Experimental Determination of (p, Ï, T) Data for Three Mixtures of

Article pubs.acs.org/jced

Experimental Determination of (p, ρ, T) Data for Three Mixtures of Carbon Dioxide with Methane for the Thermodynamic Characterization of Nonconventional Energy Gases Paper presented at the 18th Symposium on Thermophysical Properties, Boulder, CO, June 24 to 29, 2012. María E. Mondéjar,† Teresa E. Fernández-Vicente,‡ Frédérique Haloua,§ and César R. Chamorro*,† †

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

ABSTRACT: Experimental characterization of the thermodynamic behavior of gas binary mixtures containing components of fuel gases is of great importance due to the proved lack of reliable data of thermodynamic properties of mixtures. These data are essential not only for the improvement and test of the current reference equation of state for natural gases and related mixtures, GERG-2008, but also for the indirect determination of other properties. In this work density measurements of mixtures of carbon dioxide with methane are presented as a contribution to the research project EMRP ENG01 of the European Metrology Research Program, in the field of characterization of energy gases. Accurate density measurements for three binary mixtures of carbon dioxide with methane (xCO2 = 0.20, 0.40, and 0.60) were performed at temperatures between (250 and 400) K and pressures up to 20 MPa, using a single sinker densimeter with magnetic suspension coupling, 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 other authors for similar mixtures. Relatively large deviations from the equation of state observed at low temperatures suggests the possibility of higher uncertainties of the GERG model in the low temperature range. To this end, the research project EMRP ENG014 of the European Metrology Research Program, sponsored by EURAMET, addresses several joint research projects for the characterization of energy gases. The work presented in this paper is a contribution to the joint research project for the indirect determination of the calorific value of nonconventional energy gases. The present work contributes to this project with accurate density measurements of three binary mixtures of carbon dioxide with methane with different compositions, which were selected as reference mixtures for the research 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 the GERG data bank5 for these mixtures, less than half were used for the fitting of the current reference equation of state for natural gas, GERG-2004.6 Some of these data correspond to similar mixtures to those studied here. For instance, Hwang et al.7 measured (p, ρ, T) data of mixtures with a carbon dioxide molar fraction xCO2 = (0.10 to 0.90) in the temperature range from (225 to 350) K and pressures up to 35 MPa.

1. INTRODUCTION The current energy policies of the European Union are focused on the reduction of both the external energy dependence and the carbon dioxide emissions to the atmosphere, by maintaining the current energy supply and production levels. For this purpose, the use of renewable energies1 and the increase of the energy efficiency of current industrial processes are being considered as the main strategies in the short and medium term. Among the available renewable resources, biofuels are intended to replace partially or totally the use of fossil fuels which are consumed, mainly, for transportation and heating purposes. However, biofuels and other alternative fuels are characterized to have a localized production, so that its use far from the production location would increase costs and reduce their efficiency and sustainability. A solution to this problem could be based in reducing as much as possible the transportation costs of the fuels by using the current logistics networks. In this regard, several European projects2,3 are considering the “greening” of natural gas through the injection of other nonconventional fuel gases, such as biogas or coal-bed methane, in the European gas pipelines. However, due to the differences in composition between these new alternative fuel gases and natural gas, the current metrology infrastructure which is used in the gas industry must be tested and adjusted to enable the interchangeability of these new energy gases. © 2012 American Chemical Society

Received: June 19, 2012 Accepted: July 31, 2012 Published: August 17, 2012 2581

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

Journal of Chemical & Engineering Data

Article

Esper et al.8 measured the density of an equimolar mixture of carbon dioxide with methane in the range from (220 to 320) K and pressures up to 48 MPa. However, while the experimental data measured by Hwang et al.7 were used in their most for the fitting 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 temperature range from (250 to 400) K at pressures up to 20 MPa, though the lowest temperature isotherms were not carried out on all the mixtures to avoid the partial condensation of any of the components. An accurate single sinker densimeter with magnetic suspension 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 its performance for these mixtures, and the relative deviations in density of experimental data were listed and plotted versus pressure for their comparison with the above-mentioned literature data for similar mixtures The new GERG-2008 equation of state is an extension of the previous GERG-2004 equation of state for natural gases and related mixtures.6 This new equation, which is expected to be adopted as an ISO Standard (ISO 20765-2 and ISO 20765-3), covers three additional components to the 18 components covered by the previous equation, but the general mathematical structure, mixture parameters, correlations, and departure 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 of the 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 used in the fitting.5 These new, accurate (p, ρ, T) data for mixtures of carbon dioxide with methane will be complemented with speed of sound measurements on mixtures of the same composition for the indirect determination of the calorific value. Both density and speed of sound experimental data will be of great importance for the test or improvement of the current reference equation of state GERG-2008.

