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Added melting lines for many fluids - nearly all that are in REFPROP

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Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-06-09 15:48:52 +02:00
parent 2b32a18e13
commit 64946e6017
28 changed files with 809 additions and 112 deletions
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12
CoolPropBibTeXLibrary.bib
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@@ -1,6 +1,18 @@
% This file was created with JabRef 2.9.2.
% Encoding: ASCII
@ARTICLE{Abramson-HPR-2011,
author = {Evan H. Abramson},
title = {Melting curves of argon and methane},
journal = {High Pressure Research},
year = {2011},
volume = {31},
pages = {549-554},
number = {4},
owner = {Belli},
timestamp = {2014.06.09}
}
@CONFERENCE{Akasaka-DELFT-2013,
author = {Ryo Akasaka and Yukihiro Higashi and Shigeru Koyama},
title = {{A Fundamental Equation of State For Low-GWP Refrigerant HFO-1234ze(Z)}},

21
dev/fluids/Argon.json
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@@ -4,6 +4,27 @@
"ARGON"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Tegeler-JPCRD-1999",
"T_m": 87.28,
"parts": [
{
"T_0": 83.8058,
"T_max": 254.0,
"T_min": 83.806,
"a": [
-7476.2665,
9959.0613
],
"p_0": 68891,
"t": [
1.05,
1.275
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 150.687,
"Tmax": 150.68699999999976,

21
dev/fluids/CarbonDioxide.json
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@@ -7,6 +7,27 @@
"CARBONDIOXIDE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Span-JPCRD-1996",
"T_m": 216.58,
"parts": [
{
"T_0": 216.592,
"T_max": 327.6,
"T_min": 216.592,
"a": [
1955.539,
2055.4593
],
"p_0": 517950,
"t": [
1,
2
]
}
],
"type": "polynomial_in_Theta"
},
"pL": {
"T_r": 304.1282,
"Tmax": 304.1281999999994,

15
dev/fluids/CarbonMonoxide.json
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@@ -4,6 +4,21 @@
"CARBONMONOXIDE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Barreiros-JCT-1982",
"T_m": 81.63,
"parts": [
{
"T_0": 1,
"T_max": 87.5,
"T_min": 68.16,
"a": 19560.8,
"c": 2.10747,
"p_0": -142921439.2
}
],
"type": "Simon"
},
"pL": {
"T_r": 132.86,
"Tmax": 132.8599999999997,

15
dev/fluids/CycloHexane.json
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@@ -4,6 +4,21 @@
"CYCLOHEXANE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Penoncello-IJT-1995",
"T_m": 279.96,
"parts": [
{
"T_0": 279.7,
"T_max": 401.7,
"T_min": 279.47,
"a": 383400000.0,
"c": 1.41,
"p_0": 0
}
],
"type": "Simon"
},
"pL": {
"T_r": 553.6,
"Tmax": 553.5999999999988,

21
dev/fluids/Ethane.json
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@@ -4,6 +4,27 @@
"ETHANE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Buecker-JCRD-2006",
"T_m": 184.6,
"parts": [
{
"T_0": 90.368,
"T_max": 110.2,
"T_min": 90.368,
"a": [
223626315.0,
105262374.0
],
"p_0": 1.14,
"t": [
1.0,
2.55
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 305.322,
"Tmax": 305.3219999999994,

31
dev/fluids/Ethylene.json
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@@ -4,6 +4,37 @@
"ETHYLENE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Smukala-JPCRD-2000",
"T_m": 169,
"parts": [
{
"T_0": 103.989,
"T_max": 110.369,
"T_min": 103.989,
"a": [
2947001.84
],
"p_0": 122.65,
"t": [
2.045
]
},
{
"T_0": 110.369,
"T_max": 188,
"T_min": 110.369,
"a": [
6.82693421
],
"p_0": 46800000.0,
"t": [
1.089
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 282.35,
"Tmax": 282.3499999999994,

19
dev/fluids/Fluorine.json
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@@ -4,6 +4,25 @@
"FLUORINE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "deReuck-BOOK-1990",
"T_m": 85.2,
"parts": [
{
"T_0": 53.4811,
"T_max": 55.4,
"T_min": 53.4811,
"a": [
988043.478261
],
"p_0": 252,
"t": [
2.1845
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 144.414,
"Tmax": 144.41399999999967,

19
dev/fluids/IsoButane.json
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@@ -7,6 +7,25 @@
"R600a"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Buecker-JPCRD-2006B",
"T_m": 262,
"parts": [
{
"T_0": 113.73,
"T_max": 124.9,
"T_min": 113.73,
"a": [
1953637130.9
],
"p_0": 0.0219,
"t": [
6.12
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 407.817,
"Tmax": 407.81699999999915,

15
dev/fluids/Isopentane.json
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@@ -5,6 +5,21 @@
"ISOPENTANE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Reeves-JCP-1964",
"T_m": 113.22999999999999,
"parts": [
{
"T_0": 112.5,
"T_max": 212.16,
"T_min": 112.65,
"a": 591600000.0,
"c": 1.563,
"p_0": 0
}
],
"type": "Simon"
},
"pL": {
"T_r": 460.35,
"Tmax": 460.3499999999989,

15
dev/fluids/Krypton.json
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@@ -4,6 +4,21 @@
"KRYPTON"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Michels-PHYSICA-1962",
"T_m": 115.95,
"parts": [
{
"T_0": 1,
"T_max": 168.7,
"T_min": 115.77,
"a": 109479.2307,
"c": 1.6169841,
"p_0": -237497645.7
}
],
"type": "Simon"
},
"pL": {
"T_r": 209.48,
"Tmax": 209.4799999999995,

15
dev/fluids/Methane.json
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@@ -5,6 +5,21 @@
"METHANE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Abramson-HPR-2011",
"T_m": 90.7,
"parts": [
{
"T_0": 90.6941,
"T_max": 700,
"T_min": 90.6941,
"a": 208000000.0,
"c": 1.698,
"p_0": 11700.0
}
],
"type": "Simon"
},
"pL": {
"T_r": 190.564,
"Tmax": 190.56399999999954,

