Experimental Determination of (p, ρ, T) Data for Three Mixturesof Carbon Dioxide with Methane for the ThermodynamicCharacterization of Nonconventional Energy GasesPaper presented at the 18th Symposium on Thermophysical Properties, Boulder, CO, June 24 to 29, 2012.

María E. Mondejar,† Teresa E. Fernandez-Vicente,‡ Frederique Haloua,§ and Cesar R. Chamorro*,†

†Universidad de Valladolid, Paseo del Cauce, 59, E-47011 Valladolid, Spain‡Centro Espanol de Metrología, Calle del Alfar, 2, E-28760 Tres Cantos, Madrid, Spain§Laboratoire National de Metrologie et d’Essais 29, Avenue Roger Hennequin, F-78197 Trappes cedex, France

ABSTRACT: Experimental characterization of the thermodynamic behaviorof gas binary mixtures containing components of fuel gases is of greatimportance due to the proved lack of reliable data of thermodynamic prop-erties of mixtures. These data are essential not only for the improvement andtest of the current reference equation of state for natural gases and relatedmixtures, GERG-2008, but also for the indirect determination of other prop-erties. In this work density measurements of mixtures of carbon dioxide withmethane are presented as a contribution to the research project EMRPENG01 of the European Metrology Research Program, in the field of characterization of energy gases. Accurate density mea-surements for three binary mixtures of carbon dioxide with methane (xCO2

= 0.20, 0.40, and 0.60) were performed at temper-atures between (250 and 400) K and pressures up to 20 MPa, using a single sinker densimeter with magnetic suspensioncoupling, which is one of the state of the art methods for density determination over wide ranges of temperature and pressure.Experimental densities were compared with the GERG-2008 equation of state and with the experimental data reported by otherauthors for similar mixtures. Relatively large deviations from the equation of state observed at low temperatures suggests thepossibility of higher uncertainties of the GERG model in the low temperature range.

1. INTRODUCTIONThe current energy policies of the European Union are focusedon the reduction of both the external energy dependenceand the carbon dioxide emissions to the atmosphere, bymaintaining the current energy supply and production levels.For this purpose, the use of renewable energies1 and theincrease of the energy efficiency of current industrial processesare being considered as the main strategies in the short andmedium term. Among the available renewable resources,biofuels are intended to replace partially or totally the use offossil fuels which are consumed, mainly, for transportationand heating purposes. However, biofuels and other alternativefuels are characterized to have a localized production, so thatits use far from the production location would increase costsand reduce their efficiency and sustainability. A solution tothis problem could be based in reducing as much as possiblethe transportation costs of the fuels by using the currentlogistics networks.In this regard, several European projects2,3 are considering

the “greening” of natural gas through the injection of othernonconventional fuel gases, such as biogas or coal-bedmethane, in the European gas pipelines. However, due to thedifferences in composition between these new alternative fuelgases and natural gas, the current metrology infrastructurewhich is used in the gas industry must be tested and adjusted toenable the interchangeability of these new energy gases.

To this end, the research project EMRP ENG014 ofthe European Metrology Research Program, sponsored byEURAMET, addresses several joint research projects for thecharacterization of energy gases. The work presented in thispaper is a contribution to the joint research project for theindirect determination of the calorific value of nonconven-tional energy gases. The present work contributes to thisproject with accurate density measurements of three binarymixtures of carbon dioxide with methane with different com-positions, which were selected as reference mixtures for theresearch project.The density of mixtures containing carbon dioxide and

methane has been previously measured by several authors.Among all of the experimental density data collected in theGERG data bank5 for these mixtures, less than half were usedfor the fitting of the current reference equation of state fornatural gas, GERG-2004.6 Some of these data correspondto similar mixtures to those studied here. For instance, Hwanget al.7 measured (p, ρ, T) data of mixtures with a carbondioxide molar fraction xCO2

= (0.10 to 0.90) in the temperature

range from (225 to 350) K and pressures up to 35 MPa.

Received: June 19, 2012Accepted: July 31, 2012Published: August 17, 2012

Article

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© 2012 American Chemical Society 2581 dx.doi.org/10.1021/je300665n | J. Chem. Eng. Data 2012, 57, 2581−2588

Esper et al.8 measured the density of an equimolar mixture ofcarbon dioxide with methane in the range from (220 to 320) Kand pressures up to 48 MPa. However, while the experimentaldata measured by Hwang et al.7 were used in their most for thefitting of the equation of state, the data reported by Esper et al.8

were neglected.In the present work, we have measured experimental

(p, ρ, T) data of three mixtures of carbon dioxide and methane,with carbon dioxide molar fractions xCO2

= (0.199778, 0.400637,and 0.601623). The reported data were measured in the tem-perature range from (250 to 400) K at pressures up to 20 MPa,though the lowest temperature isotherms were not carried outon all the mixtures to avoid the partial condensation of any of thecomponents. An accurate single sinker densimeter with magneticsuspension coupling was used to perform these measurements.The experimental data were compared with the densities

calculated from the GERG-2008 equation of state9 to test itsperformance for these mixtures, and the relative deviations indensity of experimental data were listed and plotted versuspressure for their comparison with the above-mentioned literaturedata for similar mixturesThe new GERG-2008 equation of state is an extension of the

previous GERG-2004 equation of state for natural gases andrelated mixtures.6 This new equation, which is expected to beadopted as an ISO Standard (ISO 20765-2 and ISO 20765-3),covers three additional components to the 18 componentscovered by the previous equation, but the general mathe-matical structure, mixture parameters, correlations, and depar-ture functions for the rest of the components do not change.This equation of state is valid in a temperature range from(90 to 450) K and pressures up to 35 MPa. In the case ofthe binary mixtures containing carbon dioxide and methane,18 data sets of experimental data of density, speed of sound,isobaric heat capacity, and vapor−liquid equilibrium were usedin the fitting.5

These new, accurate (p, ρ, T) data for mixtures of carbondioxide with methane will be complemented with speed ofsound measurements on mixtures of the same composition forthe indirect determination of the calorific value. Both density andspeed of sound experimental data will be of great importancefor the test or improvement of the current reference equation ofstate GERG-2008.

