EngFire:
If you are offshore and trying to protect a structural housing, you will require over-pressure protection in the case of injecting CO2 for fire extinguishing purposes. This is not a case of whether you need it or not; depending on the amount of CO2 employed, for total safety, you should protect the enclosure from rupture or collapse. There is no economy or practical sense in doing a spreadsheet to determine IF you need it or not. The probability and hazard of overpressure is present the moment you inject CO2 for the sole purpose of putting out a fire. The subsequent resulting pressure build-up is something you inherit with the system employed and you must provide for a safe, mitigated pressure situation. And this is assuming you can safely rely on a positive liquid CO2 shutoff valve. This is sometimes difficult to accomplish due to improper, experienced mechanical design and I wouldn't put too much trust in it.
You are certainly doing the right thing by showing concern for a safe, correct design and I’d like to help.
First of all, you cannot reasonably and accurately determine the pressure build-up resulting from an injection of liquid CO2. And this has nothing whatsoever to do with the Ideal Gas Law or Johannes Diderik Van der Waals’ pioneering equation of state (which, although the first, is very inaccurate and cumbersome). The reason for this is that when you inject liquid CO2, you have no means of determining how much CO2 has been administered nor what temperature (& this will be increasing) the total gas mass is at. But even if you knew the total amount of CO2 injected, it would do you no good since the application of liquid CO2 onto a fire consists of expanding liquid CO2 into a resultant mixture of SOLID CO2 (dry ice “snow”) and GASEOUS CO2. The initial make-up of this 2-phase mixture is 50%-50% and it initially exists at -109 oF while continuously being warmed up by the fire it is suffocating and the surrounding enclosure mass. The solid CO2 sublimates (reverts to the gaseous state directly from the solid state) differentially in accordance with the surroundings and the equilibrium it is trying to establish in the enclosure. This is a very complex and dynamic heat and mass transfer model that I defy any industrious engineer to try to simulate with accuracy. It simply is never even attempted – much less done.
The practical way your problem is resolved is that a “fuse” type of apparatus is employed to rupture at a pre-determined pressure (less than the allowable for the enclosure) and release the CO2 to the atmosphere should the rupture occur. This “fuse” is usually installed in the form of a thin membrane of aluminum or other weak material that will ensure that it will fail before the structure starts to weaken. Its size (or capacity) should be based on liberal allowance for pressure build-up. Depending on the size of the protected enclosure, I don’t think a 3 ft -4 ft diameter is out of the picture. You should guide yourself by conservative design, taking into consideration the worse case scenario.
My basic recommendation is to not worry about calculating the rate of pressure buildup. Base yourself on the conservative stance that a pressure buildup will occur and that you must provide a relief device to safely protect the enclosure and personnel affected by its failure. By trying to predict the theoretical pressure (which any experienced engineer would not accept on face value) you will be putting your efforts on the effects and not the cause. Attack the problem of providing pressure relief directly and conservatively and you can’t go wrong.
