Centrifugal compressor performance prediction relies heavily on accurate modelling of thermodynamic properties using Equations of State (EOS); In particular, the gas compressibility factor (Z) and ratio of specific heat (k). There have been efforts to develop more generalised EOS such as GERG, but the challenge remains on identifying the best EOS fit for specific duties. More recent EOS including AGA8 and REFPROP’s NIST EOS haven been explored in this paper, along with some earlier ones. The boundary limits of the various EOS are herein described with comparison of the results of all of these equations on various gas mixtures encountered in real applications. The purpose of this work is to explore the more thermodynamically challenging heavy gas and mixtures. Operating points are selected to cover typical duties that are commonly encountered in LNG and offshore compression. Z and k derived from the EOS are then compared with REFPROP’s EOS as a reference and the deviations are tabulated. More specifically, Mixed Refrigerant gases are typically used for LNG liquefaction applications while CO2 gas are common in sour gas fields, hence relevant for the intended investigation. Discharge temperature is not calculated and compared between EOS in this paper; a reliable model for calculating polytropic exponents is open for further research.

1. Equations For Heavy Gases in Centrifugals
Lee Chong Jin (Team leader)
Mohd Zakiyuddin Mohd Zahari
Cheah Cang To
James Bryan
- Rotating Equipment Department, Technip Geoproduction Malaysia
August 12, 2014

2. Abstract
Centrifugal compressor performance prediction relies heavily on accurate modelling of thermodynamic properties using Equations of State (EOS); In particular, the gas compressibility factor (Z) and ratio of specific heat (k). There have been efforts to develop more generalised EOS such as GERG, but the challenge remains on identifying the best EOS fit for specific duties.
More recent EOS including AGA8 and REFPROP’s NIST EOS haven been explored in this paper, along with some earlier ones. The boundary limits of the various EOS are herein described with comparison of the results of all of these equations on various gas mixtures encountered in real applications.
The purpose of this work is to explore the more thermodynamically challenging heavy gas and mixtures. Operating points are selected to cover typical duties that are commonly encountered in LNG and offshore compression. Z and k derived from the EOS are then compared with REFPROP’s EOS as a reference and the deviations are tabulated.
More specifically, Mixed Refrigerant gases are typically used for LNG liquefaction applications while CO2 gas are common in sour gas fields, hence relevant for the intended investigation.
Discharge temperature is not calculated and compared between EOS in this paper; a reliable model for calculating polytropic exponents is open for further research.

3. Nomenclature
Symbols
( ) ( )
Abbreviations
The following are abbreviations of the different EOS names used throughout the report:
( )

4. Eq. 1
Eq. 2
Fundamentals
The Compressibility Factor, Z, is the fundamental thermodynamic property for modifying the ideal gas law to account for the real gas behavior. Z is introduced into the Ideal Gas equation [1]:
Due to the various factors involved such as having infinite possible combinations of ratios between each component in a gas mixture, it is infeasible to develop an EOS that will accurately calculate Z across a wide combination of operating conditions (in terms of gas compositions, temperatures and pressures).
With the specific heat ratio, k, polytropic exponents can be obtained and in turn gas compression can then be expressed in terms of pressure and temperature variation [2]: ( )
The power required to compress a gas is directly proportional to the gas compressibility factor, Z. For an ideal gas, Z=1 regardless of the gas’ state. Since in practice Z changes depending on the gas conditions P and T, power calculation will deviate between a real gas and ideal gas calculation by as much as the Z deviates. Similarly, k affects the accuracy of the head and power equations.
Therefore, it is worth investigating the different EOS that can be used to obtain Z and k for a specified mixture and operating condition. The EOS that are investigated in this report are tabulated in Table 1:
Equation of State
General Form of Equation
Redlich-Kwong (RK) [1]
( )√
Soave-Redlich-Kwong (SRK) [1]
( )
Peng-Robinson (PR) [1]
( ) ( )
Benedict-Webb-Rubin- Starling & Han modified by Nishiumi & Saito (BWRS- NS) [3][4]
( ) ( ) ( ) ( ) ( ) ( )
Lee-Kesler-Plöcker (LKP) [1]
( ) ( )
AGA8 [5]
Σ Σ ( ) ( )
GERG (2004) [6]
(Σ ( ) ΣΣ ( ) )
NIST [7]
Based on GERG2008 which is an updated GERG2004 EOS

5. Eq. 3
Eq. 4
Table 1: Equations of States analysed and the general form of the equation.
REFPROP, a commercially available program developed by the National Institute of Standards and Technology (NIST), performs estimation of real gas thermodynamic properties based on three models for the thermodynamic properties of pure fluids: EOS explicit in Helmholtz energy, the modified Benedict-Webb-Rubin equation of state, and an extended corresponding states (ECS) model [7]. Equation of state modules available from the REFPROP package are:-
1. AGA 8 (for pipelines)
2. GERG 2008
3. Peng-Robinson (PR)
4. NIST
The NIST EOS is primarily based on the GERG 2008 EOS (which is used in [8;9;10;11]), in turn expanded from GERG 2004 to include additional fluids (e.g. ethylene, propylene, methanol, etc.). NIST's database is widely recognised as a reliable source of reference in terms of real gas behaviour, as can be traced in both the academic and turbo-machinery industry [12;13;14;15]. Thus, with the established database in REFPROP software, the default NIST EOS will be the benchmark EOS which other EOS will be referred to for the purpose of this paper.
The standalone EOS (not included in REFPROP) compiled by the authors for the purpose of this discussion are as follows:-
1. Redlich-Kwong (RK)
2. Lee-Kesler-Plӧcker (LKP)
3. Modified Benedict, Webb, Rubin, Starling and Han by Nishiumi and Saito (BWRS-NS)
4. Soave-Redlich-Kwong (SRK)
RK and SRK EOS are relatively straightforward to model as they are cubic EOS. Virial EOS such as BWRS-NS and LKP are developed as an improvement to the former; These are EOS which represents a power series of density with temperature coefficients [1]:
The roots in these virial EOS are evaluated using the Newton-Raphson method where the initial guess for compressibility factor is set to be 0.8 for the vapor phase [1]. AGA8 which is an extended virial equation is even lengthier where it contains summations of 58 polynomial terms.
BWRS-NS is selected over the standard BWRS model for its wider range of operations; specifically in the cryogenic range [3]. Nevertheless, BWRS would still suffice for noncryogenic CO2 duties.
In the absence of REFPROP, the Multiparameter EOS such as GERG could also be modelled. GERG is represented in the Helmholtz Free Energy form in terms of reduced density and inverse reduced temperature [6]: ( ) ( ) ( )

