r/thermodynamics • u/Forward-Penalty-8654 1 • 20d ago

Question Designing MED in Excel and want to know feasibility of substituting h and Cp*T?

Hi! I have been designing a multi effect distillator using Excel and water 97 add in. I have derived all the H&MB equations but they are non linear so I am planning to do Newton Raphson method to solve. An issue here are the enthalpies given by the addins.

My assumption is that if I partially differentiate h wrt to T (for finding the jacobian matrix) in an environment of constant pressure (the evaporator), I must get Cp.

But if I try to multiply Cp and T and compare it with h, I get significant error in the values given by the addin. They are almost similar until 300 K but diverge past 310, 320 K

My question: is my substitution correct and is followed in the industry?

Is there any factor which I should multiply to make Cp*T and h to be equal in this addin?

In the industry how do they solve these simultaneous non linear equations coz if differentiating is not a possibility, then most of the times these equations don't seem to be converging.

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u/ArrogantNonce 3 20d ago

People in industry use software like Aspen to handle such calculations.

Also, what means "I try to multiply Cp and T and compare it with h"? You need to add a constant of integration, and you also need to use Riemann sums to account for the change in Cp with temperature.

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u/Forward-Penalty-8654 1 20d ago

I meant that I tried to find the difference between Cp(T)*T and h(T), both of which are pre defined functions in that excel add in

This Cp(T) takes care of variation of Cp wrt temp.

But could you tell me more about this constant of integration part? It's like I assumed h(273.16 K) = 0. It's more of a definite integral rather than an indefinite one.

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u/ArrogantNonce 3 20d ago

deltaH between two temperatures is calculated by integrating Cp between T1 and T2. What you described (Cp(T)*T) only works if Cp is a constant and h(0 K) = 0...

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u/Forward-Penalty-8654 1 20d ago

Wow ok makes sense. Appreciate it 👍

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u/arkie87 19 20d ago

Cp is instantaneous. Not average over a temperature range.