23
dev/fluids/Methanol.json
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@@ -4,6 +4,29 @@
"METHANOL"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "deReuck-BOOK-1993",
"T_m": 337.8,
"parts": [
{
"T_0": 175.61,
"T_max": 245.9,
"T_min": 175.61,
"a": [
5330770000.0,
4524780000.0,
38888610000.0
],
"p_0": 0.187,
"t": [
1,
1.5,
4
]
}
],
"type": "polynomial_in_Theta"
},
"pL": {
"T_r": 512.5,
"Tmax": 512.4999999999987,

19
dev/fluids/Nitrogen.json
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@@ -5,6 +5,25 @@
"N2"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Span-JPCRD-2000",
"T_m": 77.34,
"parts": [
{
"T_0": 63.151,
"T_max": 283.8,
"T_min": 63.151,
"a": [
12798.61
],
"p_0": 12523,
"t": [
1.78963
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 126.192,
"Tmax": 126.19199999999978,

15
dev/fluids/Oxygen.json
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@@ -5,6 +5,21 @@
"O2"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Younglove-NIST-1982",
"T_m": 90.2,
"parts": [
{
"T_0": 1,
"T_max": 63.1,
"T_min": 54.361,
"a": 227606.348,
"c": 1.769,
"p_0": -266999247.652
}
],
"type": "Simon"
},
"pL": {
"T_r": 154.581,
"Tmax": 154.58099999999973,

23
dev/fluids/ParaHydrogen.json
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@@ -5,6 +5,29 @@
"PARAHYDROGEN"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Younglove-NIST-1982",
"T_m": 18.9,
"parts": [
{
"T_0": 1,
"T_max": 22,
"T_min": 13.8033,
"a": 125746.643,
"c": 1.955,
"p_0": -21155737.752
},
{
"T_0": 1,
"T_max": 164.5,
"T_min": 22,
"a": 248578.596,
"c": 1.764739,
"p_0": -26280332.904
}
],
"type": "Simon"
},
"pL": {
"T_r": 32.938,
"Tmax": 32.93799999999992,

23
dev/fluids/Propylene.json
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@@ -4,6 +4,29 @@
"PROPYLENE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Reeves-JCP-1964",
"T_m": 88.05999999999997,
"parts": [
{
"T_0": 86.0,
"T_max": 129,
"T_min": 86.0,
"a": 319600000.0,
"c": 2.821,
"p_0": 0
},
{
"T_0": 109.6,
"T_max": 145.3,
"T_min": 129,
"a": 306400000.0,
"c": 3.871,
"p_0": 445000000.0
}
],
"type": "Simon"
},
"pL": {
"T_r": 364.211,
"Tmax": 364.2109999999991,

59
dev/fluids/Water.json
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@@ -6,6 +6,65 @@
"h2o"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "IAPWS",
"T_m": -1,
"parts": [
{
"T_0": 273.16,
"T_max": 251.165,
"T_min": 273.16,
"a": [
-1195393.37,
-80818.3159,
-3338.2686
],
"p_0": 611.657,
"t": [
3.0,
25.75,
103.75
]
},
{
"T_0": 251.165,
"T_max": 256.164,
"T_min": 251.165,
"a": [
0.299948
],
"p_0": 208566000.0,
"t": [
60
]
},
{
"T_0": 256.164,
"T_max": 273.31,
"T_min": 256.164,
"a": [
1.18721
],
"p_0": 350100000.0,
"t": [
8
]
},
{
"T_0": 273.31,
"T_max": 355,
"T_min": 273.31,
"a": [
1.07476
],
"p_0": 623400000.0,
"t": [
4.6
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 647.096,
"Tmax": 647.0959999999985,

15
dev/fluids/Xenon.json
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@@ -5,6 +5,21 @@
"XENON"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Michels-PHYSICA-1962",
"T_m": 165.02,
"parts": [
{
"T_0": 1,
"T_max": 366.4,
"T_min": 161.4,
"a": 80890.5544859,
"c": 1.589165,
"p_0": -260932309.446
}
],
"type": "Simon"
},
"pL": {
"T_r": 289.733,
"Tmax": 289.7329999999995,

19
dev/fluids/n-Butane.json
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@@ -6,6 +6,25 @@
"N-BUTANE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Buecker-JPCRD-2006B",
"T_m": 135.23,
"parts": [
{
"T_0": 134.895,
"T_max": 163.9,
"T_min": 134.895,
"a": [
558558236.4
],
"p_0": 0.653,
"t": [
2.206
]
}
],
"type": "polynomial_in_Tr"
},
"pL": {
"T_r": 425.125,
"Tmax": 425.124999999999,

15
dev/fluids/n-Pentane.json
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@@ -7,6 +7,21 @@
"R601"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Reeves-JCP-1964",
"T_m": 143.26,
"parts": [
{
"T_0": 143.5,
"T_max": 156.2,
"T_min": 143.47,
"a": 660000000.0,
"c": 1.649,
"p_0": 0.0
}
],
"type": "Simon"
},
"pL": {
"T_r": 469.7,
"Tmax": 469.69999999999914,

15
dev/fluids/n-Propane.json
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@@ -8,6 +8,21 @@
"N-PROPANE"
],
"ANCILLARIES": {
"melting_line": {
"BibTeX": "Reeves-JCP-1964",
"T_m": 85.39999999999998,
"parts": [
{
"T_0": 85.3,
"T_max": 168.63,
"T_min": 85.525,
"a": 718000000.0,
"c": 1.283,
"p_0": 0.0
}
],
"type": "Simon"
},
"pL": {
"T_r": 369.89,
"Tmax": 369.8899999999991,