6. Comparison of Z & k between different EOS
For a given pressure, temperature and gas mixture, different EOS will yield different values of Z and k. The goal would be to tabulate and understand the differences between each EOS for various gas compositions. One way to demonstrate the differences is by plotting graphs of Z and k versus pressure (at a specific temperature) for different EOS. This plot shows how the different EOS varies with each other over the range of pressures. Note that we can also choose to plot Z versus temperature for specific pressures instead, however for convention sake plots of Z versus pressure will be used (i.e. in the standard form of Nelson-Obert compressibility charts). [16]
By investigating the different EOS, if results are very similar for specific EOS for certain common gasses then the results can be interchangeable for future comparisons. In general, at lower pressure and higher temperature it is expected that the different EOS should corroborate better among each other as the conditions are approaching that of an Ideal Gas, thus yielding a more accurate and predicable model.
To ensure accurate and consistent results, the operating ranges for a given gas mixture are selected to ensure the fluid is in a pure gas state, and not as a multi-phase, liquid-phase fluid or near the critical point. This is verified by plotting a Phase Map using REFPROP NIST (i.e. vapor-liquid equilibrium curves) and ensuring the operating points chosen are in the gas phase region. Operating points are selected based on typical compressor applications of each gas, such as refrigerant compressors and high-pressure CO2 reinjection duties.
As stated previously, NIST’s EOS from the REFPROP software is widely recognized as a reliable EOS and thus will be used as the reference for a comparison datum for other EOS. REFPROP software is used to calculate Z and k for NIST, GERG, AGA8 and PR EOS. RK, SRK, BWRS-NS and LKP are not available in REFPROP and thus are compiled individually by the authors. Deviations will be quoted in terms of % deviation from NIST. Since NIST is an updated form of the GERG (2004) EOS, it is expected that the NIST and GERG2004 will have negligible deviation.
The different EOS are utilized for the calculation of Z and k for Mixed Refrigerant Gas, Pure CO2 gas and a CO2 gas mixture. For reference, Pure Methane and a Natural Gas Mixture is also investigated as the properties of methane are well-established.
Note that for mixture comparisons, RK is not used due to lack of interaction parameters on-hand. Instead, AGA8 is used. AGA8 is not used for pure fluids because in REFPROP, AGA8 is only used for mixtures and will revert back to NIST EOS when calculating pure fluids.

7. Compressibility and Cp/Cv vs Pressure Graphs
Figure 1: Compressibility Z vs Pressure for Methane gas at T=210K and T=300K
Figure 1 illustrates a typical compressibility graph of Z vs P for pure Methane using the various EOS. On the left side of the graph close to P=0 bara, it can be seen that all the EOS converges to 1. This signifies the point where the gas behaves closest to an ideal gas; the lower the P, the less collisions and force interactions between the gas molecules. As P increases, gas intermolecular forces become prevalent. This causes the gas molecules to occupy a denser space (Z reduces) than predicted by the ideal gas model. Each EOS notably branches off from each other; the different EOS models have their own set of parameters to estimate Z with varying degrees of accuracy. As P is increased even further, Z slowly increases due to the physical size of the molecules (Ideal gas model neglects gas molecule size).
At lower temperatures, the gas molecules’ kinetic energy is low enough that the interaction forces between molecules are prevalent. Thus, there is a huge variation in Z as P increases. As T is increased however, the kinetic energy of the gas molecules renders the interaction forces to be less significant which approaches the ideal gas model. Thus the curve starts to approach a flatter, straight line closer to Z=1 throughout the range of P. This trend is visible in Figure 1 by comparing the two curves at T=210K and T=300K.

8. The Critical Point of Methane is at P=46bara and T=190.6k. Thus, data to the right of the critical P line in Figure 1 in this case are within the Supercritical Region.
Figure 2: Specific Heat Ratio (k=Cp/Cv) vs Pressure for Methane gas at T=210K and T=300K
Similarly, the Specific Heat Ratios, k can be plotted versus P, as seen in Figure 2. As the ratio k=Cp/Cv and Cp>Cv in all cases, the graph for k is always above k=1. A notable feature is that near the critical point, the EOS spikes to infinity yielding erroneous results. This issue is not apparent on the Z graph, thus it is possible to obtain operating points near the critical point where values of Z appear sensible while k becomes overly sensitive. The curve slowly flattens out as Temperature is increased beyond Tc. Deviations of k also increase when P increases as the gas deviates from the Ideal Gas model.
It is not practical to present the entire range of data on this paper as this requires a 3D graph to effectively plot Z for various P and T; even then, it will be difficult to compare multiple 3d surfaces representing each EOS. Therefore, selected operating points applicable for the gas examined will be used to compare Z and k to evaluate how the EOS differ from each other.

