Simplified calculation for pressure drop for isothermal compressible gas flow 3

[PagoMitch]

Does such a thing exist for O2 at high pressure?
Searched this site, and cannot find anything similar.

I have tried several online calculators for same, with results that vary by an order of magnitude... from 22 psi to 322 psi.
On the TLV website calculator (pretty detailed, and the unit analysis worked out), their calc result (200 psi) is a far cry from their formula that I went through (22 psi)...
Also tried a couple of the Darcy and Iso compressible flow equations in Metric Crane 410 - I could never get the unit analysis to work out.

Conditions:
Client needs 0.7 kg/sec@ 1200 psi. Call it 2520kg/hr.
I have assumed to provide that volume at 1300psi to allow for a ...reasonable...pressure drop.
At 1300 psi = 115 kg/m^3 = 7.2 lb/ft^3 density.
after some conversions = 11.7 ft^3/min (0.0054 m^3/sec) mass flow.

O2 at 1300 psi (89.6 BAR)
Pipeline = Drawn copper at 265LF (81M) at 3/4" ID (19mm) - pipe and O2 tanks are indoors at appx 70-100F (21-38C)
Velocity = 63.6 feet/sec (20 m/sec)
O2 Dynamic viscosity = 0.02125 cP (22.89 x 10^-6 Pa s)
Surface roughness (Epsilon) = 0.0025 mm
Relative Roughness (Epsilon/diameter) = 0.00013
Reynolds #= 2.5Mil, Relative roughness 0.00013, Darcy FF = 0.015
O2 compressibility factor 0.308
O2 molecular weight = 32
Ratio of specific heat "k" = 1.4
Roughness coefficient = 0.0015
Mach # = 0.08; but this was from a site that yielded a pressure drop of 283 psi (???), as well as well as a Reynolds # 2X what I calculated.
A multi-hundred pressure drop for this system just does not feel right...

We have 2-bank O2 Manifold, with H size Cylinders at 2000 psi: so we have lots of P available.

Think I have everything covered above.
I think/thought we fall into the range where Darcy is still applicable; but I cannot seem to make it work.
Can anyone point me to something that has been verified to be reasonably accurate? +/- 10% or so is all I am looking for.

TIA

 

[PagoMitch]

1503-44 - No disrespect meant, but I provided the length both in my original post as well as my response:

265 linear feet/ 81 meters.

Interesting how such small differences in inputs can significantly affect the output. But there are differences:

1. I need a final pressure of 1200 psi (82.7 BAR). You used 79.9 BAR (1159 psi).
2. I am forced to use 1" OD /0.12" wall due to the pressure requirements. This results in an ID of 19.05mm. I chose 0.75" S80, which yields an ID of 18.85mm. 18.85 is as close as you can get to 19.05. Your numbers yielded 20.93mm. This impacts the calcs a lot.
3. The gas room will be exterior, not conditioned. I used 100F (38C) as a gas temp, you used 77F (25C).
4. You also used an Epsilon of 0.035, while I used 0.0025 as for hard drawn copper.

Using your last run as a start, if I change the final pressure, the pipe size, the temp, and epsilon, using 98 BAR input I still cannot get my 2500 KG/hr - I get 1600.
But once I change the length to the 81M, it works out, yielding 2516 KG/hr.
So a delta bar of 98:82.7 equates to 221 psi. yes, still hard to believe.

snickster - Yes, I believe it is a slightly modified Darcy. The "0.0625" is the pipe ID in feet. Without that the unit analysis of the calculation fails. It also fails if you do not divide the results by 144 to convert ft^2 to in^2. That said, the formula is still way off.

1503-44 again - I literally cannot use any copper pipe above 1". 1.125" pipe has the same wall, and so the pressure rating is diminished - below our operating. While 1.5" copper is available in 0.25" wall (that ought work!) Swagelok only makes bronze fittings up to 1.125". I have tried a dozen other vendors; it seems they all only make stainless; which is a no-no with high pressure O2.
If you change your last run piping to S80 (to get to the 18.85mm), you will see the reduction in capacity.
Our differences in Epsilon are also significant. I have used 0.0025 for a long time... so long that I cannot recollect or find a reference. But here is a very similar value from the "Engineering Fundamentals" (eFunda) site, using 0.0015mm. But a long way from 0.035mm.

