Thermodinamycs. Formula to calculate the efectiveness of a regenerator

[ochodoce]

Hi all.
I am a student of a university degree on Chemical Engineering in Madrid, and I have one question that I would like to have your feedback about.
It is related to Thermodynamics and, more specifically, to the formula to calculate the efectiveness of a regenerator in a Rankine or in a refrigeration cycle.

Until now, the formula that I had always used is the following one:

Efectiveness reg, version 1 = ( h cold, out - h cold, in ) / ( h hot, in - h cold, in )

In other words, the difference of enthalpies in the cold stream, (out - in), divided by the difference of entalphies between the hot and the cold streams, when entering in the regenerator.

However, in a problem of an exam, the professor has used this variation of the formula;

Efectiveness reg, version 2 = ( h cold, out - h cold, in ) / ( h * hot, in - h cold, in )
where:
h * = h ( P cold stream, T hot,in )

Thus, he is replacing the entalphy of the hot stream (in) by the value of the entalphy of the fluid at the pressure of the cold stream and the temperature of the hot stream (in)

The comparison of the results of both formulas are very different. As a consequence, the rest of the calculations of the whole problem vary a lot.

Can anyone of you give me some light on this matter? When should I use each of them? They are clearly not interchangeable, since their results are very different

Thanks very much

 

[goutam_freelance]

Version 1 is used generally.

Version-2 will give the same result as version-1 if the ideal gas cycle is used, as enthalpy depends on T only and not dependent of P.

If the actual gas cycle is used, then the normally used formulae for gas cycles can not be used any more, and enthalpy depends on pressure also. In that case, why is pressure at the cold stream used? It is logical to use the pressure of the hot stream.

Please ask your professor.

 

[ochodoce]

Hi @goutam_freelance

Thanks very much for your reply.

Your reasoning is exactly mine!

The fluid in question is metane (CH4) which cannot be considered ideal.

Just wanted to have another vision and opinion.
Unfortunately, this professor is not easy to ask ...
Anyway, that's another story.

Again, thanks very much and have a nice day