Absorption rate of CO2 in water

[sophiecentaur]

So here's an interesting topic and I would appreciate some input from the assembled brains of PF to the question. Unfortunately I can't reveal the background to this but I want to know something about the rate that small bubbles of CO2 are likely to be dissolved in water under moderate pressure and non extreme temperatures. It's a matter of flushing CO2 from plastic pipes.
I have found information about how the solubility is affected by pressure and temperature but I would really like to know how fast the process takes. The process should be reasonable short if possible.
I know that CO2 comes out of solution pretty fast with only moderate pressure drop because I have used our dreaded VacuVin for preserving a half finished bottle of wine. It works well and a lot quicker for 'airing' a cheap bottle of plonk.

 

[Bystander]

What I recall from grad school is that there is/exist catalysts/(de-)carboxylases for the process that affect the rate in very profound fashion; I'll refer you to Mentos (?) and various diet sodas used as "bombs" on Mythbusters, presumably on the telly in your neck of the woods.

 

[sophiecentaur]

Thanks for the response but the fluid is only allowed to be water / brine.
The context is not Global Warming

 

[Bystander]

water / brine.

Any "brine?" Lithium and beryllium salts have some rather peculiar behaviors.

 

[sophiecentaur]

Only NaCl or just water.

 

[Bystander]

https://www.google.com/search?q="systems:+nacl+++h2o+++co2"&rlz=1C1CHFX_enUS577US577&oq="&aqs=chrome.0.69i59l3j69i57j69i59l2.5636j0j7&sourceid=chrome&ie=UTF-8
Edit: This appears to have been studied extensively, not in the "normal" temperature range requested, but this is all that showed up.

 

[sophiecentaur]

This appears to have been studied extensively, not in the "normal" temperature range requested

There's lots of material about sequestering CO2 and geological processes. My system is to be just a few tens of minutes or perhaps hours. At least the CO2 will be in the form of bubbles - probably small ones so the net surface area vs the volume could be fairly high. Perhaps some measurements will be in order.
I was just trying to short circuit the system a bit.

 

[Chestermiller]

If the bubble radius is R, then the bubble volume is $$V=\frac{4}{3}\pi R^3$$ If the pressure is p and the temperature is T, the number of moles of CO2 in the bubble is $$n=\frac{PV}{RT}$$. If the Henry's law constant is H, the concentration of CO2 in the water at the bubble surface is $C=HP$. Assuming that CO2 concentration far from the bubble is zero, the molar rate of flow out of the bubble is $4\pi r DC$, where D is the diffusion coefficient of CO2 in water. So we have $$\frac{dn}{dt}=-\frac{P(4\pi r^2)}{RT}\frac{dR}{dT}=-4\pi rDHP$$or $$r\frac{dr}{dt}=-HDRT$$ assuming a quasi steady state diffusion profile. This assumes that the bubbles do not interact with one another, and the only transport mechanism is by molecular diffusion in the liquid. So the time for bubble collapse would be (roughly)
$$t=\frac{r_0^2}{2HDRT}$$where $r_0$ is the initial radius of the bubble. This would be an upper bound to the time of collapse.

 

[sophiecentaur]

@Chestermiller
Thanks. I think that's the sort of thing I need on the way. I can easily enough choose a representative bubble size.
I have found sources for values of most of those coefficients so I can paste them into the final equation.