EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Contents

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2 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Contents 1 Summary The enhanced revised Klosek-McKinley method Limits of the ERKM method Structure and parameters of the ERKM method The fitting and evaluation process Fitting procedure Validation with experimental data along the saturation curve Validation with experimental data at higher pressures Uncertainties of the new equation The application of the ERKM within TREND Outlook Literature Appendix A.1 Correspondence about the selection of an EOS A.2 Compositions of the measured LNG-mixtures A.3 Saturated liquid densities of the measured LNG-mixtures A.4 Additional validation tests for the saturated liquid... 26

3 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Summary The applicability of the revised Klosek and McKinley (RKM) method by McCarty [1] was expanded to represent the previously reported (p, ρ, T, x) data sets from density measurements on several LNG-mixtures [2]. The RKM was selected as it was discussed in the correspondence between VSL and RUB (see appendix A.1). Since the empirical RKM equation was developed to represent the saturation densities of LNG-mixtures within limits of 0.1 %, an application for pressures significantly higher than the saturation pressure is not possible. Therefore, an enhancement in form of a pressure-dependent term was included without changing the original RKM equation. This approach was chosen to maintain the easy to use and to implement structure of the original equation. The pressure-dependent term was originally fitted to densities of various exemplary LNG-mixtures calculated with the GERG-2008 equation of state [3] before the performance of the RKM equation was increased by taking advantage of the highly accurate experimental (p, ρ, T, x) data sets gathered in the scope of this project. The newly developed enhanced RKM (ERKM) is now able to calculate densities of LNG-mixtures at pressures of up to 10 MPa, and the temperature restriction of the equation was expanded to reach temperatures of up to 135 K. The estimated uncertainty of the newly developed equation can be set to 0.1 % for temperatures of up to 115 K and to 0.15 % for temperatures larger than 115 K up to T = 135 K. However, there are some more restrictions in using the ERKM and further details on its accuracy, which are described in more detail within the present report.

4 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August The enhanced revised Klosek and McKinley method The enhanced revised Klosek and McKinley (ERKM) method is designed as an upgrade of the revised Klosek and McKinley (RKM) method by McCarty [1]. Therefore, the original equation of the RKM method by McCarty as well as their parameters are kept in its original state. Only additional molar volumes are given to extend the temperature range. Tests with more actual data for the molar volume of methane by using calculations of the equation by Setzmann and Wagner [4] were performed, but led to strong deviations from the original behavior of the RKM. The pressure dependency is realized by an additional pressure, temperature and composition dependent term, which is given in section Limits of the ERKM method The Klosek and McKinley method [5] was designed to calculate saturation densities of mixtures of the eight main components of most LNG-compositions, which are listed in table 2.1. Since the amounts of single components have a great impact on density calculation, restrictions to the amounts of the substances have to be given. Furthermore, it is recommended to use the equation only for multi-component systems rather than binary mixtures. Table 2.1 Possible components for density calculations with the RKM and ERKM method. Component Restriction Component Restriction Methane CH 4 > 60 mol-% n-butane n-c 4 H 10 Ethane C 2 H 6 - Isobutane i-c 4 H 10 Propane C 3 H 8 - n-pentane n-c 5 H 12 Nitrogen N 2 < 4 mol-% Isopentane i-c 5 H 12 S < 4 mol-% S < 2 mol-% Σ " i 3 The temperature and pressure range where the ERKM method can be used, is given as: 100 K T 135 K p. p 10 MPa It should be noted that the attempt to use the equation at pressures below p s will most certainly result in physically incorrect values. Due to the extended range of application of the ERKM method compared to the RKM equation, the uncertainties for density calculations may exceed the originally given recommendation of 0.1 %. See section 3.4 for further details.

5 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Structure and parameters of the ERKM method As outlined above, the enhancement of the RKM method is introduced in form of an additional pressure, temperature and composition dependent term, which is added to the calculation as: with ρ 345 = M 89: v 89: 1 + f? (2.1) M 89: = x " M ", (2.2) " v 89: = x " v " " k D + k E k D x 4E x IJK, (2.3) f? = p p.,lmnn PK 1 MPa T QL T QL T D.RS, (2.4) and p.,lmnn = p.,ijk + x 4E 0.11 MPa K T 90 K x IEJU MPa K T 95 K (2.5) T QL = x " T L,", (2.6) " where: ρ LNG : density of the LNG M mix : molecular weight of the mixture M i : molecular weight of the component i, see table 2.2 v mix : 1 molar volume of the mixture expressed in dm 3 mol f p : the pressure-related expansion term p s,corr : the correction term for the saturation pressure x i : molar fraction of component i v i : molar volume of the component i at the given temperature, see table 2.3 k 1, k 2 : correction factors, see tables 2.4 and 2.5 T pc : simplified approach for a pseudo critical temperature of the mixture p s,ch4 : saturation pressure of methane, see table 2.6 T c,i : critical temperature of the component i, see table 2.7.

