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gas model: replace Redlich-Kwong with least-square quintic

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This goes back to just doing air compressibility, but using the
least-squares quintic polynomial equation that Lubomir generated based
on the Wikipedia table for air at 300K in the 1-500 bar range.

We might be able to do similar things for mixed gases..

Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
Signed-off-by: Dirk Hohndel <dirk@hohndel.org>
This commit is contained in:
Linus Torvalds 2016-03-02 14:11:53 -08:00 committed by Dirk Hohndel
parent 3f30832471
commit 3260dd9c15
1 changed files with 65 additions and 2 deletions
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67
subsurface-core/gas-model.c
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@ -13,7 +13,7 @@
*
*/
double redlich_kwong_equation(double t_red, double p_red, double z_init)
static double redlich_kwong_equation(double t_red, double p_red, double z_init)
{
return (1.0/(1.0 - 0.08664*p_red/(t_red * z_init)) -
0.42748/(sqrt(t_red * t_red * t_red) * ((t_red*z_init/p_red + 0.08664))));
@ -25,7 +25,7 @@ double redlich_kwong_equation(double t_red, double p_red, double z_init)
*/
#define STANDARD_TEMPERATURE 293.0
double gas_compressibility_factor(struct gasmix *gas, double bar)
static double redlich_kwong_compressibility_factor(struct gasmix *gas, double bar)
{
/* Critical points according to https://en.wikipedia.org/wiki/Critical_point_(thermodynamics) */
@ -46,3 +46,66 @@ double gas_compressibility_factor(struct gasmix *gas, double bar)
redlich_kwong_equation(STANDARD_TEMPERATURE/tc, bar/pc,
redlich_kwong_equation(STANDARD_TEMPERATURE/tc, bar/pc,1.0))));
}
/*
* This is a quintic formula by Lubomir I. Ivanov that has
* been optimized for the least-square error to the air
* compressibility factor table (at 300K) taken from Wikipedia:
*
* bar z_factor
* --- ------
* 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
*/
static double air_compressibility_factor(double bar)
{
double x0 = 1.0,
x1 = bar,
x2 = x1*x1,
x3 = x2*x1,
x4 = x2*x2,
x5 = x2*x3;
return + x0 * 1.0002556612420115
- x1 * 0.0003115084635183305
+ x2 * 0.00000227808965401253
+ x3 * 1.91596422989e-9
- x4 * 8.78421542e-12
+ x5 * 6.77746e-15;
}
/*
* We end up using specialized functions for known gases, because
* we have special tables for them.
*
* For now, let's do just air.
*
* We have other tables for other gases, see for example:
*
* http://ww.baue.org/library/zfactor_table.php
*
* and then we have the Redlich-Kwong function, but that seems
* to be almost too generic, and not specific enough to the very
* particular pressure and temperature ranges we care about..
*/
double gas_compressibility_factor(struct gasmix *gas, double bar)
{
#if 1
return air_compressibility_factor(bar);
#else
/* Fall back on generic function */
return redlich_kwong_compressibility_factor(gas, bar);
#endif
}