# Calculating leak rates out of high pressure cylinders

I’m trying to select a basis for a leak calculation for a room that holds a collection of CO2 and O2 high pressure cylinders. For my scenario, I am looking at a leak path that is from the high pressure cylinder (~2200 psig) to the atmosphere. The ultimate goal is to see how the current air exchange rate from the affects the steady state concentration of O2 or CO2 in the room using a simple mass balance approach.

One option I’m trying to evaluate is a leak rate out of a small hole (area of hole is 10% of the ID of the SS tubing that the gas is meant to flow through) as a proxy to a loose cylinder connection or similar issue. My confusion is in choosing between the isentropic nozzle (like a PSV) or orifice as my calculation basis. The hole in a pipe intuitively seems like an orifice problem, but I’m thinking the flow could also behave like a PSV relieving at full capacity. I’d appreciate any thoughts on the matter.

@jari001 I’m getting ready to leave the office. I’ll reply again later, but I wanted you to look at this link Fundamentals of Stack Gas Dispersion and related topics . Milton Beychok’s website may have your answer. It may not be in plain sight, so look around the website.

I’m back. Did you find Calculating Accidental Release Flow Rates
From Pressurized Gas Systems
on the Wayback Machine’s link I gave you?

Also, check out Source Terms For Accidental Discharge Flow Rates. Just choose whether you want the customary units of the United States, or SI metric units.

I think these two pages of Milton’s website is highly relevant to what you are doing. Having the leak rate with time dependency, instead of using the initial instantaneous leak rate, may be more realistic, depending on the leak rate to cylinder volume you have. Let me know your findings!

This website was really a trip back in time. I did do the calculations per those two methods, the time averaged and the instantaneous, and the depletion times were way too low in my opinion. The only two parameters I could think to change are the leak area and the coefficient of discharge, and I’d be doing that arbitrarily.

I think my premise is flawed with trying to use these types of equations for the scenario I was trying to analyze. I went the route of stipulating a leak rate out of the cylinder that had a depletion time that was more reasonable - I’m waiting to see what the MechEs have to say.

I also edited the post title to make it more accurate.

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Good, I’m glad you are making progress on this. And, I think both of Milton’s methods are based on orifice. I’m hard pressed to imagine an arbitrary leak point with the tapered, converging appearance of an isentropic nozzle.

Not sure of the situation, but I’m envisioning a large room with CO2 and O2 cylinders inside.

how about comparing the room mass to the mass of one CO2 or O2 in the cylinders and then determine the concentration. is the assumption complete mixing/even distrubution?

assume various CO2 or O2 cylinder leakage rates by guessing a time, say 5, 10, 15, . . . minutes. determine the concentrations.

if there is leakage, what is the eventual outcome or precautionary measure to take?

Fyi, there are leak sensors that can detect leakage from high-pressure sources. i think by ultrasonic methods.

In rooms where asphyxiation is possible, we have a standard of oxygen detectors, audible alarms, and green/red lights at each entrance.

This is a decompression problem. Since your situation has a pressure ratio of about 2000/15=130 you can model the whole process as choked flow and ignore the last trailing bit that isn’t.

I use this and some other NACA/NASA papers related to it:

Calculations of Flow of Air and Diatomic Gases
CHESTER W. SMITH
https://arc.aiaa.org/doi/10.2514/8.11377

Note that the paper was written in pre-pocket-calculator times so you can ignore that half of it. The same math is still used to model transient air discharges in the aviation industry.

The goal is to see if the current room air change rate could handle one cylinder leaking out pure CO2 or O2 from a loose connection.

Instead of calculating a rate, I stipulated a leak rate that would empty out a cylinder over the course of a couple hours and have asked the HVAC engineer to use that in their calculations and see what happens. We were asked by the client to determine if we’d need any special precautions like a purge fan to evacuate the gas. The “couple hours” benchmark (between 1 to 3 hours) is based on the anecdotes I have from people who have hooked up cylinders incorrectly in the past despite being trained and proficient in the skill generally.

The design of the space already has CO2 and O2 sensors tying to stack lights and sirens. Since this room is a dedicated gas storage room, the air handler for the space is once through, outside air so we’re trying to see if the current air handler can either keep the room atmosphere in a safe regime during a leak or how long it would take to clear the room out after the cylinder empties out. If the current air handler can’t keep the room safe or render it safe in a reasonable amount of time, the HVAC design will have to change to get a bigger air handler (more air changes per unit time) or we’d look into a dedicated fan system that would activate at a HiHi alarm or something.

@SparWeb I’ll see into buying that paper for my own general reference, but I’m thinking orifice and nozzle models aren’t quite right for a loose threaded connection. I have no meaningful way to adjust the leak area or coefficient of discharge to match the physical scenario - meaning I have no basis to say a particular number for those parameters is reasonable. In my OP I originally said I’d use a leak area 10% of the area of the actual pipe, but that’s still arbitrary.

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@jari001 sounds like a reasonable and practical approach to me.

Thanks jari001 & second Latexman response.

My I suggest a completely different approach.
There is no way of knowing the leakage rate of a possible improper connection.
Let’s look at worst case.
If a cylinder was to discharge immediately, in less than a minute, what would the concentration be in the room?
Would this be survivable?
Would this be hazardous?
How could this be mitigated?
Alarms? Emergency purge fans?
Would any material in the room, either as part of the construction, in storage or carried through, become a fire or explosion threat in an atmosphere of concentrated oxygen?
Many normally benign materials are subject to very rapid combustion in oxygen rich atmospheres.
An advantage of doing an evaluation based on the entire contents of the largest cylinder being released as to breathe-ability and fire hazard has the dual advantage of a conservative “worst case” approach (that may not be too much different than the 5, 10, or 15 minute approach) and the avoidance of unsure and unfamiliar calculations.
Which of the following notations would you prefer to see on an accident investigation report?

1. A fire or injury resulted when the broken fitting resulted in a gas discharge rate in excess of design criteria.
or
2. Despite the rapid discharge of gas due to a broken fitting, the resulting gas discharge rate was within design criteria and there were no resulting injuries or fires.
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