Jovani:
This is a typical, practical problem involving the gaseous equation of state. But it can have some problems and complications, mostly due to undefined basic data.
I’m guessing you are not an engineer and new to dealing with compressible fluids like nitrogen (N2), so I’ll start explaining what is going to happen in this pressure cascade system. I’ve done this before many times so I’ll define what you are going to be asked by our members:
How accurate do you want the calculations? Do you want to assume nominal diameters of your pipe - or do you want to use the actual inside diameters? If the latter, then you must furnish the schedule number or the I.D. themselves. Is the pipe all “straight” pipe - i.e., without any offsets or fittings? This affects the total test gas estimate.
Compressed gases are measure at “Standard” conditions. These conditions vary according to the industry and country you find yourself in. The usual standard conditions in Texas are: 60 oF and 14.696 psia. A standard cubic foot of gas is called Scf.
When you deal with relationships of gases, you use absolute values for pressure and temperature. That means you must convert your gauge values to absolute. For example, there is no such thing as 110 psi. It is either 110 psig (gauge) or psia (absolute). Which do you mean?
When you cascade, you usually do it through a pressure regulator. Your high pressure N2 is going to expand through the regulator and drop in temperature due to what is called the Joule-Thomson effect. This means that initially, the N2 in the pipeline is going to be lower in temperature than the temperature in the tube trailer. You are going to have to wait until the temperature in the pipeline warms up. Therefore, it makes a big difference if your pipe is underground or above ground and what will be its final temperature after it warms up. You have to define the pipe’s condition and the temperature surrounding it. As you are injecting cold gas (due to the expansion), you have to ensure you stop the gas injection before arriving at the target test pressure because the gas in the pipe will increase its pressure as it warms up due to the surroundings. An underground pipe will take a long time to warm up and reach an equilibrium temperature with the dirt around it, so you have a long wait. This can be a pain, but you have to endure it unless you can warm the expanded gas to ambient temperature as it exits the regulator and before it enters the underground pipeline.
Part of this problem - like I said, I’ve been there before - is determining if you have enough pressurized N2 in the tube trailer to finish the job or if you need more than one tube trailer. I usually piped up my trailer manifold so that I could cascade by one or several tubes at a time and left the last, fully pressurized tubes until the last cascade in order to be able to “polish” off at the desired final testing pressure.
In my time, we didn’t have electronic spreadsheets, so I made up my own paper and pencil spreadsheets and did my calculations and capacity tables on them. I recommend you use Excel spread sheets to design and make tables for the tube trailers and use these to estimate the capacities and pressures as you test.
Our members should be able to offer additional information, answers, and some useful advice.