2. EXPERIMENTAL SECTION2.1. Apparatus Description. As stated above, a single

sinker densimeter with magnetic suspension coupling wasused to perform the measurements. This apparatus, which isbased on the Archimedes' principle, is one of the state of theart methodologies for the experimental determination of thedensity of fluids10 and was originally developed by Brachthauseret al.11,12 and successively improved.13,14

The single sinker densimeter used to perform the measure-ments presented in this work has been previously describedin detail by Chamorro et al.15 and Mondejar et al.16 In thisdensimeter the buoyancy force acting on a body which isimmersed in the fluid contained in the measuring cell is mea-sured. The buoyancy force is determined by measuring thechange in the sinker mass when it is surrounded by the thermo-statized and pressurized fluid. Then, the density of the fluidcan be obtained by dividing this change in mass by the sinkervolume, as expressed in eq 1.

ρ = −m m V T p( )/ ( , )S0 Sf s (1)

Here mS0 and mSf refer to the sinker mass in a vacuum and thesinker mass in the pressurized fluid, respectively, and Vs(T,p)refers to the sinker volume affected by the fluid temperatureand pressure. The densimeter works over a temperature rangefrom (250 to 400) K and pressures up to 20 MPa.The main advantage of this densimeter is that the measuring

cell can be pressurized and thermostatized over wide pressureand temperature ranges thanks to the magnetic suspensioncoupling which transmits the sinker mass and the buoyancyforce acting on it to the balance hook without any contact.However, as stated by McLinden et al.,17 this magnetic couplinginduces a force transmission error, which consists of twoseparate effects: the apparatus effect and the fluid specific effect.The apparatus effect, which is induced due to the magneticbehavior of the apparatus itself, is here compensated for. Bycontrast, since the specific fluid effect is proportional to themagnetic susceptibility of the fluid, which is in this case verylow, the contribution of this term to the total force transmissionerror can be neglected if compared to the uncertainty in densityof the measurements.

2.2. Experimental Material. The three mixtures of carbondioxide with methane measured in this work were preparedgravimetrically in the Spanish National Metrology Institute(Centro Espanol de Metrologia, CEM) and supplied in 5 dm3

aluminum cylinders. Table 1 shows the mixture composi-tions with estimated uncertainties in molar fractions, togetherwith the mole fraction purities of the component gases and thecylinder pressures.

Pure carbon dioxide was supplied by Carburos Metalicos(Air Products) with a certified mole fraction purity of 0.99995.Pure methane was supplied by Praxair with a certified molefraction purity of 0.999995. Nitrogen used for test measure-ments was supplied by Alphagaz (Air Liquid) with a certifiedmole fraction purity of 0.999999.

2.3. Experimental Procedure. The measurements werecarried out in the homogeneous gas region along seven iso-therms at (250, 275, 300, 325, 350, 375, and 400) K andpressures up to 20 MPa. To avoid the partial condensationof carbon dioxide in the coldest parts of the densimeter,which would affect the certified composition of the mixtures,the lowest temperatures measured for each of the twomixtures with higher carbon dioxide content were 275 K,for the xCO2

= 0.40 mixture, and 300 K for the xCO2= 0.60

mixture.The measuring cell was filled with the gas mixtures up to

20 MPa approximately for each measured isotherm, by meansof a manual pump. The maximum pressure of two isothermsfor the xCO2

= 0.60 mixture was less than 20 MPa because of thelow original pressure of the prepared mixture. After a sufficient

Table 1. Molar Composition of the Studied Gas Mixturesand Purity of the Component Gases

specified purityof carbon

dioxide (xCO2)

specifiedpurity ofmethane(xCH4

)

cylinderpressure at

roomtemperature

composition (xCO2) μmol·mol−1 μmol·mol−1 MPa

0.199778 ± 0.000025 999950 999995 100.400637 ± 0.000024 999950 999995 100.601623 ± 0.000040 999950 999995 5.5

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time for the stabilization of the temperature inside the cell, themeasurement process started. Pressure steps were measuredfrom 20 MPa down to 1 MPa. The sinker mass in vacuum wasdetermined at the end of each isotherm. For each pressure step,30 replicates were measured, though only the last ten were usedto obtain the average state magnitudes.The repeatability of the density measurements was checked

in some of the isotherms by measuring some replicates of thestate points. The repeatability of the experimental densities waschecked to be less than 0.01 %.Test isotherms with nitrogen were carried out before the

measurement of each mixture to test the correct operation ofthe densimeter. Experimental densities of nitrogen werecompared with the densities calculated with the referenceequation of state for nitrogen of Span et al.18 and yielded anaverage absolute deviation less than 0.02 %, which correspondsto the uncertainty of this equation of state.

3. RESULTS AND DISCUSSION3.1. Uncertainty of the Measurements. The densimeter

has been recently modified16 to improve its measurementuncertainty. The expanded uncertainty in density is estimatedto be less than 0.12 %, while the uncertainties in temperature

and pressure are less than 4 mK and 0.015 %, respectively(k = 2). The overall uncertainty in density must include themeasurement uncertainties in temperature and pressure, andalso, the uncertainty in the composition of the mixtures, asexpressed in eq 2.

