Multi-stage compression with intercooling - Pressure ratio

We know from the previous section that the minimum air compressor work is achieved with isothermal compression. In practical way, we try to achieve that by involving some cooling during compression process that leads to Polytropic compression process.

Normally, this can be achieved by dividing air compression into 2 stages. The first stage builds up the pressure from P1 to Px then the compressed air is cooled by the intercooler and the second stage compressor builds up the pressure again from Px to the final pressure P2. See the following figures to understand how the energy can be saved by using intercooling between each stage.



























Fig.1 P-v diagram of polytropic compression process with intercooling




























Fig.2 T-s diagram of polytropic compression process with intercooling

We can see from Fig. 1 that the amount of compressor work saved is related to the pressure Px.

What is the optimal value of Px that yields maximum compressor work saved?

The total compressor work, for this case, is the summation of compressor work of each stage as follows,

w_total = w_1 + w_2

We can see that w_total will be lowest when w_1 = w_2. Thus,

P1/Px = P2/Px

or





That means the pressure ratio of each stage should be identical to get the lowest amount of work required for air compression.