237
dev/inject_melting_curves.py
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@@ -1,84 +1,96 @@
import os, json
Simon_curves = {
"n-Propane" : {
"T_0" : 85.3, "a" : 7.180e8, "c" : 1.283, "p_0" : 0.0, "T_max" : 168.63, "BibTeX" : "Reeves-JCP-1964"
"BibTeX" : "Reeves-JCP-1964", "T_m": -187.75 + 273.15, "parts": [{"T_0" : 85.3, "a" : 7.180e8, "c" : 1.283, "p_0" : 0.0, "T_max" : 168.63}]
},
"n-Pentane" : {
"T_0" : 143.5, "a" : 6.600e8, "c" : 1.649, "p_0" : 0.0, "T_max" : 156.2, "BibTeX" : "Reeves-JCP-1964"
"BibTeX" : "Reeves-JCP-1964", "T_m": -129.89 + 273.15, "parts": [{"T_0" : 143.5, "a" : 6.600e8, "c" : 1.649, "p_0" : 0.0, "T_max" : 156.2}]
},
"Isopentane" : {
"T_0" : 112.5, "a" : 5.916e8, "c" : 1.563, "p_0" : 0, "T_max" : 212.16, "BibTeX" : "Reeves-JCP-1964"
"BibTeX" : "Reeves-JCP-1964", "T_m": -159.92 + 273.15, "parts": [{"T_0" : 112.5, "a" : 5.916e8, "c" : 1.563, "p_0" : 0, "T_max" : 212.16}]
},
"Propylene" : {
"BibTeX" : "Reeves-JCP-1964", "T_m": -185.09 + 273.15, "parts": [{"T_0" : 86.0, "a" : 3.196e8, "c" : 2.821, "p_0" : 0, "T_min": 86.0, "T_max" : 129},
{"T_0" : 109.6, "a" : 3.064e8, "c" : 3.871, "p_0" : 4.450e8, "T_min": 129, "T_max" : 145.3}]
},
"Propylene" : [
{
"T_0" : 86.0, "a" : 3.196e8, "c" : 2.821, "p_0" : 0, "T_min": 86.0, "T_max" : 129, "BibTeX" : "Reeves-JCP-1964"
},
{
"T_0" : 109.6, "a" : 3.064e8, "c" : 3.871, "p_0" : 4.450e8, "T_min": 129, "T_max" : 145.3, "BibTeX" : "Reeves-JCP-1964"
}
],
"Cyclohexane" : {
"T_0" : 279.7, "a" : 383.4e6, "c" : 1.41, "p_0" : 0, "T_max" : 401.7, "BibTeX" : "Penoncello-IJT-1995"
"BibTeX" : "Penoncello-IJT-1995", "T_m": 6.81 + 273.15, "parts": [{"T_0" : 279.7, "a" : 383.4e6, "c" : 1.41, "p_0" : 0, "T_max" : 401.7}]
},
"Krypton" : {
"T_0" : 1, "a" : 109479.2307, "c" : 1.6169841, "p_0" : -237497645.7, "T_max" : 168.7, "BibTeX" : "Michels-PHYSICA-1962"
"BibTeX" : "Michels-PHYSICA-1962", "T_m": 115.95, "parts": [{"T_0" : 1, "a" : 109479.2307, "c" : 1.6169841, "p_0" : -237497645.7, "T_max" : 168.7}]
},
"Xenon" : {
"T_0" : 1, "a" : 80890.5544859, "c" : 1.5891650, "p_0" : -260932309.446, "T_max" : 366.4, "BibTeX" : "Michels-PHYSICA-1962"
"BibTeX" : "Michels-PHYSICA-1962", "T_m": 165.02, "parts": [{"T_0" : 1, "a" : 80890.5544859, "c" : 1.5891650, "p_0" : -260932309.446, "T_max" : 366.4}]
},
"CarbonMonoxide" : {
"T_0" : 1, "a" : 19560.8, "c" : 2.10747, "p_0" : -142921439.2, "T_max" : 87.5, "BibTeX" : "Barreiros-JCT-1982"
"BibTeX" : "Barreiros-JCT-1982", "T_m": 81.63, "parts": [{"T_0" : 1, "a" : 19560.8, "c" : 2.10747, "p_0" : -142921439.2, "T_max" : 87.5}]
},
"Oxygen": {
"T_0" : 1, "a" : 227606.348, "c" : 1.769, "p_0" : -266999247.652, "T_max" : 63.1, "BibTeX" : "Younglove-NIST-1982"
"BibTeX" : "Younglove-NIST-1982", "T_m": 90.2, "parts": [{"T_0" : 1, "a" : 227606.348, "c" : 1.769, "p_0" : -266999247.652, "T_max" : 63.1}]
},
"ParaHydrogen": [
{
"T_0" : 1, "a" : 125746.643, "c" : 1.955, "p_0" : -21155737.752, "T_min" : 13.8033, "T_max" : 22, "BibTeX" : "Younglove-NIST-1982"
"ParaHydrogen": {
"BibTeX" : "Younglove-NIST-1982", "T_m": 18.9, "parts": [{"T_0" : 1, "a" : 125746.643, "c" : 1.955, "p_0" : -21155737.752, "T_min" : 13.8033, "T_max" : 22},
{"T_0" : 1, "a" : 248578.596, "c" : 1.764739, "p_0" : -26280332.904, "T_min" : 22, "T_max" : 164.5}]
},
{
"T_0" : 1, "a" : 248578.596, "c" : 1.764739, "p_0" : -26280332.904, "T_min" : 22, "T_max" : 164.5, "BibTeX" : "Younglove-NIST-1982"
"Methane": {
"BibTeX" : "Abramson-HPR-2011", "T_m": 90.7, "parts": [{"T_0" : 90.6941, "a" : 0.208e9, "c" : 1.698, "p_0" : 1.17e4, "T_max" : 700}]
}
]
}
polynomial_in_Tr = {
"Argon" : {
"T_t" : 83.8058, "a" : [-7476.2665, 9959.0613], "t" : [1.05,1.275], "p_t" : 68891, "T_max" : 254.0, "BibTeX" : "Tegeler-JPCRD-1999"
"BibTeX" : "Tegeler-JPCRD-1999", "T_m": 87.28, "parts": [{"T_0" : 83.8058, "a" : [-7476.2665, 9959.0613], "t" : [1.05,1.275], "p_0" : 68891, "T_max" : 254.0}]
},
"Fluorine" : {
"T_t" : 53.4811, "a" : [988043.478261], "t" : [2.1845], "p_t" : 252, "T_max" : 55.4, "BibTeX" : "deReuck-BOOK-1990"
"BibTeX" : "deReuck-BOOK-1990", "T_m": 85.2, "parts": [{"T_0" : 53.4811, "a" : [988043.478261], "t" : [2.1845], "p_0" : 252, "T_max" : 55.4}]
},
"Nitrogen" : {
"T_t" : 63.151, "a" : [12798.61], "t" : [1.78963], "p_t" : 12523, "T_max" : 283.8, "BibTeX" : "Span-JPCRD-2000"