Here mS0 and mSf refer to the sinker mass in a vacuum and the sinker mass in the pressurized fluid, respectively, and Vs(T,p) refers to the sinker volume affected by the fluid temperature and pressure. The densimeter works over a temperature range from (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 pressure and temperature ranges thanks to the magnetic suspension coupling which transmits the sinker mass and the buoyancy force acting on it to the balance hook without any contact. However, as stated by McLinden et al.,17 this magnetic coupling induces a force transmission error, which consists of two separate effects: the apparatus effect and the fluid specific effect. The apparatus effect, which is induced due to the magnetic behavior of the apparatus itself, is here compensated for. By contrast, since the specific fluid effect is proportional to the magnetic susceptibility of the fluid, which is in this case very low, the contribution of this term to the total force transmission error can be neglected if compared to the uncertainty in density of the measurements. 2.2. Experimental Material. The three mixtures of carbon dioxide with methane measured in this work were prepared gravimetrically in the Spanish National Metrology Institute (Centro Español de Metrologia,́ CEM) and supplied in 5 dm3 aluminum cylinders. Table 1 shows the mixture compositions with estimated uncertainties in molar fractions, together with the mole fraction purities of the component gases and the cylinder pressures. Table 1. Molar Composition of the Studied Gas Mixtures and Purity of the Component Gases specified purity of methane (xCH4)

cylinder pressure at room temperature

composition (xCO2)

μmol·mol−1

μmol·mol−1

MPa

0.199778 ± 0.000025 0.400637 ± 0.000024 0.601623 ± 0.000040

999950 999950 999950

999995 999995 999995

10 10 5.5

Pure carbon dioxide was supplied by Carburos Metálicos (Air Products) with a certified mole fraction purity of 0.99995. Pure methane was supplied by Praxair with a certified mole fraction purity of 0.999995. Nitrogen used for test measurements was supplied by Alphagaz (Air Liquid) with a certified mole fraction purity of 0.999999. 2.3. Experimental Procedure. The measurements were carried out in the homogeneous gas region along seven isotherms at (250, 275, 300, 325, 350, 375, and 400) K and pressures up to 20 MPa. To avoid the partial condensation of 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 two mixtures 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 means of a manual pump. The maximum pressure of two isotherms for the xCO2 = 0.60 mixture was less than 20 MPa because of the low original pressure of the prepared mixture. After a sufficient

2. EXPERIMENTAL SECTION 2.1. Apparatus Description. As stated above, a single sinker densimeter with magnetic suspension coupling was used to perform the measurements. This apparatus, which is based on the Archimedes' principle, is one of the state of the art methodologies for the experimental determination of the density of fluids10 and was originally developed by Brachthäuser et al.11,12 and successively improved.13,14 The single sinker densimeter used to perform the measurements presented in this work has been previously described in detail by Chamorro et al.15 and Mondéjar et al.16 In this densimeter the buoyancy force acting on a body which is immersed in the fluid contained in the measuring cell is measured. The buoyancy force is determined by measuring the change in the sinker mass when it is surrounded by the thermostatized and pressurized fluid. Then, the density of the fluid can be obtained by dividing this change in mass by the sinker volume, as expressed in eq 1. ρ = (mS0 − mSf )/Vs(T , p)

specified purity of carbon dioxide (xCO2)

(1) 2582



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

time for the stabilization of the temperature inside the cell, the measurement process started. Pressure steps were measured from 20 MPa down to 1 MPa. The sinker mass in vacuum was determined at the end of each isotherm. For each pressure step, 30 replicates were measured, though only the last ten were used to obtain the average state magnitudes. The repeatability of the density measurements was checked in some of the isotherms by measuring some replicates of the state points. The repeatability of the experimental densities was checked to be less than 0.01 %. Test isotherms with nitrogen were carried out before the measurement of each mixture to test the correct operation of the densimeter. Experimental densities of nitrogen were compared with the densities calculated with the reference equation of state for nitrogen of Span et al.18 and yielded an average absolute deviation less than 0.02 %, which corresponds to the uncertainty of this equation of state.

⎛ ⎛⎛ ⎞ ⎞2 ⎛ ⎞2 ⎛ ∂ρ ⎞ ∂ρ ⎜ 2 ⎜ ⎟ uT (ρ) = ⎜u(ρ) + ⎜⎜ ⎟ u(p)⎟ + ⎜⎜⎜ ⎟ u(T )⎟⎟ ⎜ ⎠ ⎝⎝ ∂T ⎠ p , x ⎝⎝ ∂p ⎠T , x ⎠ ⎝ ⎞2 ⎞ ⎛⎛ ∂ρ ⎞ ⎟ + ⎜⎜⎜ ⎟ u(x)⎟⎟ ⎟ ⎝ ⎠ x ∂ ⎠ ⎟⎠ ⎝ T ,p

