Nitrogen for a Vessel

Enter the volume of a vessel, the pressure it is raised to and its temperature to get the nitrogen needed. Metric or oilfield units.

Inputs

Result

Nitrogen required

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Volume factor at the final pressure: –
Gas in the vessel at the final pressure: –
Gas to add, at standard conditions: –
As liquid nitrogen: –

Z from the table at these conditions

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Method

The nitrogen is the gas that has to be added to take the vessel from its starting pressure to the final pressure at constant temperature.

Volume factor of nitrogen: B = 2.8416·P / (Z·(273 + T)) in sm³/m³, with P in kPa (gauge) and T in °C. The constant stands for standard conditions of about 15 °C and 101.3 kPa.
Gas to add: the vessel volume times the difference of the factors at the final and at the starting pressure.
Liquid nitrogen: 1 m³ of liquid gives 696.5 sm³ of gas and weighs 808 kg.

Assumptions

The pressures are gauge pressures and the vessel starts with no other gas than the air at atmospheric pressure, which is not counted.
The temperature stays constant while the vessel is filled; heating from compression is not allowed for.
The compressibility factor is a single value for the whole range of pressure.
No nitrogen is lost to purging or leaks.

Uses the same volume factor and nitrogen properties as the Nitrogen Displacement tool, which reproduces a reference worksheet. Check the gas properties against a nitrogen table before you rely on a result.

Compressibility factor of nitrogen

Z corrects the ideal gas law for nitrogen at high pressure: above 1 the gas takes more room than an ideal gas, so a vessel or well holds less nitrogen in standard volumes than with Z = 1. The diagram and the table give Z for nitrogen by absolute pressure and temperature; the nitrogen tools interpolate in the table.

Compressibility factor of nitrogen
Absolute pressure	-20 °C -4 °F	0 °C 32 °F	20 °C 68 °F	40 °C 104 °F	60 °C 140 °F	80 °C 176 °F	100 °C 212 °F	120 °C 248 °F	140 °C 284 °F	160 °C 320 °F
1 bar · 15 psi	0.999	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
25 bar · 363 psi	0.984	0.990	0.995	0.999	1.002	1.004	1.006	1.007	1.008	1.009
50 bar · 725 psi	0.971	0.985	0.994	1.001	1.006	1.010	1.013	1.016	1.017	1.019
100 bar · 1,450 psi	0.963	0.985	1.001	1.013	1.021	1.028	1.033	1.037	1.039	1.041
150 bar · 2,176 psi	0.976	1.002	1.021	1.034	1.045	1.052	1.058	1.062	1.065	1.067
200 bar · 2,901 psi	1.010	1.034	1.052	1.065	1.075	1.082	1.088	1.092	1.094	1.096
250 bar · 3,626 psi	1.058	1.078	1.092	1.104	1.112	1.118	1.122	1.125	1.127	1.128
300 bar · 4,351 psi	1.117	1.130	1.140	1.148	1.153	1.157	1.160	1.161	1.161	1.161
350 bar · 5,076 psi	1.182	1.188	1.193	1.196	1.199	1.200	1.200	1.199	1.198	1.196
400 bar · 5,802 psi	1.251	1.250	1.249	1.248	1.247	1.245	1.242	1.240	1.236	1.233
450 bar · 6,527 psi	1.322	1.314	1.307	1.302	1.297	1.291	1.286	1.281	1.276	1.271
500 bar · 7,252 psi	1.394	1.380	1.368	1.357	1.348	1.340	1.332	1.324	1.317	1.310

Computed from the density of nitrogen in the NIST Chemistry WebBook (equation of state of Span et al., 2000) as Z = P·M/(ρ·R·T). Pressures are absolute, gauge pressure plus 1.013 bar. Between the points the tools interpolate linearly; outside 1–500 bar and −20 to 160 °C they use the edge value.

The tools are aids for engineers. Check the inputs and the results: responsibility for any decision stays with the user.