new data for the compressibility of gases

Thu Mar 3 13:17:06 PST 2016

hello,

the baue.org website (they haven't responded to my email yet) contains
values up to 275 bars and also has some differences in the AIR data. i
also suspect that their tables are not for 300k. on the other hand the
Wikipedia for AIR seems to be a more reliable source and was able to
find the book from which these values originate.

this is basically a patch proposal to make things more consistent and support
values above the 275 bar range up to 500 bars.

-------------------------------------------------------

new data obtained by finding two books online:

[1] PERRY’S CHEMICAL ENGINEERS’ HANDBOOK SEVENTH EDITION
pretty serious book, from which the wiki AIR values come from!

[*](Computed from pressure-volume-temperature tables in Vasserman monographs)
^ i have no idea idea what this means, but the values might not be exactly
experimental?!

the only thing this book is missing is helium, thus [2]!

http://www.unhas.ac.id/rhiza/arsip/kuliah/Sistem-dan-Tekn-Kendali-Proses/PDF_Collections/REFERENSI/Perrys_Chemical_Engineering_Handbook.pdf
page 2-165

[2] VOLUMETRIC BEHAVIOR OF HELIUM-ARGON MIXTURES AT HIGH PRESSURE AND
MODERATE TEMPERATURE.

https://shareok.org/bitstream/handle/11244/2062/6614196.PDF?sequence=1
page 108

more notes in the helium section bellow.

-------------------------------------------------------

all data sets contain Z values at 300k, while the pressures are in bars in
the 1 to 500 range!
i'm providing cubic coefficients as all of these have a R-squared (coefficient
of determination) near 0.99990 (or error in the 10e-4 range).
higher order polynomials don't really improve much on the error.

-------------------------------------------------------

air [1]:
1 0.9999
5 0.9987
10 0.9974
20 0.9950
40 0.9917
60 0.9901
80 0.9903
100 0.9930
150 1.0074
200 1.0326
250 1.0669
300 1.1089
400 1.2073
500 1.3163

coeff:
1.00073546326551309442
-0.00035836444041944628
0.00000301140653499080
-0.00000000206394800305

eq:
y = 1.00073546326551309442 - 0.00035836444041944628*x +
0.00000301140653499080*x^2 - 0.00000000206394800305*x^3

-------------------------------------------------------

nitrogen [1][*]:
1 0.9998
5 0.9990
10 0.9983
20 0.9971
40 0.9964
60 0.9973
80 1.0000
100 1.0052
200 1.0559
300 1.1422
400 1.2480
500 1.3629

coeff:
1.00030344355797817778
-0.00022528077251905598
0.00000295430303276288
-0.00000000210649996337

eq:
y = 1.00030344355797817778 - 0.00022528077251905598*x +
0.00000295430303276288*x^2 - 0.00000000210649996337*x^3

-------------------------------------------------------

oxygen [1][*]:
1 0.9994
5 0.9968
10 0.9941
20 0.9884
40 0.9771
60 0.9676
80 0.9597
100 0.9542
200 0.9560
300 0.9972
400 1.0689
500 1.1572

coeff:
1.00117935180448264158
-0.00074149079841471884
0.00000291901111247509
-0.00000000162092217461

eq:
y = 1.00117935180448264158 - 0.00074149079841471884*x +
0.00000291901111247509*x^2 - 0.00000000162092217461*x^3

-------------------------------------------------------

helium [2]:

the book has some tables with pressure values in atmosphere units. i'm
converting them
to bars. one of the relevant tables is for 323K and one for 273K
(both almost equal distance from 300K).

i construct cubic polynomials of both and apply linear interpolation
to devise a new polynomial for 300K.

this again is a linear mix operation between isotherms, which is probably not
the most accurate solution but it works.

1 1.0005
5 1.0024
10 1.0048
20 1.0096
40 1.0191
60 1.0286
80 1.0381
100 1.0476
200 1.0943
300 1.1402
400 1.1854
500 1.2297

coeff:
1.00000137322788319261
0.000488393024887620665
-0.000000054210166760015
0.000000000010908069275

eq:
y = 1.00000137322788319261 + 0.000488393024887620665*x -
0.000000054210166760015*x^2 + 0.000000000010908069275*x^3

copy-paste in google to plot a comparison between the old and new helium:
(old, new)
0.9998700261301693 + 0.0005452130351730479*x - 2.7853712233619e-7*x^2
+ 5.5935404211e-10*x^3 - 1.35114572e-12*x^4 + 2.00476e-15*x^5,
1.00000137322788319261 + 0.000488393024887620665*x -
0.000000054210166760015*x^2 + 0.000000000010908069275*x^3

-------------------------------------------------------

copy-paste to plot in google a comparison between all gases:
(air, nitrogen, oxygen, helium)
1.00073546326551309442 - 0.00035836444041944628*x +
0.00000301140653499080*x^2 - 0.00000000206394800305*x^3,
1.00030344355797817778 - 0.00022528077251905598*x +
0.00000295430303276288*x^2 - 0.00000000210649996337*x^3,
1.00117935180448264158 - 0.00074149079841471884*x +
0.00000291901111247509*x^2 - 0.00000000162092217461*x^3,
1.00000137322788319261 + 0.000488393024887620665*x -
0.000000054210166760015*x^2 + 0.000000000010908069275*x^3

N2/02 linear mix (71/21):
1 0.99972
5 0.99854
10 0.99742
20 0.99527
40 0.99235
60 0.99106
80 0.99154
100 0.99449
200 1.03492
300 1.11175
400 1.21039
500 1.31970

^pretty close to the air table, but with some error near 10e-4!

please comment and let me know if you'd like me to prepare a patch for
all the above.

lubomir
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