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 carbon dioxide molar fraction. Partial derivatives were calculated with the GERG-2008 equation of state. The standard (k = 1) overall uncertainty in density is reported in the tables below for each state point. 3.2. Discussion of the Results. Tables 2 to 4 collect 138, 100, and 77 experimental (p, ρ, T) data corresponding to the

3. RESULTS AND DISCUSSION 3.1. Uncertainty of the Measurements. The densimeter has been recently modified16 to improve its measurement uncertainty. The expanded uncertainty in density is estimated to be less than 0.12 %, while the uncertainties in temperature

Table 2. Results of the (p, ρ, T) Measurements for the Mixture of Carbon Dioxide with Methane with a Carbon Dioxide Molar Fraction xCO2 = 0.199778, where T Is the Temperature (ITS-90), p the Pressure, ρexp the Experimental Density, ρEoS the Density Calculated from the GERG-2008 Equation of State, and uT is the Standard (k = 1) Overall Uncertainty in Densitya T

p

K

MPa

250.059 250.061 250.062 250.061 250.063 250.040 250.042 250.044 250.041 250.039 250.041 250.039 250.036 250.046 250.053 250.053 250.053 275.017 275.016 275.014 275.011 275.009 275.009 275.009 275.008 275.009 275.009 275.009 275.009 275.009 275.007 275.004 275.005

17.720 17.009 16.001 14.959 14.129 11.803 11.001 10.001 9.002 7.999 6.999 6.000 4.999 3.997 2.999 2.004 0.996 19.956 19.001 17.986 17.008 16.005 15.003 14.003 13.002 12.002 11.000 10.003 9.020 8.107 7.106 6.008 5.001

ρexp kg·m

−3

317.764 310.486 298.981 285.286 272.744 227.426 207.851 181.260 154.043 128.049 104.637 84.000 65.842 49.786 35.502 22.645 10.779 276.100 266.217 254.779 242.757 229.349 214.815 199.243 182.762 165.645 148.263 131.045 114.534 99.811 84.505 68.753 55.279

T

uT 10 (ρexp − ρEoS)/ρEoS 2

0.033 0.031 0.031 0.039 0.048 0.077 0.107 0.142 0.139 0.093 0.046 −0.009 −0.042 −0.030 −0.029 −0.018 −0.020 −0.033 −0.032 −0.031 −0.029 −0.024 −0.015 −0.003 0.010 0.019 0.030 0.019 0.010 0.000 −0.002 −0.016 −0.021

kg·m

−3

0.039 0.040 0.041 0.044 0.047 0.057 0.061 0.063 0.060 0.054 0.048 0.042 0.036 0.032 0.029 0.013 0.012 0.037 0.038 0.039 0.040 0.041 0.043 0.044 0.044 0.044 0.043 0.041 0.039 0.037 0.034 0.031 0.029 2583

p

K

MPa

275.004 275.006 275.004 275.004 299.950 299.952 299.957 299.959 299.958 299.960 299.959 299.961 299.964 299.967 299.968 299.968 299.967 299.967 299.968 299.969 299.969 299.971 299.969 299.969 324.979 324.979 324.980 324.980 324.983 324.981 324.980 324.982 324.981

4.017 2.999 1.990 0.991 19.913 18.996 17.998 16.910 16.123 14.999 14.113 13.084 11.999 10.999 9.999 9.000 8.070 7.045 6.000 4.995 4.008 3.003 1.993 0.996 17.449 16.995 15.997 14.999 13.818 12.997 11.997 10.998 9.998

ρexp kg·m

−3

42.954 31.022 19.957 9.645 227.409 217.937 207.086 194.645 185.307 171.496 160.305 147.072 132.991 120.061 107.267 94.735 83.364 71.216 59.296 48.286 37.909 27.780 18.042 8.825 169.541 165.043 154.988 144.749 132.486 123.884 113.390 102.936 92.547

uT 10 (ρexp − ρEoS)/ρEoS

kg·m−3

−0.023 −0.025 0.014 0.008 −0.007 0.000 0.008 0.013 0.023 0.038 0.040 0.043 0.042 0.046 0.037 0.034 0.029 0.030 0.028 0.026 0.027 0.011 0.037 0.032 0.018 0.020 0.021 0.020 0.031 0.030 0.025 0.026 0.019

0.027 0.025 0.013 0.012 0.035 0.036 0.036 0.036 0.036 0.036 0.036 0.035 0.034 0.033 0.032 0.031 0.030 0.028 0.027 0.025 0.024 0.023 0.013 0.012 0.032 0.032 0.031 0.031 0.030 0.030 0.029 0.029 0.028