"BibTeX" : "Span-JPCRD-2000", "T_m": 77.34, "parts": [{"T_0" : 63.151, "a" : [12798.61], "t" : [1.78963], "p_0" : 12523, "T_max" : 283.8}]
},
"Ethane" : {
"T_t" : 90.368, "a" : [2.23626315e8, 1.05262374e8], "t" : [1.0, 2.55], "p_t" : 1.14, "T_max" : 110.2, "BibTeX" : "Buecker-JCRD-2006"
"BibTeX" : "Buecker-JCRD-2006", "T_m": 184.6, "parts": [{"T_0" : 90.368, "a" : [2.23626315e8, 1.05262374e8], "t" : [1.0, 2.55], "p_0" : 1.14, "T_max" : 110.2}]
},
"Isobutane" : {
"T_t" : 113.73, "a" : [1.9536371309e9], "t" : [6.12], "p_t" : 0.0219, "T_max" : 124.9, "BibTeX" : "Buecker-JPCRD-2006B"
"BibTeX" : "Buecker-JPCRD-2006B", "T_m": 262, "parts": [{"T_0" : 113.73, "a" : [1.9536371309e9], "t" : [6.12], "p_0" : 0.0219, "T_max" : 124.9}]
},
"Ethylene" : [
{
"T_t" : 103.989, "a" : [2947001.84], "t" : [2.045], "p_t" : 122.65, "T_min" : 103.989, "T_max" : 110.369, "BibTeX" : "Smukala-JPCRD-2000"
"Ethylene" : {
"BibTeX" : "Smukala-JPCRD-2000", "T_m": 169, "parts": [{"T_0" : 103.989, "a" : [2947001.84], "t" : [2.045], "p_0" : 122.65, "T_min" : 103.989, "T_max" : 110.369},
{"T_0" : 110.369, "a" : [6.82693421], "t" : [1.089], "p_0" : 46.8e6, "T_min" : 110.369, "T_max" : 188}]
},
{
"T_t" : 110.369, "a" : [6.82693421], "t" : [1.089], "p_t" : 46.8e6, "T_min" : 110.369, "T_max" : 188, "BibTeX" : "Smukala-JPCRD-2000"
}
],
"n-Butane" : {
"T_t" : 134.895, "a" : [5.585582364e8], "t" : [2.206], "p_t" : 0.653, "T_max" : 163.9, "BibTeX" : "Buecker-JPCRD-2006B"
"BibTeX" : "Buecker-JPCRD-2006B", "T_m": -137.92 + 273.15, "parts": [{"T_0" : 134.895, "a" : [5.585582364e8], "t" : [2.206], "p_0" : 0.653, "T_max" : 163.9}]
},
"Water" : {
"BibTeX" : "IAPWS", "T_m": -1, "parts": [{"T_0" : 273.16, "a" : [-0.119539337e7,-0.808183159e5,-0.333826860e4], "t" : [0.3000000e1, 0.257500e2, 0.103750e3], "p_0" : 611.657, "T_min": 273.16, "T_max" : 251.165},
{"T_0" : 251.165, "a" : [0.299948], "t" : [60], "p_0" : 208.566e6, "T_min": 251.165, "T_max" : 256.164},
{"T_0" : 256.164, "a" : [1.18721], "t" : [8], "p_0" : 350.1e6, "T_min": 256.164, "T_max" : 273.31},
{"T_0" : 273.31, "a" : [1.07476], "t" : [4.6], "p_0" : 623.4e6, "T_min": 273.31, "T_max" : 355}
]
}
}
polynomial_in_theta = {
"Methanol" : {
"T_t" : 175.61, "a" : [5.330770e9, 4.524780e9, 3.888861e10], "t" : [1, 1.5, 4], "p_t" : 0.187, "T_max" : 245.9, "BibTeX" : "deReuck-BOOK-1993"
"BibTeX" : "deReuck-BOOK-1993", "T_m": 337.8, "parts": [{"T_0" : 175.61, "a" : [5.330770e9, 4.524780e9, 3.888861e10], "t" : [1, 1.5, 4], "p_0" : 0.187, "T_max" : 245.9}]
},
"CarbonDioxide" : {
"T_t" : 216.592, "a" : [1955.5390, 2055.4593], "t" : [1, 2], "p_t" : 517950, "T_max" : 327.6, "BibTeX" : "Span-JPCRD-1996"
"BibTeX" : "Span-JPCRD-1996", "T_m": 216.58, "parts": [{"T_0" : 216.592, "a" : [1955.5390, 2055.4593], "t" : [1, 2], "p_0" : 517950, "T_max" : 327.6}]
}
}
import CoolProp
__ = 0
for fluid in CoolProp.__fluids__:
if fluid not in Simon_curves and fluid not in polynomial_in_Tr and fluid not in polynomial_in_theta:
print fluid
__ += 1
else:
print ' '*30, fluid
print __
import CoolProp.CoolProp as CP
import json, numpy as np, matplotlib.pyplot as plt, pandas
ip = 1
@@ -105,6 +117,7 @@ def plot_rho(T, rho, fit = False):
def simon():
global ip, irho
for fluid, values in Simon_curves.iteritems():
axp = figp.add_subplot(Nrow, Ncol, ip); ip += 1
axrho = figrho.add_subplot(Nrow, Ncol, irho); irho += 1
@@ -115,21 +128,36 @@ def simon():
axp.set_title(fluid)
axrho.set_title(fluid)
if not isinstance(values, list):
values = [values]
df = pandas.read_csv('melting_curves/'+fluid+'.mlt',names=['T','p','rho'])
axp.plot(df['T'], df['p'], 'o', mfc='none')
x,y = plot_rho(df['T'],df['rho'],fit = True)
axrho.plot(x,y, 'o', mfc='none')
else:
for i in ['I','II']:
df = pandas.read_csv('melting_curves/'+fluid+'-'+i+'.mlt',names=['T','p','rho'])
axp.plot(df['T'], df['p'], 'o', mfc='none')
x,y = plot_rho(df['T'],df['rho'],fit = True)
axrho.plot(x,y, 'o', mfc='none')
fname = os.path.join('fluids',fluid+'.json')
j = json.load(open(fname,'r'))
for part in values['parts']:
if 'T_min' not in part:
part['T_min'] = round(CP.Props(fluid,"Tmin"),4)
values['type'] = 'Simon'
j['ANCILLARIES']['melting_line'] = values
for i,value in enumerate(values):
Tmin = value.get('T_min',min(df['T']))
fp = open(fname,'w')
from package_json import json_options
fp.write(json.dumps(j,**json_options))
fp.close()