6 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August For calculation of the above described values and parameter, see tables 2.2 to 2.7. Table 2.2 The molar masses of the pure substances [6]. Component Molar mass M i in kg mol -1 Component Molar mass M i in kg mol -1 Methane CH n-butane n-c 4 H Ethane C 2 H Isobutane i-c 4 H Propane C 3 H n-pentane n-c 5 H Nitrogen N Isopentane i-c 5 H Table 2.3 The molar volumes of the pure substances as given by McCarty [1] as function of the given temperature. T in K -1 Molar volume v i in dm 3 mol CH 4 C 2 H 6 C 3 H 8 n-c 4 H 10 i-c 4 H 10 n-c 5 H 12 i-c 5 H 12 N a a a a a a From the original given values extrapolated molar volumes for higher temperatures.

7 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Table 2.4 The volume correction factor k 1 as given by McCarty [1]. M mix in Volume correction factor k 1 in dm 3 mol g mol K 95 K 100 K 105 K 110 K 115 K 120 K 125 K 130 K 135 K Table 2.5 The volume correction factor k 2 as given by McCarty [1]. M mix in Volume correction factor k 2 in dm 3 mol g mol K 95 K 100 K 105 K 110 K 115 K 120 K 125 K 130 K 135 K Table 2.6 The saturation pressure of pure methane calculated from the equation by Setzmann & Wagner [4]. T in K p s,ch4 in MPa T in K p s,ch4 in MPa T in K p s,ch4 in MPa

8 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Table 2.7 The critical temperatures of the pure fluids. Component Critical temperature T c,i in K Component Critical temperature T c,i in K Methane CH [4] n-butane n-c 4 H [10] Ethane C 2 H [7] Isobutane i-c 4 H [10] Propane C 3 H [8] n-pentane n-c 5 H [11] Nitrogen N [9] Isopentane i-c 5 H [12] 3 The fitting and evaluation process The original equation by Klosek and McKinley [5], the ERKM is an empirical approach to describe the density of common LNG-composition. Therefore, statistics instead of physical laws were applied to design the equation and its enhancement. The first subsection describes the procedure, which was used to develop the pressure-extension term in a short comprehensive way. Subsequently, the following subsections give an overview of the comparison to experimental data and the GERG-2008 EOS [3] as well as concluding in an uncertainty analysis. 3.1 Fitting procedure While highly accurate density measurements for multi-component LNG-mixtures are rare, the possibility to calculate them with the GERG-2008 equation of state (EOS) [3] are nearly unlimited. Since the GERG-2008 EOS showed plausible behavior when compared to the highprecision measurements [2] at pressures above the saturation pressure, calculations from this equation for various exemplary LNG-compositions were used to adjust the added term. The fitting to those data was performed using the Levenberg-Marquardt algorithm [13,14,15] after an appropriate structure of the term was found. To emphasize the fitted parameters, eq. (2.4) can be expressed using f p as the pressure expansion term with the constants k 3 and k 4 : f? = p p.,lmnn k W X YZ X YZ PX [ \. (3.1) Within the expansion term f p, the correction for the saturation pressure is required to avoid increasing deviations in the saturation density from the RKM method at higher temperatures, which would have been caused by the rising saturation pressure as can be observed in figure 3.1.

9 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Figure 3.1: Saturation pressures of the experimentally investigated LNG-compositions compared to pure methane and two selected binary mixtures calculated with the GERG-2008 EOS [3] plotted versus temperature. Figure 3.1 shows the saturation pressures of the experimentally investigated LNG-mixtures and selected binary mixtures to underline the need of the correction terms that were introduced in eq. (2.5). While the LNG-compositions mostly coincide with the saturation pressure of pure methane, a high amount of nitrogen or ethane can substantially affect the saturation pressure. The calculation of a pseudo-critical temperature of the respective mixture using eq. (2.6) serves as an indication for influences of the components in the critical temperature. Due to this simplified approach, the values do not perfectly agree with values exemplarily obtained from the GERG-2008 EOS and are, therefore, labeled as pseudo values.

