Vapor-Phase (p, Ï, T, x) Behavior and Virial ... - ACS Publications

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Vapor-Phase (p, ρ, T, x) Behavior and Virial Coefficients for the Binary Mixture (0.05 Hydrogen + 0.95 Carbon Dioxide) over the Temperature Range from (273.15 to 323.15) K with Pressures up to 6 MPa Mohamed A. Ben Souissi, Reiner Kleinrahm, Xiaoxian Yang, and Markus Richter* Thermodynamik, Ruhr-Universität Bochum, D−44780 Bochum, Germany ABSTRACT: Accurate density measurements on a binary (hydrogen + carbon dioxide) mixture with a hydrogen mole fraction of 0.05362 were carried out at temperatures T = (273.15, 293.15, and 323.15) K with pressures up to the dew-point pressure or 6.0 MPa, whichever was lower. The gas mixture was prepared gravimetrically. A wellproven two-sinker magnetic suspension densimeter was utilized for the measurements, and a preheating device for the gas sample was specially designed and integrated in order to avoid condensation when filling and flushing the densimeter. Considering all measurement uncertainties in temperature, pressure, density, and composition, the combined expanded uncertainty (k = 2) in density was estimated to be less than or equal to 7.4 × 10−4ρ. The relative deviations of the experimental densities from the GERG-2008 equation of state were less than 0.4%, which is clearly within the uncertainty of this equation. Sorption effects were carefully investigated, and a large impact on the reproducibility of the density measurements on the order of 6 × 10−4ρ (k = 2) was observed. Values and uncertainties of the second and third virial coefficients were determined by fitting a third-order virial equation to the experimental results. The second interaction virial coefficient was determined as well.

1. INTRODUCTION Carbon dioxide-rich mixtures have been attracting a great deal of interest in recent years due to the increasing applications in the field of chemical synthesis and processing,1 refrigeration engineering,2 enhanced oil recovery,3 and carbon capture and storage (CCS)4,5 as well as in solvation science.6−8 Lots of density measurements were carried out on carbon dioxide-rich mixtures in the past 5 years, e.g., on carbon dioxide + nitrogen, carbon dioxide + argon, and carbon dioxide + oxygen by Mantovani et al.;9 on carbon dioxide + nitrogen + argon and carbon dioxide + methane by Yang et al.;10,11 on carbon dioxide + hydrogen by Sanchez-Vicente et al.;12 on carbon dioxide + argon in our previous work;13,14 and on many more. In the present work, we focused on the binary (hydrogen + carbon dioxide) system. The currently available experimental (p, ρ, T, x) data12,15−20 for this particular system are summarized in Table 1. After a study of these experimental data, an obvious lack of accurate experimental data was observed, and especially no experimental data are available for this binary system at pressures lower than 10 MPa with carbon dioxide mole fractions larger than 0.90. To fill this data gap, we investigated the (p, ρ, T, x) behavior of a binary (hydrogen + carbon dioxide) mixture with a hydrogen mole fraction of 0.05362 at T = (273.15, 293.15, and 323.15) K with pressures up to the dew-point pressure or 6.0 MPa, whichever was lower. © 2017 American Chemical Society

Measurements were conducted with a two-sinker magnetic suspension densimeter, and the measuring points are depicted in Figure 1 in a pressure versus temperature phase diagram. The phase envelope and the critical point (as well as other fluid properties of interest in this work) were calculated with the GERG-2008 equation of state (EOS)21,22 as implemented in the NIST REFPROP database.23 The GERG-2008 EOS is currently the reference EOS for natural gas and similar mixtures. However, it is an empirical EOS, and the accuracy in predicting thermodynamic properties relies on the quality of the underlying experimental data. For the binary (hydrogen + carbon dioxide) system, not enough accurate experimental data were available to develop a binaryspecific departure function;21 thus, the uncertainty of the GERG-2008 EOS in calculating densities in the gas-phase and phase boundaries could be as high as 0.010ρ and 0.050ρ24 (or more), respectively. Please note that the new multiparameter EOS optimized for combustion gases (EOS-CG)25 has not been improved with respect to the (hydrogen + carbon dioxide) system. Therefore, efforts are still required to improve Special Issue: Memorial Issue in Honor of Ken Marsh Received: February 23, 2017 Accepted: June 30, 2017 Published: July 19, 2017 2973