# if not isinstance(values, list):
# values = [values]
# df = pandas.read_csv('melting_curves/'+fluid+'.mlt',names=['T','p','rho'])
# axp.plot(df['T'], df['p'], 'o', mfc='none')
# x,y = plot_rho(df['T'],df['rho'],fit = True)
# axrho.plot(x,y, 'o', mfc='none')
# else:
# for i in ['I','II']:
# df = pandas.read_csv('melting_curves/'+fluid+'-'+i+'.mlt',names=['T','p','rho'])
# axp.plot(df['T'], df['p'], 'o', mfc='none')
# x,y = plot_rho(df['T'],df['rho'],fit = True)
# axrho.plot(x,y, 'o', mfc='none')
for i, value in enumerate(values['parts']):
Tmin = value.get('T_min',CP.Props(fluid,"Tmin"))
Tmax = value['T_max']
T = np.linspace(Tmin, Tmax, 200)
@@ -155,35 +183,50 @@ def Tr():
axp.set_title(fluid)
axrho.set_title(fluid)
fname = os.path.join('fluids',fluid+'.json')
j = json.load(open(fname,'r'))
for part in values['parts']:
if 'T_min' not in part:
part['T_min'] = round(CP.Props(fluid,"Tmin"),4)
values['type'] = 'polynomial_in_Tr'
j['ANCILLARIES']['melting_line'] = values
fp = open(fname,'w')
from package_json import json_options
fp.write(json.dumps(j,**json_options))
fp.close()
if fluid == 'Ethylene':
T = [104.003, 104.059, 104.13, 104.2, 104.27, 104.41, 104.55, 104.69, 104.83, 104.969, 105.108, 105.386, 106.077, 106.764, 107.446, 111.384, 119.283, 127.136, 158.146, 188.621]
p = np.array([0.1, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 10, 15, 20, 25, 50, 75, 100, 200, 300])*1e6
axp.plot(T,p,'*')
if not isinstance(values, list):
values = [values]
df = pandas.read_csv('melting_curves/'+fluid+'.mlt',names=['T','p','rho'])
axp.plot(df['T'], df['p'], 'o', mfc='none')
x,y = plot_rho(df['T'],df['rho'],fit = True)
axrho.plot(x,y, 'o', mfc='none')
else:
for i in ['I','II']:
df = pandas.read_csv('melting_curves/'+fluid+'-'+i+'.mlt',names=['T','p','rho'])
axp.plot(df['T'], df['p'], 'o', mfc='none')
x,y = plot_rho(df['T'],df['rho'],fit = True)
axrho.plot(x,y, 'o', mfc='none')
# if not isinstance(values, list):
# values = [values]
# df = pandas.read_csv('melting_curves/'+fluid+'.mlt',names=['T','p','rho'])
# axp.plot(df['T'], df['p'], 'o', mfc='none')
# x,y = plot_rho(df['T'],df['rho'],fit = True)
# axrho.plot(x,y, 'o', mfc='none')
#
# else:
# for i in ['I','II']:
# df = pandas.read_csv('melting_curves/'+fluid+'-'+i+'.mlt',names=['T','p','rho'])
# axp.plot(df['T'], df['p'], 'o', mfc='none')
# x,y = plot_rho(df['T'],df['rho'],fit = True)
# axrho.plot(x,y, 'o', mfc='none')
for i,value in enumerate(values):
Tmin = value.get('T_min',min(df['T']))
for i,value in enumerate(values['parts']):
Tmin = value.get('T_min',CP.Props(fluid,"Tmin"))
Tmax = value['T_max']
T = np.linspace(Tmin, Tmax, 200)
a = value['a']
t = value['t']
T_t = value['T_t']
p_t = value['p_t']
T_t = value['T_0']
p_t = value['p_0']
RHS = 0
for i in range(len(a)):
@@ -196,7 +239,7 @@ def Tr():
def theta():
global ip, irho
for fluid, value in polynomial_in_theta.iteritems():
for fluid, values in polynomial_in_theta.iteritems():
axp = figp.add_subplot(Nrow, Ncol, ip); ip += 1
axrho = figrho.add_subplot(Nrow, Ncol, irho); irho += 1
@@ -207,29 +250,45 @@ def theta():
axp.set_title(fluid)
axrho.set_title(fluid)
a = value['a']
t = value['t']
T_t = value['T_t']
p_t = value['p_t']
fname = os.path.join('fluids',fluid+'.json')
j = json.load(open(fname,'r'))
for part in values['parts']:
if 'T_min' not in part:
part['T_min'] = round(CP.Props(fluid,"Tmin"),4)
values['type'] = 'polynomial_in_Theta'
j['ANCILLARIES']['melting_line'] = values
Tmin = T_t
Tmax = value['T_max']
T = np.linspace(Tmin, Tmax, 200)
fp = open(fname,'w')
from package_json import json_options
fp.write(json.dumps(j,**json_options))
fp.close()
RHS = 0
for i in range(len(a)):
RHS += a[i]*(T/T_t - 1)**t[i]
for value in values['parts']:
a = value['a']
t = value['t']
T_t = value['T_0']
p_t = value['p_0']
Tmin = T_t
Tmax = value['T_max']
T = np.linspace(Tmin, Tmax, 200)
RHS = 0
for i in range(len(a)):
RHS += a[i]*(T/T_t - 1)**t[i]
p = p_t*(RHS + 1)
#df = pandas.read_csv('melting_curves/' + fluid + '.mlt', names=['T','p','rho'])
#axp.plot(df['T'], df['p'], 'o', mfc='none')
axp.plot(T, p)
p = p_t*(RHS + 1)
df = pandas.read_csv('melting_curves/' + fluid + '.mlt', names=['T','p','rho'])
axp.plot(df['T'], df['p'], 'o', mfc='none')
axp.plot(T, p)
x,y = plot_rho(df['T'],df['rho'],fit = True)
axrho.plot(x,y, 'o', mfc='none')
#x,y = plot_rho(df['T'],df['rho'],fit = True)
#axrho.plot(x,y, 'o', mfc='none')
if __name__=='__main__':
simon()

