and Pressures up to 1000 bar
Sara Anwar and John J. Carroll Gas Liquids Engineering, Ltd.
Calgary, Alberta, Canada
Scrivener Publishing 3 Winter Street, Suite 3
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and Pressures up to 1000 bar
Sara Anwar and John J. Carroll Gas Liquids Engineering, Ltd.
Calgary, Alberta, Canada
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Contents
1 Density (kg/m3) of Saturated Carbon Dioxide l
2 Enthalpy (J/mol) of Saturated Carbon Dioxide 3
3 Entropy (J/mol ·Κ) of Saturated Carbon Dioxide 5
4 Heat Capacity, C,, (J/mol · K) of Saturated Carbon Dioxide 7
5 Density (kg/m3) of Carbon Dioxide as a Function of Temperature and Pressure 9
6 Enthalpy (J/mol) of Carbon Dioxide as a Function of Temperature and Pressure 149
7 Entropy (J/mol ·Κ) of Carbon Dioxide as a Function of Temperature and Pressure 289
8 Heat Capacity, Cp, (J/mol · K) of Carbon Dioxide as a Function of Temperature and Pressure 429
V l l
Acknowledgement
The authors are grateful to Gas Liquids Engineering (GLE) for provided the time to compile this book. In particular we are indebted to the company principles Doug Mackenzie and Jim Maddocks. We would also like to thank Peter Griffin of GLE for his continuing support of this project.
IX
Preface
Like water, carbon dioxide is one of the most studied substances in the annals of science. It has a readily accessible critical point (30.98°C and 73.77 bar), and it is relatively safe (compared with hydrocarbons and toxic chemicals such as hydrogen sulfide). The measurements have been criti- cally reviewed and complex, highly accurate equations of state have been developed.
In the 21st century carbon dioxide has become an important social chemical. It has been impli- cated in global climate change, and governments are scrambling to deal with emissions of C0 2 to the environment, including taxing emitters. Carbon dioxide may one day rival other commodities.
This is the most comprehensive collection of data on the thermodynamic properties of carbon dioxide ever published, and much of this information is now no longer available in such a ready format anywhere else. The authors hope that this volume will become a standard reference work for engineers, chemists, and scientists everywhere, who are studying, working with, or hoping to combat carbon dioxide.
xi
Introduction
Presented in this book are tabulated properties for pure carbon dioxide. The properties are based on the equation of state of Span and Wagner (1996). Although Span and Wagner (1996) also included tabular properties, the properties given here are at fine intervals of temperature and pressure and make rapid interpretation much easier.
The range of temperatures and pressure was selected as being appropriate for the application of carbon dioxide sequestration. However, the tabulated data are not limited to that application.
The first tables in this book are for the properties of saturated carbon dioxide. The pressures, therefore, that are given in these tables are the vapor pressure of pure C0 2 and they end at the criti- cal point. One thing that looks unusual is that the heat capacity, C , is infinite at the critical point, but this is true by definition.
Derived Properties
From the tables provided in this book several other properties can be calculated directly. This sec- tion provides the formulae to perform these calculations.
Molar Volume
The molar volume, v, is basically the reciprocal of the density and can be calculated using the fol- lowing definition:
v = ^ - (i) p
where: v is the molar volume, m3/kmol M is the molar mass of carbon dioxide, 44.010 kg/kmol p is the density, kg/m 3
Compressibility Factor
The compressibility factor, z, can be calculated from the values in the density tables using the fol- lowing definition:
M P (2) p R (t + 273.15)
where: z is the compressibility factor, dimensionless M is the molar mass of carbon dioxide, 44.010 kg/kmol P is the total pressure, bar p is the density, kg/m 3
R is the universal gas constant, 0.083 145 bar«m3/kmol»K T is the temperature, °C
xiu
Specific Properties
The tabulated values for the enthalpy, entropy, and heat capacity are on a molar basis. In order to convert them to the specific property (per unit mass), divide by the molar mass of carbon dioxide (44.010 g/mol).