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Table 2. continued T

p

K

MPa

324.981 324.980 324.979 324.978 324.979 324.980 324.980 324.980 324.980 324.981 349.966 349.965 349.966 349.967 349.966 349.967 349.968 349.966 349.967 349.966 349.968 349.968 349.969 349.969 349.967 349.967 349.970 349.970 349.970 349.970 349.970 349.970 349.970 349.970 349.970 349.970

9.000 8.002 7.001 6.004 5.002 3.992 2.999 1.994 0.998 0.998 16.757 15.750 14.991 13.996 12.997 11.997 10.996 9.997 9.000 8.028 6.999 6.998 5.998 5.998 4.998 4.998 3.998 3.998 2.998 2.998 1.993 1.993 1.993 0.998 0.998 0.998

ρexp kg·m

−3

82.311 72.237 62.343 52.708 43.259 34.000 25.159 16.469 8.115 8.114 142.049 133.311 126.643 117.828 108.933 100.011 91.104 82.241 73.462 64.986 56.125 56.121 47.627 47.626 39.289 39.288 31.094 31.093 23.064 23.063 15.159 15.158 15.159 7.505 7.504 7.505

T


0.012 0.006 0.004 0.000 −0.002 −0.005 −0.004 0.002 −0.013 −0.009 0.031 0.029 0.026 0.021 0.016 0.018 0.012 0.008 0.004 0.021 0.030 0.020 0.023 0.004 0.002 0.000 0.007 0.008 0.004 0.001 0.000 −0.002 0.004 0.005 −0.002 −0.011

kg·m

−3

0.027 0.026 0.025 0.024 0.023 0.022 0.021 0.012 0.012 0.012 0.028 0.028 0.027 0.027 0.026 0.025 0.025 0.024 0.023 0.012 0.012 0.028 0.023 0.023 0.022 0.021 0.020 0.020 0.012 0.012 0.022 0.021 0.020 0.020 0.012 0.012

p

K

MPa

374.944 374.945 374.946 374.943 374.946 374.947 374.945 374.946 374.945 374.946 374.944 374.947 374.947 374.947 374.945 374.945 374.945 374.947 374.950 374.949 400.014 400.015 400.015 400.015 400.016 400.015 400.014 400.016 400.018 400.016 400.015 400.015 400.018 400.016 400.017

19.939 19.082 17.988 16.989 15.993 14.991 13.993 12.993 11.994 10.994 9.995 8.883 7.930 6.997 6.002 4.999 3.997 2.998 2.000 0.992 14.809 13.990 12.989 11.991 10.991 9.993 8.994 7.996 7.002 5.997 4.999 3.998 2.998 1.994 0.998

ρexp kg·m

−3

150.707 144.421 136.285 128.742 121.141 113.416 105.670 97.863 90.049 82.233 74.421 65.767 58.389 51.228 43.652 36.102 28.651 21.319 14.112 6.941 101.918 96.226 89.239 82.244 75.222 68.212 61.204 54.210 47.282 40.322 33.446 26.613 19.845 13.127 6.531


kg·m−3

0.016 0.012 0.011 0.008 0.005 0.002 −0.002 −0.005 −0.010 −0.006 −0.012 −0.016 −0.022 −0.020 −0.028 −0.031 −0.033 −0.037 −0.010 0.004 −0.013 −0.011 −0.013 −0.011 −0.013 −0.017 −0.012 −0.020 −0.024 −0.022 −0.026 −0.023 −0.033 −0.018 −0.018

0.027 0.027 0.026 0.026 0.026 0.025 0.025 0.024 0.024 0.023 0.023 0.022 0.022 0.021 0.020 0.020 0.019 0.019 0.012 0.012 0.024 0.023 0.023 0.022 0.022 0.021 0.021 0.023 0.020 0.020 0.019 0.019 0.018 0.018 0.012

2

Expanded (k = 2) uncertainties of each state point magnitude are: u(T) = 3.9 mK, u(p) = 3.5·10−3 + 7.5·10−5p MPa (for pressures above 2 MPa) or u(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.

a

250 K and pressures between (9 and 11) MPa, which experience larger deviations above this band. Experimental densities of the two mixtures with a higher content of carbon dioxide show, however, negative deviations which increase with pressure and carbon dioxide content, as can be seen in Figures 2 and 3. The observed deviations follow a similar behavior in both cases. It is remarkable that similar behaviors of the experimental data with respect to the equation of state to that observed at 250 K in the mixture with carbon dioxide content xCO2 = 0.20 can be also found at (275 and 300) K for the mixtures with carbon dioxide content xCO2 = (0.40 and 0.60), respectively. For this reason, it could be concluded that these high deviations, observed in the middle pressure range, may be due to the proximity of the experimental data to the saturation curve and the critical point, as it can be observed in Figure 4, where the saturation curve for each mixture is depicted together with the experimental points at the lowest isotherm measured for each mixture.