10 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Validation with experimental data along the saturation curve Due to the good representation of saturated liquid densities by the RKM method and for consistency of the results, it was considered particularly important that this trend is maintained to the greatest possible extend during the adjustment process. Therefore, diagrams for the saturation densities as similarly seen in previous reports [2] were closely observed. These diagrams can be seen in figure 3.2 and show the RKM equation as well as experimental data points [2,16,17] beside the ERKM method in comparison to the GERG-2008 EOS [3]. Figure 3.2: Comparison of the experimental saturated liquid density data [2,16,17], the RKM method [1] and the newly developed ERKM method to the GERG-2008 EOS [3] plotted versus temperature T for the investigated LNG-compositions (see appendix A.2). It should be emphasized that the zero line in these plots represents the GERG-2008 EOS, while the other data are labeled underneath the plots. In these diagrams, it can be observed that the values calculated from the new ERKM method are nearly the same of those gained from McCarty s RKM. Both simplified approaches show a better representation of the experimental data than the GERG-2008 EOS does. The experimental saturated liquid densities for the plotted LNG-mixtures are added to this report and can be found in appendix A.2. In this comparison,

11 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August small deviations between the ERKM and RKM method result from the fact that f p does not become exactly zero for the pressures along the saturated liquid line. However, the approximation chosen for p s,corr (eq. 2.5) is considered a reasonable compromise between numerical effort and consistency on the saturated liquid line. 3.3 Validation with experimental data at higher pressures The enhancement of the pressure dependency was the primary objective in developing the ERKM method. While the RKM method is solely usable at saturation conditions, the applicable pressure range now reaches up to 10 MPa. In figure 3.3, the newly developed equation is shown in comparison to experimental data as well as calculations with the RKM method [1] and the GERG-2008 EOS [3] at the temperatures and pressures at which measurements in the homogeneous liquid were carried out. The results shown in figure 3.3 prove a good representation of the experimental data, which were measured in the course of this project [2] and earlier work [16,17]. Most of the data can be represented within a 0.1 % density-deviation range, and only data at temperatures beyond 125 K exceed this limit. In these pressure-related plots, the calculations with the RKM method show a good representation at very small pressures but deviate strongly with higher pressures as it was expected. The highest deviation observed of the RKM method was 2.2 % at the upper temperature limit of 135 K and the highest measured pressure of 7.98 MPa for LNG-Norway. While calculations with the GERG-2008 EOS [3] show a good agreement with the experimental data and the ERKM method for most of the compositions, the calculations for LNG-Mix #5 deviate strongly by up to 0.23 % from the measurements. Further validation tests with older available LNG-data from Rodosevich and Miller [18], Hiza and Haynes [19] and Haynes [20] were performed and can be found in appendix A.4 along with tests for pure methane [21] and a binary methane-ethane mixture [22].

12 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Figure 3.3: Comparison of homogeneous liquid-phase density data from experiments [2,16,17], the RKM method [1] and the GERG-2008 EOS [3] to the newly developed ERKM method plotted versus pressure p for the investigated LNG-compositions (see appendix A.2). Only low pressure data of the RKM method are shown in the plots since data points that are off-scale were dispensed due to clarity. 3.4 Uncertainties of the new equation An estimation of the accuracy of the ERKM method can be derived from the comparison of the method to the available set of accurate experimental data. Figure 3.4 shows the complete sets of measurements that were produced in course of this project and before [2,16,17] as well as an estimated uncertainty.

13 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Figure 3.4: Comparison of density data from experiments [2,16,17], the RKM method [1] and the GERG-2008 EOS [3] to the newly developed ERKM method plotted versus temperature T (left) and pressure p (right) including the estimated uncertainty of the ERKM method. As already discussed in section 3.3, the measured data points are mostly represented within deviations of 0.1 %. Only at higher temperatures as the experimental data at 125 K and 135 K, the deviations exceed this limit. McCarty [1] discussed the phenomenon that the inclusion of nitrogen caused higher deviations at temperatures above 115 K and, therefore, restricted the use of the RKM method to this limit. However, due to the newly available data, it was possible to fit the additional pressure term to higher temperature and pressure data. This way, the ERKM method is also applicable at temperatures higher than 115 K. Even though, deviations larger than 0.1 % could only be observed at temperatures of 125 K and above, the estimated uncertainty for calculations higher than 115 K is precautionary set to 0.15 %. In conclusion, the estimated uncertainties are stated as: 0.1 % for 100 K T 115 K 0.15 % for 115 K < T 135 K