9. Pure Methane
Methane is the simplest alkane molecule and the main constituent in natural gas, serving as a reference to establish the comparisons between EOS. Selected points are chosen rather than presenting all the data on a graph here as it is impractical to overlay all the data of the various EOS.
Operating Point 1 represents boil-off gas conditions. Operating points 2-7 represent typical values of a natural gas compressor.
Operating Point
1
2
3
4
5
6
7
Pressure, bar a
1.01
13.82
24.41
24.6
105.66
56.42
128.94
Temp, K
115
320
320
350
350
380
380
Table 2: Selected Operating Points for Pure Methane
Note that the critical point of methane is at 46bara, 191K. None of the operating points are selected near this value.
-0.5
0
0.5
1
1.5
2
1
2
3
4
5
6
7
%Deviation Z
Operating Points
Deviation of Z for Pure Methane
Z GERG
Z LKP
Z BWRSNS
Z SRK
Z PR
Z RK

10. Figure 3 & 4: Deviation of Z and k for Pure Methane
Z: With reference to NIST, it can be seen that for Z most of the EOS agree with each other within these ranges; exhibiting deviations <0.5% except for SRK at higher P and T. LKP appears to be the most consistent throughout the range with the lowest deviations. SRK on the other hand appears to deviate more as P and T increases by up to nearly 2%. What appears promising is that even at low T of 115K (i.e. near boil-off gas conditions), the EOS all fall within 0.4%< deviation.
k: Specific heat ratios (k) on the other hand do not follow the same trend even with the same operating conditions. It is apparent that SRK has generally the least deviations this time, however the trend indicates that k for SRK gradually shifts to negative deviation as P increase. For BWRS-NS the opposite is observed; k gradually shifts to positive deviation as P increase. LKP and PR demonstrates stable deviations throughout the range. Again, at 115K, the EOS are within 0.5%< deviation.
Hence for Z, all the EOS throughout the range (even for low T) fall within +- 0.5% deviation except for SRK at higher P (>50bara). For k, all the EOS throughout the range (even for low T) fall within +- 0.5% deviation except for RK at higher P (>50bara).
-2
-1.5
-1
-0.5
0
0.5
1
1
2
3
4
5
6
7
%Deviation k
Operating Points
Deviation of k for Pure Methane
k GERG
k LKP
k BWRSNS
k SRK
k PR
k RK

11. Natural Gas Mixture
The difficulty of modeling mixtures arises from the interactions between the different components. Thus, more reliable EOS consider the interactions by using binary interaction parameters. By considering the effects between each pair of compounds in a mixture and taking an average, a more accurate result for the calculation of EOS parameters is obtained. Hence, it is expected that the EOS will result in higher deviations for mixtures than pure components.
With the analysis of EOS for pure Methane, it can be predicted that a natural gas composition will exhibit similar trends for Z and k. A sample typical natural gas mixture consisting of 82% methane is analysed using similar operating points to pure methane gas. The exact composition can be found in Appendix A.
Operating Point
1
2
3
4
5
6
Pressure, bar a
10.91
21.42
24.3423
102.8026
55.93
126.52
Temp, K
320
320
350
350
380
380
Table 3: Selected Operating Points for Natural Gas Mixture
-1
-0.5
0
0.5
1
1.5
2
2.5
1
2
3
4
5
6
%Deviation Z
Operating Points
Deviation of Z for Natural Gas
Z GERG
Z LKP
Z BWRSNS
Z SRK
Z PR
Z AGA8

12. Figure 5 & 6: Deviation of Z and k for Natural Gas Mixture
As predicted, the results of the graphs (Figures 1 & 3, 2 & 4) for natural gas are similar to the pure Methane gas graph except with slightly more deviations.
Z: For Natural Gas data, it is observed that LKP gives stable results; with less than 0.5% deviation for each data. However, the results show that AGA8 show the least deviation throughout the range; demonstrating great correlation with NIST for natural gas mixtures. As predicted, SRK again exhibits large deviations up to 2% at high P and T. PR has low deviations in this range but may overshoot at higher P and T; same goes for BWRS-NS.
k: AGA8 represents the closest EOS to NIST but deviates more significantly at the higher P>100bara (around 0.5%). SRK still models k well comparatively (around 0.25% at most) despite poor comparison with Z, however k continues to deviate more negatively as P and T increase. PR basically demonstrates to be a worse SRK in this mixture. LKP remains fairly consistent with deviations throughout the range around 0.25%.
Overall, it can be concluded that for the ranges above, AGA8 resembles closest to NIST for this methane-predominant mixture. Otherwise, LKP is also a strong contender for Z, and LKP/SRK for k. However within the P and T ranges analysed above, most EOS do agree well with each other as deviations are at most 1%. Therefore for a natural gas mixture with similar composition to the above, any of the above EOS can be used and a deviation of not more than 1% for Z and k can be expected (except for RK and SRK at higher P).
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
2
3
4
5
6
%Deviation k
Operating Points
Deviation of k for Natural Gas
k GERG
k LKP
k BWRSNS
k SRK
k PR
k AGA8

