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‘Graphical’ Evaluation to Calculate the Number of Transfer Units – Problem Description

Reference:

This is from E.M. Rosen and R. N. Adams, “A Review of Spreadsheet Usage in Chemical Engineering Calculations”, Computers and Chemical Engineering, Vol. 11, No. 6, pp. 723-736, but they took it from Henley and Seader, “Equilibrium Stage Separation Operations in Chemical Engineering”, Wiley, NY 1981 pg. 653.  I don’t have a copy of the book, so, I may not include everything.  If you do and want to add to this, please do.  Also, why do we chem e’s always have to have such long titles?  And why do we always have to include ‘chemical engineering’ in the title?  Like we’ll forget or something.

Problem Description:

Rosen and Adams were using the spreadsheet to set up an interpolation and ‘table look up’ function with the data.  Usually, you use this approach when you have a ‘packed’ column that doesn’t have ‘discrete’ trays/stages.  They didn’t really describe the column arrangement or the components involved.  Okay, okay, I’ll go the library and get a copy of the Henley and Rosen book so that I know more about the problem.  They used the spreadsheet to set up the data, interpolate and estimate so they had values at even locations.  With that data table, they set up a four-interval Newton-Coates integration to calculate the number of transfer units.  Here is what the data looks like set up using arrays in Scipy.

X and X* Equlibrium Data as Scipy Arrays

X and X* Equlibrium Data as Scipy Arrays

You usually get this type of data from the equilibrium operating diagram for the system you are working with.  X* is the equilibrium concentration.  Consult Henley and Seader or look at a Perry’s Chemical Engineer’s handbook for more detail.  Treybal, “Mass Transfer Operations” is another good text you may want to consult.

Essentially, you’ll be doing and integration as follows:

N(OG) = ∫(1 – x)lm/((1 – x)*(x – x*)) dx

with (1 – x)lm = ((1 – x) – (1 – x*))/(ln((1 – x)/(1 – x*)))

N(OG) = Number of transfer units based on the gas phase resistance to mass transfer

This is what we have, let’s post on our programming approach.

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