14 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August The application of the ERKM within TREND The ERKM was implemented in the open source software package TREND (Thermodynamic Reference & Engineering Data) [23] of the chair of thermodynamics at Ruhr-University Bochum. The software package includes highly accurate equations of state in terms of the Helmholtz free energy as well as mixture models such as the GERG-2008 EOS [3] for a wide range of fluids, but inhabits also simplified equations such as the COSTALD correlation [24]. An interface programmed for MS Excel [25] facilitates the application of the software. The usage of certain equations and mixture models can be controlled by using different integer numbers as equation or mixture type as it can be seen in figure 4.1. To use the ERKM method, these numbers has to be set to 81. While the implemented fundamental equations of state are able to calculate a variety of thermodynamic properties, the ERKM method is restricted to calculate densities. Calculations can be performed by using the function call DEOS(INPUT, PROP1, PROP2, FLUIDS, MOLFRACTIONS, EOSTYPE, PATH) within the Excel interface. The variables of this formula are described in table 4.1. For more detailed information, see the TREND Excel Manual [26]. Table 4.1 Description of the variables of the DEOS-formula [24]. Variable INPUT PROP1/PROP2 FLUIDS MOLFRACTION EOSTYPE PATH Description The input code indicates the types and combination of the property inputs PROP1 and PROP2, e.g. TP for a state point at a given temperature (PROP1) and pressure (PROP2) or TLIQ for a saturated liquid state point at a given temperature (PROP1), PROP2 can be set to an arbitrary number in this case. It is recommended to use rather the ERKM method with the input code TP along with the value of the saturation pressure or the RKM method along with the input code TLIQ. If the input code TLIQ is applied on the ERKM method, the saturation pressure of pure methane is used and causes greater deviations from the RKM method. The first and second input property, e.g. 100 for the temperature in Kelvin and 1 for the pressure in MPa, when TP is used as input code. The list of components can be either an array of cells or one string separated by semicolons, e.g. methane;ethane;nitrogen. The fluid names have to match the names in the fluid files in spelling and case. The mole fractions of the given components can be either an array of cells or one string separated by semicolons, e.g. 0.84;0.11;0.05. The sum of the fractions has to be 1. The EOSTYPE is split into the equation type, which had to be set for each fluid and a mixing rule. While the equation type is for more than one fluid an array of cells, the mixing rule is a single cell. It can also be written in one string separated by semicolons, e.g. 81;81;81;81 for the use of three fluids including the last number as the mixing rule. While 81 resembles the ERKM method, 8 can be used for the RKM method. Path of the directory, where the fluid files are stored, e.g. D:\TREND\

15 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August * not applicable for the RKM method. Figure 4.1: Excel interface of the TREND software package [23] with annotations for using the ERKM method.

16 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Outlook The outcome of the development of an additional pressure-dependent term for the RKM method showed promising results. Due to the small data set, the evaluation of its accuracy should be continued as soon as new data sets are available. While the equation showed a good representation for LNG-compositions, binary mixtures or mixtures with a high content of secondary components such as nitrogen are subject of future development.