mixtures with carbon dioxide content xCO2 = (0.199778, 0.400637, and 0.601623), respectively. The relative deviations between the reported densities and the densities calculated with the GERG-2008 equation of state and the standard (k = 1) overall uncertainty in density for each state point are also given. Each state point magnitude value was obtained as the average of the last 10 values of the 30 replicate measurements of each pressure step. Figures 1 to 3 depict the relative deviations from the GERG2008 equation of state versus pressure of the experimental data presented in Tables 2 to 4, respectively. The shaded band represents the estimated uncertainty in density of the equation of state when predicting the density of gaseous mixtures of methane 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 the GERG-2008 equation of state at temperatures above 250 K for the mixture with a carbon dioxide content xCO2 = 0.20. The relative deviations are within a 0.1 % band, except for those at 2584



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Table 3. Results of the (p, ρ, T) Measurements for the Mixture of Carbon Dioxide with Methane with a Carbon Dioxide Molar Fraction xCO2 = 0.400637, where T Is the Temperature (ITS-90), p the Pressure, ρexp the Experimental Density, ρEoS the Density Calculated from the GERG-2008 Equation of State, and uT is the Standard (k = 1) Overall Uncertainty in Densitya T

p

K

MPa

275.037 275.030 275.029 275.028 275.027 275.025 275.026 275.026 275.025 275.025 275.024 299.956 299.959 299.963 299.962 299.963 299.965 299.962 299.964 299.962 299.961 299.962 299.962 299.961 299.959 299.958 299.958 299.955 299.956 299.955 299.958 324.978 324.982 324.982 324.980 324.981 324.981 324.981 324.981 324.981 324.982 349.957 349.957 349.957 349.956 349.956 349.959 349.961 349.960 349.961

18.801 18.001 16.092 14.108 12.002 10.000 8.000 6.001 4.004 1.988 0.993 19.476 18.999 18.059 17.009 15.998 15.001 14.155 12.999 11.999 11.022 10.002 9.004 8.000 7.015 5.998 4.989 3.993 3.002 1.993 0.997 18.944 18.002 16.007 14.017 12.012 9.999 8.002 6.001 4.000 1.991 19.605 18.996 17.983 17.007 15.999 15.109 13.996 12.993 12.104

ρexp kg·m

−3

390.124 379.515 350.142 310.634 255.941 195.639 139.096 92.953 56.051 25.515 12.256 320.040 313.315 299.322 282.477 265.042 246.757 230.531 207.592 187.444 167.877 147.892 129.067 111.044 94.308 78.017 62.859 48.790 35.604 22.975 11.181 255.776 242.914 214.240 184.283 153.688 123.602 95.147 68.467 43.763 20.901 225.084 218.051 206.113 194.397 182.088 171.117 157.279 144.787 133.748

T


−0.037 −0.105 −0.128 −0.113 −0.011 0.139 0.071 −0.011 −0.049 −0.026 −0.023 −0.243 −0.242 −0.237 −0.223 −0.200 −0.169 −0.144 −0.115 −0.098 −0.084 −0.092 −0.098 −0.102 −0.101 −0.105 −0.103 −0.101 −0.094 −0.064 −0.072 −0.131 −0.115 −0.082 −0.063 −0.057 −0.054 −0.051 −0.039 −0.024 −0.007 −0.158 −0.154 −0.148 −0.141 −0.134 −0.122 −0.125 −0.121 −0.121

kg·m

−3

0.046 0.048 0.053 0.061 0.070 0.069 0.056 0.044 0.035 0.013 0.012 0.046 0.047 0.048 0.049 0.050 0.051 0.051 0.051 0.050 0.048 0.046 0.043 0.040 0.037 0.035 0.032 0.030 0.028 0.013 0.012 0.042 0.043 0.042 0.041 0.039 0.036 0.033 0.030 0.027 0.013 0.038 0.037 0.037 0.037 0.036 0.036 0.035 0.034 0.033

p

K

MPa

349.960 349.960 349.961 349.962 349.962 349.962 349.961 349.962 349.961 349.961 349.962 374.950 374.951 374.948 374.950 374.951 374.952 374.949 374.948 374.949 374.951 374.951 374.951 374.951 374.951 374.950 374.948 374.950 374.949 374.951 374.951 400.018 400.017 400.016 400.017 400.018 400.016 400.017 400.016 400.016 400.016 400.017 400.017 400.017 400.016 400.018 400.017 400.015 400.013 400.015

10.998 9.992 8.999 7.996 6.996 5.996 4.997 4.006 2.997 1.994 0.997 19.906 18.989 17.990 16.992 15.943 14.992 13.993 12.992 11.950 11.009 9.997 8.995 7.996 6.996 5.997 4.998 3.995 2.998 1.988 0.993 19.946 18.983 17.986 16.908 15.988 14.990 13.958 12.938 11.992 10.992 9.991 7.996 6.996 5.997 4.997 4.000 2.998 1.989 0.998