ρ ρ ρ ρ

ρ

= + ∂∂

+ ∂∂

+ ∂∂

⎜ ⎟

⎜ ⎟

⎛

⎝⎜⎜⎜

⎛

⎝⎜⎜⎛⎝⎜

⎞⎠⎟

⎞

⎠⎟⎟

⎛⎝⎜⎜⎛⎝

⎞⎠

⎞⎠⎟⎟

⎛⎝⎜⎜⎛⎝

⎞⎠

⎞⎠⎟⎟

⎞

⎠⎟⎟⎟

u up

u pT

u T

xu x

( ) ( ) ( ) ( )

( )

TT x p x

T p

2

,

2

,

2

,

2 1/2

(2)

Here, uT(ρ) is the standard (k = 1) total uncertainty in density,p is the pressure, T is the temperature, and x is the carbondioxide molar fraction. Partial derivatives were calculated withthe GERG-2008 equation of state. The standard (k = 1) overalluncertainty in density is reported in the tables below for eachstate point.

3.2. Discussion of the Results. Tables 2 to 4 collect 138,100, and 77 experimental (p, ρ, T) data corresponding to the

Table 2. Results of the (p, ρ, T) Measurements for the Mixture of Carbon Dioxide with Methane with a Carbon Dioxide MolarFraction xCO2

= 0.199778, where T Is the Temperature (ITS-90), p the Pressure, ρexp the Experimental Density, ρEoS the DensityCalculated from the GERG-2008 Equation of State, and uT is the Standard (k = 1) Overall Uncertainty in Densitya

T p ρexp uT

K MPa kg·m−3 102(ρexp − ρEoS)/ρEoS kg·m−3

250.059 17.720 317.764 0.033 0.039250.061 17.009 310.486 0.031 0.040250.062 16.001 298.981 0.031 0.041250.061 14.959 285.286 0.039 0.044250.063 14.129 272.744 0.048 0.047250.040 11.803 227.426 0.077 0.057250.042 11.001 207.851 0.107 0.061250.044 10.001 181.260 0.142 0.063250.041 9.002 154.043 0.139 0.060250.039 7.999 128.049 0.093 0.054250.041 6.999 104.637 0.046 0.048250.039 6.000 84.000 −0.009 0.042250.036 4.999 65.842 −0.042 0.036250.046 3.997 49.786 −0.030 0.032250.053 2.999 35.502 −0.029 0.029250.053 2.004 22.645 −0.018 0.013250.053 0.996 10.779 −0.020 0.012275.017 19.956 276.100 −0.033 0.037275.016 19.001 266.217 −0.032 0.038275.014 17.986 254.779 −0.031 0.039275.011 17.008 242.757 −0.029 0.040275.009 16.005 229.349 −0.024 0.041275.009 15.003 214.815 −0.015 0.043275.009 14.003 199.243 −0.003 0.044275.008 13.002 182.762 0.010 0.044275.009 12.002 165.645 0.019 0.044275.009 11.000 148.263 0.030 0.043275.009 10.003 131.045 0.019 0.041275.009 9.020 114.534 0.010 0.039275.009 8.107 99.811 0.000 0.037275.007 7.106 84.505 −0.002 0.034275.004 6.008 68.753 −0.016 0.031275.005 5.001 55.279 −0.021 0.029

T p ρexp uT

K MPa kg·m−3 102(ρexp − ρEoS)/ρEoS kg·m−3

275.004 4.017 42.954 −0.023 0.027275.006 2.999 31.022 −0.025 0.025275.004 1.990 19.957 0.014 0.013275.004 0.991 9.645 0.008 0.012299.950 19.913 227.409 −0.007 0.035299.952 18.996 217.937 0.000 0.036299.957 17.998 207.086 0.008 0.036299.959 16.910 194.645 0.013 0.036299.958 16.123 185.307 0.023 0.036299.960 14.999 171.496 0.038 0.036299.959 14.113 160.305 0.040 0.036299.961 13.084 147.072 0.043 0.035299.964 11.999 132.991 0.042 0.034299.967 10.999 120.061 0.046 0.033299.968 9.999 107.267 0.037 0.032299.968 9.000 94.735 0.034 0.031299.967 8.070 83.364 0.029 0.030299.967 7.045 71.216 0.030 0.028299.968 6.000 59.296 0.028 0.027299.969 4.995 48.286 0.026 0.025299.969 4.008 37.909 0.027 0.024299.971 3.003 27.780 0.011 0.023299.969 1.993 18.042 0.037 0.013299.969 0.996 8.825 0.032 0.012324.979 17.449 169.541 0.018 0.032324.979 16.995 165.043 0.020 0.032324.980 15.997 154.988 0.021 0.031324.980 14.999 144.749 0.020 0.031324.983 13.818 132.486 0.031 0.030324.981 12.997 123.884 0.030 0.030324.980 11.997 113.390 0.025 0.029324.982 10.998 102.936 0.026 0.029324.981 9.998 92.547 0.019 0.028

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mixtures with carbon dioxide content xCO2= (0.199778, 0.400637,

and 0.601623), respectively. The relative deviations betweenthe reported densities and the densities calculated with theGERG-2008 equation of state and the standard (k = 1)overall uncertainty in density for each state point are alsogiven. Each state point magnitude value was obtained as theaverage of the last 10 values of the 30 replicate measurementsof each pressure step.Figures 1 to 3 depict the relative deviations from the GERG-

