Bottle Headspace Pressure

[chin19]

Hi all,

I'm trying to get my head around a chemical engineering problem and was hoping someone could advise me on how to solve it.

I have a closed soft drink bottled at 5g/L of CO2 with known temperature, headspace pressure, headspace volume and liquid volume. I want to work out the maximum pressure that would be exerted on the cap from the headspace if the bottle was heated to 70°C. I'm not sure what the best way to approach this is, 1) should I determine the volume reduction in the headspace from the liquid expansion and then work out how this changes the headspace pressure from an EoS? 2) Would I then also need to work out any further pressure increase from CO2 dropping out of solution and trying to reach equilibrium or would this not contribute to the headspace pressure, rather the headspace pressure determines how much of the CO2 is dissolved within the liquid?

Any help is greatly appreciated.

Best regards,
chin18

 

[danschwind]

chin18,

This is an interesting question. I'm not sure if I'm correct, but:

- Consider PV = nRT for the sake of simplicity (use a more rigorous EoS to solve your problem).

- There will be an expansion of liquid volume that will reduce the available headspace, therefore V will reduce.

- T will increase.

- n will increase as more CO2 comes out of solution (due to temperature).

 

[LittleInch]

I think you need to do both.

So a graph like this

https://www.engineeringtoolbox.com/carbon-dioxide-d_1000.html

would seem to help.

The expansion of liquid will not be great but if the head space is small then it might be significant.

Liquids are not totally incompressible, nor is the vessel truly rigid so that adds further complications.

Sounds like a bit of an iterative operation as more pressure will inhibit the release of CO2 due to temperature and more pressure from temperature will inhibit a bit the expansion of the liquid, plus the liquid compression and vessel expansion.

Can't you just try it and measure it?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[SuperSalad]

Sorry, my original comment was totally wrong and I erased it, gas solubility decreases with temperature as the energy increase causes more gas to escape the liquid. So, both the liquid and the gas behavior is needed to accurately predict the pressure, but the gas behavior will have much more effect on your pressure than the relatively inconsequential volume increase of the liquid.

Andrew H.

http://www.mototribology.com

 

[apetri]

if you know composition and initial condition then you can solve a constant volume (the volume of the bottle) flash operation at specified temperature to get the final pressure, I do not know how much accurate a extended EOS or a Helmholtz based model can be for your CO2 mixture (you should include all components with significant impact on properties), I utilize regularly the V-P or V-T flash operations available in Prode Properties, see

http://www.prode.com

, for solving similar problems, mainly to estimate the discharge temperatures for PSVs protecting vessels, anyway, with mixtures of hydrocarbons (see PSV case) results are quite accurate...

 

[LittleInch]

Supersalad All depends on the relative size of the head space.

If you think of something like a 2 litre coke bottle the head space is really small compared to the volume.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[IRstuff]

The size of the head space is irrelevant, since the equilibrium pressure is what is achieved by the amount of carbonation. My recollection is that pressure is something like 90 psi, max, at high ambient temperatures, which is why a 2L bottle wall feels stiff before the cap is opened, and you can almost never get back to the same level of stiffness afterwards.

TTFN (ta ta for now)
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[3DDave]

As long as the headspace is larger than the volumetric expansion of the liquid over the volumetric expansion of the bottle due to temperature rise then the pressure should be driven by the CO2 pressure. But if the container was fully rigid and there was no initial headspace, then the liquid's attempt at expansion would drive much higher pressures.

Which is sort of what happens when a soda bottle is put into a freezer and the ice expands.

That analysis needs its own thread, but I bet the reality is the bottlers do a lot of practical testing rather than making a bunch of time-step calculations to represent the initial formation of ice, concentration of the syrup, the movement of CO2 between the water, the headspace, and the syrup, the contraction of the bottle/can, the changing properties with temperature, and the expansion of the ice and then contraction as it cools further during the progressive formation.

Fill it up to some level. Cap it off. Toss it in to the oven or the freezer, and see what happens.

The tricky part is the solubility of the CO2 in the soft drink. From painful experience I believe that this is not a constant across soft drinks. Example - Blueberry New York Seltzer. I worked adjacent to a grocery store and would get one of these as an afternoon break. All sorts of flavors. But I recall only this one because I would get to my desk, gently set it down, still cold from the store refrigerator, and undo the cap just like any of the other 25 or so flavors. But this one flavor would practically explode. Caught me unawares the first time and I figured I'd not paid attention to handling it. The second time of having to get a pile of paper towels I noted the flavor. There was no third time as I undid the cap as if defusing a bomb. And sure enough, carefully handled, gently set down, the instant I cracked the cap seal, the bottle went substantially to foam. It took many minutes to allow enough CO2 to escape in tiny increments of time before it was safe to remove the cap for a sip. No other flavor was as willing to rapidly shed the CO2 like blueberry.

A similar effect is seen in the Mentos vs soda bottle experiments. Apparently certain diet colas are exceptional for this.

From this I gather that the ability to retain CO2 depends on the composition of the soft drink. I believe it is not as simple as nucleation as the New York Seltzers are perfectly clear and have no obvious places inside the body of the fluid to start nucleation; while the Mentos candies do supply nucleation, if that's all there is why is it so much more effective in some soft drinks over others?

In summary, I think that experiments will have to be done to find the solubility of CO2 for any particular soft drink at various pressures across the temperature range before any calculation for a particular case can be done.

I see there's a formula called Henry's Law, but one has to know the solubility constant and it only applies to conditions where the only variable is partial pressure. And then there's this:

https://chemistry.stackexchange.com...arbon-dioxide-content-of-a-soda-can-or-bottle

 

[mdepeche]

if you do not know the components in the mixture robably the best solution is to heat the bottle and measure the resulting pressure, as already suggested by LittleInch,
if you know (or can guess) the composition, the approach suggested by APetri can help to estimate the final pressure,
assuming a constant volume for the container (bottle) seems a reasonable assumption for metal containers at relatively low pressures (say < 100...200 psi),
for aqueous mixtures and vapor headspace (vapor/liquid volumes > 0.01) the pressure will not show large variations from, say, 60 to 150 F, an increase of 1.5 or so (depending from fluids properties),
instead, if you reduce the amount of vapor you'll observe much larger variations due to influence of liquid phase...

 

[georgeverghese]

On Pro/ II - Simsci, you can get this sorted out using an adiabatic constant volume flash unit operation at 70degC. A manual calculation is possible, but would involve a few iterations with trial values of final head space pressure. Contribution of thermal expansion of liquid space would be very small in comparison to the contribution of net release of CO2 from liquid phase to vapor phase and may hence be ignored.

 

[moltenmetal]

Don't forget that some soft drinks contain more than just water and CO2- they contain other acids, which shift the CO2/water equilibrium.

 

[3DDave]

Related:

https://www.youtube.com/watch?v=Uk6YMWwV_Oo

Weird Soda Behavior Explained
•Jan 18, 2020