96
include/CoolPropFluid.h
View File

@@ -112,6 +112,7 @@ struct ConductivityCriticalSimplifiedOlchowySengersData{
qD = 2e9; //[m]
// Set to invalid number, can be provided in the JSON file
// Default is 1.5*Tc
T_ref = _HUGE;
}
};
@@ -365,14 +366,105 @@ public:
}
};
class MeltingLine
struct MeltingLinePiecewiseSimonSegment
{
long double T_0, a, c, p_0, T_max, T_min;
};
struct MeltingLinePiecewiseSimonData
{
std::vector<MeltingLinePiecewiseSimonSegment> parts;
};
struct MeltingLinePiecewisePolynomialInTrSegment
{
std::vector<long double> a, t;
long double T_0, p_0, T_max, T_min;
};
struct MeltingLinePiecewisePolynomialInTrData
{
std::vector<MeltingLinePiecewisePolynomialInTrSegment> parts;
};
struct MeltingLinePiecewisePolynomialInThetaSegment
{
std::vector<long double> a, t;
long double T_0, p_0, T_max, T_min;
};
struct MeltingLinePiecewisePolynomialInThetaData
{
std::vector<MeltingLinePiecewisePolynomialInThetaSegment> parts;
};
class MeltingLineVariables
{
public:
enum MeltingLineVariablesEnum{
MELTING_LINE_SIMON_TYPE,
MELTING_LINE_POLYNOMIAL_IN_TR_TYPE,
MELTING_LINE_POLYNOMIAL_IN_THETA_TYPE,
MELTING_LINE_NOT_SET
};
long double evaluate(int OF, int GIVEN, long double value)
{
if (type == MELTING_LINE_NOT_SET){throw ValueError("Melting line curve not set");}
if (OF == iP && GIVEN == iT){
long double T = value;
if (type == MELTING_LINE_SIMON_TYPE){
// Need to find the right segment
for (std::size_t i = 0; i < simon.parts.size(); ++i){
MeltingLinePiecewiseSimonSegment &part = simon.parts[i];
if (T >= part.T_min && T <= part.T_max){
return part.p_0 + part.a*(pow(T/part.T_0,part.c)-1);
}
}
throw ValueError("unable to calculate melting line (p,T) for Simon curve");
}
else if (type == MELTING_LINE_POLYNOMIAL_IN_TR_TYPE){
// Need to find the right segment
for (std::size_t i = 0; i < polynomial_in_Tr.parts.size(); ++i){
MeltingLinePiecewisePolynomialInTrSegment &part = polynomial_in_Tr.parts[i];
if (T >= part.T_min && T <= part.T_max){
long double summer = 0;
for (std::size_t i =0; i < part.a.size(); ++i){
summer += part.a[i]*(pow(T/part.T_0,part.t[i])-1);
}
return part.p_0*(1+summer);
}
}
throw ValueError("unable to calculate melting line (p,T) for polynomial_in_Tr curve");
}
else if (type == MELTING_LINE_POLYNOMIAL_IN_THETA_TYPE){
// Need to find the right segment
for (std::size_t i = 0; i < polynomial_in_Theta.parts.size(); ++i){
MeltingLinePiecewisePolynomialInThetaSegment &part = polynomial_in_Theta.parts[i];
if (T >= part.T_min && T <= part.T_max){
long double summer = 0;
for (std::size_t i =0; i < part.a.size(); ++i){
summer += part.a[i]*pow(T/part.T_0-1,part.t[i]);
}
return part.p_0*(1+summer);
}
}
throw ValueError("unable to calculate melting line (p,T) for polynomial_in_Theta curve");
}
else{
throw ValueError("only Simon supported now");
}
}
else{
throw ValueError("only melt(P,T) supported now");
}
}
std::string BibTeX;
long double T_m; ///< Melting temperature at 1 atmosphere
MeltingLinePiecewiseSimonData simon;
MeltingLinePiecewisePolynomialInTrData polynomial_in_Tr;
MeltingLinePiecewisePolynomialInThetaData polynomial_in_Theta;
int type;
MeltingLineVariables(){type = MELTING_LINE_NOT_SET;};
};
struct Ancillaries
{
SaturationAncillaryFunction pL, pV, rhoL, rhoV;
MeltingLine melting_line;
MeltingLineVariables melting_line;
SurfaceTensionCorrelation surface_tension;
};

14
include/rapidjson/rapidjson_include.h
View File

@@ -100,6 +100,20 @@ namespace cpjson
return out;
};
/// A convenience function to get a long double array compactly
inline std::vector<long double> get_long_double_array(rapidjson::Value &v, std::string name)
{
std::vector<long double> out;
if (!v.HasMember(name.c_str())){ throw CoolProp::ValueError(format("Does not have member [%s]",name.c_str())); }
if (!v[name.c_str()].IsArray()) { throw CoolProp::ValueError("input is not an array"); }
for (rapidjson::Value::ValueIterator itr = v[name.c_str()].Begin(); itr != v[name.c_str()].End(); ++itr)
{
if (!itr->IsNumber()){throw CoolProp::ValueError("input is not a number");}
out.push_back(itr->GetDouble());
}
return out;
};
/// A convenience function to get a string array compactly
inline std::vector<std::string> get_string_array(rapidjson::Value &v)
{