2008 equation of state versus pressure of the experimental datapresented in Tables 2 to 4, respectively. The shaded bandrepresents the estimated uncertainty in density of the equationof state when predicting the density of gaseous mixtures ofmethane and carbon dioxide, which is 0.1 %.As can be observed in Figure 1, there is an exceptionally

good agreement between the experimental densities and theGERG-2008 equation of state at temperatures above 250 K forthe mixture with a carbon dioxide content xCO2

= 0.20. Therelative deviations are within a 0.1 % band, except for those at

250 K and pressures between (9 and 11) MPa, whichexperience larger deviations above this band.Experimental densities of the two mixtures with a higher

content of carbon dioxide show, however, negative deviationswhich increase with pressure and carbon dioxide content,as can be seen in Figures 2 and 3. The observed deviationsfollow a similar behavior in both cases. It is remarkable thatsimilar behaviors of the experimental data with respect to theequation of state to that observed at 250 K in the mixturewith carbon dioxide content xCO2

= 0.20 can be also foundat (275 and 300) K for the mixtures with carbon dioxidecontent xCO2

= (0.40 and 0.60), respectively. For this reason, itcould be concluded that these high deviations, observed inthe middle pressure range, may be due to the proximity ofthe experimental data to the saturation curve and the criticalpoint, as it can be observed in Figure 4, where the satura-tion curve for each mixture is depicted together with theexperimental points at the lowest isotherm measured for eachmixture.

Table 2. continued

T p ρexp uT

K MPa kg·m−3 102(ρexp − ρEoS)/ρEoS kg·m−3

324.981 9.000 82.311 0.012 0.027324.980 8.002 72.237 0.006 0.026324.979 7.001 62.343 0.004 0.025324.978 6.004 52.708 0.000 0.024324.979 5.002 43.259 −0.002 0.023324.980 3.992 34.000 −0.005 0.022324.980 2.999 25.159 −0.004 0.021324.980 1.994 16.469 0.002 0.012324.980 0.998 8.115 −0.013 0.012324.981 0.998 8.114 −0.009 0.012349.966 16.757 142.049 0.031 0.028349.965 15.750 133.311 0.029 0.028349.966 14.991 126.643 0.026 0.027349.967 13.996 117.828 0.021 0.027349.966 12.997 108.933 0.016 0.026349.967 11.997 100.011 0.018 0.025349.968 10.996 91.104 0.012 0.025349.966 9.997 82.241 0.008 0.024349.967 9.000 73.462 0.004 0.023349.966 8.028 64.986 0.021 0.012349.968 6.999 56.125 0.030 0.012349.968 6.998 56.121 0.020 0.028349.969 5.998 47.627 0.023 0.023349.969 5.998 47.626 0.004 0.023349.967 4.998 39.289 0.002 0.022349.967 4.998 39.288 0.000 0.021349.970 3.998 31.094 0.007 0.020349.970 3.998 31.093 0.008 0.020349.970 2.998 23.064 0.004 0.012349.970 2.998 23.063 0.001 0.012349.970 1.993 15.159 0.000 0.022349.970 1.993 15.158 −0.002 0.021349.970 1.993 15.159 0.004 0.020349.970 0.998 7.505 0.005 0.020349.970 0.998 7.504 −0.002 0.012349.970 0.998 7.505 −0.011 0.012

T p ρexp uT

K MPa kg·m−3 102(ρexp − ρEoS)/ρEoS kg·m−3

374.944 19.939 150.707 0.016 0.027374.945 19.082 144.421 0.012 0.027374.946 17.988 136.285 0.011 0.026374.943 16.989 128.742 0.008 0.026374.946 15.993 121.141 0.005 0.026374.947 14.991 113.416 0.002 0.025374.945 13.993 105.670 −0.002 0.025374.946 12.993 97.863 −0.005 0.024374.945 11.994 90.049 −0.010 0.024374.946 10.994 82.233 −0.006 0.023374.944 9.995 74.421 −0.012 0.023374.947 8.883 65.767 −0.016 0.022374.947 7.930 58.389 −0.022 0.022374.947 6.997 51.228 −0.020 0.021374.945 6.002 43.652 −0.028 0.020374.945 4.999 36.102 −0.031 0.020374.945 3.997 28.651 −0.033 0.019374.947 2.998 21.319 −0.037 0.019374.950 2.000 14.112 −0.010 0.012374.949 0.992 6.941 0.004 0.012400.014 14.809 101.918 −0.013 0.024400.015 13.990 96.226 −0.011 0.023400.015 12.989 89.239 −0.013 0.023400.015 11.991 82.244 −0.011 0.022400.016 10.991 75.222 −0.013 0.022400.015 9.993 68.212 −0.017 0.021400.014 8.994 61.204 −0.012 0.021400.016 7.996 54.210 −0.020 0.023400.018 7.002 47.282 −0.024 0.020400.016 5.997 40.322 −0.022 0.020400.015 4.999 33.446 −0.026 0.019400.015 3.998 26.613 −0.023 0.019400.018 2.998 19.845 −0.033 0.018400.016 1.994 13.127 −0.018 0.018400.017 0.998 6.531 −0.018 0.012

aExpanded (k = 2) uncertainties of each state point magnitude are: u(T) = 3.9 mK, u(p) = 3.5·10−3 + 7.5·10−5pMPa (for pressures above 2 MPa) oru(p) = 1.8·10−4 + 6.0·10−5p MPa (for pressures of 2 MPa or below) and u(ρ) = 2.3·10−2 + 1.1·10−4ρ kg·m−3.

