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Calculation of required cylinder compression for a multistage reciprocating compressor
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r = stage pressure ratio
R = compression pressure ratio
for a two stage
r = R1/2 for a three stage

r = R1/3 for example, a 3 stage compressor requiring a final pressure of 64bar would have the following interstage pressures 1st stage.

1bar compressed to 4bar
2nd stage 4bar compressed to 16bar
3rd stage 16bar compressed to 64bar

It would appear that most of the work is being carried out in the final stage, this is untrue as with the increase in pressure is a complimentary reduction in volume, if the temperature conditions remain the same then work will be equally divided between the stages.

By reducing the suction pressure, the cylinder is required to do more work on the air before the discharge valve opens. This means that the air will be delivered at a higher pressure. The higher temperature can lead to problems with the cylinder lubrication as well as a drop in efficiency as well as carbonising of the oil and increased deposits on the valves and piston rings and interstage passages. In the extreme it can lead to seizure and possible diesel detonation of the oil laden air.

The reduction in pressure at the suction can be due to a partially blocked suction filter or partially choked suction valve. The lower pressure conditions in the cylinder at the start of compression can cause oil laden air to be drawn from the crankcase up the liner. This oil can lead to increased deposits in the compressor as well as further downstream in the distribution system

(P1.V1)/ T1 = (P2. V2)/T2

and

(P1/P2).(T2/T1) = (V2/V1)

P1.V1g = P2.V2g

and

P1/P2 = V2g/V1g From these we get;
T2 = T1. (P2/P1) (g -1)/g
g = 1.4
and if we take for and example
P1 = 0.4 bar
P2 = 1 bar
Pf = 5 bar
Tinitial = 300 K we end with final temperatures for the two compression's of
T1= 617 K and T2 = 475 K
from the graph it can be clearly seen that losses due to the bump clearance has increased and the period of constant pressure delivery has been reduced.