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# PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates? 3

## PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

(OP)
I am working on calculating the pressure drop in piping upstream and downstream of a PSV, which is new to me. Since my company (very small - I'm the only engineer) has no simulation software or any other software to handle these kinds of calculations, I am using the Darcy-Weisbach formula to calculate the pressure drop at this time. My calculated Reynolds number comes out very low (~50) and my overall calculations don't seem reasonable because of it.

I have been converting SCFD to ACFD, then to ACFS to find the ACTUAL velocity to use in the Darcy-Weisbach equation. Should I be using STANDARD or ACTUAL flow rates for this kind of calculation involving velocity?

Conditions:
Required Flow: 4 MMSCFD
Operating Pressure: 350 psig
Set Pressure: 400 psig
Temperature: 100 F
MW: 17.4
Density: 0.05 lb/ft^3 (using SG*air density)
Viscosity: 0.013 cP
Inlet Pipe ID: 1.61 in (NPS 2 SCH STD)
Outlet Pipe ID: 2.067 in (NPS 3 SCH STD)

Actual CFD: 0.153 MMACFD (compared to 4.0 MMSCFD)
Actual CFS: 1.767 ACFS
Inlet Velocity: 125 ft/s = (ACFS/Area Inlet)
Outlet Velocity: 75.8 ft/s = (ACFS/Area Outlet)
Inlet Re: 64.5
Outlet Re: 50.2
Inlet f = 0.992 (64/Re)
Outlet f = 1.274 (64/Re)
Inlet Pipe Pressure Loss: 1.869 psid
Outlet Pipe Pressure Loss: 2.40 psid

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

More importantly is you say you're the only engineer (PE?) but haven't done these calculations before and presumably have no one to review your evaluation of the relief scenarios and calculations. This is unacceptable imo.

Relief calculations are process safety devices that shouldn't be done on a whim or analyzed by people not fluent in their details (without proper review/oversight).

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

A gas PSV scenario with laminar flows? I doubt it.

Use actual flows for inlet and outlet dP.

Back up and tell us about the scenario and PSV size. Is it a proportional or full flow PSV? Is it a 1.5H2?

Has your boss ever sized a PSV?

Good Luck,
Latexman

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

Also note your relief piping pressure drops (inlet & outlet) must be acceptable for the capacity of the relief valve, not merely your required flow calculated based of the scenario. This is required by code.

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

At a minimum, you need to really study API 520 Parts I and II and API 521.

AND DON"T DOUBLE POST!!!

Good Luck,
Latexman

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

(OP)
RVAmeche: I am a PE, my background is mostly I&C but I'm a Mechanical engineer through education. I agree that it isn't acceptable and I'm working on changing it, but the company doesn't seem to want to change things... I'm working on changing my situation.

Latexman: Posting corrected. I'll try to explain more, but please keep in mind that up until now I have only ever had a working knowledge of the PSV basics and have never done any related calculations. I'm aware that I'm ignorant on the subject, but I'm trying to fix that. No one here has ever sized PSVs and have always relied on vendors. One potential customer is asking for verification of inlet and outlet pressure loss for the PSVs specified, which is what is leading to this inquiry.

Scenario: PSV used to limit the outlet pressure of one PCV (PCV1) to the inlet of a second PCV (PCV2) in series in the event that PCV1 fails. Maximum inlet pressure of PCV2 is 400 psig. Flow is 3-4 MMSCFD.

PSV: 1.5F2 per vendor, Model RV10, MFR BMD. I can't find any mention of proportional or full flow in the literature. I am also working on building a PSV sizing spreadsheet for future use. It almost matches the vendor, but is overly conservative still.

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

3 MMSCFD looks right for the capacity of a 1.5F2 PSV set at 400 psig + 10% OP. My tool said 5800 PPH.

Your Reynolds numbers look way off. For a 1.61" inlet I got 1.14x10^6 and a 2.067" outlet I got 8.86x10^5. Check your units and conversions. If turbulent, that'll make your f's wrong, so you'll need to re-visit that.

Can you characterize the length and fittings (ΣK) of the inlet and outlet?

Good Luck,
Latexman

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

(OP)
Latexman: Thanks, I knew it was something simple like that. I wasn't converting absolute viscosity into lbf-s/ft^2. My resulting Reynolds numbers are almost the same as yours now.

I'm using pipe lengths of 2 feet both upstream and downstream, with one elbow downstream included in the K values for the minor losses (K=1.5). My total head loss comes out to be 83 feet for the inlet and 158 feet for the outlet, correlating to a 0.029 psid and 0.055 psid for inlet and outlet, respectively, using a density of 0.05 lbm/ft^3 (dP=rho*g/gc*dH). It still seems low to me, but I don't have anything to compare it to.

I included a screen shot of my workbook in case that provides any clarity about my fumbling.

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

It is always best to define what your standard conditions are. The differences are small, but it is good practice.

The Darcy-Weisbach equation requires the actual velocity. Therefore you must calculate the actual volumetric flow. I agree with your 1.767 ACFS at the set condition.

In calculating the Reynolds number you must either use the standard formula of Re = (density x velocity x diameter) / viscosity with a consistent set of units, or you must use a dimensional form of the equation designed for the units you have. I always prefer to use consistent units (SI if possible).

