pressurizing

Simple way to look at it:

Forget about the constants (R & molecular weight etc) - they are constant .

Assume also that the temperature remains constant (as I assume you're going to start and finish at 0°C).

To increase pressure to 1 barg, you need 2 x V of gas (where V is volume of vessel); that is, you need to add 1 x V of gas. By extension, to increase the pressure to 20 barg you need to add 20 x V.

The flow rate is therefore ((20 x V) / 30) litres per minute (assuming V is in litres).

could you please to explain more how did you calculate multiplying factor of 2 for each 1 bar pressure increase?

I didn't say "multiplying factor of 2 for each 1 bar pressure increase" - I said "add the same volume again for each 1 bar increase" (or that's what I meant, if you read carefully).

P x V = "a constant" (at constant temperature).

Start with a cylinder with the piston retracted, so that the volume contained is 2V, at some arbitrary pressure P. Move the piston in, to reduce the volume to V. Keeping the temperature before and after the same, the pressure must now be 2P (since P x 2V = 2P x V).

Extend this to an initial volume 3V, and move the piston to reduce back to V. Now P x 3V = 3P x V, etc.

john

your explanation does'nt cover my request. because in method that is explained by you, pressure is increasing by decreasing volume. but I want to increase pressure with injection nitrogen. therefore mole content of nitrogen is changing with time. on the other hand, mass is changing with time

1. You did not state that the vessel was not initially filled with nitrogen. I assumed this, which I believed to be a reasonable assumption.

2. How accurate do you need your result to be? In the atmosphere, the concentration of non-nitrogen components is about 12%. If you add 20 times the volume of pure nitrogen, this concentration reduces to very slightly over 1%. Is this a "real life" question, or some hypothetical setup from an exam question? This is an engineering site - not a homework solution service. In "real life", you would have to set up an extremely complex thermal control system to keep the gas temperature constant while adding the nitrogen.

Deldari,

Assume the system is the gas in the vessel at any given time. Also the filling process is adiabatic, no heat transfer to the vessel walls or to the surroundings. Assume ideal gas behavior.

There are two working equations necessary to solve this problem. This is also an unsteady-state problem since things are changing with respect to time.

m-balance

n^f = nⁱ + (nⁱⁿ)t

e-balance

d(nU) = Hⁱⁿdnⁱⁿ

The first thing you need to calc is the temperature rise. This can be accomplished by solving the e-balance. The equation simplified is:

T^f = Tⁱⁿ(C_p/C_v)

The mole flow can be found by combining the original e-balance and m-balance then simplifying.

You should arrive at this equation for molar flow:

n = nⁱ[(T^f/Tⁱ)^Cv/R - 1]/t where nⁱ = PⁱV/RTⁱ

Hope this helps!

- David

I agree with your approach to solving this problem, but I wonder about the consideration of mixing of the gases during expansion into the vessel. It seems that the solution would be bounded by assumptions of plug-slow and CSTR models.

The energy balance can be tailored to account for initial gas conditions.

The compression ratio is 21:1. The difference between initial moles and final moles at least a magnitude different. I neglected any initial gas temperature contributions.

The equation stated for temperature rise does exactly that by assuming an evacuated vessel. In simplifying I dropped initial gas terms. Keeping them in won't let you solve for T final explicitly. More of a headache if you ask me.

what a load. remember KISS keep it simple stupid.

answer (density of N2 full - density of N2 empty) * volume tank / time = answer is pounds per time.

go to NIST workbook and get density at conditions or use PV=znRT or other EOS.