DOI: 10.1021/acs.jced.7b00213 J. Chem. Eng. Data 2017, 62, 2973−2981

Journal of Chemical & Engineering Data

Article

Table 1. Review of Density Measurements on Hydrogen + Carbon Dioxide T range/K

p range/MPa

mole fraction of H2

author

year

273−473 323.15−423.15 303.15−343.15 273−350 278.15−298.15 308−343 288.15−333.15

5.1−50.7 0.1−6.0 0.6−12.7 0.2−26.3 4.8−19.3 20.1−48.9 11.7−22.7

0.47, 0.74 0.2341, 0.8633 0.36−0.49 0.50, 0.75 0.10−0.16 0.065−0.244 0.020, 0.075, 0.100

Kritschewsky and Markov15 Mallu and Viswanath16 Abadio and McElroy17 Jaeschke et al.18 Bezanehtak et al.19 Cipollina et al.20 Sanchez-Vicente et al.12

1940 1990 1993 1997 2002 2007 2013

valves, which are exposed to a temperature below the gas mixture’s dew point. There has been experimental evidence demonstrating that the uncertainty of the density measurement of mixtures increases due to sorption effects.13,14,26,27 Nevertheless, no mathematical approach is currently available to quantitatively determine the impact of sorption effects in advance of experimental studies. Therefore, when accurate experimental data are the goal, one proven way to minimize the detrimental effects of sorption is to flush the measuring cell using “fresh” sample gas from the gas cylinder, as suggested by Richter and Kleinrahm.26 Figure 1. Pressure−temperature phase diagram of the investigated (0.05362 hydrogen + 0.94638 carbon dioxide) mixture: + , density values measured in the present work at T = (273.15, 293.15, and 323.15) K; *, critical point; − , phase boundary calculated with the GERG-2008 equation of state of Kunz and Wagner.21

2. EXPERIMENTAL SECTION 2.1. Apparatus Description. The technique of the twosinker magnetic suspension densimeter was developed by Kleinrahm and Wagner28 in the 1980s. Our present two-sinker apparatus was specially built to measure densities of pure gases and natural gas mixtures over the temperature range from (273.15 to 323.15) K with pressures up to 12 MPa. This particular apparatus was described in detail in previous work;29,30 it was overhauled for recent studies in our group.13,14,26 Detailed information about this general type of instrument can be found elsewhere.28,31,32 Here, we just briefly explain the measuring principle, and only the new preheating device designed to avoid condensation of the gas mixture sample during filling of the densimeter is discussed in more detail. Density measurements were carried out using two specially matched sinkers made of stainless steel: a hollow sphere (VS ≈ 107 cm3; mS ≈ 123 g; ρS ≈ 1.16 g·cm−3) and a solid ring (VR ≈ 15.6 cm3; mR ≈ 123 g; ρR ≈ 7.90 g·cm−3). The sinker surfaces (A ≈ 109 cm2) were polished electrolytically, and afterward

the available EOS, and our new experimental data could serve as a reliable input. In the context of the measurements it is worthwhile to mention that a key challenge in accurate gas density measurements of mixtures is to avoid a compositional distortion caused by surface phenomena such as adsorption and desorption26 or capillary condensation. Such phenomena become particularly distinct when approaching dew-point conditions. Once the composition of the gas mixture is altered, the property under investigation changes and that leads to an experimental result with a larger uncertainty. Situations where a phase transition is most likely encountered are (1) a pressure drop when a gas mixture sample is withdrawn from a high pressure cylinder through a pressure regulator and (2) a temperature drop when mixture sample flows through tubes or

Figure 2. Schematic diagram of the preheating device. The tube (outer diameter, 6 mm; inner diameter, 4 mm) of the preheater is made of stainless steel, and it is about 4 m long. A heating band (about 6 m long) is wrapped around the tube. Its electrical power of at most 300 W is controlled by a two-point controller. 2974