H = h / M
where: H is the specific enthalpy, kj/kg h is the molar enthalpy, kj/kmol (or J/mol) M is the molar mass of carbon dioxide, 44.010 kg/kmol
S = s / M
where: S is the specific entropy, kJ/kg»K s is the molar entropy, kJ /kmol 'K (or J/moleK) M is the molar mass of carbon dioxide, 44.010 kg/kmol
CP = C P / M
where: Cp is the specific heat capacity, kJ/kg»K Cp is the molar heat capacity, kJ/kmol«K (or J/mol#K) M is the molar mass of carbon dioxide, 44.010 kg/kmol
Internal Energy
The internal energy, U, in kj/kg can be calculated the following definition:
100 P
P
where: U is the specific internal energy, kj/kg H is the specific enthalpy, kj/kg P is the pressure, bar p is the density, kg/m 3
Alternatively, the molar internal energy, u, in J/mol can be calculated from:
. 1000 M P u = h (4)
P
where: u is the molar internal energy, J/mol M is the molar mass of carbon dioxide, 44.010 kg/kmol h is the molar enthalpy, J/mol
Linear Interpolation
The tables provided are at fine grids of temperature and pressure. However, for more accurate cal- culations the tables should be interpolated. The grid is sufficiently fine that linear interpolation is satisfactory.
y = VX1 — X2 /
(x-x1) + y1 (5)
One must be careful not to interpolate across the vapor pressure.
INTRODUCTION XV
Example 1 What is the enthalpy of carbon dioxide at 50°C and 6.25 bar?
Answer: From Table 9 at 50°C:
P = 6 bar h = 734.0 J/mol (point 1) P = 7bar h = 698.4 J/mol (point 2)
Interpolating:
= 725.1 J/mol
Example 2 What is the enthalpy of carbon dioxide at 71.3°C and 18 bar.
Answer: From Table 9:
= 1193.1 J/mol
and n 2 5 2 . 2 - n 7 0 . 8 - , 2 5 2 2
3 y 17.5-20 ) = 1235.9 J/mol
These interpolations are summarized in the following table:
71 °C
72°C
17.5 bar
1209.5 J/mol
1252.2 J/mol
18 bar
1193.1 J/mol
1235.9 J/mol
20 bar
1127.4 J/mol
1170.8 J/mol
Interpolate with the temperature (the italicized values in the above table).
( 1193.1-1235.9 V ^ „ ^ , . , ,„„., y = l 7 W 2 J(71.3-71) + 1193.1
= 1205.9 J/mol
Fig. 1 Schematic of the Joule-Thomson Expansion
Τ , , Ρ ι , ^ , β ,
Fig. 2 Schematic of the Compression of a Gas Stream
I pi ' 2 ' ' ' 2 ' 2
Sample Calculations
Presented in this section are some sample calculations based on classical thermodynamics, which demonstrate some applications for the tables.
Joule-Thomson Expansion
One of the classic examples in thermodynamics is the expansion of a fluid across a valve (or a porous plug), which is a constant enthalpy process. The process is shown in Fig. 1. The specification of this process is given the temperature and the pressure of the inlet (state 1) and the pressure at the outlet (state 2), calculate the temperature of the outlet stream. Since this is an isenthalpic process, we also know that:
h1 = h2
Isentropic Compression
An ideal compressor is an isentropic process (i.e. the change in entropy of the stream is zero). A sim- ple schematic of a compression process is shown in Fig. 2. The specification for a compressor is the inlet temperature and pressure and the outlet pressure (or equivalently the compression ratio). For the ideal case:
S1 = S 2
Thus the outlet of the compressor is specified by P2 and s2 from which the other properties can be calculated.
The ideal, adiabatic work compression can then be calculated from the difference in the enthalpies:
w* = h2 - hj
where w* is the ideal, adiabatic work of compression, J/mol
Example 3
Calculate the temperature drop when a carbon dioxide stream is throttled from 7 bar and 50°C to 1 bar.