13. Mixed Refrigerant Gas
Mixed refrigerant gas consists of a wider range of heavier hydrocarbons compared to a typical natural gas mixture and therefore has a significantly heavier molecular weight. Since the longer chain hydrocarbon molecules come into the picture, their size and interaction are important to consider. A sample gas consisting primarily of Methane, Ethylene and Butane is investigated for the following operating conditions:
Operating Point
1
2
3
4
5
6
Pressure, bar a
3.35
16.73
16.73
43.48
43.48
56.86
Temp, K
300
310
390
360
400
400
Table 4: Selected Operating Points for Mixed Refrigerant Gas
Note that the critical point of this mixture is at 103bara, 334K. The operating P typically do not exceed the critical P. GERG2004 does not contain parameters for ethylene and propylene, therefore is excluded from the analysis of this mixed refrigerant composition.
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
1
2
3
4
5
6
%Deviation Z
Operating Points
Deviation of Z for Mixed Refrigerant Gas
Z LKP
Z BWRSNS
Z SRK
Z PR
Z AGA8

14. Figure 7 & 8: Deviation of Z and k for Mixed Refrigerant Gas
Z: Compared to the primarily Methane mixture, some larger deviations can be observed. PR and BWRS-NS appears to be the more stable EOS; with a deviations below 1%. The other EOS demonstrates inconsistent trends even at lower P; AGA8 and LKP exceed 1% deviation at higher P to T ratios.
K: Again, trends appear inconsistent especially for AGA8. The most stable EOS appears to be BWRS-NS, however there is excellent correlation between EOS at Operating Points 1 and 3 (i.e. at relatively lower P values with sufficient T).
Overall, BWRS-NS seems like a safer option for Z and k to compare with NIST for this heavier hydrocarbon mixture especially at higher pressure and temperature conditions. However, PR performs relatively well too for computing Z. The other EOS are expected to deviate at least 1% at higher P.
-1.5
-1
-0.5
0
0.5
1
1.5
1
2
3
4
5
6
%Deviation k
Operating Points
Deviation of k for Mixed Refrigerant Gas
k LKP
k BWRSNS
k SRK
k PR
k AGA8

15. Pure Carbon Dioxide
Carbon Dioxide (CO2) is more difficult to model accurately, as its properties are far from an ideal gas. As it is a linear molecule, it has a high acentric factor (i.e. highly non-spherical). This affects the interaction between the molecules in the gas, yielding inaccurate values of Z and k if not taken into account. CO2 is of interest in oil & gas for CO2 reinjection, thus high pressure ranges are investigated for comparison.
Operating Point
1
2
3
4
5
6
7*
8
9
10
Pressure, bar a
32
48.1
54.1
62.9
79.6
95.6
100.6
416.8
481
520
Temp, K
310
350
320
370
400
420
320
400
400
430
Table 5: Selected Operating Points for Pure Carbon Dioxide
*The critical point of CO2 is at 73.77bara, 304.1K. Operating point 7 is reasonably close and therefore may result in anomalous results.
Figure 9 & 10: Deviation of Z and k for Pure CO2 Gas
-4
-2
0
2
4
6
8
10
12
14
1
2
3
4
5
6
7
8
9
10
%Deviation Z
Operating Points
Deviation of Z for Pure CO2
Z GERG
Z LKP
Z BWRSNS
Z SRK
Z PR
Z RK
-20
-15
-10
-5
0
5
10
1
2
3
4
5
6
7
8
9
10
%Deviation k
Operating Points
Deviation of k for Pure CO2
k GERG
k LKP
k BWRSNS
k SRK
k PR
k RK

16. Z: Below the critical point, LKP and BWRS-NS have the lowest deviations to NIST (<1%). At P=100.57bara and T=320K which is close to the critical point of CO2, most EOS have massive deviations with NIST. At this point, only LKP demonstrates astonishingly high correlation with NIST, while the other EOS deviates by at least 7%. RK performs surprisingly well throughout these conditions, deviating at most 2% throughout the range. RK does not take acentric factor into account when calculating Z and k, thus for CO2 it was expected that RK will have large deviations from NIST. Beyond the critical point - at supercritical conditions (Operating Points 8, 9, 10), some EOS exhibits larger inconsistencies to NIST; with SRK having up to 8% deviations. In general however, LKP and PR shows the most consistent deviation with NIST at around 1% even in supercritical regions.
k: Massive deviations can be seen throughout the range, with average deviations at least 2% among the EOS. This is because k is more sensitive than Z - especially near the critical point; k theoretically shoots to infinity while Z is not affected. Below the critical point, BWRS-NS and surprisingly RK demonstrate excellent correlation with NIST. In the supercritical region, each EOS deviates by large amounts with each other and thus, it is unsafe to draw a general conclusion as to the validity of the EOS models.
Thus, for Z it is generally safe to use LKP as the EOS with the lowest deviation to NIST. PR may be used for Z in the supercritical region (about 1% Deviation). However for k, it is advised there will be deviations between EOS of at least 2% in the supercritical region. Otherwise, below the critical point BWRS-NS and RK does comparatively well (<1.5% Deviation).

