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# 521 Fire Alternate Methods

4.4.13.2.4.4 fire thermal expansion fire psv supercritical fluid

10 replies to this topic
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### #1 therossboss

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Posted 19 April 2022 - 10:58 AM

All,

I am working on a PSV study for a natural gas processing plant. I started working on the fire sizing or the PSVs in the hot oil system. The facility uses Therminol-55 for the heating fluid.

These PSVs are set at 150 psig with relief pressure of 181.5 psig (1.21*150 psig). The Therminol-55 datasheet lists the pseudocritical pressure as 191 psia (site atmospheric pressure is 13.3 psia) so the relief pressure exceeds the pseudocritical pressure and fluid would be in dense phase. Based on the Therminol-55 datasheet, I used the alternative methods for supercritical relief in API 521 6th edition 4.4.13.2.4.4 to calculate relief rate and direct integration from Annex B in API 520 pt I to calculate orifice size.

The problem I encountered is that I am getting very different results depending on which equation I use from 4.4.13.2.4.4. I am using a time step of 3 seconds and total time is adjusted until I obtain peak flow rates. Equation 14 results in larger relief rates at later time steps, so at a greater temperature. Equation 15 results in smaller relief rates at earlier time steps and lower temperatures. When I use 520 pt I Annex B to calculate the mass flux through the PSV, I am obtaining different values due to the difference in starting temperature from the two equations in 4.4.13.2.4.4. When using equation 14 with higher relief temperature, the mass flux is much less than if using equation 15. The larger relief rate and lower mass flux when using equation 14 results in a much larger relief valve.

Has anyone else encountered this issue? I am not sure which equation from 521 4.4.13.2.4.4 to use as I obtain different results from both. The biggest difference I see between the two is that in equation 14, the volume to be relieved is calculated based on the heat input and resulting enthalpy and density changes instead of equation 15 where the mass to be relieved is calculated just based on the initial volume and the density changes.

Edited by therossboss, 15 July 2022 - 11:11 AM.

### #2 PaoloPemi

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Posted 19 April 2022 - 01:43 PM

there are a few threads discussing this topic at cheresources.com,
the procedure (direct integration) shouldn't be complex to code providing you have a software which solves the several intermediate V-H (before release) or V-P flash operations (I use Prode Properties with PRX or similar EOS packages),
the inputs are vessel volume as constant (see API for details) and heat absorbed at each step estimated with the methods discussed in API,
for the details about the selection of correct thermodynamic package and the methods to adopt with Aspen you may ask the vendor for assistance...

### #3 therossboss

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Posted 22 April 2022 - 08:35 AM

Thanks PaoloPemi.

I can do the flash steps to find the relief rates and then isentropic flash to find orifice area, but depending on which equation I use from 4.4.13.2.4.4 (eqn 14 or 15), I have two different results and can be a big enough change to require a different orifice size. 521 says that both can be used, but I obtain different results. I would have expected the results to be similar if both can be used. Have you experienced similar differences? I notice it with both high pressure NGLs above the cricondenbar and for heat medium oil above cricondenbar.

Which equation do you recommend using? Equation 14 written in terms of volume or 15 written in terms of mass?

### #4 PaoloPemi

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Posted 22 April 2022 - 11:14 AM

with reference to API 521 2020
4.4.13.2.4.4 Alternative Methods
If the user considers that the preceding assumptions in 4.4.13.2.4 are not appropriate, more rigorous methods of calculations may be specified...

if you solve a V-H or V-P flash operation as discussed in my previous post the solution will include the different contributes (fluid compressibility, phase equilibria..) accuracy depending from EOS capability to model fluid properties.

or (see API) the expansion of volume and incremental mass to be relieved can be calculated from the Equation (15) and Equation (16) ...

Edited by PaoloPemi, 22 April 2022 - 11:15 AM.

### #5 therossboss

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Posted 27 September 2022 - 02:04 PM

PaoloPemi,

Do you obtain a different result depending on which equation you use?

### #6 PaoloPemi

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Posted 28 September 2022 - 02:28 AM

for a general discussion see (API 521 2020) chapter 4.3.2 Effects of Pressure, Temperature, and Composition

to answer your question, in dense phase (no change of phase) when calculating area there are little differences between methods based on direct / numerical integration and simple methods considering real fluid properties (see for example Proper relief-valve sizing requires equation mastery, Hydrocarbon Processing Dec. 2011)

### #7 therossboss

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Posted 05 October 2022 - 12:56 PM

But what about the two equations in API 521 4.4.13.2.4.4, eqn 14 and 15 in 6th edition? Depending on which equation I use, I am getting different results from both.

### #8 PaoloPemi

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Posted 06 October 2022 - 04:15 AM

the direct integration method proceeds starting at the initial operating pressure and temperature, assuming the pressure increases via a constant volume process until the relieving pressure is reached,
you can solve each step with the V-P(H) or equivalent flash operations available in thermodynamic libraries as Prode Properties or process simulators,

for fluids without a phase change (e.g. gases, non flashing liquids, or supercritical fluids) API 521 2014 indicates  equations 14,15 in 4.4.13.2.4.4 Alternative Methods

with these equations you estimate fluid dV and (being V container constant) the incremental mass to be relieved ,

for a rigorous solution including also multi phase you should consider the above mentioned tools

Edited by PaoloPemi, 06 October 2022 - 04:25 AM.

### #9 therossboss

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Posted 06 October 2022 - 04:29 PM

6th ed. API 521 4.4.13.2.4.4 has equations to solve the incremental relief, either in terms of mass (eqn 15) or volume (eqn 14). Have you compared your results using these two equations? Do you get the same answer from each?

I do not get the same answer for some fluids above cricondenbar such as NGLs and hot oils. I am curious which equation (14 or 15) you and others use.

Edited by therossboss, 06 October 2022 - 04:54 PM.

### #10 PaoloPemi

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Posted 07 October 2022 - 04:21 AM

to calculate the mass to be released I use the same methodology (direct integration) but I solve flash operations with the software tools mentioned in previous posts.
Why do you presume equation 14 and 15 are equivalent ?
Equation 14 includes the contributes  Q (heat input into the system expressed in Kj) and Hn (enthalpy of fluid expressed in Kj/Kg), one could suspect some derivation including latent heat, but....
while equation 15 allows to calculate the incremental mass to be released given the volume of container (Vo)  and the variation of fluid density

Edited by PaoloPemi, 07 October 2022 - 04:45 AM.

### #11 breizh

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Posted 08 October 2022 - 09:09 PM

Hi,

A few documents to support your query.

Normally you should not get big differences.

BTW you can prepare a specification sheet and submit it to reputable vendors (Pentair, Leser and others) or you can download their software. Ultimately you can use simulators.

Good luck

Breizh