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they were galvanically gold-plated to obtain a surface finish that is as smooth as possible. To measure the density of a gas sample, both sinkers were weighed alternately with an analytical balance (readability, 0.00001 g) while being immersed in the gas sample within the measuring cell. A magnetic suspension coupling was employed to transmit the gravity and buoyancy forces on the sinkers to the balance, thus isolating the gas sample (inside the pressure tight measuring cell) from the balance, which was placed under ambient conditions. The force transmission error of the magnetic suspension coupling, which was described in detail by McLinden et al.,33 was very small. Due to the weak magnetic properties of the coupling housing, its influence on the density measurement was less than 1.0 × 10−5ρ, and the effect of the magnetic properties of the fluid (fluid-specific effect) was also less than 1.0 × 10−5ρ. These two sources of error were included in the combined expanded uncertainty (k = 2) in density measurement of 1.5 × 10−4ρ. The density of the gas under investigation was determined by ρgas (T , p) =

Figure 3. Pressure−enthalpy phase diagram of the binary mixture (0.05362 hydrogen + 0.94638 carbon dioxide). Density values measured in the present work: ○, T = 273.15 K; ◊, T = 293.15 K; ▽, T = 323.15 K. The phase boundary (illustrated by the thick solid line) was calculated with the GERG-2008 equation of state of Kunz and Wagner.21 The solid points (●) illustrate an example for the experimental procedure (with the help of arrows) to attain the first measurement point (4) at T = 273.15 K, where state point (1) indicates the condition of the gas mixture inside the sample cylinder; see explanation in section 2.1.

* * ) (mS − mR ) − (mS,fluid − mR,fluid VS(T , p) − VR (T , p)

(1)

where m and V are the mass and the volume of the sinker, m* is the weighing value of the sinker, and the subscripts refer to the two sinkers. The two sinkers had nearly the same mass (mS − mR ≈ 0.000765 g), the same surface area, and the same surface material, but had a significant difference in volume (VS − VR ≈ 91.4 cm3). According to this, the buoyancy effect was very large, and, therefore, even the low-density range of gases could be measured accurately. Moreover, the adsorption of gas on the sinker surfaces was approximately compensated for because both sinkers had the same surface area (A ≈ 109 cm2) and the same surface material, and, to specifically mention this feature once again, the surface was very smooth. A smooth surface is a fundamental feature of a sinker to minimize the sorption effects. To avoid condensation of the gas sample in the filling lines, a preheating device was specially designed and integrated. The device is shown schematically in Figure 2. Preheating of the gas sample becomes particularly relevant when a sample cylinder is charged with a large amount of gas mixture in order to have enough source material with an exactly known composition for a comprehensive measurement campaign, e.g., with different measurement apparatuses. Therefore, the gas mixture is usually stored in the sample cylinder at a supercritical pressure, and before use the cylinder is heated at the bottom to create fluid convection for mixing. Considering a pressure versus temperature diagram as shown in Figure 1, nothing out of the ordinary can be observed. However, illustrating the measuring points in a pressure versus enthalpy phase diagram, such as in Figure 3, makes clear that expanding the fluid mixture from the sample cylinder (point 1 in Figure 3) into the densimeter’s measuring cell leads temporarily to state points in the two-phase region, i.e., point 5 in Figure 3 (due to adiabatic expansion, h1 = h5). Thus, the sample will partially condense and substantially distort the composition of the gas mixture inside the measuring cell. To avoid this, a heat exchanger (gas preheater) was installed between the pressure regulator at the gas cylinder and a second pressure regulator (see Figure 2) before the inlet of the densimeter. In our system, the gas mixture inside the cylinder was usually heated to T = 323.15 K, and the pressure was about 14.0 MPa; see point 1 in Figure 3. The pressure regulator at the gas cylinder was also heated and only used to slightly reduce the pressure, keeping the gas at a supercritical