17. CO2 Gas mixture
For CO2 reinjection purposes, a 95% CO2 gas mixture is analysed. Again, similar operating points are selected inline with the pure CO2 gas for comparison purpose; It is expected that the trends of both graphs should be similar.
Operating Point
1
2
3
4
5
6
7**
8
9
10
Pressure, bar a
30.99
46.29
52.84
60.36
75.9
90.75
100.85
415.61
475.1
536.18
Temp, K
310
350
320
370
400
420
320
400
400
430
Table 6: Selected Operating Points for CO2 Gas Mixture
**The critical point of CO2 is at 73.77bara, 304.1K. Since this gas mixture consists of 95% CO2, the mixture’s critical point is expected to be very similar to pure CO2. Operating point 7 is reasonably close and therefore may result in anomalous results.
Figure 11 & 12: Deviation of Z and k for CO2 Gas Mixture
-2
0
2
4
6
8
1
2
3
4
5
6
7
8
9
10
%Deviation Z
Operating Points
Deviation of Z for CO2 Gas Mixture
Z GERG
Z LKP
Z BWRSNS
Z SRK
Z PR
Z AGA8
-10
-8
-6
-4
-2
0
2
4
6
8
10
1
2
3
4
5
6
7
8
9
10
%Deviation k
Operating Points
Deviation of k for CO2 Gas Mixture
k GERG
k LKP
k BWRSNS
k SRK
k PR
k AGA8

18. Z: Similar to the pure CO2 graph, LKP demonstrates consistently low deviations throughout the range. However for mixtures, the correlation between AGA8 and NIST is unrivalled; only deviating notably near the critical point. At P higher than Tc, LKP and PR compares reasonably well with NIST at 1% deviation but AGA8 correlates much better.
k: Similar to pure CO2, BWRS-NS correlates well with NIST below the critical point (<1% Deviation). Near the critical point, all of the EOS examined tend to deviate significantly; PR, SRK and BWRS-NS deviates around 8-10%. In the supercritical region, again it is not possible to establish with confidence the validity of the results due to the large deviations between EOS.
A similar conclusion for CO2 mixture can be drawn; LKP is fairly reliable for Z across the range, and BWRS-NS correlates well with NIST below the critical point for k. However, AGA8 demonstrates the best comparison with NIST for both Z and k for CO2.
Conclusion
The selection of a reliable EOS ensures more accurate calculation of a compressor’s power and discharge temperature. By establishing NIST as a datum, results of Z and k of different EOS for Mixed Refrigerant and CO2 duties were compared.
For predominantly methane based mixtures, most EOS agree well with each other as the properties of methane are well established (0.5% average deviation for Z and k). However, heavier hydrocarbon mixtures such as Mixed Refrigerants and CO2 gas demonstrate larger deviations among EOS. The results are summarised in Table 7. The following EOS are therefore recommended (with some caution):
Mixture
Recommended EOS
Remarks (% Deviation with respect to NIST EOS)
Z
k
Mixed Refrigerants
BWRS-NS, PR
BWRS-NS
<0.5% for Z and k (BWRS-NS),
<1% for Z (PR)
Pure CO2 (gas)
LKP/BWRS- NS
BWRS-NS
<1% for Z and <0.5% for k
Pure CO2 (supercritical)
LKP/PR
-
1% for Z, k inconclusive
CO2 Gas Mixtures (gas)
AGA8
AGA8
<0.2% for Z and <1% for k
LKP/BWRS- NS
BWRS-NS
<1% for Z and k
CO2 Gas Mixtures (supercritical)
LKP/PR
-
1% for Z, k inconclusive
Table 7: Summary of EOS comparisons with NIST EOS
The findings are generally in agreement with those of authorities such as Sandberg [17] and Lüdtke [18], where BWRS and LKP are already shown to be reliable EOS models.
This also emphasizes the need for vendors to justify their EOS selection when providing quotes to consultant engineers - especially for mixed refrigerants and CO2. Typically, datasheets of compressors provided by vendors do not clarify the EOS used in calculation of the Z and k values. Therefore, it is not possible to verify the values as different EOS will have deviations between each other. Clarification will ensure consistency between both parties, and consequently better confidence to the operator/end-user of the compressor.

19. References
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[16] Yunus A. Cengel, Michael A. Boles (2005) Thermodynamics: An Engineering Approach 5th Edition, McGraw-Hill College, Boston, MA
[17] Mark R. Sandberg (2005) Equation of State Influences on Compressor Performance Determination, 34th Turbomachinery Symposium
[18] H. K. Lüdtke (2004) Process Centrifugal Compressor: Basics, Function,
Operation, Design, Application, 1st Edition, Springer

