# Multi-stage compression with intercooling

1. Nov 10, 2010

### 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

(sorry for my rough english)

2. Nov 10, 2010

### 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...

Wikipedia: Temperature-Entropy Diagram

3. Nov 10, 2010

### 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:
$$\frac{Pinlet}{Pi1}$$=$$\frac{Pi2}{Pi1}$$=$$\frac{Pi3}{Pi2}$$=$$\frac{Poutlet}{Pi3}$$

4. Nov 10, 2010

### 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, $$n = 4$$.

5. Nov 11, 2010

### exergetic

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