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 -- _______________________________________________ subsurface mailing list [email protected] http://lists.subsurface-divelog.org/cgi-bin/mailman/listinfo/subsurface
