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cstr with 5 solution case - MC15, update

HarveyHensley
Visitor

cstr with 5 solution case - MC15, update

Since there is such a lack of chemical engineering worksheets on this site, I am submitting the attached model to give users an example of Mathcad for CHE.  It is a model of a simple CSTR with two reactions.  Although this is an academic case, it illustrates several features:  natural math notation, use of state variables for reactors, use of solve blocks, including parameterized blocks.  The plots (2D and 3D) aid in the engineering analysis of the results.

A CSTR can be easily modeled in process simulation packages.  However, this solution offers some insight that I might have missed if I had not done this model in Mathcad first.  After doing this model, I now try to emulate this approach using the sensitivity studies options in the process simulators.

You will see a highlighted area in the worksheet where the actual model of the reactor begins.  Everything above that point describes the fluids and reactions.  I have built other models that can be substituted for the reactor section.

The model is in Mathcad 15.  The file is documented, but I must admit that further documentation would be needed if this were to be released as a report to non-Mathcad users.

If there are errors, please let me know. The results agree with those reported by the original sources.  If anyone has constructive suggestions for improvements, please let me know.

I will not have the time to help students do homework with this model, but it may be useful as a learning guide.

Update 10/28/2012

I am uploading a new version of the worksheet.  The main change is the formatting of the worksheet.  I have included this worksheet as an example in my reactor modeling book, so the text and math fonts have changed.  Some of the math changed to be consistent with the rest of the book, but the basic approach has not changed from the previous worksheet.

There has been some discussion in the Community about math fonts and the layout of worksheets for documentation purposes.  I would greatly appreciate any critique of the styles and layout and any suggestions for improvement.

The worksheet is in version 15. 

9 REPLIES 9

Re: cstr with 5 solution case - MC15, update

Very interesting calculation!

Welcome to the cooperation!

http://twt.mpei.ac.ru/TTHB/New-Chem-Kin/En-ChemKin.html

Re: cstr with 5 solution case - MC15, update

Thank you for your excellent paper. I think it is appropriate to show also the author opininalny version which was published in the EEC.multistationarity.GIF

Viktor

Re: cstr with 5 solution case - MC15, update

Great, it would be good a stability local analysis of the multiple steady-states

Re: cstr with 5 solution case - MC15, update

Figure E8.4 is the key to the stable region for a given operating point.  As I pointed out in the worksheet, the stable points are on the positive slopes of the red curve.  If the reactor has no heat exchange (adiabatic), then the allowable range of feed temperature can be determined by changing the feed temperature to move that curve left and right.  If there is heat exchange, then the allowable range of heating or cooling can be determined by moving the vertical curve left and right.

If operation is desired for the middle stable point, then startup is tricky.  I've modeled the dynamics of the startup in another example in my book.  However, more likely inert would be added to the system to increase the stability.

Re: cstr with 5 solution case - MC15, update

I have a question about adding inert in the worksheet

when I change the inlet condition to (A B C inert) = ( 0.9  0  0  0.1), every solve block works fine except the last solve block,( the one with energy, mass and mass fraction balance failed).

I have tried to change the initial guess based on the contour plots but I cannot get the last solve block to converge. Can anyone tell me what I might be doing wrong? 

Re: cstr with 5 solution case - MC15, update

Henry,

I tried it and it worked fine.  Originally, I tried it with the initial guesses and that worked, then I modified the outlet temperature to tout = 14 (480 K) leaving the other optimal settings unchanged.  That worked also.

Please attach your worksheet so I can examine it.

Re: cstr with 5 solution case - MC15, update

Cannot attach file in document...will put it in discussion

I suspect it is because I have 15.0.0.436 [006041742 instead of the latest version....because the only thing I did to the original file is change the

mfin to (0.8 0 0 0.2),  I tried different tout index too but no luck... all changes is highlighted in red

Re: cstr with 5 solution case - MC15, update

Henry,

I don't think it is caused by your MC15 version, although it might be.  After you select the optimum space time and outlet temperature indexes, you need to select the inlet temperature index using Fig 8.3.  Using the Tout index on the vertical axis, go across the plot to the desired heat exchange curve, 0 if adiabatic.  Then read the Tin index on the bottom axis.

Try that.  If that doesn't work, then send the file in a discussion as you mentioned. 

Re: cstr with 5 solution case - MC15, update

Thanks Harvey, now I better understand the worksheet.

When I changed the mfin to (0.8 0 0 0.2),  the optimum space time is still 10 min and tout index is 14, if I want an adiabatic Qm, I have to pick tin index of 18, which is Tin = 340 K.  and the worksheet converge. 

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