20 replies to this topic

[chemtoli]

how to calculate each mass fraction flow rate for the given separator system with One feed and two products (W &D). Each stream has four components of mass fraction flow rate as it shown in pdf. I tried to calculate but I couldn't 

Attached Files

•  material balance.pdf   38.81KB   26 downloads

[Pilesar]

Material balance problems have blocked many students from deciding to not become chemical engineers. This is a key skill that is essential to learn. Don't be satisfied until you master it. Find example problems and really learn methods for solving these. Simultaneous equations are needed. Good luck.

[breizh]

Hi,

As suggested you need to solve all the system of equations simultaneously.

8 unknowns it means 8 equations, 3 equations are missing in your document.

The way I did it was to use solver in excel.

 Good luck.

Breizh 

[Pilesar]

The excel file is interesting and I learned from it. I have not used excel 'solver' much at all but often use 'goal seek'. I will look for other problems where I can use the solver. For this material balance, I added over a dozen additional constraints to get the answer but I think there should be a way to calculate how many constraints are theoretically needed. My Excel 2003 doesn't seem to flag whether a problem is over-specified and the reports generated seem pretty poor, Maybe the newer versions provide more diagnostics.

[chemtoli]

Hi,

As suggested you need to solve all the system of equations simultaneously.

8 unknowns it means 8 equations, 3 equations are missing in your document.

The way I did it was to use solver in excel.

 Good luck.

Breizh 

 

Dear Breizh, 

 

Could you tell me which are those three missing equations because I need to solve this problem mathematically than by excel. Anyway I am very grateful for the help you are continuously offering me.

[breizh]

Hi,

Sum xfi = 1

Sum xdi =1

Sum xwi =1

Edit

Note: Unfortunately, equations above are not sufficient enough to get a single solution using excel. More work to be done.

Can you please share with us where the examples are coming from?

 

Breizh 

[latexman]

From my past distillation studies, always remember the MESH equations. The acronym MESH stands for the independent equations for material balances, equilibrium relationships, summation equations and heat (enthalpy) balances.

Breizh gave you the summation equations.

[Pilesar]

Also constrain against negative values since there may be multiple solutions otherwise. Solvers don't always go in the direction that you intend. They do not know the big picture and solving stops when a solution is found even if it is in an impractical region. Initial guesses can help but not always.

Edited by Pilesar, 01 July 2023 - 08:41 AM.

[Pilesar]

Just using eight equations may not be enough. Only independent equations count. I had to add a few more to the spreadsheet to balance each component.

[chemtoli]

Just using eight equations may not be enough. Only independent equations count. I had to add a few more to the spreadsheet to balance each component.

 

dear Pilesar

 

can you tell as which other equations did you added 

[Pilesar]

Mass balance each component since there is no reaction. In=Out.

[chemtoli]

Hi 

 

Is there any missing equation for this case.

 

I tried to learn about DOF but I couldn't understand much. Also I tried to find similar examples on internet but I couldn't find case where all mass fractions of feed components are unknown. Please if someone have any reference or ebook for these kind of problems. 

 

Thank you so much!

Attached Files

•  matba equations.png   26.37KB   0 downloads
•  fundamentals-of-material-balances-with-applications-to-nonreactive.pdf   8.34MB   15 downloads

[chemtoli]

Hi,

Sum xfi = 1

Sum xdi =1

Sum xwi =1

Edit

Note: Unfortunately, equations above are not sufficient enough to get a single solution using excel. More work to be done.

Can you please share with us where the examples are coming from?

 

Breizh 

 

dear Breizh 

this was one of the problems presented in the test of the subject "Material Balance of chemical engineering" I don't where our assistant got it.

[Pilesar]

Why not try to find solution using the equations you listed? Then you will know whether the equations are sufficient to find a solution! Degrees of Freedom are sometimes found by 'this didn't work, there must be a Degree of Freedom difficulty. Let's try making changes.'

[breizh]

HI,

8 unknows means 8 independent equations. 

From equation 3 you get access to xbf .

Have you ever considered the case where the missing data have the same value? let say xcd and xdd and /or xaw and xcw ? This works in excel.

Breizh 

[latexman]

Show us your DOF attempt.  Here's mine.    

 

SV = 3 streams x 4 components = 12

IB = 4 components = 4

IC = 4 (xbw, xdw, xad, xbd)

F = 3 (F, W, D)

SR = 0 or 1?  (does xbw = 0.15 and xbd = 0.4 constitutes a split fraction?)

DOF = SV - IB - IC - F - SR

DOF = 12 - 4 - 3 - 3 - 0 or 1 = 2 or 1; NOT 0!

So, in either case, underspecied.

Therefore, don't waste your time.

[Pilesar]

Underspecified does not mean there is no solution. For example, 'x + y = 12' is underspecified, but x=5, y=7 is a solution! The original problem has more than one solution.

Edited by Pilesar, 03 July 2023 - 10:19 AM.

[latexman]

 

Therefore, don't waste your time.

 

Clarifying . . . looking for the solution.  What was the teacher assistant's objective with this problem?  A DOF, a general solution to an infinite number of solutions, or both?  OP?

[chemtoli]

Show us your DOF attempt.  Here's mine.    

 

SV = 3 streams x 4 components = 12

IB = 4 components = 4

IC = 4 (xbw, xdw, xad, xbd)

F = 3 (F, W, D)

SR = 0 or 1?  (does xbw = 0.15 and xbd = 0.4 constitutes a split fraction?)

DOF = SV - IB - IC - F - SR

DOF = 12 - 4 - 3 - 3 - 0 or 1 = 2 or 1; NOT 0!

So, in either case, underspecied.

Therefore, don't waste your time.

 

Dear latexman,

 

Could you explain in more detailed form what did you mean "SR = 0 or 1?  (does xbw = 0.15 and xbd = 0.4 constitutes a split fraction?)". What is split fraction? Anyway thank you so much for your DOF.

[chemtoli]

HI,

8 unknows means 8 independent equations. 

From equation 3 you get access to xbf .

Have you ever considered the case where the missing data have the same value? let say xcd and xdd and /or xaw and xcw ? This works in excel.

Breizh 

 

Dear Breizh, I really can't find words to thank you for your effort and kindness that you are doing to help me solve many problems so far. As I said earlier in this case firstly  I have to solve this problem  mathematically than in Excel. I've sent an email to my teacher's assistant to ask about the case where the missing data have the same value, but he's not answering me back!

[latexman]

Dear latexman,

 

Could you explain in more detailed form what did you mean "SR = 0 or 1?  (does xbw = 0.15 and xbd = 0.4 constitutes a split fraction?)". What is split fraction? Anyway thank you so much for your DOF.

 

You should read or re-read your attachment in post #12.  Split fraction is mentioned in there.