I have responded to this question a lot of times in the past and I will quote from a seminar I gave on this subject in the past:
In understanding compressors, it is more important to consider the compressor ratio than the discharge pressure.
The compression ratio per stage, R, is based on absolute pressures and the number of stages required. To minimize power usage, one should initially select an equal compression ratio in each stage. The number of compression stages is arrived at by dividing the total work done equally between all the stages of compression. The compression ratio is defined as follows:
R = (Pd/Ps)1/n
where,
Pd = discharge pressure, absolute
Ps = suction pressure, absolute
n = number of compression stages
The ultimate compression ratios supplied by a compressor manufacturer will only approximate the calculated, ideal, equal ratios because the manufacturer is limited by the existing, pre-designed cylinder sizes available to a compressor package.
It is desirable to limit discharge temperatures to below 121 – 135 °C (250 – 275 °F) to ensure adequate packing life and to avoid cylinder lube oil degradation. At temperatures above 149 °C (300 °F), eventual lube oil degradation is likely, and if oxygen is present, ignition is possible. This specific hazard has occurred in Air Separation plants in the past and is well documented. Under no circumstances should the discharge temperature be allowed to exceed 177 °C (350 °F).
Employing a “non-lube” design doesn’t remove the temperature limitation on the cylinder. Polymers and plastics employed as piston and rider rings are also subject to the same temperature limit.
The discharge temperature can be lowered by cooling the suction gas or reducing the compression ratios per stage by adding more stages of compression. Depending on the gas, a compression ratio between 2 and 3.75 is the usual practice.
The compression ratio per stage is limited for any reciprocating compressor by the need to limit the discharge temperature. As the ratio per stage increases, the discharge temperature increases.
Normal compression ratio limits per stage vary from slightly over 1.0 for booster service to roughly 4.0 for special high ratio machines. Staging compression is efficient because it saves compression power. For example, by installing a second stage, one may cool the gas discharged from the first stage – which is the suction to the second stage. The actual volume of gas to be compressed is then lower than it would have been if the gas had continued to be compressed in a single stage compressor without interstage cooling. The energy saved by performing the compression in two stages. This savings must be balanced by the cost for increased piping and equipment, energy lost due to pressure drop in interstage piping, and increased maintenance costs. Note that staging is, in reality, an approach to Isothermal Compression - which is the most efficient method of compression.