 

[pierreick]

Hi,
Considering your data: roughness 0.0025 mm; compressibility factor 0.943 (Peng Robinson @ 30C & 89.6 bar); L= 81 m.
using my own calculation spreadsheet:

Results (isothermal compressible flow) T= 30C

Pin 96.52 bars (1400PSI); Pout 82.730 bars (1200 PSI); mass flow rate 2461 kg/h



Pierre

 

[1503-44]

No worries. Accepted.
I thought roughness of tubing is 0.0005 in x 25mm/in = 0.0125mm, then I used something else.
It's very, very late here and Steel is permanently embedded in my brain.

These are the values of roughness that I have used for the last 100 yrs. Below.
Copper 0.0015mm
Slick epoxy coating at 0.0001" = 0.0025mm

At least things seem to be converging.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[Snickster]

You sure you want to use copper tubing and fittings. Seems like stainless steel with swagelok fittings and valves will be more appropriate for high pressure process lines which this is.

 

[Latexman]

Snickster, Cu is a much better choice in O2 service. 316 stainless steel has been shown to combust at a pressure of 3.45 MPa (500 psi) in 100% oxygen at ambient temperature, so no.

Good Luck,
Latexman

 

[PagoMitch]

pierreick - That pretty much matches mine.

1503-44 - Yep. I am glad they are converging as well! It is amazing how much time this...calculation process has taken; but then again, this is almost rocket science.

Snickster/Latexman - Yes, other than some older NASA docs (which are still floating around, and recommend SS for all systems over 700 psi - see below), SS has significant safety issues over 500 psi.

Thanks again all.

 

[katmar]

A good starting point for a calculation like this, where you know the outlet conditions and the pressure drop is not too high a fraction of the inlet pressure, is to determine the physical properties at the outlet and then to calculate the pressure drop for incompressible (i.e. liquid) flow.

Fluid:
Flow = 2520 kg/h, Outlet pressure = 1215 psia, temperature = 38C,
Density = 108.8 kg/m3 (from Peng-Robinson) , visc = 0.022 cP

Pipe:
ID = 18.85 mm, roughness = 0.0025 mm, Length = 81 m

Pressure drop for incompressible flow = 239 psi

Now you can calculate the inlet conditions for the calculated inlet pressure and test the pressure drop calculation using isothermal compressible flow.

Inlet pressure = 1215 + 239 = 1454 psia, density = 130.9 kg/m3

Pressure drop is now 218.4 psi. It is reasonable to get a lower result than under the incompressible assumption because now the average density is higher and the average velocity is lower.

You could iterate to get an exact match for the outlet pressure but 1450 psia or 1439 psig is probably a good enough design figure.

As you might expect, all calculations done with Uconeer and AioFlo

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[Prometheus21]

Hello,

I'm guessing this is a sort of continuation of your previous question,

https://www.eng-tips.com/viewthread.cfm?qid=508255,

where you asked about O2 piping material(?).

Based on the information you have given I can't help but wonder on certain elements:

Required mass flow: At 1300 psi = 115 kg/m^3. - This is achievable with a much smaller ID tubing. 3/4" ID (19mm) seems excessive.

O2 at 1300 psi (89.6 BAR)- fairly low pressure. In a practical setting you can reduce the ID size, and use 316L. As I explained in the other thread it is fully possible to void the velocity limitations under certain conditions. 316L is safely used all the way up to 230 bar in the industry, and have been for decades, even at near sonic velocities. Yes, combustion at 3.45 MPa has been provoked, but don't disregard the empirical data collected from the industry after 60+ years. But lets say stainless steel all of a sudden has gotten more dangerous the last few years:

Why not use Monel 400 or Cu-Ni 90-10(?),You will have a stronger tubing material with the same exemption pressure of 20,6 MPa (3000 psi), completely voiding the velocity limitations in both impingement and non-impingement sites and allowing for a smaller tube ID, allowing for more common fittings to be used.