ρexp kg·m

−3

120.117 107.869 95.944 84.128 72.606 61.357 50.399 39.808 29.337 19.234 9.474 200.428 191.188 180.961 170.605 159.599 149.562 138.951 128.320 117.260 107.319 96.695 86.283 76.011 65.890 55.925 46.138 36.485 27.088 17.763 8.773 180.087 171.465 162.405 152.527 144.024 134.744 125.097 115.556 106.702 97.363 88.043 69.645 60.542 51.540 42.637 33.883 25.200 16.590 8.251


kg·m−3

−0.113 −0.099 −0.114 −0.111 −0.102 −0.097 −0.090 −0.088 −0.080 −0.059 −0.077 −0.154 −0.150 −0.146 −0.141 −0.140 −0.134 −0.135 −0.128 −0.128 −0.119 −0.119 −0.114 −0.108 −0.100 −0.093 −0.081 −0.074 −0.053 −0.057 −0.028 −0.068 −0.061 −0.071 −0.069 −0.068 −0.070 −0.069 −0.068 −0.067 −0.058 −0.058 −0.050 −0.040 −0.036 −0.013 0.024 0.049 0.072 0.054

0.032 0.031 0.030 0.029 0.028 0.027 0.025 0.024 0.023 0.013 0.012 0.034 0.034 0.033 0.033 0.032 0.032 0.031 0.030 0.030 0.029 0.028 0.027 0.026 0.025 0.024 0.024 0.023 0.022 0.013 0.012 0.031 0.031 0.030 0.030 0.029 0.029 0.028 0.028 0.027 0.026 0.026 0.024 0.024 0.023 0.022 0.021 0.021 0.012 0.012

2


a

temperatures are compared in Figures 5 to 7 to confirm if the unexpected deviations observed in Figures 1 to 3 have been previously reported by other authors. Figures 5, 6, and 7 depict the relative deviations in density for mixtures with a carbon

The new experimental data reported in this work for mixtures of carbon dioxide with methane are here compared with the literature data mentioned in the introduction section for mixtures with a similar composition. Only the data at low 2585



Article

Table 4. Results of the (p, ρ, T) Measurements for the Mixture of Carbon Dioxide with Methane with a Carbon Dioxide Molar Fraction xCO2 = 0.601623, where T Is the Temperature (ITS-90), p the Pressure, ρexp the Experimental Density, ρEoS the Density Calculated from the GERG-2008 Equation of State, and uT Is the Standard (k = 1) Overall Uncertainty in Densitya T

p

ρexp

uT

T

p

ρexp

K

MPa

kg·m−3

102(ρexp−ρEoS)/ρEoS

kg·m−3

K

MPa

kg·m−3

102(ρexp−ρEoS)/ρEoS

kg·m−3

299.992 299.988 299.986 299.985 299.985 299.985 299.984 299.984 299.983 299.985 299.982 299.982 299.983 324.979 324.979 324.979 324.979 324.978 324.979 324.979 324.979 324.978 324.978 324.978 324.979 324.979 349.967 349.966 349.967 349.967 349.964 349.965 349.964 349.964 349.964 349.964 349.965 349.965 349.965

13.154 12.026 11.027 10.024 8.998 8.020 7.023 5.998 5.000 4.002 2.999 1.997 0.998 13.000 12.028 11.000 10.012 8.997 7.997 6.999 6.000 5.007 3.999 2.998 1.998 0.998 17.545 16.999 16.013 15.003 14.000 12.999 11.997 10.997 10.006 8.990 7.995 6.998 5.999

316.638 278.580 243.914 209.959 177.625 149.665 124.089 100.533 79.906 61.193 44.005 28.195 13.599 230.103 207.668 184.504 162.979 141.882 122.177 103.638 86.135 69.768 54.118 39.437 25.579 12.447 268.385 259.069 242.000 224.302 206.656 189.085 171.692 154.626 138.104 121.625 106.042 90.920 76.355

−0.445 −0.313 −0.194 −0.150 −0.152 −0.167 −0.164 −0.156 −0.138 −0.095 −0.056 −0.036 −0.017 −0.332 −0.308 −0.275 −0.261 −0.243 −0.220 −0.188 −0.168 −0.142 −0.093 −0.061 −0.036 −0.026 −0.441 −0.430 −0.408 −0.384 −0.348 −0.318 −0.284 −0.260 −0.238 −0.218 −0.176 −0.175 −0.156