Answer: At 7 bar and 50°C the enthalpy is 698.4 J/mol (from Table 6). At 1 bar, from Table 6 we have the following:
INTRODUCTION xvii
By linear interpolation:
/ 4 4 _ 4 5 \ y = _ (698.4 - 678.2) + 44 y V 678.2 -716.5 Γ
= 44.5°C
So the exit temperature is 44.5°C, a cooling of about 5.5 Celsius degrees.
Example 4
The suction pressure is 3.5 bar and the temperature is 50°C. For a discharge pressure is 10 bar calcu- lated the discharge temperature and the work of compression.
Answer: The flowing properties are for carbon dioxide at 50°C at 3 and 4 bar are from Tables x and y and the value at 3.5 bar is interpolated from these values.
entropy
enthalpy
3 bar
-6.214 J/moLK
839.3 J/mol
3.5 bar
-7.448 J/moUK
821.9 J/mol
4 bar
-8.682 J/mol.K
804.4 J/mol
From Table 11 at 10 bar, it can be seen that the discharge temperature is between 130° and 131°C, because the entries in the table span the entropy value at 50°C and 3.5 bar (-7.448 J/mol K). In fact, from these vales it can be seen that the discharge temperature is almost exactly 131°C. For many cases this may be sufficiently accurate.
However the values for the entropy can be used to interpolate the temperature more accurately as shown below:
entropy
enthalpy
130°C
-7.583 J/mol.K
3916.2 J/mol
130.99°C
-7.448 J/mohK
3958.4 J/mol
131°C
-7.447 J/mol.K
3958.8 J/mol
Í 1 3 0 1 3 1 V-7.583—7.448) + 130 3 1-7.583—7.447 P '
= 130.99°C
Finally the ideal, adiabatic work of compression is the change in enthalpy:
w* = 3958.4 - 821.9 = 3136.5 T/mol
xviii CARBON DIOXIDE THERMODYNAMIC PROPERTIES HANDBOOK
Conversion factors
-20°C -10°C
0°C 10°C 20°C 30°C 50°C
100°C 150°C 200°C 250°C
= ^ ° F = 14°F = 32°F = 50°F = 68°F = 86°F = 122°F = 212°F = 302°F = 392°F = 482°F
Reference Span, R. and W. Wagner, "A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa", /. Phys. Chem. Ref. Data, 25,1509-1596, (1996).
1 Density (kg/m3) of Saturated Carbon Dioxide
Table 1 Density (kg/m3) of Saturated Carbon Dioxide
Temp (°C) -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
Press (bar) 19.70 20.31 20.94 21.58 22.24 22.91 23.59 24.29 25.01 25.74 26.49 27.25 28.03 28.82 29.63 30.46 31.30 32.16 33.04 33.94 34.85 35.78 36.73
Liquid 1031.7 1027.0 1022.3 1017.6 1012.8 1008.0 1003.1 998.1 993.1 988.1 982.9 977.7 972.5 967.1 961.7 956.2 950.6 945.0 939.2 933.4 927.4 921.4 915.2
Vapor 51.70 53.40 55.15 56.96 58.82 60.73 62.70 64.73 66.81 68.97 71.18 73.47 75.83 78.26 80.77 83.36 86.03 88.79 91.65 94.60 97.65
100.8 104.1
Temp (°C) 9
10 11 12 13 14 15 16 17 18 19 20 21 22 22 23 24 25 26 27 28 29 29.5
Press (bar) 43.92 45.02 46.15 47.30 48.47 · 49.66 50.87 52.11 53.37 54.65 55.96 57.29 58.65 60.03 60.03 61.44 62.88 64.34 65.84 67.36 68.92 70.51 71.32
Liquid 868.4 861.1 853.6 845.9 837.9 829.7 821.2 812.4 803.3 793.8 783.8 773.4 762.4 750.8 750.8 738.4 725.0 710.5 694.5 676.4 655.3 629.4 613.3
Vapor 130.7 135.2 139.8 144.7 149.8 155.1 160.7 166.7 172.9 179.6 186.6 194.2 202.3 211.1 211.1 220.6 231.1 242.7 255.9 271.0 289.1 312.0 326.6
1
2 C A R B O N DIOXIDE THERMODYNAMIC PROPERTIES H A N D B O O K
Table 1 Density (kg/m3) of Saturated Carbon Dioxide (cont.)
