Is there a reason why yeast sugar and water will not create enough pressure to explode a pressure barrel With enough sugar will the yeast create pressure indefinitely?
Actually, this does happen - but, perhaps 'explode' is a bit of a dramatic term to use... 'Spring a leak' is more like it; because the building pressure would pop the seal of the barrel in order to off-gas.
Check out this thread from the Homebrewing beta: Flat beer after priming in a pressure barrel
That's probably the main culprit (CO2 leak).
Also, this brewer describes the exact same scenario occurring during a couple of his brews due to a specific yeast:
I decided to dig into this because I have been home brewing off and on for 20 years and never really used a pressure barrel.
Pressure Barrels seem to be more widely used in the UK and Australian markets than in the USA where we use Cornelius kegs instead.
Pressure barrels are made out of plastic and come in a variety of sizes, the most common seem to be about the 5 gallon/25 liter size.
To use a pressure barrel you move your freshly fermented beer into this vessel and prime with some type of sugar and let it sit for a couple of weeks while it builds up carbonation. Then you serve from the tap.
They are designed to withstand a lot of pressure, but I am sure there is a theoretical limit that I couldn't find. However, they do come with a pressure relief valve in the lid that limits the pressure to give you carbonation within certain parameters and to protect you from the scenario asked above.
I did find this on a pdf on the web:
Whichever cap you have they are designed to release excess pressure, sometimes barrels may bulge under the pressure, but the cap should automatically release when needed. If needed pressure can be released manually by slightly opening the lid by unscrewing and allowing CO2 out, if for example the holes on the cap had become blocked. Between brews check the caps are clean and free from any build up which could stop them from releasing pressure, and make sure they are well cleaned in clean warm water to ensure the rubber 'bands' are not stuck in position with any sticky liquid that may have come into contact with them.
Let say, for argument's sake, that the pressure relief valve was stuck and you put waaaay too much priming sugar in. I don't think the pressure barrel would ever explode. There are two weak points that would probably fail before it go to that point and that's the lid and the serving valve which would both probably vent before it got to that pressure.
So, to answer this question, there is almost zero chance it would explode and would probably just have a leak of some type with infinite yeast and sugar.