Real gas (Z)

What it's for

Real gases at cylinder pressure hold fewer or more moles than the ideal gas law predicts. The compressibility factor Z corrects for that. The library uses it, when you opt in with useRealGas, for free-gas volumes, blending, cascades and boosters.

Formulas

A virial fit per component:

Z_{i} (P) = 1 + a_{i} P + b_{i} P^{2} + c_{i} P^{3}

Mixed linearly by mole fraction:

Z_{m i x} = 1 + \sum_{i} F_{i} (Z_{i} - 1)

The ideal-gas pressure that holds the same moles, normalised so that 1 atm maps to 1 atm:

P_{i d e a l} = P \frac{Z (P_{a t m})}{Z (P)}

$P$ : absolute pressure, bar. Always absolute, never gauge.
$P_{a t m} = 1.01325$ bar.
$a_{i}, b_{i}, c_{i}$ : fit coefficients for component $i$ (table below).
$F_{i}$ : fraction of component $i$ (O₂, N₂, He).

Coefficients

Gas	a	b	c
o2	-7.18092073703e-4	2.81852572808e-6	-1.50290620492e-9
n2	-2.19260353292e-4	2.92844845532e-6	-2.07613482075e-9
he	4.87320026468e-4	-8.83632921053e-8	5.33304543646e-11

Assumptions and limits

Valid for 0 to 500 bar absolute. Outside that range the functions throw a RangeError.
The coefficient source does not state its reference temperature. Treat results as room-temperature approximations.
realPressureForIdealEquivalent uses fixed-point iteration and throws if the answer leaves the model range.
Z is evaluated at absolute pressure everywhere in the library.

Sources

Coefficients come from atdotde/realblender (a Python script), as used by Subsurface and by the GasPlanner scuba-physics library (MIT, copyright 2018 JirkaPok). See THIRD_PARTY_NOTICES.md.

Examples

import { AIR, gas } from 'dive-math/gas'
import { mixZ, idealEquivalentPressure } from 'dive-math/real-gas'
mixZ(AIR, 207) // => 1.0402
mixZ(gas(1), 207) // => 0.9588
idealEquivalentPressure(gas(0.25, 0.25), 200) // => 192.05

API

See the real-gas API reference.

Real gas (Z) ​

What it's for ​

Formulas ​

Coefficients ​

Assumptions and limits ​

Sources ​

Examples ​

API ​