77
src/Backends/Helmholtz/Fluids/FluidLibrary.h
View File

@@ -311,7 +311,7 @@ protected:
EOS.reduce.rhomolar = cpjson::get_double(reducing_state,"rhomolar");
EOS.reduce.p = cpjson::get_double(reducing_state,"p");
/// todo: define limits of EOS better
/// \todo: define limits of EOS better
EOS.limits.Tmin = cpjson::get_double(satminL_state, "T");
EOS.Ttriple = EOS.limits.Tmin;
@@ -804,6 +804,71 @@ protected:
fluid.transport.epsilon_over_k = Tc/1.3593; // [K]
}
void parse_melting_line(rapidjson::Value &melting_line, CoolPropFluid & fluid)
{
fluid.ancillaries.melting_line.T_m = cpjson::get_double(melting_line, "T_m");
fluid.ancillaries.melting_line.BibTeX = cpjson::get_string(melting_line, "BibTeX");
if (melting_line.HasMember("type"))
{
std::string type = cpjson::get_string(melting_line, "type");
if (!type.compare("Simon"))
{
rapidjson::Value &parts = melting_line["parts"];
for (rapidjson::Value::ValueIterator itr = parts.Begin(); itr != parts.End(); ++itr)
{
MeltingLinePiecewiseSimonSegment data;
data.a = cpjson::get_double((*itr),"a");
data.c = cpjson::get_double((*itr),"c");
data.T_min = cpjson::get_double((*itr),"T_min");
data.T_max = cpjson::get_double((*itr),"T_max");
data.T_0 = cpjson::get_double((*itr),"T_0");
data.p_0 = cpjson::get_double((*itr),"p_0");
fluid.ancillaries.melting_line.simon.parts.push_back(data);
}
fluid.ancillaries.melting_line.type = MeltingLineVariables::MELTING_LINE_SIMON_TYPE;
}
else if (!type.compare("polynomial_in_Tr"))
{
rapidjson::Value &parts = melting_line["parts"];
for (rapidjson::Value::ValueIterator itr = parts.Begin(); itr != parts.End(); ++itr)
{
MeltingLinePiecewisePolynomialInTrSegment data;
data.a = cpjson::get_long_double_array((*itr),"a");
data.t = cpjson::get_long_double_array((*itr),"t");
data.T_min = cpjson::get_double((*itr),"T_min");
data.T_max = cpjson::get_double((*itr),"T_max");
data.T_0 = cpjson::get_double((*itr),"T_0");
data.p_0 = cpjson::get_double((*itr),"p_0");
fluid.ancillaries.melting_line.polynomial_in_Tr.parts.push_back(data);
}
fluid.ancillaries.melting_line.type = MeltingLineVariables::MELTING_LINE_POLYNOMIAL_IN_TR_TYPE;
}
else if (!type.compare("polynomial_in_Theta"))
{
rapidjson::Value &parts = melting_line["parts"];
for (rapidjson::Value::ValueIterator itr = parts.Begin(); itr != parts.End(); ++itr)
{
MeltingLinePiecewisePolynomialInThetaSegment data;
data.a = cpjson::get_long_double_array((*itr),"a");
data.t = cpjson::get_long_double_array((*itr),"t");
data.T_min = cpjson::get_double((*itr),"T_min");
data.T_max = cpjson::get_double((*itr),"T_max");
data.T_0 = cpjson::get_double((*itr),"T_0");
data.p_0 = cpjson::get_double((*itr),"p_0");
fluid.ancillaries.melting_line.polynomial_in_Theta.parts.push_back(data);
}
fluid.ancillaries.melting_line.type = MeltingLineVariables::MELTING_LINE_POLYNOMIAL_IN_THETA_TYPE;
}
else{
throw ValueError(format("melting line type [%s] is not understood for fluid %s", type.c_str(), fluid.name.c_str()));
}
}
else{
throw ValueError(format("melting line does not have \"type\" for fluid %s", fluid.name.c_str()));
}
};
/// Parse the critical state for the given EOS
void parse_states(rapidjson::Value &states, CoolPropFluid & fluid)
{
@@ -936,6 +1001,16 @@ public:
parse_surface_tension(fluid_json["ANCILLARIES"]["surface_tension"], fluid);
}
// Melting line
if (!(fluid_json["ANCILLARIES"].HasMember("melting_line"))){
if (get_debug_level() > 0){
std::cout << format("Melting line curves are missing for fluid [%s]\n", fluid.name.c_str()) ;
}
}
else{
parse_melting_line(fluid_json["ANCILLARIES"]["melting_line"], fluid);
}
// Parse the environmental parameters
if (!(fluid_json.HasMember("ENVIRONMENTAL"))){
if (get_debug_level() > 0){

15
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
View File

@@ -115,6 +115,17 @@ long double HelmholtzEOSMixtureBackend::calc_molar_mass(void)
}
return summer;
}
long double HelmholtzEOSMixtureBackend::calc_melt_p_T(long double T)
{
if (is_pure_or_pseudopure)
{
return components[0]->ancillaries.melting_line.evaluate(iP, iT, T);
}
else
{
throw NotImplementedError(format("calc_melt_p_T not implemented for mixtures"));
}
}
long double HelmholtzEOSMixtureBackend::calc_surface_tension(void)
{
if (is_pure_or_pseudopure)
@@ -1591,8 +1602,8 @@ long double HelmholtzEOSMixtureBackend::calc_speed_sound(void)
long double d2ar_dDelta2 = d2alphar_dDelta2();
long double d2ar_dDelta_dTau = d2alphar_dDelta_dTau();
long double d2ar_dTau2 = d2alphar_dTau2();
long double R_u = static_cast<long double>(_gas_constant);
long double mm = static_cast<long double>(_molar_mass);
long double R_u = gas_constant();
long double mm = molar_mass();
// Get speed of sound
_speed_sound = sqrt(R_u*_T/mm*(1+2*_delta.pt()*dar_dDelta+pow(_delta.pt(),2)*d2ar_dDelta2 - pow(1+_delta.pt()*dar_dDelta-_delta.pt()*_tau.pt()*d2ar_dDelta_dTau,2)/(pow(_tau.pt(),2)*(d2ar_dTau2 + d2a0_dTau2))));

