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Performance Optimisation 3098 Technical Manual
A-4
COMPRESSIBILITY FACTOR
The normal or base density (
ρ
s
) is given by the equation:
ρρ
s
s
s
P
P
t
t
= x x x
Z
Z
s
A5
Where:
P
s
, t
s
& Z
s
= Values of pressure, temperature and compressibility at standard conditions.
ρ
, P, t & Z = Values of density, pressure, temperature and compressibility at measurement
conditions.
The basic operation of the instrument allows the pressure/temperature ratio to be considered constant, hence equation A5
reduces to:
ρρ
s
s
K
Z
Z
=
ρ
ρ
sF
KZ = A6
Where: K = The calibration constant.
Z
F
= The compressibility factor.
The Z factor for gases or gas mixtures may be obtained from reference sources or may be derived from:
For Nitrogen at 20°C:
ZPx = 10 238 10
4
.(. )−
−
A7
Where: P = The gas pressure in bar absolute.
For a methane-based gas mixture at 20°C:
[]
ZPxxMxMxI = 10 17 10 6 10 113 10 7 2 10
45 52 3
.. (). ().()++ − +
−− − −
A8
Where: P = The gas pressure in bar absolute.
M = The mean molecular weight of gas.
I = Volume/mole fraction of inerts, e.g. N
2
and CO
2
.
The Z factors of the calibration gases and the sample gases should be calculated at both base and operating conditions in
order to establish the compressibility factor V
F
and then tabulated as shown
by the example in Table A2.
COMBINATION OF
V
F
AND
Z
F
By combining equations A4 and A6, gives:
ρ
ρ
siFF
KVZ =
A9
The combination of V
F
and Z
F
should also be tabulated as shown in Table A2. The combined factor E
F
can then be used to
determine the anticipated measurement errors on sample gases when using the two selected calibration gases. Furthermore,
the tabulated results can be plotted to show the error trends and uncover the most suitable calibration gas selection and/or
calibration offset to give minimum measurement error on the sample gases, see fig. A1.
Table A1 is provided to identify the variables used in equations A10 and A11.