The density at the set conditions will be close to 1.2 lb/ft3. I agree with your inlet velocity of 125 ft/s. The diameter of 1.61 inches must be expressed as 1.61/12 = 0.134 ft. The viscosity of 0.013 cP is equivalent to 8.7e-6 lb/ft.s. These values give a Re No of 2.3e6 and with a standard pipe roughness of 0.002 inch the Moody friction factor will be 0.021.

You have not given the pipe lengths so I cannot comment on the calculated pressure drops. Remember that with the vapor piping there could be an extreme increase in the velocity over the length of the pipe and I would not recommend using Darcy-Weisbach in these circumstances. Search for the isothermal compressible flow equation in your handbooks, or on the web, or right here in the forums. The velocity head in the exiting gas is also likely to be significant.

Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

You seem to be using density at atmospheric pressure not at 400 psi?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

I got inlet density = 1.72 lb/CF. I modelled a MW = 17.4 as 96.63% NH3 and 3.37% N2. Z was 0.764.

Inlet dP = 0.4 psi = 0.1% of SP. I used 1 contraction and 2' of 1.5" sch. 40 pipe

Outlet dP = 11.7 psi = 2.9% of SP. I used 2' of 2" sch. 40 pipe, one elbow, and, of course, one exit.

Your outlet velocity = 75.8 ft/sec is way too slow. At the tailpipe outlet, the pressure may be near atmospheric pressure and the velocity may be near Mach 1 with your system.

Good Luck,
Latexman

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

(OP)
Katmar: Thanks for the density check. I wasn't converting it like you said. It looked weird but since it wasn't my most unknown matter I wasn't looking at it closely yet. I will look into the isothermal compressible flow approach. I have seen that brought up but I also still see a lot of the D.W. method too. I can include both.

It is always best to define what your standard conditions are. The differences are small, but it is good practice.
Ts = 60 F, Ps = 14.7 psia - this was reflected in my workbook calculations but not explicitly shown

The density at the set conditions will be close to 1.2 lb/ft3. I agree with your inlet velocity of 125 ft/s. The diameter of 1.61 inches must be expressed as 1.61/12 = 0.134 ft. The viscosity of 0.013 cP is equivalent to 8.7e-6 lb/ft.s. These values give a Re No of 2.3e6 and with a standard pipe roughness of 0.002 inch the Moody friction factor will be 0.021.
Once I corrected the density I'm nearly matching these Numbers.

You have not given the pipe lengths so I cannot comment on the calculated pressure drops. Remember that with the vapor piping there could be an extreme increase in the velocity over the length of the pipe and I would not recommend using Darcy-Weisbach in these circumstances. Search for the isothermal compressible flow equation in your handbooks, or on the web, or right here in the forums. The velocity head in the exiting gas is also likely to be significant.
I have been using 2 feet on the inlet and outlet at this point. In the outlet line, I have included one elbow with a K=1.5.

LittleInch: You're right, I got it updated to be about 1.11 lbm/ft^3 using the ideal gas law equations.

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

(OP)
Latexman: I'm still pretty far off of your dP calculations, but now at least I know where to shoot for. After fixing the things addressed by previous points in this post, I don't immediately see where I'm going wrong with the Darcy Weisbach method here.

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

2
The problem is the actual flow on the outlet pipe. It will not be = to the inlet flow on a volumetric flow rate basis. Inlet is at 400ish psig and outlet is at atmospheric pressure at the exit. Huge difference. My guess is you have Mach 1 at the exit.

The outlet dP has to be solved backwards, from atmospheric pressure at the exit and calculated back to the PSV outlet flange where you have the backpressure on the PSV.

Good Luck,
Latexman

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

Latexman's comment regarding the pressure in the outlet pipe is extremely important. The back pressure from the outlet piping should usually be limited to 10 % of the PSV set pressure. With a limit of 40 psig I would design for around 30 psig.

Guessing this pressure allows us to determine the density and velocity of the vapor at the start of the outlet pipe. Latexman has calculated a Z of 0.764 but I had used 1.0. I cannot find the gas composition and using the higher Z will be more conservative so I will stick with it. Certainly in the outlet pipe Z will be very close to 1.0. This makes the density at 45 psia (= 30 psig + 15 psia atm) 0.13 lb/ft3.

My approach would then be to try a mass flow of 2.12 lb/s in pipes of various diameters to calculate the pressure drop - and to ensure the calculated pressure drop is less than 30 psid and the exit velocity is reasonable.

In fact, with such a short exit pipe you could pretty much ignore the pressure drop along the pipe and just investigate the exit velocity. Once the gas has dropped to atmospheric pressure your density would be around 0.046 lb/ft3 and the exit velocities would be
2" - 1978 ft/s
3" - 898 ft/s
4" - 521 ft/s
6" - 230 ft/s

On this basis I would select at least the 4" line and preferably the 6". Also, get someone competent to check the reaction force on the elbow in the outlet pipe.

Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

### RE: PSV Inlet/Outlet Piping Pressure Loss - Actual or Standard Flow Rates?

(OP)
Thank you Latexman and Katmar. This has given me much more to investigate and I will be doing a more thorough effort on this since the customer deadline for the information they requested has passed.

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