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The new experimental data reported in this work formixtures of carbon dioxide with methane are here comparedwith the literature data mentioned in the introduction sectionfor mixtures with a similar composition. Only the data at low

temperatures are compared in Figures 5 to 7 to confirm if theunexpected deviations observed in Figures 1 to 3 have beenpreviously reported by other authors. Figures 5, 6, and 7 depictthe relative deviations in density for mixtures with a carbon

Table 3. Results of the (p, ρ, T) Measurements for the Mixture of Carbon Dioxide with Methane with a Carbon Dioxide MolarFraction xCO2

= 0.400637, where T Is the Temperature (ITS-90), p the Pressure, ρexp the Experimental Density, ρEoS the DensityCalculated from the GERG-2008 Equation of State, and uT is the Standard (k = 1) Overall Uncertainty in Densitya

T p ρexp uT

K MPa kg·m−3 102(ρexp − ρEoS)/ρEoS kg·m−3

275.037 18.801 390.124 −0.037 0.046275.030 18.001 379.515 −0.105 0.048275.029 16.092 350.142 −0.128 0.053275.028 14.108 310.634 −0.113 0.061275.027 12.002 255.941 −0.011 0.070275.025 10.000 195.639 0.139 0.069275.026 8.000 139.096 0.071 0.056275.026 6.001 92.953 −0.011 0.044275.025 4.004 56.051 −0.049 0.035275.025 1.988 25.515 −0.026 0.013275.024 0.993 12.256 −0.023 0.012299.956 19.476 320.040 −0.243 0.046299.959 18.999 313.315 −0.242 0.047299.963 18.059 299.322 −0.237 0.048299.962 17.009 282.477 −0.223 0.049299.963 15.998 265.042 −0.200 0.050299.965 15.001 246.757 −0.169 0.051299.962 14.155 230.531 −0.144 0.051299.964 12.999 207.592 −0.115 0.051299.962 11.999 187.444 −0.098 0.050299.961 11.022 167.877 −0.084 0.048299.962 10.002 147.892 −0.092 0.046299.962 9.004 129.067 −0.098 0.043299.961 8.000 111.044 −0.102 0.040299.959 7.015 94.308 −0.101 0.037299.958 5.998 78.017 −0.105 0.035299.958 4.989 62.859 −0.103 0.032299.955 3.993 48.790 −0.101 0.030299.956 3.002 35.604 −0.094 0.028299.955 1.993 22.975 −0.064 0.013299.958 0.997 11.181 −0.072 0.012324.978 18.944 255.776 −0.131 0.042324.982 18.002 242.914 −0.115 0.043324.982 16.007 214.240 −0.082 0.042324.980 14.017 184.283 −0.063 0.041324.981 12.012 153.688 −0.057 0.039324.981 9.999 123.602 −0.054 0.036324.981 8.002 95.147 −0.051 0.033324.981 6.001 68.467 −0.039 0.030324.981 4.000 43.763 −0.024 0.027324.982 1.991 20.901 −0.007 0.013349.957 19.605 225.084 −0.158 0.038349.957 18.996 218.051 −0.154 0.037349.957 17.983 206.113 −0.148 0.037349.956 17.007 194.397 −0.141 0.037349.956 15.999 182.088 −0.134 0.036349.959 15.109 171.117 −0.122 0.036349.961 13.996 157.279 −0.125 0.035349.960 12.993 144.787 −0.121 0.034349.961 12.104 133.748 −0.121 0.033

T p ρexp uT

K MPa kg·m−3 102(ρexp − ρEoS)/ρEoS kg·m−3

349.960 10.998 120.117 −0.113 0.032349.960 9.992 107.869 −0.099 0.031349.961 8.999 95.944 −0.114 0.030349.962 7.996 84.128 −0.111 0.029349.962 6.996 72.606 −0.102 0.028349.962 5.996 61.357 −0.097 0.027349.961 4.997 50.399 −0.090 0.025349.962 4.006 39.808 −0.088 0.024349.961 2.997 29.337 −0.080 0.023349.961 1.994 19.234 −0.059 0.013349.962 0.997 9.474 −0.077 0.012374.950 19.906 200.428 −0.154 0.034374.951 18.989 191.188 −0.150 0.034374.948 17.990 180.961 −0.146 0.033374.950 16.992 170.605 −0.141 0.033374.951 15.943 159.599 −0.140 0.032374.952 14.992 149.562 −0.134 0.032374.949 13.993 138.951 −0.135 0.031374.948 12.992 128.320 −0.128 0.030374.949 11.950 117.260 −0.128 0.030374.951 11.009 107.319 −0.119 0.029374.951 9.997 96.695 −0.119 0.028374.951 8.995 86.283 −0.114 0.027374.951 7.996 76.011 −0.108 0.026374.951 6.996 65.890 −0.100 0.025374.950 5.997 55.925 −0.093 0.024374.948 4.998 46.138 −0.081 0.024374.950 3.995 36.485 −0.074 0.023374.949 2.998 27.088 −0.053 0.022374.951 1.988 17.763 −0.057 0.013374.951 0.993 8.773 −0.028 0.012400.018 19.946 180.087 −0.068 0.031400.017 18.983 171.465 −0.061 0.031400.016 17.986 162.405 −0.071 0.030400.017 16.908 152.527 −0.069 0.030400.018 15.988 144.024 −0.068 0.029400.016 14.990 134.744 −0.070 0.029400.017 13.958 125.097 −0.069 0.028400.016 12.938 115.556 −0.068 0.028400.016 11.992 106.702 −0.067 0.027400.016 10.992 97.363 −0.058 0.026400.017 9.991 88.043 −0.058 0.026400.017 7.996 69.645 −0.050 0.024400.017 6.996 60.542 −0.040 0.024400.016 5.997 51.540 −0.036 0.023400.018 4.997 42.637 −0.013 0.022400.017 4.000 33.883 0.024 0.021400.015 2.998 25.200 0.049 0.021400.013 1.989 16.590 0.072 0.012400.015 0.998 8.251 0.054 0.012

aExpanded (k = 2) uncertainties of each state point magnitude are: u(T) = 3.9 mK, u(p) = 3.5·10−3 + 7.5·10−5pMPa (for pressures above 2 MPa) oru(p) = 1.8·10−4 + 6.0·10−5p MPa (for pressures of 2 MPa or below) and u(ρ) = 2.3·10−2 + 1.1·10−4ρ kg·m−3.

