Air Pressure Equalization Between 2 Vessels

[tm1274]

Hello Everyone, I am working on a project with a friend and neither of us have any formal training in engineering but we generally are quick learners. We are both familiar with many of the gas laws and are trying to calculate the equalization pressure between 2 cylinders/vessels or tanks used in Fire Fighting and SCUBA diving. The second part of the task is to calculate the number of transfills or fills that can be accomplished with a bank of storage cylinders, but we can address this part after calculating equalization. The specific criteria we are working with are as follows for the pressure equalization part:

P1 (Supply Cylinder Pressure) = 6000 PSIG Initial
V1 (Supply Cylinder Volume in Liters) = 43.28
P2 (Receiver Pressure) = 0 PSIG Initial, 4500 PSIG Final after transfer
V2 (Receiver Volume in Liters) = 9.06

I realize that the transfer of the air from one cylinder to the other will generate heat and there will be some loss of pressure after the receiver cools down, so if temperature will play a bigger role to be more accurate, we can use 70 degrees Fahrenheit as the ambient temperature. I am also not sure if the "Z Factor" or compressibility factor should be part of the equation to achieve a reasonably accurate equalization pressure between the 2 cylinders.

I have spent days searching online to get a better understanding of how to calculate this and have seen a few different methods, all of which seem to have a different answer but I would like to achieve an accurate value if possible.
Can someone please help me to determine how to accurately calculate the equalization pressure of the 2 cylinders and if I need more information to accomplish this part of the task?

 

[JBA]

Below you will find attached my "best effort" Excel calculation method, including the comprehensibility factor, for your application. I believe these calculations are accurate but you still should do some verification checking to confirm this.
While I was at it, I included the capability to adjust the number of supply and scuba tanks used; and, included one successive charging column to address the effects of falling supply tank pressure with repetitive charging cycles on one Supply Tank Fill Note: This can be expanded across a the page to address a series of such cycles.
I hope this gives you at least a start on dealing with your problem. It also gave me a chance to learn a bit more about the Z factor application.

 

[tm1274]

Wow! That was so much more help than I expected. I may be wrong in how I am reading the spreadsheet but the 1st cycle shows a Supply Tank Remaining Pressure of 5964.39 psig, after the first fill. Wouldn't the initial pressure equalization between the Supply Cylinder and the SCUBA tank lower the Supply by considerably more? The pressure equalization part of the project has me stumped so I could be totally wrong about my way of thinking.

 

[JBA]

We are not equalizing the pressure in the scuba tank with that in the supply tank. The equation ignoring the temperature effects because the tank temperatures are equal is very straight forward.

It is: V scuba tank air / V supply tank air = V scuba tank / V supply tank * P scuba tank / P supply tank * Z scuba tank / Z supply tank

 

[SteamKing]

Below you will find attached my "best effort" Excel calculation method, including the comprehensibility factor,

I think you mean the "compressibility" factor here.

 

[JBA]

I believe the supply tank pressure reduction is directly proportional to the gas volume reduction in the tank so I used P2 = P1 * V2/V1 to get that value.

At the same time upon doing a bit of investigating, I am having some trouble reversing the supply tank loss to equal the scuba tank gain so I am going to have to do a bit of work to resolve that before I am ready to make any firm conclusion about the accuracy of my sheet.

 

[JBA]

tm1274, you were correct about the error in tank pressure reduction and it was caused by an error in my tank volume reduction calculation. It took awhile but I think I now have everything corrected; and at the same time I have done a bit more.
First, I have integrated an equation for Z at a range of pressures to provide more accurate Z values than the increments in the table, but this equation, as indicated, is only valid at 70°F so if you want to change either of the tanks temperatures the a new equation will be required (or the insertion of an alternate Z value from the referenced website table)
I have also placed boxes around those tank properties that can varied for variations in tank size(s) and pressure(s)
You will also find that there are two pages with different methods of calculating the number of scuba tanks that can be filled before the supply tank pressure drops below the required scuba tank pressure. Although each method has different capabilities in tank size and pressure adjustments, the main reason I am providing both is that the single column calculation indicates one more allowable tank filling than the multi stage calculation and I don't know which will show to be more accurate of the two methods. Hopefully you willbe able to determine that by your own testing.
You will see some other small variations in formatting, etc, but those are not worthy of any explanations.
The new revised Revision A workbook is attached below, so check it out and get back to me with any concerns, questions or suggested changes. Hopefully I did a better job on the calculation accuracy this time.
I am just glad you voiced your concerns and motivated me to revisit the original program.