Jutesh:
Bobby is correct and his advice is what a process or project engineer does when confronted with a compressor application.
It makes no rational or process sense to design a 2-stage reciprocating compressor based on making the 1st stage and 2nd stage discharge temperatures equal. That is not a typical concern. Neither is “simulating” a compressor realistic or practical. You have certain process conditions which are fixed or which will be set by the compressor’s performance under steady-state, continuous operation performance. These conditions are normally the suction pressure and the ultimate discharge pressure. This assumes there is NO INTERMEDIATE 2ND STAGE SUCTION STREAM. In other words, what goes in the 1st stage comes out the 2nd stage.
If the above is the case, you normally expect the compressor manufacturer to design the machine such that the two stages are mechanically balanced - the power requirements are equally divided between the stages. This is done for obvious mechanical design operation and sets the parameter that allows you to derive the following equation to determine the theoretically desired intermediate, 2nd stage discharge pressure. The theoretical minimum power with perfect intercooling and no inter-stage pressure drop is obtained by making the compression ratio equal in all stages. The derived equation is:
Rn = (RT)1/n
Where,
Rn = Best compression ratio per stage;
RT = The over-all compression ratio of the machine;
n = the number of stages.
In your case the number of stages = 2. With the above equation you easily find the theoretical best compression ratio in each stage and the intermediate pressure. Knowing the intermediate pressure you can then estimate the intermediate discharge temperature. You now have estimated a THEORETICALLY balanced machine.
HOWEVER, this is NOT the compressor that will be quoted to you by all manufacturers. The quoted machine will be "close" to the expected, not the exact estimated intermediate discharge conditions. The suction and discharge pressures will be as you specified, but the intermediate pressure (and discharge temperature) will be somewhat different than that estimated. The reason is not because you assumed ideal conditions in your estimate; the main reason is because all reciprocating compressor manufacturers have already designed and established their standard, cast, compressor cylinder sizing and they are not about to design and cast a special one for your application since this would drive their manufacturing costs sky-high and they wouldn’t be competitive. Every bidder will apply their “best fit” compressor cylinders to the machine they can warrant as performing the duty you specify.
So you see, the identification of the intermediate discharge pressure and temperature should be only of general process interest to you in evaluating the performance and application - if the intermediate pressure does not affect your process (which I assume it does not). The actual, real-life design is always in the hands of the final, selected manufacturer and what cylinders he applies to your specification. The total purchased price of any reciprocating compressor (and I’ve specified and bought many, many of them) is totally dependent on what you specify in your detailed data sheet. I have to assume you are (or will) using a standard API reciprocating compressor Data Sheet - or equivalent.
That is why I fully support and reinforce what Bobby Strain has so succinctly and correctly stated.
I hope this experience helps.