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Table 4. Results of the (p, ρ, T) Measurements for the Mixture of Carbon Dioxide with Methane with a Carbon Dioxide MolarFraction xCO2

= 0.601623, where T Is the Temperature (ITS-90), p the Pressure, ρexp the Experimental Density, ρEoS the DensityCalculated from the GERG-2008 Equation of State, and uT Is the Standard (k = 1) Overall Uncertainty in Densitya

T p ρexp uT

K MPa kg·m−3 102(ρexp−ρEoS)/ρEoS kg·m−3

299.992 13.154 316.638 −0.445 0.082299.988 12.026 278.580 −0.313 0.083299.986 11.027 243.914 −0.194 0.081299.985 10.024 209.959 −0.150 0.075299.985 8.998 177.625 −0.152 0.067299.985 8.020 149.665 −0.167 0.060299.984 7.023 124.089 −0.164 0.053299.984 5.998 100.533 −0.156 0.047299.983 5.000 79.906 −0.138 0.042299.985 4.002 61.193 −0.095 0.037299.982 2.999 44.005 −0.056 0.034299.982 1.997 28.195 −0.036 0.013299.983 0.998 13.599 −0.017 0.012324.979 13.000 230.103 −0.332 0.058324.979 12.028 207.668 −0.308 0.056324.979 11.000 184.504 −0.275 0.053324.979 10.012 162.979 −0.261 0.050324.978 8.997 141.882 −0.243 0.047324.979 7.997 122.177 −0.220 0.044324.979 6.999 103.638 −0.188 0.041324.979 6.000 86.135 −0.168 0.038324.978 5.007 69.768 −0.142 0.035324.978 3.999 54.118 −0.093 0.032324.978 2.998 39.437 −0.061 0.030324.979 1.998 25.579 −0.036 0.013324.979 0.998 12.447 −0.026 0.012349.967 17.545 268.385 −0.441 0.050349.966 16.999 259.069 −0.430 0.050349.967 16.013 242.000 −0.408 0.049349.967 15.003 224.302 −0.384 0.048349.964 14.000 206.656 −0.348 0.047349.965 12.999 189.085 −0.318 0.046349.964 11.997 171.692 −0.284 0.044349.964 10.997 154.626 −0.260 0.042349.964 10.006 138.104 −0.238 0.040349.964 8.990 121.625 −0.218 0.038349.965 7.995 106.042 −0.176 0.036349.965 6.998 90.920 −0.175 0.034349.965 5.999 76.355 −0.156 0.033

T p ρexp uT

K MPa kg·m−3 102(ρexp−ρEoS)/ρEoS kg·m−3

349.965 4.998 62.325 −0.134 0.031349.964 3.999 48.857 −0.114 0.029349.965 2.998 35.891 −0.090 0.027349.964 1.990 23.359 −0.065 0.013349.965 0.998 11.480 −0.081 0.012374.951 19.532 256.935 −0.285 0.044374.949 17.994 235.519 −0.269 0.043374.951 15.992 206.960 −0.249 0.041374.950 13.986 178.061 −0.227 0.040374.949 12.011 149.810 −0.207 0.037374.949 11.001 135.612 −0.184 0.036374.950 9.999 121.712 −0.174 0.035374.949 9.002 108.159 −0.159 0.033374.949 7.997 94.764 −0.143 0.032374.947 6.997 81.764 −0.117 0.031374.947 5.998 69.087 −0.099 0.029374.946 4.998 56.733 −0.081 0.028374.949 3.998 44.717 −0.065 0.027374.948 2.992 32.974 −0.049 0.025374.948 1.986 21.560 −0.014 0.013400.011 19.496 225.213 −0.349 0.039400.012 18.983 219.081 −0.345 0.038400.012 17.985 207.041 −0.337 0.038400.011 16.982 194.837 −0.328 0.037400.012 15.990 182.686 −0.319 0.037400.012 14.992 170.428 −0.310 0.036400.011 13.992 158.126 −0.302 0.035400.011 13.008 146.047 −0.296 0.034400.012 11.996 133.703 −0.279 0.033400.011 10.988 121.519 −0.248 0.032400.012 8.993 97.725 −0.216 0.030400.012 7.995 86.056 −0.199 0.029400.011 6.111 64.557 −0.153 0.027400.012 4.996 52.160 −0.137 0.026400.012 3.996 41.273 −0.125 0.025400.011 2.995 30.592 −0.092 0.024400.012 1.984 20.042 −0.085 0.013400.011 0.993 9.916 −0.080 0.012

aExpanded (k = 2) uncertainties of each state point magnitude are: u(T) = 3.9 mK, u(p) = 3.5·10−3 + 7.5·10−5pMPa (for pressures above 2 MPa) oru(p) = 1.8·10−4 + 6.0·10−5p MPa (for pressures of 2 MPa or below) and u(ρ) = 2.3·10−2 + 1.1·10−4ρ kg·m−3.