Temp (°C) 3 4 5 6 7 8
Press (bar) 37.70 38.69 39.70 40.72 41.77 42.83
Liquid 909.0 902.6 896.0 889.4 882.5 875.6
Vapor 107.5 111.0 114.6 118.4 122.3 126.4
Temp (°C) 30.0 30.2 30.4 30.6 30.8 30.98
Press (bar) 72.14 72.47 72.80 73.13 73.47 73.77
Liquid 593.3 583.5 572.0 557.7 537.4 467.6
Vapor 345.1 354.3 365.3 379.1 399.2 467.6
Enthalpy (J/mol) of Saturated Carbon Dioxide
Table 2 Enthalpy (J/mol) of Saturated Carbon Dioxide
Temp (°C) -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
Press (bar) 19.70 20.31 20.94 21.58 22.24 22.91 23.59 24.29 25.01 25.74 26.49 27.25 28.03 28.82 29.63 30.46 31.30 32.16 33.04 33.94 34.85 35.78
Liquid
-15506 -15411 -15316 -15220 -15123 -15027 -14929 -14831 -14733 -14634 -14535 -14435 -14334 -14232 -14130 -14027 -13924 -13820 -13714 -13608 -13501 -13393
Vapour
-3075.8 -3079.5 -3084.1 -3089.5 -3095.8 -3102.9 -3111.0 -3120.0 -3130.0 -3141.0 -3153.1 -3166.2 -3180.4 -3195.8 -3212.3 -3230.2 -3249.3 -3269.7 -3291.6 -3314.9 -3339.8 -3366.2
Vaporization
12430 12332 12232 12130 12028 11924 11818 11711 11603 11493 11382 11268 11153 11037 10918 10797 10675 10550 10423 10293 10162 10027
Temp (°C)
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 29.5
Press (bar) 43.92 45.02 46.15 47.30 48.47 49.66 50.87 52.11 53.37 54.65 55.96 57.29 58.65 60.03 61.44 62.88 64.34 65.84 67.36 68.92 70.51 71.32
Liquid
-12488 -12369 -12248 -12124 -11999 -11872 -11741 -11609 -11473 -11333 -11190 -11043 -10890 -10732 -10567 -10394 -10210 -10013
-9798.2 -9557.1 -9273.2 -9103.6
-3646.8 -3692.2 -3740.6 -3792.0 -3846.7 -3905.0 -3967.2 -4033.8 -4105.0 -4181.6 -4264.1 -4353.2 -4450.0 -4555.7 -4671.8 -4800.4 -4944.5 -5108.3 -5298.5 -5526.7 -5816.6 -6001.2
Vaporization
8841.7 8676.7 8507.1 8332.5 8152.4 7966.5 7774.2 7574.8 7367.5 7151.6 6926.0 6689.4 6440.1 6176.2 5895.1 5593.2 5265.5 4904.9 4499.7 4030.4 3456.6 3102.4
3
4 CARBON DIOXIDE THERMODYNAMIC PROPERTIES H A N D B O O K
Table 2 Enthalpy (J/mol) of Saturated Carbon Dioxide (cont.)