20. Appendix A – Gas Mixture Compositions
Gas composition
Natural Gas Mixture
Mixed Refrigerant
CO2 Gas Mixture
Mole fraction
Methane
0.829700
0.257800
0.041018
Nitrogen
0.060810
0.079780
0.001157
Carbon dioxide
0.029040
0.000000
0.947150
Ethane
0.042890
0.002530
0.005496
Propane
0.017600
0.016730
0.002540
n-Butane
0.005328
0.047480
0.000393
i-Butane
0.003198
0.215113
0.000558
n-Pentane
0.001838
0.000078
0.000131
i-Pentane
0.001929
0.001319
0.000210
n-Hexane
0.001500
0.000000
0.000245
n-Heptane
0.004157
0.000000
0.001103
Water
0.002010
0.000000
0.000000
Ethylene
0.000000
0.378900
0.000000
Propylene
0.000000
0.000270
0.000000
Appendix B – Tabulated values of Z and k of the gas compositions for various EOS
NIST, GERG, AGA8 and PR EOS calculations are done via REFPROP software. RK, SRK, LKP and BWRS-NS calculations are compiled by the authors independantly.
Pure Methane
Pressure, bar a
Temp, K
Z NIST
Z GERG
Z LKP
Z BWRS-NS
Z SRK
Z PR
Z RK
1.01
115
0.9671
0.9674
0.9667
0.9685
0.9704
0.9699
0.9691
%Deviation to NIST
0.00
0.03
-0.05
0.14
0.34
0.29
0.20
13.82
320
0.9820
0.9820
0.9826
0.9806
0.9830
0.9790
0.9808
%Deviation to NIST
0.00
0.00
0.06
-0.14
0.10
-0.30
-0.12
24.41
320
0.9687
0.9687
0.9697
0.9665
0.9706
0.9639
0.9667
%Deviation to NIST
0.00
0.00
0.11
-0.22
0.20
-0.49
-0.20
24.59628
350
0.9786
0.9786
0.9793
0.9763
0.9809
0.9750
0.9766
%Deviation to NIST
0.00
0.00
0.07
-0.24
0.24
-0.36
-0.20
105.6605
350
0.9280
0.9280
0.9315
0.9306
0.9429
0.9260
0.9248
%Deviation to NIST
0.00
0.00
0.38
0.28
1.61
-0.21
-0.34
56.42
380
0.9706
0.9706
0.9718
0.9675
0.9772
0.9667
0.9668
%Deviation to NIST
0.00
0.00
0.12
-0.31
0.68
-0.39
-0.39
128.94
380
0.9525
0.9525
0.9563
0.9583
0.9700
0.9532
0.9479
%Deviation to NIST
0.00
0.01
0.40
0.61
1.84
0.07
-0.48
Pure Methane
Pressure, bar a
Temp, K
k NIST
k GERG
k LKP
k BWRS-NS
k SRK
k PR
k RK
1.01
115
1.3693
1.3697
1.3760
1.3733
1.3680
1.3627
1.3709
%Deviation to NIST
0.00
0.03
0.49
0.29
-0.10
-0.48
0.12
13.82
320
1.3250
1.3250
1.3221
1.3222
1.3266
1.3293
1.3229
%Deviation to NIST
0.00
0.00
-0.21
-0.21
0.12
0.32
-0.16
24.41
320
1.3504
1.3503
1.3464
1.3469
1.3539
1.3579
1.3472
%Deviation to NIST
0.00
-0.01
-0.30
-0.26
0.26
0.56
-0.24
24.60
350
1.3232
1.3231
1.3197
1.3206
1.3252
1.3288
1.3201
%Deviation to NIST
0.00
-0.01
-0.26
-0.20
0.15
0.42
-0.23
105.66
350
1.4822
1.4818
1.4761
1.4844
1.4803
1.4905
1.4597
%Deviation to NIST
0.00
-0.02
-0.41
0.15
-0.13
0.56
-1.52
56.42
380
1.3445
1.3443
1.3401
1.3433
1.3465
1.3521
1.3380
%Deviation to NIST
0.00
-0.02
-0.33
-0.09
0.15
0.56
-0.48
128.94
380
1.4462
1.4456
1.4412
1.4502
1.4398
1.4490
1.4223
%Deviation to NIST
0.00
-0.04
-0.35
0.28
-0.45
0.19
-1.66
Natural Gas Mixture

21. Pressure, bar a
Temp, K
Z NIST
Z GERG
Z LKP
Z BWRS-NS
Z SRK
Z PR
Z AGA8
10.91
320
0.9811
0.9811
0.9819
0.9802
0.9817
0.9781
0.9811
%Deviation to NIST
0.00
0.00
0.08
-0.09
0.06
-0.31
0.00
21.42
320
0.9632
0.9632
0.9647
0.9617
0.9647
0.9578
0.9634
%Deviation to NIST
0.00
0.00
0.15
-0.16
0.16
-0.56
0.01
24.3423
350
0.9711
0.9711
0.9722
0.9693
0.9734
0.9665
0.9713
%Deviation to NIST
0.00
0.00
0.12
-0.19
0.24
-0.47
0.02
102.8026
350
0.9003
0.9004
0.9032
0.9049
0.9164
0.8972
0.9025
%Deviation to NIST
0.00
0.01
0.32
0.51
1.78
-0.35
0.24
55.93
380
0.9579
0.9579
0.9596
0.9558
0.9650
0.9528
0.9585
%Deviation to NIST
0.00
0.00
0.17
-0.22
0.74
-0.54
0.05
126.52
380
0.9286
0.9287
0.9315
0.9365
0.9480
0.9285
0.9305
%Deviation to NIST
0.00
0.01
0.32
0.85
2.09
-0.01
0.21
Natural Gas Mixture
Pressure, bar a
Temp, K
k NIST
k GERG
k LKP
k BWRS-NS
k SRK
k PR
k AGA8
10.91
320
1.2921
1.2921
1.2898
1.2899
1.2938
1.2958
1.2921
%Deviation to NIST
0.00
-0.01
-0.18
-0.18
0.13
0.28
0.00
21.42
320
1.3206
1.3205
1.3168
1.3172
1.3247
1.3279
1.3204
%Deviation to NIST
0.00
-0.01
-0.29
-0.26
0.31
0.55
-0.02
24.3423
350
1.2991
1.2990
1.2958
1.2964
1.3023
1.3053
1.2986
%Deviation to NIST
0.00
-0.01
-0.26
-0.21
0.25
0.47
-0.04
102.8026
350
1.4820
1.4817
1.4783
1.4798
1.4840
1.4923
1.4743
%Deviation to NIST
0.00
-0.02
-0.25
-0.14
0.14
0.70
-0.52
55.93
380
1.3258
1.3256
1.3215
1.3235
1.3296
1.3345
1.3241
%Deviation to NIST
0.00
-0.02
-0.32
-0.17
0.29
0.65
-0.13
126.52
380
1.4414
1.4410
1.4387
1.4411
1.4374
1.4448
1.4342
%Deviation to NIST
0.00
-0.03
-0.19
-0.02
-0.27
0.24
-0.50
Mixed Refrigerant
Pressure, bar a
Temp, K
Z NIST
Z LKP
Z BWRS-NS
Z SRK
Z PR
Z AGA8
3.35
300
0.9762
0.9781
0.9754
0.9765
0.9747
0.9722
%Deviation to NIST
0.00
0.19
-0.08
0.03
-0.16
-0.42
16.73
310
0.8870
0.8963
0.8835
0.8890
0.8808
0.8664
%Deviation to NIST
0.00
1.04
-0.40
0.22
-0.70
-2.33
16.73
390
0.9504
0.9552
0.9487
0.9526
0.9457
0.9440
%Deviation to NIST
0.00
0.50
-0.18
0.23
-0.49
-0.68
43.48
360
0.8225
0.8371
0.8180
0.8302
0.8149
0.7985
%Deviation to NIST
0.00
1.78
-0.55
0.94
-0.92
-2.92
43.48
400
0.8838
0.8945
0.8806
0.8919
0.8773
0.8705
%Deviation to NIST
0.00
1.21
-0.36
0.92
-0.73
-1.51
56.86
400
0.8498
0.8630
0.8470
0.8621
0.8450
0.8346
%Deviation to NIST
0.00
1.55
-0.34
1.45
-0.57
-1.79
Mixed Refrigerant
Pressure, bar a
Temp, K
k NIST
k LKP
k BWRS-NS
k SRK
k PR
k AGA8
3.35
300
1.1959
1.1943
1.1959
1.1955
1.1960
1.1859
%Deviation to NIST
0.00
-0.13
0.00
-0.03
0.01
-0.84
16.73
310
1.2778
1.2692
1.2798
1.2799
1.2796
1.2908
%Deviation to NIST
0.00
-0.67
0.16
0.17
0.14
1.02
16.73
390
1.1823
1.1801
1.1827
1.1859
1.1854
1.1750
%Deviation to NIST
0.00
-0.18
0.03
0.30
0.26
-0.62
43.48
360
1.3471
1.3331
1.3517
1.3606
1.3577
1.3659
%Deviation to NIST
0.00
-1.04
0.34
1.00
0.78
1.40
43.48
400
1.2513
1.2446
1.2530
1.2598
1.2589
1.2496
%Deviation to NIST
0.00
-0.54
0.14
0.68
0.61
-0.13
56.86
400
1.2989
1.2901
1.3023
1.3096
1.3074
1.2988
%Deviation to NIST
0.00
-0.67
0.26
0.82
0.65
-0.01
Pure Carbon Dioxide
Pressure, bar a
Temp, K
Z NIST
Z GERG
Z LKP
Z BWRS-NS
Z SRK
Z PR
Z RK