17 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Literature 1 R.D. McCarty, J. Chem. Thermodynamics 14.9 (1982) R. Lentner, M. Richter, R. Kleinrahm, R. Span, Report - Deliverables REG D3 and D4 / JRP D4.1.2 and D4.1.3, Bochum, O. Kunz, W. Wagner, J. Chem. Eng. Data 57 (2012) U. Setzmann, W. Wagner, J. Phys. Chem. Ref. Data 20.6 (1991) J. Klosek, C. McKinley, Proc. First Intern. Conf. on LNG, Chicago (1968). 6 M.E. Wieser, M. Berglund, IUPAC Technical Report, Pure and Applied Chemistry (2009) D. Buecker, W. Wagner, J. Phys. Chem. Ref. Data, 35.1 (2006) E.W. Lemmon, M.O. McLinden, W. Wagner, J. Chem. Eng. Data, 54 (2009) R. Span, E.W. Lemmon, R.T. Jacobsen, W. Wagner, A. Yokozeki, J. Phys. Chem. Ref. Data, 29.6 (2000) D. Buecker, W. Wagner, J. Phys. Chem. Ref. Data, 35.2 (2006) R. Span, W. Wagner, Int. J. Thermophys., 24.1 (2003) E.W. Lemmon, R. Span, J. Chem. Eng. Data, 51 (2006) K. Levenberg, Quart. Appl. Math. 2 (1944) D. Marquardt, J. Appl. Math. 11 (1963) J.J. Moré, Numerical Analysis, Dundee (1977) 16 M. Richter, R. Kleinrahm, R. Lentner, R. Span, J. Chem. Thermodynamics 93 (2016) M. Richter, R. Lentner, R. Kleinrahm, R. Span, GERG Project 1.67: Final Report Phase 2, October J. B. Rodosevich, R.C. Miller, AIChE Journal 19.4 (1973) M.J. Hiza, W. M. Haynes, J. Chem. Thermodynamics 12.1 (1980) W.M. Haynes, J. Chem. Thermodynamics 14.7 (1982) R. Kleinrahm, W. Wagner, J. Chem. Thermodynamics 18.8 (1986) R. Lentner, M. Richter, R. Kleinrahm, R. Span, Personal communication (2016). 23 R. Span, T. Eckermann, S. Herrig, S. Hielscher, A. Jäger, M. Thol, TREND. Thermodynamic Reference and Engineering Data 2.0. Lehrstuhl für Thermodynamik, Ruhr- Universität Bochum. 24 G.H. Thomson, K.R. Brobst, R.W. Hankinson, AiChE J. 28 (1982)

18 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Microsoft Corporation (2015): Excel 2016, Microsoft, Redmond, USA. 26 R. Span, T. Eckermann, S. Herrig, S. Hielscher, A. Jäger, M. Thol (2015): TREND User Manual for the Microsoft Excel Interface, Version 2.0.1, November 2015.

19 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Appendix A.1 Correspondence about the selection of an EOS The selection of a suitable EOS for improvements with help of the new experimental data that were obtained in the course of this project was discussed between Mr. G. Nieuwenkamp (VSL), Dr. A. van der Veen (VSL) and Prof. Dr.-Ing. M. Richter (RUB) and is concluded within the following quoted from the 3 rd Ferbruary 2016: Dear Gerard and Adriaan, According to our telephone conference of January 21, I wanted to send you a short memo about our work on the deliverables ENG60 LNG II JRP D4.2.2 and D4.2.3, which deal with the improvement of a selected EOS for the calculation of saturated liquid densities of LNG and the development of a software tool enabling such calculations. The comparison of our new experimental data for six different LNG composition with three EOS (Revised Klosek McKinley Method RKM, GERG-2008 and COSTALD) revealed that the performance of the RKM for the calculation of saturated liquid densities of LNG is remarkably good and the best among the three tested EOS. The good agreement of our experimental data and values calculated from the RKM does actually not really require a substantial improvement. The RKM method does only work for the calculation of saturated liquid densities of LNG and is only temperature-dependent. Nevertheless, this method seems to be a feasible starting point for improvements also considering the amount of time that we have in our JRP. We think it would be extremely useful for industry and in terms of suggesting an amendment for ISO 6578 or the GIIGNL LNG Custody Transfer Handbook to implement a pressure dependent calculation of density. This would be valid for a temperature range from (105 to 135) K with pressures up to 10 MPa. A fine tuning of the calculation of saturated liquid densities would be carried out as well. The changed RKM will be implemented in the thermodynamic property software package TREND" of our institute, which is very comprehensive and does also include the GERG-2008/EOS-CG, the COSTALD method and many more options for property calculations for mixtures and pure substances as well. We offer to distribute TREND to all project partners and the stakeholders including the changed RKM.

