# CO2 [ppm] exposure relative to room volume [m^3] and air ventilation

#### Dijana

Hi All,

I am trying to find out how much CO2 (ppm) would be released into a ventilated room (m3) from a faulty pressurized gas cylinder to calculate risk associated. Would anyone be able to help me with a formula? I was trying to work with V=nRT/P but wasn't sure how do I translate the outcome to get the ppm released relative to room m3 and air ventilation that works against the CO2 exposure? Time of exposure varies in this dynamic process so time would be another variable that needs to be considered.

Co2 gas cylinder: F size (22kg) - liquid phase >99.9% (v/v)
Cylinder pressure: 5700 kPa
Outlet pressure (reduced through regulator): 150 kPa
Connection outlet: 10 mm
Room size: 60.5 m3
Air ventilation: 161 L/sec
Room temperature: 20 degrees Celsius

I guess there is a difference if CO2 is released before or after the regulator regarding the pressure difference?

Appreciate your help with this.
Dijana

#### jim mcnamara

Mentor
Is this a class assignment?

#### Dijana

Hi Jim, this is not for an assignment. This is part of a risk assessment for occupational health and safety.

#### russ_watters

Mentor
Hi All,

I am trying to find out how much CO2 (ppm) would be released into a ventilated room (m3) from a faulty pressurized gas cylinder to calculate risk associated. Would anyone be able to help me with a formula? I was trying to work with V=nRT/P but wasn't sure how do I translate the outcome to get the ppm released relative to room m3 and air ventilation that works against the CO2 exposure? Time of exposure varies in this dynamic process so time would be another variable that needs to be considered.

Co2 gas cylinder: F size (22kg) - liquid phase >99.9% (v/v)
Cylinder pressure: 5700 kPa
Outlet pressure (reduced through regulator): 150 kPa
Connection outlet: 10 mm
Room size: 60.5 m3
Air ventilation: 161 L/sec
Room temperature: 20 degrees Celsius

I guess there is a difference if CO2 is released before or after the regulator regarding the pressure difference?

Appreciate your help with this.
Dijana
Welcome to PF! The steady state dilution equation is just the ratio of the contaminant entering to the total volume leaving the room, in any units as long as they are consistent. For example, 1 liter per second of CO2 in 100 l/s of exhaust would be 1% or 10,000 ppm.

The real problem here is that you don't seem to have any idea what the leak rate might be. You'll need a way to estimate it. I assume this is a real world issue? Perhaps fixing or testing the cylinder or testing the room would be the better/safer option.

#### jrmichler

For a risk assessment, you assume that the entire cylinder is discharged instantly. You calculate the volume at room temperature and pressure of 22 kg of CO2. Then you calculate the percentage CO2 in the room. Ventilation is not included because the cylinder is discharged instantly. Then you find the maximum safe concentration of CO2. Then compare.

How can a cylinder discharge instantly? If it tips over and breaks off the valve. How can it do that if it's chained in place? Because it's not chained in place when an empty cylinder is replaced with a full one. Or a cylinder cart tips over. Or something runs into it. Or somebody opens the valve wide to see what happens. Or somebody removes the regulator to change cylinders without closing the valve. Risk assessments are always based on worst cases.

#### Dijana

Hi All,

Happy New Year! Thank you All for the very helpful responses.
Dijana

#### berkeman

Mentor
For a risk assessment, you assume that the entire cylinder is discharged instantly.
I was going to ask about the extra issue of the density of CO2 being different from air, but it sounds like for this specific calculation that is irrelevant, right?

#### CWatters

Homework Helper
Gold Member
The density of CO2 at STP is around 1.96 grams per litre, or 1.96kg per m^3.

The volume V in m^3 is about..

V = mass/density
= 22/1.93
= 11.4 m^3

Check my maths.

Just a heads up... I think CO2 is heavier than air so there might be the potential for it to form a layer at ground level or flow out of one room into another room or a basement displacing the air. Especially as it could/will be colder.

#### russ_watters

Mentor
I was going to ask about the extra issue of the density of CO2 being different from air, but it sounds like for this specific calculation that is irrelevant, right?
That's a tough one, and it comes up a lot for liquid nitrogen where the offgassing is cold. Typically CO2 is expected to mix, so you locate the sensor at "breathing zone" height. Cold vapor from dry ice will drop, but the concentration you are testing for is way below the immediately dangerous concentration. CO2 is a poison vs N2 which is an asphyxiate. For LN2 if the concentration at 4' elevation is in the danger zone and an occupant stumbles on the way to the door, they might not get back up. So the O2 depletion sensor is low.

The alarm points tend to be conservative though. Also, it can sometimes be tough to differentiate between normal exposure and emergencies for the purpose of alarms, but for this example it is clear.

#### CWatters

Homework Helper
Gold Member
Another heads up... I just looked for C02 alarms on eBay and it looks like many vendors mix up Carbon Monoxide and Carbon Dioxide. I don't know if a CO detector also responds to CO2 but I suggest you be very careful to buy/install an alarm from a reputable company.

#### Tom.G

Just to be conservative:
As @CWatters pointed out, consider that the CO2 volume in the cylinder is 1/5 the volume of the room. Since CO2 is much denser than air it won't stay mixed for long, if at all. That implies there will be a layer of essentially 100% CO2 from the floor up to 1/5 the room ceiling height. Depending on the circulation from both a jet of CO2 leaving the cylinder and ventilation, this layer will eventually be somewhat thinner with the air above having some unknown concentration. The upper air concentration depends strongly on the ventilation details. For instance if the air inlet is at ceiling level and the exit at the floor, the mixing will be mostly due to turbulence and convection. If the air exhaust is at the ceiling, I would expect rather more mixing.

Cheers,
Tom

#### russ_watters

Mentor
Since CO2 is much denser than air it won't stay mixed for long, if at all. That implies there will be a layer of essentially 100% CO2 from the floor up to 1/5 the room ceiling height.
Others have said similar things, but please consider that in the atmosphere normally there is 450ppm or so (and in a heavily occupied office maybe 1000ppm) all the time and quite thoroughly mixed. Air is not still enough for the CO2/N2/O2 to stratify much unless it comes out cold and slow.

#### jim mcnamara

Mentor
I would think the total mass release of CO2 would have a small bearing - especially in case of a small room. Somewhat like @jrmichler mentions above.

Ex: a limnic eruption from Lake Nyos in the Northwest of Cameroon killed people and livestock in 25 villages, all due to massive outgassing of CO2 from the lake. No small rooms, but a huge volume of gas which cooled and flowed downhill. Normally the lake "fizzes" like freshly poured soda, a rockslide caused 100000 metric tons of gas to be release, like shaking the soda bottle violently

https://en.wikipedia.org/wiki/Lake_Nyos_disaster

ppm levels for CO2
In many confined spaces, there is a direct relationship between low concentrations of oxygen and elevated concentrations of CO2. In the case of a confined space where CO2 is generated as a byproduct of aerobic bacterial action, a concentration of 19.5 percent O2 (the hazardous condition threshold for oxygen deficiency in most jurisdictions) would be associated with an equivalent concentration of at least 1.4 percent ( = 14,000 ppm) CO2. This is substantially higher than the generally accepted workplace exposure limit for CO2 (5,000 ppm calculated as an 8-hour TWA).
https://ohsonline.com/Articles/2006/07/Carbon-Dioxide-Measures-Up-as-a-Real-Hazard.aspx This site is not the official US gov't site - which has issues right now.

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