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# Gibbs Free Energy Direct Minimization Calculations

## Gibbs Free Energy Direct Minimization Calculations

(OP)
Dear Expert,
I am trying to conduct Gibbs Free Energy Direct Minimization Calculations using Excel spreadsheet.I am following the procedures published in the attached PDF file. However, I am facing a problem in the initial estimate described in the paper (Highlighted in Yellow). In fact,I'm not able to understand how the author is solving that problem and how to implement it in my excel file.
What I could understand is that while solver is conducting the iteration process it comes to a value of yi of zero which leads to ln(0) math error and stop the iteration.
My target is to make my excel file be user friendly to those who are not having idea to guess the initial estimates of (ni)s

### RE: Gibbs Free Energy Direct Minimization Calculations

To me, on looking at eqn 4, ln 0 appears only when

Z=B
or when
B/Z = -1, or B=-Z

So, one constraint is that the range of values permitted for B is given by -Z < B < Z

And as you say, additionally, another constraint is yi > 0

Does this help ?

I have worked on the same problem for steam reforming equilibrium many years ago with the aim to monitor and track steam reformer nickel catalyst activity, but using a simpler approach where the thermodynamic K values for the steam reforming and shift reactions are given as polynomial functions of temp. This approach you have now uses a more basic principle of Gibbs free energy being at a minimum and doesnt need to compute K values - looks numerically much more difficult.

### RE: Gibbs Free Energy Direct Minimization Calculations

(OP)
Dear georgeverghese
I think the problem is taking place during the iteration of ni i.e. at some time yi will be assigned a zero (yi=0)and in turn the term RT ∑(ni ln yi) will have math error and stop iteration. Anyway, I could solve the problem by avoiding zero value of yi by "if" function in excel sheet such that yi will never assign zero value. For example, cells from c14 to H14 will take values > 0 and if they are divided by total number of moles they will have value >0 as well. (see the attached spreadsheet)

I am just trying to solve this problem to use this excel later on to expect flue gas composition of primary reformer in ammonia plant including NOx, SOx and CO formation in flue gas.

### RE: Gibbs Free Energy Direct Minimization Calculations

Okay, there is another cell I53 in your first spreadsheet also that refers to these iterative values for yi.

By the way, why do the cells in I52 and I53 use the initial ni values in cells C13 to G13- should they not use the iterative values in cells C14 to G14 ?

### RE: Gibbs Free Energy Direct Minimization Calculations

(OP)
georgeverghese,
Yes you are right I have missed that.

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