"Pipe and O2 tanks are indoors at appx 70-100F (21-38C)- 2000 psi cylinder pressure"
So the tanks are connected to a reduction valve with an inlet filter, allowing for the pressure to be reduced to 89,6 bar while removing some of the possible particulates. I have seen certain applications where an additional filter has installed downstream for extra safety. This has a tendency to create quite the pressure drop, just beware of that possibility, and take it into account if that is the case.

As for the initial question of "Simplified calculation for pressure drop for isothermal compressible gas flow" you seem to be getting all the help you need

 

[EdStainless]

I am really curious about when the properties of SS in oxygen changed.
In 1966 DMIC Report 224 " At lower temperatures, the 300 series stainless steels do not ignite when ruptured in 2000psi oxygen at 572F."
Considering that in commercial aircraft the high-pressure oxygen bottles are nearly all SS (usually 21-6-9, Nitonic 40) and these operate at 3,000-10,000psi depending on the application.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[Prometheus21]

Not to hijack the thread, but it hasnt.
Ever since Union Cabride Industrial Gases inc.got renamed to Praxair they started putting a lot more focus on gas safety, to the extreme (In large part due to the Bhopal accident). It is a reason Praxair gs-38 was one of (if not THE most) strictest degreasing standards, and is often followed even today. When they merged with Linde plc in 2020 thats when the focus on the use of stainless steel in oxygen service really became a primary focus.
I will not be surprised if they want to completely phase out SS within the next 5- years. Guess we will find out

 

[pierreick]

Hi Harvey,
Well done even I don't understand why you used the Darcy Weisbach equation (incompressible fluid). It's just an iterative calculation on P inlet knowing P outlet to get the appropriate flow rate using the relevant equation for compressible flow.
Anyway, I encourage everyone to get a copy of Uconeer and AioFlow from Katmar software, best in the class.
Pierre

 

[katmar]

Pierre, the main reason I suggested starting with an incompressible model is that the OP seemed unsure of the equation/units to use for an isothermal compressible calculation. The incompressible calculation serves as a sanity check when you are getting results that vary by a factor of 10. For someone who is confident of their tools for doing the compressible calculation then I agree with you 100% that you simply plug the numbers in and run a few iterations. Unfortunately my earlier post definitely did not do a good job of explaining that. Harvey

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[EdStainless]

The main reason that we used SS for high pressure lines was flow.
We used 21-6-9 aircraft hydraulic tubing.
1" OD x 0.052" wall is rated at 3000psi service and fatigue tested at 4500psi.
This stuff has very tight dimensions, very smooth ID, high strength, and infinite fatigue resistance at 4500psi.
There is a whole range of sizes available and they all have the same properties.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[PagoMitch]

Wow. Thought this was done...

Katmar - I believe we are in agreement with the final numbers for DP and flow.

Prometheus21 - Yes, same project. Smaller tubing also causes higher velocities. With the 1" tube with 0.12" wall, I have 0.75" ID, yielding a velocity of about 21 m/sec. This is also close to the Eng Toolbox - and others - recommended limits of 20-30 m/sec. You are correct in that this pressure/velocity places the selection above the impingement and non-impingement curves per CGA G-4.4, requiring exempt materials. I could indeed go smaller; but the cost difference between 1/2" copper and 1" copper in minimal, but the velocity and pressure drop would rise significantly. As well, in the event of a regulator valve failure (it happens) the line would see full O2 tank pressure of 2400 psi, with velocity increasing significantly. In that event, I have tried to keep the (potential) velocity as low as practicable with the 1" tubing selection; Swagelok does not make bronze fittings above 1".

Copper is the most readily available material around here, even in my required 0.12" wall, and is available cleaned and capped to meet NFPA 99 (my background is more in Hospital gases, but cleaned and capped is still valid in this industrial setting). It (and also 316SS) is also suitable for Swagelok fittings, which the client has directed us to use. Swageloks are rather pricey, but compared to specifying, monitoring, testing, and resolving welding and brazing QC issues (historically for our client, primarily caused by lack of knowledge and care exhibited on the part of lowest bid contractors), they are significantly cheaper in the long run. As with many things, sometimes the easiest way to solve a problem is to go around it.

