10 replies to this topic

[ThroatwobblerMangrove]

Does anyone have an equation that is something like:V(t,T,P) = <insert equation here>, where V(t,T,P) is the function for volumes of CO2, t = time, T = temperature, P = PSI.It would be interesting to know so that I could crank the pressure up and know at what time t that I should start turning it down. Anyone have this?

[ThroatwobblerMangrove]

Does anyone have an equation that is something like:V(t,T,P) = <insert equation here>, where V(t,T,P) is the function for volumes of CO2, t = time, T = temperature, P = PSI.It would be interesting to know so that I could crank the pressure up and know at what time t that I should start turning it down. Anyone have this?

Does surface area come into play here? How about the gravity of the beer?

[ThroatwobblerMangrove]

Does surface area come into play here? How about the gravity of the beer?

I suspect both of those things do. This would probably be very similar to a heat transfer problem so we'd have to bust out some partial differential equations.

[ThroatwobblerMangrove]

And you guys call yourselves beer nerds, pppppfffttt.

[ANUSTART]

Chart. Look at numbers. No do math.

[ThroatwobblerMangrove]

Chart. Look at numbers. No do math.

the charts seemingly only deal with equilibrium.

[MtnBrewer]

Does surface area come into play here? How about the gravity of the beer?

I don't know about gravity but certainly surface area will matter. It won't matter in how much CO₂ is dissolved but it will matter in the rate at which it's dissolved. I don't know what the exact equation would be but I'm pretty sure that it would take the general form of D = E - e^-rt, where D is the amount of dissolved CO₂, E is the amount at equilibrium and r is a factor governing the rate. In other words, the amount of dissolved CO₂ would asymptotically approach the equilibrium value. E would be dependent on temperature and pressure and r may depend on these things as well.

[RommelMagic]

My equation is (P+T)+ M= ?, whereas P=pressure, T=time, M=mouthfeel and the question mark is where it is determined if the beer is ready or not.

[ThroatwobblerMangrove]

I don't know about gravity but certainly surface area will matter. It won't matter in how much CO₂ is dissolved but it will matter in the rate at which it's dissolved. I don't know what the exact equation would be but I'm pretty sure that it would take the general form of D = E - e^-rt, where D is the amount of dissolved CO₂, E is the amount at equilibrium and r is a factor governing the rate. In other words, the amount of dissolved CO₂ would asymptotically approach the equilibrium value. E would be dependent on temperature and pressure and r may depend on these things as well.

that's not a bad thought, the rate of transfer will certainly be dependent on the CO2 deltas (similar to temperature deltas in heat transfer).

[3rd party JKor]

Unfortunately, it's even more complicated than that. The equation MB posted only works if you assume the keg is well mixed. In reality, there will be a concentration gradient of carbonic acid from the top to the bottom of the keg unless you are continuously agitating it. Not only do you need to calculate the amount of CO2 that passes the phase boundary, which is driven by co2 pressure, surface area and the concentration of carbonic acid at the liquid surface, you also need to know the diffusion rate of carbonic acid away from the phase boundary.The equations to solve for this are not overwhelmingly difficult, the problem is getting realistic values for the rate constants. It's one of those things that you either need to scour brewing science literature for, or do the experiments yourself.

[ThroatwobblerMangrove]

Unfortunately, it's even more complicated than that. The equation MB posted only works if you assume the keg is well mixed. In reality, there will be a concentration gradient of carbonic acid from the top to the bottom of the keg unless you are continuously agitating it. Not only do you need to calculate the amount of CO2 that passes the phase boundary, which is driven by co2 pressure, surface area and the concentration of carbonic acid at the liquid surface, you also need to know the diffusion rate of carbonic acid away from the phase boundary.The equations to solve for this are not overwhelmingly difficult, the problem is getting realistic values for the rate constants. It's one of those things that you either need to scour brewing science literature for, or do the experiments yourself.

yeah - I found some literature and the constants are hiding a lot of details I think.