22. 31.96
310
0.8448
0.8448
0.8406
0.8418
0.8469
0.8329
0.8454
%Deviation to NIST
0.00
0.00
-0.49
-0.35
0.25
-1.41
0.07
48.07
350
0.8503
0.8503
0.8487
0.8476
0.8554
0.8377
0.8418
%Deviation to NIST
0.00
0.00
-0.18
-0.31
0.60
-1.48
-1.00
54.05
320
0.7487
0.7487
0.7418
0.7437
0.7542
0.7329
0.7459
%Deviation to NIST
0.00
0.00
-0.93
-0.67
0.74
-2.12
-0.38
62.86
370
0.8415
0.8415
0.8413
0.8390
0.8508
0.8300
0.8280
%Deviation to NIST
0.00
0.00
-0.03
-0.30
1.10
-1.36
-1.61
79.61
400
0.8551
0.8550
0.8575
0.8535
0.8702
0.8473
0.8366
%Deviation to NIST
0.00
-0.01
0.28
-0.19
1.77
-0.90
-2.16
95.62
420
0.8605
0.8603
0.8647
0.8598
0.8808
0.8561
0.8386
%Deviation to NIST
0
-0.01
0.49
-0.07
2.37
-0.51
-2.54
100.57
320
0.3642
0.3644
0.3638
0.3924
0.4137
0.3910
0.3730
%Deviation to NIST
0.00
0.05
-0.11
7.73
13.58
7.36
2.40
416.84
400
0.8037
0.8036
0.8119
0.8301
0.8757
0.8210
0.8152
%Deviation to NIST
0.00
-0.01
1.03
3.30
8.97
2.16
1.44
480.90
400
0.8678
0.8677
0.8766
0.8910
0.9366
0.8763
0.8804
%Deviation to NIST
0.00
-0.01
1.01
2.67
7.93
0.98
1.44
520.02
430
0.9357
0.9355
0.9471
0.9671
1.0063
0.9454
0.9334
%Deviation to NIST
0.00
-0.02
1.21
3.36
7.55
1.03
-0.25
Pure Carbon Dioxide
Pressure, bar a
Temp, K
k NIST
k GERG
k LKP
k BWRS-NS
k SRK
k PR
k RK
31.96
310
1.5324
1.5327
1.5608
1.5408
1.5688
1.5702
1.5105
%Deviation to NIST
0.00
0.02
1.85
0.55
2.38
2.47
-1.43
48.07
350
1.5125
1.5123
1.5374
1.5196
1.5551
1.5586
1.5056
%Deviation to NIST
0.00
-0.01
1.65
0.47
2.82
3.05
-0.46
54.05
320
1.8137
1.8142
1.8838
1.8396
1.9101
1.9177
1.7882
%Deviation to NIST
0.00
0.03
3.87
1.43
5.32
5.74
-1.40
62.86
370
1.5344
1.5341
1.5611
1.5421
1.5801
1.5856
1.5330
%Deviation to NIST
0.00
-0.02
1.74
0.50
2.98
3.34
-0.09
79.61
400
1.5093
1.5089
1.5321
1.5146
1.5451
1.5525
1.5111
%Deviation to NIST
0.00
-0.02
1.51
0.35
2.38
2.86
0.12
95.62
420
1.5059
1.5055
1.5278
1.5102
1.5347
1.5434
1.5082
%Deviation to NIST
0.00
-0.03
1.46
0.29
1.91
2.49
0.15
100.57
320
7.1967
7.1328
6.9563
5.8332
7.4018
7.4032
5.8767
%Deviation to NIST
0.00
-0.89
-3.34
-18.95
2.85
2.87
-18.34
416.84
400
1.9801
1.9762
2.0692
2.1368
1.8982
1.9317
1.6844
%Deviation to NIST
0.00
-0.20
4.50
7.91
-4.14
-2.45
-14.93
480.90
400
1.9129
1.9087
2.0017
2.0962
1.8230
1.8595
1.6220
%Deviation to NIST
0.00
-0.22
4.64
9.58
-4.70
-2.79
-15.21
520.02
430
1.8221
1.8178
1.9000
1.9570
1.7314
1.7594
1.5766
%Deviation to NIST
0.00
-0.23
4.28
7.41
-4.98
-3.44
-13.47