20 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Currently the original version of the RKM is being implemented in TREND, which makes the fitting work much easier. We are making good progress so that the software distribution and reporting should be realistic for the end of March. Attached you find the manual of TREND, which might convey an impression about its capabilities. If you have further questions, please do not hesitate to ask. Best regards, Markus

21 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August A.2 Compositions of the measured LNG-mixtures Table A1 Composition (mole-fraction), expanded uncertainties (k = 2) for each component and molar mass M of the studied natural-gas mixture (type LNG 2 ). Component Mole-fraction (certificate) a Mole-fraction (normalized) Expanded uncertainty (k = 2) [mole-fraction (certificate) a ] CH C 2 H C 3 H n-c 4 H i-c 4 H n-c 5 H i-c 5 H N M / (g mol 1 ) a As reported in the certificate of VSL (Dutch Metrology Institute). Mole-fractions were determined by comparison with an appropriate set of primary standard gas mixtures in accordance with the International Standard ISO 6143:2001. Uncertainties were determined in accordance with GUM. Table A2 Composition (mole-fraction), expanded uncertainties (k = 2) for each component and molar mass M of the studied natural-gas mixture (type LNG 5 ). Component Mole-fraction (certificate) a Mole-fraction (normalized) Expanded uncertainty (k = 2) [mole-fraction (certificate) a ] CH C 2 H C 3 H n-c 4 H i-c 4 H n-c 5 H i-c 5 H N M / (g mol 1 ) a As reported in the certificate of VSL (Dutch Metrology Institute). Mole-fractions were determined by comparison with an appropriate set of primary standard gas mixtures in accordance with the International Standard ISO 6143:2001. Uncertainties were determined in accordance with GUM. Table A3 Composition (mole-fraction), expanded uncertainties (k = 2) for each component and molar mass M of the studied natural-gas mixture (type LNG 7 ).

22 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Component Mole-fraction (certificate) a Mole-fraction (normalized) Expanded uncertainty (k = 2) [mole-fraction (certificate) a ] CH C 2 H C 3 H n-c 4 H i-c 4 H n-c 5 H i-c 5 H N M / (g mol 1 ) a As reported in the certificate of VSL (Dutch Metrology Institute). Mole-fractions were determined by comparison with an appropriate set of primary standard gas mixtures in accordance with the International Standard ISO 6143:2001. Uncertainties were determined in accordance with GUM. Table A4 Composition (mole-fraction), expanded uncertainties (k = 2) for each component and molar mass M of the studied natural-gas mixture (type LNG-Libya ). Component Mole-fraction (certificate) a Mole-fraction (normalized) Expanded uncertainty (k = 2) [mole-fraction (certificate) a ] CH C 2 H C 3 H n-c 4 H N M / (g mol 1 ) a As reported in the certificate of VSL (Dutch Metrology Institute). Mole-fractions were determined by comparison with an appropriate set of primary standard gas mixtures in accordance with the International Standard ISO 6143:2001. Uncertainties were determined in accordance with GUM.

23 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Table A5 Composition (mole-fraction), expanded uncertainties (k = 2) for each component and molar mass M of the studied natural-gas mixture (type LNG-Norway ). Component Mole-fraction (certificate) a Mole-fraction (normalized) Expanded uncertainty (k = 2) [mole-fraction (certificate) a ] CH C 2 H C 3 H n-c 4 H N M / (g mol 1 ) a As reported in the certificate of VSL (Dutch Metrology Institute). Mole-fractions were determined by comparison with an appropriate set of primary standard gas mixtures in accordance with the International Standard ISO 6143:2001. Uncertainties were determined in accordance with GUM. Table A6 Composition (mole-fraction), expanded uncertainties (k = 2) for each component and molar mass M of the studied natural-gas mixture (type LNG-Oman ). Component Mole-fraction (certificate) a Mole-fraction (normalized) Expanded uncertainty (k = 2) [mole-fraction (certificate) a ] CH C 2 H C 3 H n-c 4 H N M / (g mol 1 ) a As reported in the certificate of VSL (Dutch Metrology Institute). Mole-fractions were determined by comparison with an appropriate set of primary standard gas mixtures in accordance with the International Standard ISO 6143:2001. Uncertainties were determined in accordance with GUM.