0.082 0.083 0.081 0.075 0.067 0.060 0.053 0.047 0.042 0.037 0.034 0.013 0.012 0.058 0.056 0.053 0.050 0.047 0.044 0.041 0.038 0.035 0.032 0.030 0.013 0.012 0.050 0.050 0.049 0.048 0.047 0.046 0.044 0.042 0.040 0.038 0.036 0.034 0.033

349.965 349.964 349.965 349.964 349.965 374.951 374.949 374.951 374.950 374.949 374.949 374.950 374.949 374.949 374.947 374.947 374.946 374.949 374.948 374.948 400.011 400.012 400.012 400.011 400.012 400.012 400.011 400.011 400.012 400.011 400.012 400.012 400.011 400.012 400.012 400.011 400.012 400.011

4.998 3.999 2.998 1.990 0.998 19.532 17.994 15.992 13.986 12.011 11.001 9.999 9.002 7.997 6.997 5.998 4.998 3.998 2.992 1.986 19.496 18.983 17.985 16.982 15.990 14.992 13.992 13.008 11.996 10.988 8.993 7.995 6.111 4.996 3.996 2.995 1.984 0.993

62.325 48.857 35.891 23.359 11.480 256.935 235.519 206.960 178.061 149.810 135.612 121.712 108.159 94.764 81.764 69.087 56.733 44.717 32.974 21.560 225.213 219.081 207.041 194.837 182.686 170.428 158.126 146.047 133.703 121.519 97.725 86.056 64.557 52.160 41.273 30.592 20.042 9.916

−0.134 −0.114 −0.090 −0.065 −0.081 −0.285 −0.269 −0.249 −0.227 −0.207 −0.184 −0.174 −0.159 −0.143 −0.117 −0.099 −0.081 −0.065 −0.049 −0.014 −0.349 −0.345 −0.337 −0.328 −0.319 −0.310 −0.302 −0.296 −0.279 −0.248 −0.216 −0.199 −0.153 −0.137 −0.125 −0.092 −0.085 −0.080

0.031 0.029 0.027 0.013 0.012 0.044 0.043 0.041 0.040 0.037 0.036 0.035 0.033 0.032 0.031 0.029 0.028 0.027 0.025 0.013 0.039 0.038 0.038 0.037 0.037 0.036 0.035 0.034 0.033 0.032 0.030 0.029 0.027 0.026 0.025 0.024 0.013 0.012

uT


a

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

Figure 1. Percentage density deviations of experimental (p, ρ, T) data of the (0.20 CO2 + 0.80 CH4) binary mixture from density values ρEoS calculated from the GERG-2008 equation of state versus pressure: □, 250 K; ◇, 275 K; △, 300 K; ×, 325; +, 350 K; ○, 375 K; ∗, 400 K. 2586



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

Figure 6. Percentage density deviations of experimental (p, ρ, T) data of binary mixtures of carbon dioxide with methane from density values ρEoS 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 (xCO = 0.40, T = 300 K); ×, Esper et al.8 (xCO = 0.47, 2 2

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 of state for these mixtures.

Figure 4. Comparison between the reported experimental density data at the lowest temperature isotherms and the saturation curve for each mixture. Blue and □: xCO2 = 0.20; Orange and ◇: xCO2 = 0.40; Red and △: xCO2 = 0.60.

Figure 7. Percentage density deviations of experimental (p, ρ, T) data of binary mixtures of carbon dioxide with methane from density values ρEoS 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 estimated uncertainty of the equation of state for these mixtures.

Table 5 collects statistical magnitudes of the experimental data 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, AAD is the average absolute deviation defined in eq 3, rms refers to the root-mean-square defined in eq 4, and MaxD represents the maximum relative deviation in the considered data set. Both experimental data measured by Esper et al.8 and by Hwang et al.,7 for a carbon dioxide molar fraction of xCO2 = 0.67, were not used in the fitting of the GERG-2004 equation of state.

Figure 5. Percentage density deviations of experimental (p, ρ, T) data of binary mixtures of carbon dioxide with methane from density values ρEoS calculated from the GERG-2008 equation of state versus pressure, for CO2 molar compositions (xCO2 = 0.20, 0.29) at low temperatures and pressures up to 20 MPa: ◆, this work (xCO2 = 0.20, T = 250 K); ▲, this work (xCO = 0.20, T = 275 K); △, Hwang et al.7 (xCO = 0.29, 2 2 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 of state for these mixtures.

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 found in the experimental data of the literature for similar mixtures, at low temperatures and medium pressures. In the case of the mixtures with a carbon dioxide content of xCO2 ≈ 0.60, the maximum deviations occur at high pressures.