Figure 1. Percentage density deviations of experimental (p, ρ, T) dataof the (0.20 CO2 + 0.80 CH4) binary mixture from density values ρEoScalculated from the GERG-2008 equation of state versus pressure: □,250 K; ◇, 275 K; △, 300 K; ×, 325; +, 350 K; ○, 375 K; ∗, 400 K.

Figure 2. Percentage density deviations of experimental (p, ρ, T) dataof the (0.40 CO2 + 0.60 CH4) binary mixture from density values ρEoScalculated from the GERG-2008 equation of state versus pressure: ◇,275 K; △, 300 K; ×, 325; +, 350 K; ○, 375 K; ∗, 400 K.

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dioxide content xCO2= (0.20, 0.29), xCO2

= (0.40, 0.47) and xCO2=

(0.60, 0.67), respectively, at temperatures of 300 K or below.It can be seen that the observed high deviations are also foundin the experimental data of the literature for similar mixtures,at low temperatures and medium pressures. In the case ofthe mixtures with a carbon dioxide content of xCO2

≈ 0.60, themaximum deviations occur at high pressures.

Table 5 collects statistical magnitudes of the experimentaldata reported in this work and those measured by Esper et al.8

and Hwang et al.,7 where n is the number of data points, AADis the average absolute deviation defined in eq 3, rms refersto the root-mean-square defined in eq 4, and MaxD representsthe maximum relative deviation in the considered dataset. Both experimental data measured by Esper et al.8 andby Hwang et al.,7 for a carbon dioxide molar fraction of xCO2

=0.67, were not used in the fitting of the GERG-2004 equationof state.

∑ρ ρ

ρ=

−

=nAAD

110

i

ni i

i1

2 ,exp ,EoS

,EoS (3)

∑ρ ρ

ρ=

−

=

⎛⎝⎜⎜

⎞⎠⎟⎟n

rms1

i

ni i

i1

,exp ,EoS

,EoS

2

(4)

Figure 3. Percentage density deviations of experimental (p, ρ, T) dataof the (0.60 CO2 + 0.40 CH4) binary mixture from density values ρEoScalculated from the GERG-2008 equation of state versus pressure: △,300 K; ×, 325; +, 350 K; ○, 375 K; ∗, 400 K.

Figure 4. Comparison between the reported experimental density dataat the lowest temperature isotherms and the saturation curve for eachmixture. Blue and □: xCO2

= 0.20; Orange and ◇: xCO2= 0.40; Red

and △: xCO2= 0.60.

Figure 5. Percentage density deviations of experimental (p, ρ, T) dataof binary mixtures of carbon dioxide with methane from density valuesρEoS calculated from the GERG-2008 equation of state versus pressure,for CO2 molar compositions (xCO2

= 0.20, 0.29) at low temperaturesand pressures up to 20 MPa: ◆, this work (xCO2

= 0.20, T = 250 K);▲, this work (xCO2

= 0.20, T = 275 K); △, Hwang et al.7 (xCO2= 0.29,

T = 280 K); □, Hwang et al.7 (xCO2= 0.29, T = 260 K). The shaded

0.1 % band represents the estimated uncertainty of the equation ofstate for these mixtures.

Figure 6. Percentage density deviations of experimental (p, ρ, T) dataof binary mixtures of carbon dioxide with methane from density valuesρEoS calculated from the GERG-2008 equation of state versus pressure,for CO2 molar compositions (xCO2

= 0.40, 0.47) at low temperatures

and pressures up to 20 MPa: ▲, this work (xCO2= 0.40, T = 275 K);

◆, this work (xCO2= 0.40, T = 300 K); ×, Esper et al.8 (xCO2

= 0.47,

T = 289 K); □, Esper et al.8 (xCO2= 0.47, T = 300 K). The shaded

0.1 % band represents the estimated uncertainty of the equation ofstate for these mixtures.

Figure 7. Percentage density deviations of experimental (p, ρ, T) dataof binary mixtures of carbon dioxide with methane from density valuesρEoS calculated from the GERG-2008 equation of state versus pressure,for CO2 molar compositions (xCO2

= 0.60, 0.67) at low temperatures

and pressures up to 20 MPa: ◆, this work (xCO2= 0.60, T = 300 K); +,

Hwang et al.7 (xCO2= 0.67, T = 275 K); ◇, Hwang et al.7 (xCO2

= 0.67,

T = 300 K). The shaded 0.1 % band represents the estimateduncertainty of the equation of state for these mixtures.

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4. CONCLUSIONNew experimental (p, ρ, T) data of three mixtures of carbondioxide with methane, with carbon dioxide molar composi-tions xCO2

= (0.20, 0.40, and 0.60), were accurately measured aspart of the research project AMRP ENG01 of the EuropeanMetrology Research Program for the characterization of non-conventional energy gases. Density data were measured alongseven isotherms in the temperature range from (250 to 400) Kand pressures up to 20 MPa using a single sinker densimeter withmagnetic suspension coupling.Experimental densities were compared with the densities

estimated from the GERG-2008 equation of state. Relativedeviations showed a very good agreement between the experi-mental data and the equation of state for the mixture with thelowest content of carbon dioxide, except at 250 K and mediumpressures where unexpected higher deviations were found.However, deviations of the densities reported for the othertwo mixtures increase with pressure. A similar behavior to thatobserved at 250 K in the first mixture can be also seen for theminimum temperature isotherms in the other two mixtures.The new data were compared with the experimental densities

reported by other authors for mixtures with a similar com-position, and the same behavior could be observed at lowtemperatures and medium pressures.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: cescha@eii.uva.es.FundingSupport for this work came from the Programa Nacional deFormacio n de Profesorado Universitario (FPU), projectENE2009-14644-C02-01 of the Spanish Ministry of Scienceand Innovation, Junta de Castilla y Leon reference GR 152, andfrom the research project AMRP ENG01 of the EuropeanMetrology Research Program.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank the Spanish National Metrology Institute (CentroEspanol de Metrologia, CEM) for the preparation of the threebinary mixtures analyzed in this work.