24 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August A.3 Saturated liquid densities of the measured LNG-mixtures Table 2 Saturated liquid densities a ρ sat,exp for LNG 2 b and their relative deviations from densities ρ sat,gerg calculated with the GERG-2008 equation of state of Kunz and Wagner [..], where p is the pressure and T is the temperature (ITS-90). T / K p / MPa ρ exp / (kg m 3 ) 100 (ρ sat,exp ρ sat,gerg ) / ρ sat,gerg a The saturated liquid densities were determined by extrapolation of the densities along isotherms in the homogenous liquid region to the vapor pressure. The vapor pressure was calculated from the GERG-2008 equation of state of Kunz and Wagner. Its uncertainty was reported by the authors to be (1 to 3)%. b The expanded uncertainty (k = 1.73) in temperature is U(T) = K. The expanded uncertainty (k = 1.73) in pressure is U(p) = 0.01% p max. The relative expanded combined uncertainty (k = 2) in density is U C (ρ)/ρ = 0.044%. Table 4 Saturated liquid densities a ρ sat,exp for LNG 5 b and their relative deviations from densities ρ sat,gerg calculated with the GERG-2008 equation of state of Kunz and Wagner [..], where p is the pressure and T is the temperature (ITS-90). T / K p / MPa ρ exp / kg m (ρ sat,exp ρ sat,gerg ) / ρ sat,gerg a The saturated liquid densities were determined by extrapolation of the densities along isotherms in the homogenous liquid region to the vapor pressure. The vapor pressure was calculated from the GERG-2008 equation of state of Kunz and Wagner. Its uncertainty was reported by the authors to be (1 to 3)%. b The expanded uncertainty (k = 1.73) in temperature is U(T) = K. The expanded uncertainty (k = 1.73) in pressure is U(p) = 0.01% p max. The relative expanded combined uncertainty (k = 2) in density is U C (ρ)/ρ = 0.044%

25 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Table 6 Saturated liquid densities a ρ sat,exp for LNG 7 b and their relative deviations from densities ρ sat,gerg calculated with the GERG-2008 equation of state of Kunz and Wagner [..], where p is the pressure and T is the temperature (ITS-90). T / K p / MPa ρ exp / kg m (ρ sat,exp ρ sat,gerg ) / ρ sat,gerg a The saturated liquid densities were determined by extrapolation of the densities along isotherms in the homogenous liquid region to the vapor pressure. The vapor pressure was calculated from the GERG-2008 equation of state of Kunz and Wagner. Its uncertainty was reported by the authors to be (1 to 3)%. b The expanded uncertainty (k = 1.73) in temperature is U(T) = K. The expanded uncertainty (k = 1.73) in pressure is U(p) = 0.01% p max. The relative expanded combined uncertainty (k = 2) in density is U C (ρ)/ρ = 0.044%. Table 8 Saturated liquid densities a ρ sat,exp for LNG-Libya b and their relative deviations from densities ρ sat,gerg calculated with the GERG-2008 equation of state of Kunz and Wagner [..], where p is the pressure and T is the temperature (ITS-90). T / K p / MPa ρ exp / (kg m 3 ) 100 (ρ sat,exp ρ sat,gerg ) / ρ sat,gerg c a The saturated liquid densities were determined by extrapolation of the densities along isotherms in the homogenous liquid region to the vapor pressure. The vapor pressure was calculated from the GERG-2008 equation of state of Kunz and Wagner. Its uncertainty was reported by the authors to be (1 to 3)%. b The expanded uncertainty (k = 1.73) in temperature is U(T) = K. The expanded uncertainty (k = 1.73) in pressure is U(p) = 0.01% p max. The relative expanded combined uncertainty (k = 2) in density is U C (ρ)/ρ = 0.044%. c In comparison to previous reports adjusted value after revised data analysis.

26 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Table 10 Saturated liquid densities a ρ sat,exp for LNG-Norway b and their relative deviations from densities ρ sat,gerg calculated with the GERG-2008 equation of state of Kunz and Wagner [..], where p is the pressure and T is the temperature (ITS-90). T / K p / MPa ρ exp / (kg m 3 ) 100 (ρ sat,exp ρ sat,gerg ) / ρ sat,gerg c a The saturated liquid densities were determined by extrapolation of the densities along isotherms in the homogenous liquid region to the vapor pressure. The vapor pressure was calculated from the GERG-2008 equation of state of Kunz and Wagner. Its uncertainty was reported by the authors to be (1 to 3)%. b The expanded uncertainty (k = 1.73) in temperature is U(T) = K. The expanded uncertainty (k = 1.73) in pressure is U(p) = 0.01% p max. The relative expanded combined uncertainty (k = 2) in density is U C (ρ)/ρ = 0.044%. c In comparison to previous reports adjusted value after revised data analysis. Table 10 Saturated liquid densities a ρ sat,exp for LNG-Oman b and their relative deviations from densities ρ sat,gerg calculated with the GERG-2008 equation of state of Kunz and Wagner [..], where p is the pressure and T is the temperature (ITS-90). T / K p / MPa ρ exp / (kg m 3 ) 100 (ρ sat,exp ρ sat,gerg ) / ρ sat,gerg c c c a The saturated liquid densities were determined by extrapolation of the densities along isotherms in the homogenous liquid region to the vapor pressure. The vapor pressure was calculated from the GERG-2008 equation of state of Kunz and Wagner. Its uncertainty was reported by the authors to be (1 to 3)%. b The expanded uncertainty (k = 1.73) in temperature is U(T) = K. The expanded uncertainty (k = 1.73) in pressure is U(p) = 0.01% p max. The relative expanded combined uncertainty (k = 2) in density is U C (ρ)/ρ = 0.044%. c In comparison to previous reports adjusted value after revised data analysis.

