1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
|
/* gas-model.c */
/* gas compressibility model */
#include <stdio.h>
#include <stdlib.h>
#include "dive.h"
/*
* This gives an interative solution of hte Redlich-Kwong equation for the compressibility factor
* according to https://en.wikipedia.org/wiki/Redlich–Kwong_equation_of_state
* in terms of the reduced temperature T/T_crit and pressure p/p_crit.
*
* Iterate this three times for good results in our pressur range.
*
*/
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))));
}
/*
* At high pressures air becomes less compressible, and
* does not follow the ideal gas law any more.
*/
#define STANDARD_TEMPERATURE 293.0
static double redlich_kwong_compressibility_factor(struct gasmix *gas, double bar)
{
/* Critical points according to https://en.wikipedia.org/wiki/Critical_point_(thermodynamics) */
double tcn2 = 126.2;
double tco2 = 154.6;
double tche = 5.19;
double pcn2 = 33.9;
double pco2 = 50.5;
double pche = 2.27;
double tc, pc;
tc = (tco2 * get_o2(gas) + tche * get_he(gas) + tcn2 * (1000 - get_o2(gas) - get_he(gas))) / 1000.0;
pc = (pco2 * get_o2(gas) + pche * get_he(gas) + pcn2 * (1000 - get_o2(gas) - get_he(gas))) / 1000.0;
return (redlich_kwong_equation(STANDARD_TEMPERATURE/tc, bar/pc,
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
}
|