AAD =

rms =

2587

n

ρi ,exp − ρi ,EoS

1 n

∑

1 n

2 ⎛ρ − ρi ,EoS ⎞ i ,exp ⎜ ⎟ ∑⎜ ⎟ ρi ,EoS ⎠ i=1 ⎝

i=1

102

ρi ,EoS

(3)

n

(4)



Article

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

year

experimental technique

n

102·AAD

this work, xCO2 = (0.20)

2012

single sinker densimeter

138

0.022

0.142

0.031

2012


100

0.095

−0.243

0.107

this work, xCO2 = (0.60)

2012


77

0.198

−0.445

0.226 0.862

Esper et al., xCO2 = (0.47)

1997

Burnett-isochoric

118

0.388

−3.073

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

4. CONCLUSION New experimental (p, ρ, T) data of three mixtures of carbon dioxide with methane, with carbon dioxide molar compositions xCO2 = (0.20, 0.40, and 0.60), were accurately measured as part of the research project AMRP ENG01 of the European Metrology Research Program for the characterization of nonconventional energy gases. Density data were measured along seven isotherms in the temperature range from (250 to 400) K and pressures up to 20 MPa using a single sinker densimeter with magnetic suspension coupling. Experimental densities were compared with the densities estimated from the GERG-2008 equation of state. Relative deviations showed a very good agreement between the experimental data and the equation of state for the mixture with the lowest content of carbon dioxide, except at 250 K and medium pressures where unexpected higher deviations were found. However, deviations of the densities reported for the other two mixtures increase with pressure. A similar behavior to that observed at 250 K in the first mixture can be also seen for the minimum 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 composition, and the same behavior could be observed at low temperatures and medium pressures.

(3) Marcogaz Final Recommendation. Injection of Gases from NonConventional 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 High Accuracy Compressibility Factor Measurements. GERG Tech. Monogr., 1997; Vol. 4. (6) Kunz, O.; Klimeck, R.; Wagner, W.; Jaeschke, M. The GERG2004 Wide-Range Reference Equation of State for Natural Gases and Other 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 + methane mixtures 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. Volumetric behavior 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 of State for Natural Gases and Other Mixtures: An Expansion of GERG2004. J. Chem. Eng. Data 2012, in press. (10) Wagner, W.; Kleinrahm, R. Densimeters for very accurate density measurements of fluids over large ranges of temperature, pressure, and density. Metrologia 2004, 2, S24−S39. (11) Brachthäuser, K.; Kleinrahm, R.; Lösch, H. W.; Wagner, W. Entwicklungeinesneuen Dichtemeßverfahrens und Aufbau einer Hochtemperatur-Hochdruck-Dichtemeßanlage; VDI-Verlag, Düsseldorf, 1993. (12) Wagner, W.; Brachthäuser, K.; Kleinrahm, R.; Lösch, H. W. A new, accurate single-sinker densitometer for temperatures from 233 to 523 K at pressures up to 30 MPa. Int. J. Thermophys. 1995, 2, 399−411. (13) Klimeck, J. Weiterentwicklung einer Ein-Senkkörper-Dichtemeßanlage und Präzisionsmessungen der thermischen Zustandsgrößen von Kohlendioxid, Argon, Stickstoff und Methan; Ruhr-Universität Bochum, 1997. (14) Klimeck, J.; Kleinrahm, R.; Wagner, W. An accurate singlesinker densimeter and measurements of the (p, ρ, T) relation of argon and nitrogen in the temperature range from (235 to 520) K at pressures 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) gas mixtures at temperatures between 240 and 400 K and pressures up to 20 MPa using an accurate single-sinker densimeter. J. Chem. Thermodyn. 2006, 7, 916−922. (16) Mondéjar, M. E.; Segovia, J. J.; Chamorro, C. R. Improvement of the measurement uncertainty of a high accuracy single sinker densimeter via setup modifications based on a state point uncertainty analysis. Measurement 2011, 9, 1768−1780. (17) McLinden, M. O.; Kleinrahm, R.; Wagner, W. Force transmission 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 thermodynamic properties of nitrogen for temperatures from 63.151 to 1000 K and pressures to 2200 MPa. J. Phys. Chem. Ref. Data 2000, 6, 1361−1401.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

Support for this work came from the Programa Nacional de Formación de Profesorado Universitario (FPU), project ENE2009-14644-C02-01 of the Spanish Ministry of Science and Innovation, Junta de Castilla y León reference GR 152, and from the research project AMRP ENG01 of the European Metrology Research Program. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank the Spanish National Metrology Institute (Centro Español de Metrologia,́ CEM) for the preparation of the three binary mixtures analyzed in this work.

■

102·MaxD

this work, xCO2 = (0.40) 8

■

102·rms

REFERENCES

(1) European Parliament. European Parliament Resolution on the International Conference for Renewable Energies, Bonn, Germany; Resolution. P5_TA(2004)0276; 2004. (2) Florrisson, O.; Pinchbeck, D. Biogas and others in natural gas operations (BONGO): a project under development; 23rd World Gas Conference, Amsterdam, 2006. 2588


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