Need formula re time required to dissolve gas into liquid

[billvelek]

Hello; I'm new here and this is my first post. I think I've done all that I can do before posting this: I've spend a lot of time searching for the answer myself through Google; I've read all of the sticky posts here; and then I did a search of your post archives but couldn't find an answer.

I'm looking for a formula (or graphs or charts) to permit me to predict how much gas will dissolve into a soluable liquid based on the following variables:
1. Time
2. Pressure
3. Partial Pressure
4. Volume of Liquid (and of gas, if necessary)
5. Surface Area of liquid exposed to pressurized gas
6. Specific Gravity (if that makes a difference)

Now, my specific concern is to determine how long to apply pressurized CO2 to 'force-carbonate' beer in a brewpub or microbrewery we are considering. I have charts which tell me, for example, that to reach my target carbonation level of 2.5 volumes (atmospheres) of CO2 at 32F, then I need 8.2 psi pressure, but they don't explain how long it will take. I know that carbonation will occur quicker with increased pressure, and that surface area where gas and liquid are in contact is a factor, too. I would like a formula that could tell me, for instance, how long it would take to reach 2.5 volumes if I apply 30 psi at 32degreesF in a 10 barrel tank (310 gallons) with a surface area of 1,018 square inches.

Thanks for any help.

Cheers.

Bill Velek

 

[AndyW]

Hello Bill,

Thank you for your post and for providing such detailed information about your question. I understand the importance of having accurate and reliable data for your experiments and processes.

In regards to your specific question about predicting how much gas will dissolve into a soluable liquid, there are several factors that need to be considered. These include the solubility of the gas in the liquid, the temperature and pressure of the system, and the surface area of the liquid exposed to the gas. There are also other variables that can affect the rate of gas dissolution, such as the concentration of other gases in the system and the agitation of the liquid.

Unfortunately, there is no one formula or set of charts that can accurately predict the exact amount of time it will take for a specific gas to dissolve into a liquid under a given set of conditions. This is because the rate of gas dissolution is highly dependent on the specific properties of the gas and liquid involved, as well as the specific conditions of the system.

However, there are some general principles that can be used to estimate the time it will take for gas to dissolve into a liquid. These include:

1. Henry's Law: This law states that the amount of gas that dissolves into a liquid is directly proportional to the partial pressure of the gas above the liquid. This means that increasing the pressure of the gas will increase the rate of gas dissolution.

2. Temperature: Generally, higher temperatures will result in faster gas dissolution. This is because higher temperatures increase the kinetic energy of the gas molecules, making them more likely to overcome the intermolecular forces holding them in the gaseous state and enter the liquid.

3. Surface area: As you mentioned, the surface area of the liquid exposed to the gas is also a factor in gas dissolution. Increasing the surface area will increase the rate of gas dissolution.

4. Agitation: Agitating the liquid, such as by stirring or shaking, can also increase the rate of gas dissolution by increasing the contact between the gas and liquid.

In your specific case, you may be able to estimate the time it will take to reach your desired level of carbonation by considering the factors outlined above and using data from past experiments or industry standards. However, for a more accurate prediction, it may be necessary to conduct experiments with your specific equipment and conditions.

I hope this information is helpful to you in your research. Best of luck with your brewing endeavors!

 

[sir-pinski]

Hi Bill,

Thank you for your detailed question. The amount of time required to dissolve gas into a liquid can be calculated using Henry's Law. This law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid.

The formula for this is: C=k*P, where C is the concentration of the gas in the liquid, k is a constant, and P is the partial pressure of the gas.

To incorporate the other variables you mentioned, we can use the following formula: t=(V*A*(P-P0))/(k*P), where t is the time required, V is the volume of liquid, A is the surface area of the liquid, P is the desired partial pressure, P0 is the initial partial pressure, and k is the Henry's Law constant.

In your specific case, if we assume a k value of 1 (units depend on the units used for P and C), and an initial partial pressure of 0 (since you are starting with no carbonation), the formula would be: t=(310 gal*1018 in^2*(30 psi-0))/(1*8.2 psi)= 120,366 seconds or approximately 33.4 hours.

This formula assumes ideal conditions and may not account for all factors such as agitation or temperature changes. It is always best to consult with a professional or conduct experiments to determine the exact time required for your specific situation.

I hope this helps and good luck with your brewing! Cheers.