I am still on the fence re: an O2 filter. Per my readings, they can become the source of an impingement event, even in a non-impingement setting; although I would think the all-copper material should prevent this. That said, in the dozens of Hospital Med gas systems I have designed, we have never specified a filter, and never had a problem with downstream outlets. Then again, 55 psig is a long way from 1400 psig.

EdStainless/Prometheus21 - Re: use of SS. I am just the dumb designer. When the applicable Code state that Copper has an exemption pressure of 3000 psi, and 316SS has an exemption pressure of 325 psi, and I am at 1500 psi, there is no question on my decision. Wish I could reconcile others' long term use of SS for high pressure O2; but that is not my job...I have been involved with (2) court cases in my 40 years practicing. Both were favorable to our firm; and both came down to "What Codes did you follow when you designed this?". Both were also experiences I would rather not go thru again.

pierrick/katmar - I started with Darcy, as it was the easiest to use; and this problem appeared to meet the conditions where Darcy was suitable - where the estimated DP was less than 10% of initial P. Turned out that I was somewhat (18%) above that, and getting 10X differences from what I expected. Then I went back to my old 1988 CRANE 410 for isothermal/compressible flow, and then found the calculator for same.

pierrick - Thanks for those recommendations.

EdStainless - responded to above re: exemption pressures.

Thanks again all.

 

[Prometheus21]

You know engineers, we love a good discussion..

Your arguments are valid and on point.

"...difference between 1/2" copper and 1" copper in minimal, but the velocity and pressure drop would rise significantly. As well, in the event of a regulator valve failure (it happens) the line would see full O2 tank pressure of 2400 psi, with velocity increasing significantly"

Fair point. If the pressure drop wasn't an issue then I would argue the use of a pressure relief valve + a built in failsafe to shutdown the system if these conditions occur. That again would require proper ventilation, which is mandatory where I'm from (Scandinavian region), but maybe not in other countries.

From what I can see the NFPA 99 requires all equipment to be cleaned iaw. CGA G-4.1. Which is fine. not great, but fine.

"As with many things, sometimes the easiest way to solve a problem is to go around it." - I concur. Sometimes its even easier to not take on a customer, simply because you know they will screw up *something* and blame your company for any fallout. I have personally blacklisted 2 companies (albeit smaller ones) due to failing to implement proper maintenance routines in O2 systems. In both cases people were disabled for life. In both cases people got horrific injuries due to other peoples pure incompetence.

Disregard my comment on the O2 filter. If everything is cleaned and installed properly then the inlet filter on the reduction valve is sufficient. This filter should be switched out periodically, but no one ever does it unfortunately. And you are right, it does indeed become a source of an impingement event, been there, seen it, experienced it.

I'm not going even try to comprehend the amount of codes and standards you guys have overseas, not my forte. Follow the codes, no doubt. "Fortunately" for me we have a standard that specifically states that as long as you can show a long and successful service life the material is approved. Extremely vague and up for interpretations.

 

[pierreick]

Hi,
For those interested I've attached my calculation note.

Pierre

 

[1503-44]

Thank you.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[goutam_freelance]

Applying the Crane isothermal flow formula

w=0.7 kg/s,
f=0.015,
D=19 mm,
L=89 m,
P1'=1300 psia
density =115 kg/m^3
calculated P2'=994 psia(not 1200 psia)
Please check if diameter needs to be upgraded

 

[pierreick]

Hi Goutam,
The requirement from OP:
Client needs 0.7 kg/sec@ 1200 psi. Call it 2520kg/hr. This means you need to calculate Inlet Pressure to satisfy the client's request.
Note: The data you are using are not accurate. Let you read the entire thread.

Similar result using equations 1-27 or 1-28 but need iterations to get the right answer.

Pierre

 

[goutam_freelance]

Hi pierreick,

Thank you for your observations. I was a little lazy in not going through all the threads.

I have recalculated based on updated data as available and which as given below after several iterations.

The required inlet pressure is 1425 psia. But it is very sensitive to actual ID of tubes..

Hope the above information will be of some use.


Engineers, think what we have done to the environment !

https://www.linkedin.com/in/goutam-das-59743b30/