CO2 Quantity required based on temp

[DM2]

I'm trying to write a formula in EXCEL that will tell me how much liquid CO2 I need, given the volume, and temperature of a particular space. I need this as part of another formula to resolve some quantity calculations for Fire Protection.

NFPA 12, Appendix D, offers the following formula that I'm trying to tweak in EXCEL:

[tab]X = 2.0303 (Log₁₀[100/100-C])
[tab]Where:
[tab][tab]X = Volume of CO2 expressed in ft³
[tab][tab]C = Desired Concentration (usually 34%)

The result is ft³ so I then divide by 9 (i.e. 1 lb of CO₂ expands to 9 ft³ at 86°F).

My problem is that this is based on the expansion of CO₂ at 86°F at 1 atmosphere. The temperatures I'm dealing in range from 40°F to 400°F. Normally I won't worry about this due to how CO₂ is packaged in cylinders (i.e. 25, 50, 75, 100, or 120lb capacity cylinders). The problem is I need to determine the leak rate from an opening and add CO₂ accordingly. The added CO₂ can vary anywhere from 1 to 30 lbs per minute over more than 20 minutes. If I can't get more accurate, I'll find myself adding several cylinders at a cost of $2,500.00 each (installed).

Does anyone know how I might modify this formula to allow me to insert different temperatures, and possible pressures?

Regards,
Dan

 

[Montemayor]

Dan:

I don’t have a copy of NFPA 12, so I have a lot of trouble understanding what you are working with and what it is that you are trying to control.

I suspect that you are trying to keep a fire extinguished or trying to create and maintain an inert atmosphere where combustion can’t take place. I think your NFPA equation determines the volumetric quantity of CO2 that will mitigate a fire in a given environment. The “X” in the equation is volume of CO2 measured at 14.696 psia and 86 oF.

Since the specific volume of CO2 gas while at 14.696 psia and 86 oF is 9.0109 ft3/lb CO2, then you can obtain the CO2 mass by dividing X by 9 to obtain lbs of CO2 required.

All produced CO2 is measured in lbs of mass - not in volumetric terms. The average, normal cylinder contains 50 lbs of CO2 liquid at 1,046.3 psia and 86 oF. The normal manner of applying CO2 as a fire extinguisher is to expand the high pressure (HP) liquid in the cylinder down to atmospheric conditions. I believe that you are trying to find a method by which you can measure the mass amount of CO2 applied to an external environment in order to control the % of inert gas there. Am I correct?

The problem in correlating the amount of released liquid CO2 and the desired amount of CO2 vapor created is that the measuring of the liquid CO2 is very difficult and impractical. I have never seen a mass meter on this type of application. Usually, the mixed amount of CO2 “snow” and CO2 vapor (both at -109 oF) is done at one time, totally in excess (hopefully) of what would be required to extinguish any fire in the environment. You are using a relationship that predicts a volume of CO2 vapor at 86 oF/ however the product of ANY LIQUID CO2 expansion to atmosphere is a mixture of “snow” (dry ice) and CO2 vapor – both at a very cold -109 oF (definitely not 86 oF).

I don’t know how you could “modify” the NFPA formula since I don’t know what exactly it is supposed to predict.