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# Sizing of PSV - Calculation of the Upstream Relieving Pressure 2

## Sizing of PSV - Calculation of the Upstream Relieving Pressure

(OP)
I am reviewing the sizing of a PSV for a pentanes product storage tank.

Current PSV Size: 3K4

Set Pressure: 3.4 barg

Maximum allowable Backpressure: 0.29 barg [1.30 bara]

Vessel data
ID = 2.5 m, Ls/s = 10.9 m, Liquid depth = 2.63 m, elevation = 1.2 m and so I am calculating wetted area to be around 75.65 m^2.
MAWP/Design Pressure = 16.0 barg

Gas Properties at relief
MW = 71.72
T1 = 87.21
Z = 0.8688
k = 1.064
Heat of vapourisation = 304.1 kJ/kg

Area is paved and fire-fighting exists.

Calculated relieving load is approx. 25,679 kg/hr

Now the problem:
I calculate relieving pressure as follows:
MAWP: 16 barg
Max. Accumulation Pressure: 1.21 x 16 barg = 19.36 barg
Set Pressure: 3.4 barg
Allowable Overpressure: 19.36 barg - 3.4 barg = 15.96 bar
Barometric Pressure: 1.01325 bar
Relieving Pressure: 3.4 barg + 15.96 bar + 1.01325 bar = 20.37 bar [2037.33 kPa (abs)]

Calculating required area for critical flow yields an orifice area of approx. 764.88 mm^2 requiring a J orifice.

But then this is where it gets interesting:

When I enter these same values into Lesser's Valvestar and Emerson's PRV^2Size (screenshot attached)....they calculate a Q orifice.

I reckon the problem emanates from the calculation of the relieving pressure. It appears the designer wanted to obtain a smaller relief device - by setting the vessel MAWP so high.

Please share your thoughts - did I approach the hand calculation the wrong way?

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

Hi Again.
I just took one look at the Emerson PRV2 calculation. It has taken 3.4 + 21% as the set pressure hence a large Q orifice has been calculated. PRV sizing is about what the PRV will pass at a predetermined pressure. Normally MAWP = Set Pressure.

What is important to understand here is what is the normal operating pressure and also to understand why the MAWP is so high unless it purposely over engineered for a reason.

Per ISO-4126, only the term Safety Valve is used regardless of application or design.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

Can you also check your vessel dimensions? Depth of fluid cannot be greater than vessel diameter.
Re my earlier comment. Inlet relieving pressure is calculated as Set Pressure 3.4 barg x 1.21 + 1.01325 = 5.13 bar abs as used in calculation.
Vessel Operating/Working pressure should be 90 % of 3.4 = 3.06 barg Nowhere is the working/operating pressure stated.
See attached page/figure 15 from API-520

Per ISO-4126, only the term Safety Valve is used regardless of application or design.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

(OP)
@The Obturator (Mechanical)...thank you very much as ever.

Sorry, the liquid depth is 2.130 m. Also, the vessel operates between 0.3 barg to 0.6 barg.

Yes, normally, PSV is set = vessel MAWP. It may also be set below the MAWP in accordance with API 520.

Indeed, API 520 defines the upstream relieving pressure as:

"this is the set pressure plus the allowable overpressure plus atmospheric pressure"

Allowable overpressure = Maximum Accumulated pressure (1.21 x MAWP) - PSV set pressure

I am attaching the allowable overpressure calculation from Table 4 API 520 as reference. A similar case is presented in there; where the PSV set pressure was below the MAWP of the vessel. I followed this approach.

Therefore, I suspect the Emerson/Leser Valvestar software are both calculating the allowable overpressure wrongly.
It appears the designer has adopted a clever strategy to reduce the relief valve size. As to whether more savings can be made on much stronger vessel compared to savings on the relief valve is another issue altogether.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

The Table 4 you referenced from API-520, lower section, for set pressures below MAWP, does in fact then use a higher overpressure to result in the same absolute, accumulated relieving pressure.

I see how you followed that, but it does appear an extreme overpressure which is why its not picked up by vendor sizing. I'll need to find more infoo on such a case. In the meantime maybe some other contributors on here can advise.

The normal operating pressure advised now which is OK for a set pressure of 3.4 barg.

Per ISO-4126, only the term Safety Valve is used regardless of application or design.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

(OP)
Thank you @The Obturator. Will be waiting patiently to hear from you when you have any new information.

Would be interesting to hear the views from other subject matter experts when faced with such a case.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

Using a sizing pressure = max. allowable accumulation is within Code.

Does all the attached piping spec(s) support this strategy?

Good Luck,
Latexman

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

I haven't used either of those sizing programs, but it's pretty obvious that the program is doing the sizing at 1.21(SetP) rather than 1.21(MAWP).

If you're OK with allowing the relieving pressure to rise to the limit, 1.21MAWP, then the work-around is to enter the MAWP for the set P. You can then chose to actually set the PSV at any lower value. Regardless of that lower set P the PSV will still prevent the relieving pressure from exceeding 1.21MAWP. I can't think of a reason for setting the PSV below the MAWP, unless you want to limit the relieving pressure to a value that's below the allowable limit. But, possibly there is a sensible reason in your case - I just don't know.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

I ran a calculation using Emerson PRV2
There is a facility to enter other overpressure rather than % Looks strange but I tried using MAWP 16 bar as set pressure and also 3.4 bar set + 15.96 bar overpressure. You get the same result! A "J" Orifice. My calculations for both are attached (note % OP = 469.41%).