■ REFERENCES(1) European Parliament. European Parliament Resolution on theInternational Conference for Renewable Energies, Bonn, Germany;Resolution. P5_TA(2004)0276; 2004.(2) Florrisson, O.; Pinchbeck, D. Biogas and others in natural gasoperations (BONGO): a project under development; 23rd World GasConference, Amsterdam, 2006.

(3) Marcogaz Final Recommendation. Injection of Gases from Non-Conventional Sources into Gas Networks; Marcogaz: Brussels, 2006.(4) Characterization of energy gases; EMRP ENG01 N 912/2009/EC;Euramet: Braunschweig, Germany, 2010−2013.(5) Jaeschke, M.; Humphreys, A. E.; Van Caneghem, P.; Fauveau, M.;Janssen-van Rosmalen, R.; Pellei, Q. The GERG Databank of HighAccuracy Compressibility Factor Measurements. GERG Tech. Monogr.,1997; Vol. 4.(6) Kunz, O.; Klimeck, R.; Wagner, W.; Jaeschke, M. The GERG-2004 Wide-Range Reference Equation of State for Natural Gases andOther Mixtures. GERG Tech. Monogr. Fortsch., 2007.(7) Hwang, C.; Iglesias-Silva, G. A.; Holste, J. C.; Hall, K. R.;Gammon, B. E.; Marsh, K. N. Densities of carbon dioxide + methanemixtures from 225 to 350 K at pressures up to 35 MPa. J. Chem. Eng.Data 1997, 5, 897−899.(8) Esper, G. J.; Bailey, D. M.; Holste, J. C.; Hall, K. R. Volumetricbehavior of near-equimolar mixtures for CO2 + CH4 and CO2 + N2.Fluid Phase Equilib. 1989, 49, 35−47.(9) Kunz, O.; Wagner, W. The GERG-2008 Wide-Range Equation ofState for Natural Gases and Other Mixtures: An Expansion of GERG-2004. J. Chem. Eng. Data 2012, in press.(10) Wagner, W.; Kleinrahm, R. Densimeters for very accuratedensity measurements of fluids over large ranges of temperature,pressure, and density. Metrologia 2004, 2, S24−S39.(11) Brachthauser, K.; Kleinrahm, R.; Losch, H. W.; Wagner, W.Entwicklungeinesneuen Dichtemeßverfahrens und Aufbau einer Hoch-temperatur-Hochdruck-Dichtemeßanlage; VDI-Verlag, Dusseldorf, 1993.(12) Wagner, W.; Brachthauser, K.; Kleinrahm, R.; Losch, H. W. Anew, accurate single-sinker densitometer for temperatures from 233 to523 K at pressures up to 30 MPa. Int. J. Thermophys. 1995, 2, 399−411.(13) Klimeck, J. Weiterentwicklung einer Ein-Senkkorper-Dichteme-ßanlage und Prazisionsmessungen der thermischen Zustandsgroßenvon Kohlendioxid, Argon, Stickstoff und Methan; Ruhr-UniversitatBochum, 1997.(14) Klimeck, J.; Kleinrahm, R.; Wagner, W. An accurate single-sinker densimeter and measurements of the (p, ρ, T) relation of argonand nitrogen in the temperature range from (235 to 520) K atpressures up to 30 MPa. J. Chem. Thermodyn. 1998, 12, 1571−1588.(15) Chamorro, C. R.; Segovia, J. J.; Martin, M. C.; Villamanan, M.A.; Estela-Uribe, J. F.; Trusler, J. P. M. Measurement of the (pressure,density, temperature) relation of two (methane plus nitrogen) gasmixtures at temperatures between 240 and 400 K and pressures up to20 MPa using an accurate single-sinker densimeter. J. Chem.Thermodyn. 2006, 7, 916−922.(16) Mondejar, M. E.; Segovia, J. J.; Chamorro, C. R. Improvementof the measurement uncertainty of a high accuracy single sinkerdensimeter via setup modifications based on a state point uncertaintyanalysis. Measurement 2011, 9, 1768−1780.(17) McLinden, M. O.; Kleinrahm, R.; Wagner, W. Forcetransmission errors in magnetic suspension densimeters. Int. J.Thermophys. 2007, 2, 429−448.(18) Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W.;Yokozeki, A. A reference equation of state for the thermodynamicproperties of nitrogen for temperatures from 63.151 to 1000 K andpressures to 2200 MPa. J. Phys. Chem. Ref. Data 2000, 6, 1361−1401.

Table 5. Statistical Comparison of the Experimental Density Measurements Reported in This Work and by Other Authors, withRespect to the GERG-2008 Equation of State

source year experimental technique n 102·AAD 102·rms 102·MaxD

this work, xCO2= (0.20) 2012 single sinker densimeter 138 0.022 0.142 0.031

this work, xCO2= (0.40) 2012 single sinker densimeter 100 0.095 −0.243 0.107

this work, xCO2= (0.60) 2012 single sinker densimeter 77 0.198 −0.445 0.226

Esper et al.,8 xCO2= (0.47) 1997 Burnett-isochoric 118 0.388 −3.073 0.862

Hwang et al.,7 xCO2= (0.29) 2011 pycnometer 41 0.233 −0.826 0.315

Hwang et al.,7 xCO2= (0.67) 2011 pycnometer 49 0.440 −1.7 0.569

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