Safety Relief Valve - recip compressor closed outlet 2

[130684]

Dears,

I would like to consult you in solving an issue regarding a closed outlet scenario at the outlet of a reciprocating compressor.

Data:
I have a 2 stage reciprocating compressor, compressing a mixture of isobutane, hexane and nitrogen.
The 2'nd stage suction parameters are P0=4.14 bar and T0=35 C and 342 m3/h (@760 mmHG, 0C)which is almost equivalent to 563 kg/h. The normal discharge parameters of the 2'nd stage are P1=16.3 bar and T1=110 C (predicted; and 35 C adiabatic, don't know exactly what it means). The kW for 2'nd stage is 20.

Requirements:
I have to check the relief valve downstream of this compressor (relief flow, relief conditions and valve size) for the CLOSED OUTLET scenario. The relief pressure is 110%xSPrv = 1.1 x 17.2 barg = 18.9 barg. The relief flow I suppose it's the flow that compressor is able to provide, 563 kh/h, but I don't know exactly HOW TO CALCULATE THE RELIEF TEMPERATURE.

Cmpressibility of gas(@inlet pressure) is 0.985. I assume ideal gas behaviour
Cp/Cv = 1.22.

In case of closed outlet, is the compression process still polytropic?
Can I use the equation: T2 = T1(P2/P1)^(1-(1/n))?

Does the compressor efficiency matters in calculating the temperature? If I had an efficiency curve, could I have been able to use Hysys for calculation?


Thank you in advance for your support,

 

[Latexman]

No aftercooler? Then the temperature going into the PSV is the same as the temperature coming out of the 2nd stage. A PSV is traditionally treated as isentropic, so you should use:

T2 = T1(P2/P1)^(1-(1/k)) where k = Cp/Cv

Good luck,
Latexman

 

[130684]

Great! Thank you! So my approach is correct (n = k = Cp/Cv).

The PSV is between 2'nd stage discharge vessel and aftercooler; the valve that might be closed is downstream of the aftercooler. I suppose it will have a bit of effect on gas cooling.

Kind regards,

 

[zdas04]

You need to be really careful about terminology here. Nothing about a recip is polytropic. It really does fall pretty close to being adiabatic. Closing the outlet does not change the process from adiabatic to polytropic. Closing the outlet on a dynamic machine changes it from polytropic to no-flow (so power usage drops to windage losses). That is a tough PSV to size. For a recip you really don't reach a dead-head condition until you run out of power and the engine dies or the breaker trips.

The P1 and P2 that you use are really important. The equation that Latexman gave you works after the suction check valves and before the discharge check valves. Both those valves have a non-zero cracking pressure. I always use P1=P(suction header)+P(atm)-5 psi and P2=P(discharge header)+P(atm)+10 psig. This minor tweak will make a significant difference in calculated temperature. If you know actual cracking pressure, use them, otherwise the 5 and 10 psi gets very close to the assumptions in the manufactures programs.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[Latexman]

I meant P1 = inlet to PSV and P2 = outlet from PSV.

Good luck,
Latexman

 

[130684]

Thank you for your helpful answers,

I apologize, in my first post it's an error. The question should have been if i could calculate the relieving temperature with the following relation: T2 = T0(P2/P0)^(1-(1/k)) (and not using T1 and P1 which are the normal discharge parameters).

T0 = suction pressure of the 2'nd stage, K
P0 = suction pressure of the 2'nd stage, atm
P2 = relief pressure, atm
k = Cp/Cv

 

[zdas04]

Latexman,
The equation you put in is not the equation for cooling through a PSV. It is the equation for adiabatic heating. Like in a PD compressor

130648,
That is exactly the equation I would use for the case you were asking about. Needs to be in absolute units and I would account for the cracking pressure of the valves, but that is the right equation.



David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[Latexman]

Traditionally, PSV calculations assume frictionless and adiabatic (and therefore isentropic) for flow in a very, very short nozzle. Since it is assumed adiabatic, frictionless nozzle flow, it is the equation for adiabatic cooling (and heating).

Good luck,
Latexman

 

[dcasto]

The compressor efficiency is not that important and neither is the discharge temperature. Make a few attempts to size the relief valve and change the discharge temp 10 deg C, the decreased volume capacity of the relief valve isn't that much and you'll be selecting a relief valve that will have excess capacity.

zadas, I have had plenty of discharge reliefs go off and the engine keeps on going In this case, the poster needs to clarify his set pressure, is the maop of the system 17.2 barg and therefore the relief must me set at 17.2 and be fully opened at 18.9? In any case a 1 to 2 barg increase in pressure isn't that much work that the engine has take up.

 

[zdas04]

That isn't what I said!!! I said that a dead ended recip will increase pressure until the engine dies or the motor trips. If a PSV opens (or a pipe ruptures) then it is no longer dead ended and everything keeps running. I've had PSV's go off on recips as well and it just makes noise and a mess, no big deal. I've also had one recip dead ended with a stuck PSV that never opened. Luckily the engine died on over hp (under speed) before anything came apart.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[dcasto]

my bad zdas