Note also;-
a. I used 20'C as a operating temperature (required in calculation for valve selection but not for sizing)
b. Minimum PRV size required is 2" x J x 3" CL 150 x CL 150 Conventional design
c. My Wetted area calculation came to 72.84 m2
d. My calculated flow 172,215 kg/hr
e. Observe outlet piping suitability as per Latexman's note

Strange one this, and I would look further into why the vessel is so over engineered. Effectively, the PRV will never open

Second calculation follows in next post.

Per ISO-4126, only the term Safety Valve is used regardless of application or design.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

(OP)
@The Obturator - Thank you for the great effort. As we all agree by now. As outlined in API 520 Table 4, the relieving pressure = Pset (gauge) + allowable overpressure (gauge) + barometric pressure. Allowable overpressure = Maximum Accumulation (1.XX x MAWP) - Pset. Glad you re-produced my results.

I think that the valve will start to simmer as we approach 3.4 barg and then pop once we reach 3.4 barg but never reach full lift as long as internal vessel pressure never reaches the maximum accumulated pressure which is 19.36 barg (1.21 x 16 barg). And i have no idea whether this is a good idea or not.

Another concern I have is that when we size using the 1.21 x Pset approach and arrive at the Q orifice, the rated capacity is over 60%. I am not very comfortable with such a high % over capacity. I remember reading somewhere on this forum that a relief device is considered unacceptably oversized if the excess capacity exceeds 25 % or so. Correct me if I am wrong.

Note d: I am sure you meant 17,215 kg/hr; with this relief load and J (2 J 3) orifice selection, I calculate rated capacity as 19,277 kg/hr (Kd = 0.975).

@don1980 : I think I will prefer the software are modified to calculate the Maximum Accumulation as 1.XX x MAWP rather than 1.XX x Pset. I would like to point it out to the developers.

@Latexman - Verification of Piping specs below.

Preliminary verification of 2 " Inlet Piping and 3 " Outlet Piping
Inlet Piping: NPS 2", SCH STD/40, ID = 52.48 mm, assumed piping length is 1.0 m and using Darcy-Weisbach Equation, pressure loss = 0.1536 bar which is about 4.52% of Pset (3.40 barg). This exceeds the code limit of 3% of Pset.

Outlet Piping: NPS 3", SCH STD/40, ID = 77.92 mm, assumed length = 1.50 m. Pressure just outlet of PSV = MABP = 0.29 barg. With calculated pressure drop of 0.46 bar and Mach No. evaluated at the point just outlet of the tailpipe (point of lowest pressure and highest velocity in tail pipe) - Mach No. = 2.4 Mach. Well over the 0.7 Mach code limit.

Verification of 3" Inlet Piping & 4" Outlet Piping
With a 3" NPS inlet piping, ID = 77.92 mm & pressure loss is approx. 0.58 % and is well below the 3 % of Pset specified in the code.
A 4" NPS outlet piping (ID = 102.26 mm) results in Mach No. = 1.00, which exceeds the 0.7 Mach No limit.

Conclusion: A 2 J 3 may not be adequate. For the 3 J 4 case, outlet piping size may need to be increased to meet Mach No. specification.

Note: In all cases piping material is carbon steel, roughness = 0.015 mm. Reasonable accuracy is expected with the use of Darcy-Weisbach.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

All Spring Loaded PRV will simmer before set pressure.

API designs will reach full lift within 10% . They have been designed and laboratory tested to do that acc to ASME VIII. I would be asking the selected PRV vendor if their design has the capability of such high overpressure. You don't want to use a design that has no built in lift stop that could then bind the spring and /or overpressurise its design.

You're right, this overpressure is not a good idea. Are the original designers aware of what they had done and why?

Minimum flow for satisfactory operation of a spring PRV on compressible fluid varies with whoever you ask. Typically 30 % is a minimum figure, but you have to equate other factors such as inlet geometry, pressure drop, ring setting etc.It is not a moot point here. Restricted lift can solve such issues.

Other calculation attached.

I noted also your pipin comments. Just one observation. You start by discussing a 2" size inlet. I understand this would be for the valve now calculated. I query the size since existing valve has a 3" inlet.

Per ISO-4126, only the term Safety Valve is used regardless of application or design.

### RE: Sizing of PSV - Calculation of the Upstream Relieving Pressure

Sometimes massive over design makes sense, what if the vessel contained "methyl ethyl death" at one time, and they never, ever wanted an emission to the atmosphere? And, sometimes one must use surplus equipment, so WYSIWYG (what you see, is what you get).

#### Quote (Latexman)

Does all the attached piping spec(s) support this strategy?
My primary concern was, is the adjacent piping/pipe spec(s) good for the 16 barg MAWP? This will be another indication whether the original designer wanted to use 1.21(Pset) or 1.21(MAWP).

Good Luck,
Latexman

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