27 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August A.4 Additional validation tests for the saturated liquid Component Mole-fraction CH C 2 H 6 - C 3 H 8 - n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N 2 - Figure A.1: Comparison of saturation density data from the experiment by Kleinrahm and Wagner [21], the RKM method [1] and the ERKM method to the GERG-2008 EOS [3] versus temperature T for pure methane. The values for the RKM method are identical to those of the ERKM method. Component Mole-fraction CH C 2 H C 3 H 8 - n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N 2 - Figure A.2: Comparison of saturation density data from the experiment by Lentner et al. [XXX], the RKM method [1] and the ERKM method to the GERG-2008 EOS [3] versus temperature T for the binary mixture of methane and ethane.

28 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Component Mole-fraction CH C 2 H C 3 H n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N 2 - Component Mole-fraction CH C 2 H C 3 H 8 - n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N Component Mole-fraction CH C 2 H 6 - C 3 H n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N Figure A.3: Comparison of saturation density data from the experiment by Rodosevich and Miller [18], the RKM method [1] and the ERKM method to the GERG-2008 EOS [3] versus temperature T for several methane-rich mixtures. Red marked composition entries indicate amounts that exceed the allowances of the ERKM- and RKM method.

29 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Component Mole-fraction CH C 2 H C 3 H n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N Component Mole-fraction CH C 2 H C 3 H n-c 4 H i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N 2 - Component Mole-fraction CH C 2 H C 3 H n-c 4 H i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N Figure A.4: Comparison of saturation density data from the experiment by Haynes [20], the RKM method [1] and the ERKM method to the GERG-2008 EOS [3] versus temperature T for several methane-rich mixtures. Red marked composition entries indicate amounts that exceed the allowances of the ERKM- and RKM method.

30 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Component Mole-fraction CH C 2 H C 3 H n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N 2 - Component Mole-fraction CH C 2 H C 3 H n-c 4 H i-c 4 H n-c 5 H 12 - i-c 5 H 12 - N 2 - Component Mole-fraction CH C 2 H 6 - C 3 H n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N Figure A.5: Comparison of saturation density data from the experiment by Hiza and Haynes [19], the RKM method [1] and the ERKM method to the GERG-2008 EOS [3] versus temperature T for several methane-rich mixtures. Red marked composition entries indicate amounts that exceed the allowances of the ERKM- and RKM method.

31 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Component Mole-fraction CH C 2 H C 3 H n-c 4 H 10 - i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N Component Mole-fraction CH C 2 H C 3 H n-c 4 H 10 - i-c 4 H n-c 5 H 12 - i-c 5 H 12 - N Component Mole-fraction CH C 2 H C 3 H n-c 4 H i-c 4 H 10 - n-c 5 H 12 - i-c 5 H 12 - N Figure A.6: Comparison of saturation density data from the experiment by Hiza and Haynes [19], the RKM method [1] and the ERKM method to the GERG-2008 EOS [3] versus temperature T for several methane-rich mixtures. Red marked composition entries indicate amounts that exceed the allowances of the ERKM- and RKM method.

32 EMRP JRP ENG60 LNG II: Report Deliverables REG D5 to D8 / D4.2.1 to D4.2.4, August Component Mole-fraction CH C 2 H C 3 H n-c 4 H i-c 4 H n-c 5 H 12 - i-c 5 H 12 - N Figure A.7: Comparison of saturation density data from the experiment by Hiza and Haynes [19], the RKM method [1] and the ERKM method to the GERG-2008 EOS [3] versus temperature T for a methane-rich mixtures. Red marked composition entries indicate amounts that exceed the allowances of the ERKM- and RKM method. The experimental determined saturation pressures deviated strongly by up to 0.2 % from those calculated with the GERG-2008 EOS.