Temp (°C) 2 3 4 5 6 7 8
Press (bar) 36.73 37.70 38.69 39.70 40.72 41.77 42.83
Liquid
Vapour
Vaporization
Temp (°C)
Press (bar) 72.14 72.47 72.80 73.13 73.47 73.77 73.77
Liquid
Vapour
Vaporization
0.000
Table 3 Entropy (J/mol»K) of Saturated Carbon Dioxide
Temp (°C) -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
Press (bar) 19.70 20.31 20.94 21.58 22.24 22.91 23.59 24.29 25.01 25.74 26.49 27.25 28.03 28.82 29.63 30.46 31.30 32.16 33.04 33.94 34.85 35.78
Liquid
-83.89 -83.53 -83.16 -82.80 -82.43 -82.07 -81.70 -81.34 -80.97 -80.61 -80.24 -79.88 -79.51 -79.14 -78.77 -78.40 -78.03 -77.66 -77.28 -76.91 -76.53 -76.16
Vapour
-34.79 -35.01 -35.22 -35.44 -35.66 -35.88 -36.10 -36.32 -36.54 -36.77 -36.99 -37.22 -37.44 -37.67 -37.90 -38.14 -38.37 -38.61 -38.85 -39.09 -39.33 -39.58
Vaporization
49.10 48.52 47.94 47.36 46.77 46.19 45.60 45.02 44.43 43.84 43.25 42.66 42.06 41.47 40.87 40.27 39.66 39.05 38.44 37.82 37.20 36.58
Temp (°C) 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 29.5
Press (bar) 43.92 45.02 46.15 47.30 48.47 49.66 50.87 52.11 53.37 54.65 55.96 57.29 58.65 60.03 61.44 62.88 64.34 65.84 67.36 68.92 70.51 71.32
Liquid
-73.05 -72.64 -72.24 -71.82 -71.41 -70.98 -70.55 -70.12 -69.67 -69.22 -68.75 -68.27 -67.78 -67.27 -66.74 -66.18 -65.60 -64.97 -64.29 -63.52 -62.61 -62.07
Vapour
-41.71 -42.00 -42.30 -42.60 -42.92 -43.24 -43.57 -43.92 -44.28 -44.65 -45.04 -45.45 -45.88 -46.34 -46.83 -47.36 -47.94 -48.57 -49.29 -50.13 -51.17 -51.82
Vaporization
31.34 30.64 29.94 29.22 28.49 27.74 26.98 26.20 25.39 24.56 23.71 22.82 21.89 20.93 19.91 18.82 17.66 16.40 14.99 13.38 11.44 10.25
5
6 C A R B O N DIOXIDE THERMODYNAMIC PROPERTIES H A N D B O O K
Table 3 Entropy (J/mol»K) of Saturated Carbon Dioxide (cont.)
Temp (°C) 2 3 4 5 6 7 8
Press (bar) 36.73 37.70 38.69 39.70 40.72 41.77 42.83
Liquid
Vapour
Vaporization
Temp ( 30.0 30.2 30.4 30.6 30.8 30.97 30.98
Press (bar) 72.14 72.47 72.80 73.13 73.47 73.77 73.77
Liquid
Vapour
Vaporization
4 Heat Capacity, Cp, (J/mol · K) of Saturated Carbon Dioxide
Table 4 Heat Capacity, Cp, (J/mol*K) of Saturated Carbon Dioxide
Temp (°C) -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
Press (bar) 19.7 20.31 20.94 21.58 22.24 22.91 23.59 24.29 25.01 25.74 26.49 27.25 28.03 28.82 29.63 30.46 31.3 32.16 33.04 33.94 34.85 35.78 36.73
Liquid 95.29 95.80 96.33 96.88 97.46 98.07 98.70 99.36
100.1 100.8 101.5 102.3 103.2 104.1 105.0 106.0 107.0 108.1 109.3 110.6 111.9 113.3 114.8
Vapour 56.74 57.54 58.37 59.23 60.13 61.07 62.05 63.07 64.13 65.25 66.41 67.64 68.92 70.26 71.68 73.18 74.76 76.42 78.19 80.07 82.07 84.20 86.47
Temp (°C) 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 29.5 30.0
Press (bar) 43.92 45.02 46.15 47.3 48.47 49.66 50.87 52.11 53.37 54.65 55.96 57.29 58.65 60.03 61.44 62.88 64.34 65.84 67.36 68.92 70.51 71.32 72.14
Liquid 129.1 131.9 135.0 138.4 142.2 146.5 151.2 156.6 162.7 169.8 178.0 187.6 199.2 213.3 231.0 253.8 284.6 328.3 394.9 508.3 745.8 999.6
1555
Vapour 108.3 112.6 117.3 122.6 128.5 135.0 142.5 150.9 160.6 171.8 185.0 200.7 219.6 242.9 272.2 310.2 361.4 434.0 544.8 734.6
1133 1554 2457
7
8 C A R B O N DIOXIDE THERMODYNAMIC PROPERTIES HANDBOOK
Table 4 Heat Capacity, Cp (J/mol»K) of Saturated Carbon Dioxide (cont.)
