of non-linear operating lines. In that case, I still need the operating lines on my x-y plot in order to draw a line from my maroon dot to my dark blue dot. No matter the situation, I need the McCabe-Thiele diagram in order to use the Ponchon-Savarit method.

I hope this makes my troubles more clear.

 

[maistral]

Ah. I see where the problem is coming from. The drawing itself is incorrect... I think. Your first stage is drawn correctly. Your second stage and onwards that... isn't, though (I think). You need to begin dropping your line from the vapor curve, not from the liquid curve (it would be pointless, it'd look like you're calculating the maximum reflux)

I'll whip up a Paint diagram for you. Hold on.

 

[maistral]

Here it is:
https://www.facebook.com/media/set/?set=a.859119010791315&type=1&l=6475572c9f

I'm sorry for adding it on such an informal site as Facebook, lol (I don't know if those kinds of things matter here, I just really wanted to help). In that diagram the light-blue lines are the stages. You may want to compare it with a traditional McCabe graph.

 

[gfd43tg]

Thanks for showing your work step by step in the images. I was unaware that it was supposed to be from the vapor curve that I do the next line.

 

[maistral]

You're welcome. Good luck! :)