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ptc-52063361-Visitor
1-Visitor
August 7, 2013
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Population balance modelling - Rkadapt and Minerr

  • August 7, 2013
  • 1 reply
  • 3685 views

I'm looking for help solving a problem with a topic I haven't seen any previous example on here of, population balance modeling. In this case the onset of crystallization. The aim is to solve a system of differential equations which represent the crystal population. The first sheet I've attached "Population balance method of moments.mcd" does this reasonably successfully. But I've had to specifty the values for nucleation and growth coefficients (kb, b, kg & g). What I would like to do now is to calculate values for these coefficients so that the model data and experimental data match. The concept is similar to the discussion over here http://communities.ptc.com/thread/43738 were Minerr was used to determine kinetic coefficients to match experimental data. I suspect the issue i'm having is regards to the fact that although the population balance equations are a function of dt, what I'm actually wanting to minise the error for is a function of cooling rate, beta. The second sheet I've attached "Population balance method of moments with minerr.mcd" is my attempt at implementing one of the solutions detailed in the mentioned thread, but my stumbling block seems to be around the programming portion.

Thanks in advance,

Cameron

Best answer by Werner_E

Sorry, I forgot to attch the worksheet.

Strange enough upon reloading the worksheet I get different results (a better fit and the guess values didn't change much).

population2.png

1 reply

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Werner_E25-Diamond I
25-Diamond I
August 7, 2013

I spot some errors in you minerr sheet

- beta should be a vector, not a range variable

- it seems you have copied the expressions using "augment" from the sheet you mentioned and didn't know what augment is meant for. Augment simply merges together two or more matrices or vectors with the same number of rows to create a bigger matrix. It doesn't make any sense to apply augment to a single vector, the output woul be just that vector again.

Was the intention that MinErr should try to make DeltaT.max equal to DeltaT.max_exp? How could that be? You supply 19 different values for better, so the first vector would have 19 elements, while the second you have defined with only 12!

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ptc-52063361-VisitorAuthor
1-Visitor
August 7, 2013

If i set beta equal to beta_exp then that would create at vector both with 12 elements correct?

For the given statement then, if it's only a single vector should it just be a case of:

Delta.T.max(beta, kb,b, kg, g) = Delta.T.max_exp?

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Werner_E25-Diamond IAnswer
25-Diamond I
August 7, 2013

Sorry, I forgot to attch the worksheet.

Strange enough upon reloading the worksheet I get different results (a better fit and the guess values didn't change much).

population2.png

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