Temp (°C) 3 4 5 6 7 8
Press (bar) 37.7 38.69 39.7 40.72 41.77 42.83
Liquid 116.4 118.1 120.0 122.0 124.2 126.5
Vapour 88.91 91.53 94.36 97.41
100.7 104.3
Liquid 2010 2831 4678
16920 42140
0 0
5 Density (kg/m3) of Carbon Dioxide as a Function of Temperature and Pressure
Table 5 Density (kg/m3) of Carbon Dioxide as a Function of Temperature and Pressure
Temp (°C) -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
lbar 2.109 2.100 2.092 2.084 2.075 2.067 2.059 2.051 2.043 2.035 2.027 2.019 2.011 2.003 1.996 1.988 1.980 1.973 1.965 1.958 1.951 1.944 1.936
2 bar 4.255 4.237 4.220 4.202 4.185 4.168 4.151 4.134 4.118 4.101 4.085 4.069 4.052 4.036 4.021 4.005 3.989 3.974 3.958 3.943 3.928 3.913 3.898
3 bar 6.441 6.413 6.386 6.358 6.332 6.305 6.279 6.252 6.227 6.201 6.176 6.150 6.125 6.101 6.076 6.052 6.028 6.004 5.980 5.956 5.933 5.910 5.887
4 bar 8.667 8.629 8.591 8.553 8.516 8.479 8.443 8.407 8.371 8.336 8.300 8.266 8.231 8.197 8.163 8.130 8.097 8.064 8.031 7.999 7.967 7.935 7.903
5 bar 10.94 10.89 10.84 10.79 10.74 10.69 10.65 10.60 10.55 10.51 10.46 10.42 10.37 10.33 10.28 10.24 10.20 10.16 10.11 10.07 10.03 9.989 9.948
6 bar 13.25 13.19 13.13 13.07 13.01 12.95 12.89 12.83 12.77 12.72 12.66 12.60 12.55 12.49 12.44 12.38 12.33 12.28 12.23 12.18 12.12 12.07 12.02
7 bar 15.62 15.54 15.47 15.39 15.32 15.25 15.17 15.10 15.03 14.96 14.90 14.83 14.76 14.70 14.63 14.56 14.50 14.44 14.37 14.31 14.25 14.19 14.13
9
10 C A R B O N DIOXIDE THERMODYNAMIC PROPERTIES H A N D B O O K
Table 5 Density (kg/m3) of Carbon Dioxide as a Function of Temperature and Pressure (cont.)
Temp (°C) 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
l b a r 1.929 1.922 1.915 1.908 1.901 1.894 1.887 1.880 1.874 1.867 1.860 1.854 1.847 1.841 1.834 1.828 1.821 1.815 1.809 1.803 1.796 1.790 1.784 1.778 1.772 1.760 1.754 1.748 1.743 1.737 1.731 1.725 1.720 1.714 1.709 1.703 1.697 1.692 1.687 1.681 1.676