Multi-stage compression with intercooling

[exergetic]

Hi everybody!
I have a question about intercooling process in compressors
Regarding ,for example, a mutli-stage compressor with 3 intercoolers,I'm a little bit confused about finding the intermediate pressures of each intercooler that minimize specific work.I'm able to find the intermediate pressure only if there'ls only one intercooler,using well known statement:

where Px is the intermediate pressure at which intercooling process happens, P1 and P2 the inlet and the oulet pressure in the compressor.

Could anyone help me?
http://air-compressors-info.blogspot.com/2007/12/multi-stage-compression-with.html"

Thanks in advance.
(sorry for my rough english)

 

[Mech_Engineer]

Are you familiar with thermodynamic processes, and how they are mapped on a thermodynamic properties chart (such as a T-S or P-V diagram)? A multi-staged compression cycle with intercooling would be pretty easy to visualize on a T-S diagram...

http://en.wikipedia.org/wiki/Temperature_entropy_diagram"

 

[exergetic]

Yes,I have some familiarity with thermodynamics.But I know how to represent this process on T-s chart.Instead I would understand,in case of more than 1 intercooling process, how to calculate pressure values at which intercoolers must work for minimizing specific work.Could be correct to state that the minimum specific work is obtained when all pressure ratios equate each other?In other words when:
$$\frac{Pinlet}{Pi1}$$=$$\frac{Pi2}{Pi1}$$=$$\frac{Pi3}{Pi2}$$=$$\frac{Poutlet}{Pi3}$$

 

[jack action]

Yes, all pressure ratios from each compressor must be the same and it is found this way:

$$P_{r}=\sqrt[n]{\frac{P_{out}}{P_{in}}}$$

Where $$n$$ is the number of compressors.

So with 3 intercoolers, $$n = 4$$.

 

[exergetic]

Ok,thanks a lot for your help.I appreciated it.