37
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.h
View File

@@ -17,10 +17,10 @@ class FlashRoutines;
class HelmholtzEOSMixtureBackend : public AbstractState {
protected:
std::vector<CoolPropFluid*> components; ///< The components that are in use
bool is_pure_or_pseudopure; ///< A flag for whether the substance is a pure or pseudo-pure fluid (true) or a mixture (false)
std::vector<long double> mole_fractions; ///< The mole fractions of the components
std::vector<long double> mole_fractions_liq, ///< The mole fractions of the saturated liquid
std::vector<long double> mole_fractions_liq, ///< The mole fractions of the saturated liquid
mole_fractions_vap, ///< The mole fractions of the saturated vapor
K, ///< The K factors for the components
lnK; ///< The natural logarithms of the K factors of the components
@@ -37,7 +37,7 @@ public:
friend class FlashRoutines; // Allows the static methods in the FlashRoutines class to have access to all the protected members and methods of this class
friend class TransportRoutines; // Allows the static methods in the TransportRoutines class to have access to all the protected members and methods of this class
//friend class MixtureDerivatives; //
//friend class MixtureDerivatives; //
// Helmholtz EOS backend uses mole fractions
bool using_mole_fractions(){return true;}
@@ -46,7 +46,7 @@ public:
std::vector<long double> &get_K(){return K;};
std::vector<long double> &get_lnK(){return lnK;};
shared_ptr<HelmholtzEOSMixtureBackend> SatL, SatV; ///<
shared_ptr<HelmholtzEOSMixtureBackend> SatL, SatV; ///<
void update(long input_pair, double value1, double value2);
@@ -69,19 +69,19 @@ public:
void set_excess_term();
/// Set the mole fractions
/**
/**
@param mole_fractions The vector of mole fractions of the components
*/
void set_mole_fractions(const std::vector<long double> &mole_fractions);
const std::vector<long double> &get_mole_fractions(){return mole_fractions;};
/// Set the mass fractions
/**
/**
@param mass_fractions The vector of mass fractions of the components
*/
void set_mass_fractions(const std::vector<long double> &mass_fractions){throw std::exception();};
long double calc_molar_mass(void);
long double calc_gas_constant(void);
@@ -118,6 +118,7 @@ public:
long double calc_d2alpha0_dDelta_dTau(void);
long double calc_d2alpha0_dTau2(void);
long double calc_melt_p_T(long double T);
long double calc_surface_tension(void);
long double calc_viscosity(void);
long double calc_viscosity_dilute(void);
@@ -137,7 +138,7 @@ public:
std::string calc_name(void);
long double calc_alphar_deriv_nocache(const int nTau, const int nDelta, const std::vector<long double> & mole_fractions, const long double &tau, const long double &delta);
/**
\brief Take derivatives of the ideal-gas part of the Helmholtz energy, don't use any cached values, or store any cached values
@@ -163,7 +164,7 @@ public:
\sa Table B5, GERG 2008 from Kunz Wagner, JCED, 2012
*/
long double calc_alpha0_deriv_nocache(const int nTau, const int nDelta, const std::vector<long double> & mole_fractions, const long double &tau, const long double &delta, const long double &Tr, const long double &rhor);
void calc_reducing_state(void);
SimpleState calc_reducing_state_nocache(const std::vector<long double> & mole_fractions);
@@ -183,11 +184,11 @@ public:
void mass_to_molar_inputs(long &input_pair, double &value1, double &value2);
// ***************************************************************
// ***************************************************************
// ***************************************************************
// ************* PHASE DETERMINATION ROUTINES ******************
// ***************************************************************
// ***************************************************************
// ***************************************************************
void T_phase_determination_pure_or_pseudopure(int other, long double value);
void p_phase_determination_pure_or_pseudopure(int other, long double value);
void DmolarP_phase_determination();
@@ -197,8 +198,8 @@ public:
// ***************************************************************
// ******************* SOLVER ROUTINES *************************
// ***************************************************************
// ***************************************************************
// ***************************************************************
long double solver_rho_Tp(long double T, long double p, long double rho_guess = -1);
long double solver_rho_Tp_SRK(long double T, long double p, int phase);
long double solver_for_rho_given_T_oneof_HSU(long double T, long double value, int other);
@@ -310,7 +311,7 @@ public:
\f[
n\left(\frac{\partial \ln \phi_i}{\partial n_j}\right)_{T,p} = n\left(\frac{\partial^2n\alpha^r}{\partial n_j \partial n_i} \right)_{T,V}+1+\frac{n}{RT}\frac{\left(\frac{\partial p}{\partial n_j}\right)_{T,V,n_i}\left(\frac{\partial p}{\partial n_i}\right)_{T,V,n_j}}{\left(\frac{\partial p}{\partial V}\right)_{T,\bar n}}
\f]
which is also equal to
which is also equal to
\f[
n\left(\frac{\partial \ln \phi_i}{\partial n_j}\right)_{T,p} = n\left(\frac{\partial^2n\alpha^r}{\partial n_j \partial n_i} \right)_{T,V}+1-\frac{\hat v_i}{RT}\left[n\left(\frac{\partial p}{\partial n_j}\right)_{T,V,n_i}\right]
\f]
@@ -320,7 +321,7 @@ public:
/// Gernert Equation 3.115
/// Catch test provided
long double mixderiv_dln_fugacity_coefficient_dxj__constT_p_xi(int i, int j);
/// Gernert Equation 3.130
/// Catch test provided
long double mixderiv_dpdxj__constT_V_xi(int j);
@@ -390,7 +391,7 @@ public:
\f]
GERG 2004 Monograph equation 7.47:
\f{eqnarray*}{
n\left( \frac{\partial}{\partial n_j}\left(n\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_j} \right) \right)_{T,V,n_i} &=& \left( \frac{\partial}{\partial \delta}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\tau,\bar x}\cdot n\left(\frac{\partial\delta}{\partial n_j}\right)_{T,V,n_i}\\
n\left( \frac{\partial}{\partial n_j}\left(n\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_j} \right) \right)_{T,V,n_i} &=& \left( \frac{\partial}{\partial \delta}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\tau,\bar x}\cdot n\left(\frac{\partial\delta}{\partial n_j}\right)_{T,V,n_i}\\
&+& \left( \frac{\partial}{\partial \tau}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\tau,\bar x}\cdot n\left(\frac{\partial\tau}{\partial n_j}\right)_{T,V,n_i}\\
&+& \left( \frac{\partial}{\partial x_j}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\delta,\tau,x_i}-\sum_{k=1}^{N}x_k \left( \frac{\partial}{\partial x_k}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\delta,\tau,x_i}\\
\f}
@@ -404,7 +405,7 @@ public:
\f]
*/
long double mixderiv_nddeltadni__constT_V_nj(int i);
/// GERG 2004 Monograph equation 7.49
/** The derivative term
\f[