23. CO2 Mixture
Pressure, bar a
Temp, K
Z NIST
Z GERG
Z LKP
Z BWRS-NS
Z SRK
Z PR
Z RK
30.99
310
0.8551
0.8551
0.8529
0.8524
0.8575
0.8439
0.8556
%Deviation to NIST
0
0.00
-0.26
-0.31
0.29
-1.30
0.06
46.29
350
0.8613
0.8613
0.8613
0.8589
0.8666
0.8496
0.8617
%Deviation to NIST
0
0.00
0.01
-0.27
0.62
-1.35
0.05
52.84
320
0.7655
0.7654
0.7619
0.7612
0.7716
0.7508
0.7665
%Deviation to NIST
0
0.00
-0.47
-0.56
0.80
-1.91
0.13
60.36
370
0.8538
0.8537
0.8551
0.8515
0.8629
0.8431
0.8542
%Deviation to NIST
0
0.00
0.16
-0.26
1.08
-1.25
0.06
75.90
400
0.8673
0.8672
0.8708
0.8659
0.8817
0.8600
0.8680
%Deviation to NIST
0
-0.01
0.41
-0.16
1.66
-0.84
0.08
90.75
420
0.8728
0.8727
0.8780
0.8723
0.8919
0.8684
0.8738
%Deviation to NIST
0
-0.01
0.59
-0.06
2.19
-0.50
0.11
100.85
320
0.4357
0.4357
0.4281
0.4510
0.4743
0.4505
0.4434
%Deviation to NIST
0
-0.01
-1.74
3.52
8.87
3.40
1.77
415.61
400
0.8243
0.8242
0.8325
0.8533
0.8948
0.8419
0.8243
%Deviation to NIST
0
-0.01
1.00
3.52
8.55
2.13
0.01
475.10
400
0.8838
0.8837
0.8922
0.9098
0.9513
0.8934
0.8829
%Deviation to NIST
0
-0.01
0.95
2.94
7.64
1.09
-0.10
536.18
430
0.9712
0.9709
0.9827
1.0044
1.0388
0.9787
0.9703
%Deviation to NIST
0
-0.03
1.18
3.42
6.97
0.78
-0.09
CO2 Mixture
Pressure, bar a
Temp, K
k NIST
k GERG
k LKP
k BWRS-NS
k SRK
k PR
k AGA8
30.99
310
1.5054
1.5056
1.5263
1.5119
1.5362
1.5377
1.5052
%Deviation to NIST
0
0.01
1.39
0.44
2.05
2.15
-0.01
46.29
350
1.4840
1.4838
1.5028
1.4894
1.5200
1.5233
1.4856
%Deviation to NIST
0
-0.01
1.27
0.37
2.43
2.65
0.11
52.84
320
1.7469
1.7471
1.7961
1.7661
1.8252
1.8319
1.7463
%Deviation to NIST
0
0.01
2.82
1.10
4.48
4.87
-0.03
60.36
370
1.5012
1.5010
1.5214
1.5069
1.5397
1.5448
1.5043
%Deviation to NIST
0
-0.02
1.34
0.38
2.56
2.90
0.20
75.90
400
1.4764
1.4761
1.4938
1.4801
1.5068
1.5135
1.4813
%Deviation to NIST
0
-0.02
1.17
0.25
2.06
2.51
0.33
90.75
420
1.4718
1.4714
1.4885
1.4746
1.4964
1.5043
1.4782
%Deviation to NIST
0
-0.02
1.13
0.19
1.67
2.21
0.43
100.85
320
5.0262
5.0257
5.2633
4.5261
5.4992
5.4315
4.7783
%Deviation to NIST
0
-0.01
4.72
-9.95
9.41
8.06
-4.93
415.61
400
1.9311
1.9274
2.0184
2.0756
1.8556
1.8852
1.9485
%Deviation to NIST
0
-0.19
4.52
7.48
-3.91
-2.37
0.90
475.10
400
1.8743
1.8701
1.9616
2.0466
1.7921
1.8248
1.8853
%Deviation to NIST
0
-0.23
4.66
9.19
-4.38
-2.64
0.59
536.18
430
1.7721
1.7681
1.8483
1.9062
1.6873
1.7131
1.7843
%Deviation to NIST
0
-0.23
4.30
7.57
-4.79
-3.33
0.69