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

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>

subsurface-core/gas-model.c

@@ -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
+}