Gas Thermal Expansion Relief Flow Calculation

[jennymd]

Hi guys,

I am designing a PSV to protect piping and a hairpin that heats gas from 41 deg. C (29 barg) to 288 deg.C. The PSV is going to be located in the cold inlet piping.
The case that I'm analyzing reflects a block outlet that derivates in thermal expansion of the gas.
I checked by simulation that I have a vapor phase and not a supercritical fluid @ the Pset of 37.7 barg (Paccumulation 41.5 barg).
I calculated the relieving temperature using the following expression derived from the ideal gas law:

To = Po / P x T (eq.1)
were
P = Operating Pressure
T = Temperature
Po = PSV Relieving Pressure
To = Relief Temperature

I'm looking for fundamental information that relates the Ideal Gas Law with the duty equation (Q = m x Cp x DeltaT), in order to determine the RELIEF FLOW.
Basically I need confirmation of this derivation (of if you know about another methodology):

dP/dt = d(Z N R T / V)/dt = 0
= Z R / V * d(N T)/dt = 0
d(NT)/dt = N dT/dt + T dN/dt = 0
= N Q / N Cp + T dN/dt = 0
dN/dt = - Q / T / Cp

Thanks for your time,
JD

 

[EGT01]

JD,

My suggestion would be to just refer you to API RP-521 and not try to re-invent the wheel unless your situation requires it.

In API 521 you will find a section that discusses the effects of fire on the unwetted surface of a vessel and offers a way to determine the required relief rate for vessels containing super-critical fluids, gases or vapors. The method presented there is based on the perfect gas laws and I would think you could use the same basic methods for your situation with the heat input from your heat exchanger.

If a more rigorous approach is needed, API 521 includes 2 references that you may want to review...

I. Heitner, T. Trautmauis, and M. Morrissey, “Relieving Requirements for Gas Filled Vessels Exposed to Fire,” 1983 Proceedings-Refining Department, Volume 62, American Petroleum Institute, Washington, D.C., pp. 112-122.

I. 0. Francis and W. E. Shackelton, “A Calculation of Relieving Requirements in the Critical Region,” 1985 Proceedings-Rejining Department, Volume 64, American Petroleum Institute, pp. 179-182.

For a more recent reference, check in the archives at the Chemical Engineering Progress website for...

Ryan Ouderkirk, Fluor Corp., "Rigorously Size Relief Valves for Supercritical Fluids", CEP, August 2002.

Of the API references, I've only seen the one by Francis and Shackelton and it is similar to what you find in the more recent CEP article I mentioned. The methods presented in these basically ends up determining the relief rate as a function of the change in specific volume of the fluid in the vessel with respect to time so that's all I'll comment on the derivation that you've proposed.

ET