state; see point 2 in Figure 3. The line between the two pressure regulators and the second pressure regulator were heated to a temperature of approximately 350 K. Initially, the line was pressurized to approximately p ≈ 12 MPa. Hence, the gas was heated isobarically from point 2 to point 3, as shown in Figure 3. Then, the second pressure regulator and valve 1 (see Figure 2) were opened to flush the line with the sample gas until the temperature sensor before the second pressure regulator reached T ≈ 350 K, which took only a few seconds. After that, valve 1 was closed and valve 2 was opened (see Figure 2), and the sample gas mixture could be expanded into the measuring cell without a phase transition; see the change from point 3 to point 4 in Figure 3. Then, density measurements could be carried out along isotherms at the desired pressure. 2.2. Experimental Material. The binary (hydrogen + carbon dioxide) mixture was prepared gravimetrically with a custom-made mixture preparation system. The detailed description of our sample preparation procedure and the mixture preparation system can be found in section 6 of the dissertation of Schäfer.34 The pure components are described in Table 2; they were used as received without further gas analysis or purification. The concentrations were determined to be 0.05362 mole fraction hydrogen and 0.94638 mole fraction carbon dioxide, respectively. The molar mass of the gas mixture was Mgrav = 41.7580 g·mol−1. The expanded uncertainty (k = 2) in composition due to the mixture preparation was estimated to be 0.00040 mole fraction, which corresponds to an expanded uncertainty (k = 2) in molar mass of 0.0168 g·mol−1. 2.3. Experimental Procedures. Hydrogen is known for its ability to diffuse into solid materials at high pressures, and it is hardly returning to the gas phase at low pressures. However, based on the testing of Richter et al.,35 the quantity of hydrogen likely to diffuse into the sinkers and the measuring cell wall would be on the order of only 10 μg. Carbon dioxide is inclined to adsorb on the solid surfaces inside the measuring cell at high pressures, and subsequently, it would desorb back to the gas phase at low pressures. Moreover, carbon dioxide is known for 2975



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Table 2. Sample Information chemical name

molar mass/ (g·mol−1)

source

purity/(mol fraction)

purification method

hydrogen carbon dioxide

2.0159 44.0095

Air Liquide Air Liquide

0.999990a 0.999995b

none none

a Impurities (stated by supplier): x(H2O) ≤ 5.0 × 10−6, x(O2) ≤ 1.0 × 10−6, x(CmHn) ≤ 0.1 × 10−6, x(N2) ≤ 5.0 × 10−6, and x(CO/CO2) ≤ 0.1 × 10−6. bImpurities (stated by supplier): x(H2O) ≤ 2.0 × 10−6, x(O2) ≤ 1.0 × 10−6, x(CmHn) ≤ 0.1 × 10−6, x(N2) ≤ 2.0 × 10−6, x(CO) ≤ 0.5 × 10−6, and x(NOx) ≤ 0.1 × 10−6.

less than or equal to 7.4 × 10−4ρ, as listed in Table 4 for each measuring point.

its affinity to diffuse into, elastomer seals, and hydrogen can diffuse into elastomers and permeate through them. Thus, nonnegligible sorption effects occur, which have to be examined carefully. To investigate sorption effects in the course of obtaining reliable experimental data, different types of measurement runs were carried out; all measurements were performed along isotherms. After the measuring cell was evacuated for about 9 h, it was slowly filled with the sample gas mixture to the highest desired pressure. Then, isothermal measurements were conducted, and immediate, overnight, and flushing points were determined successively. The nomenclature of the different measurement runs is according to the work of Richter and Kleinrahm:26 immediate point - measurement run without special preparation, e.g., cell only filled or pressure reduced, and adequate equilibration time (about (1−2) h) was allowed before starting the actual density measurement; overnight point - measurement run without special preparation after one or more nights of waiting (minimum time, 14 h); flushing point before the measurement run, the measuring cell was flushed with “fresh“ sample gas at the temperature and pressure of interest and adequate equilibration time was allowed. At each (T, p) state point, at least two replicate measurements were taken. To improve the accuracy of the value (mS,fluid * − mR,fluid * ) in eq 1, the sinkers were generally exchanged 30 times, and an average of 30 single values was calculated.

Table 4. Experimental (p, ρ, T, x) Data for the (0.05362 Hydrogen + 0.94638 Carbon Dioxide) Mixture and Relative Deviations of the Experimental Densities ρexp from Densities Calculated with the GERG-2008 Equation of State21 ρGERG where p is the Pressure, T is the Temperature (ITS-90), and Uc(ρexp)/ρexp is the Relative Combined Expanded Uncertainty (k = 2) in Densitya p/MPa

3. RESULTS AND DISCUSSION 3.1. Uncertainty in Measurement. The “Guide to the Expression of Uncertainty in Measurement”,36 commonly known as GUM, was used to determine the measurement uncertainty. We used the same methodology as described by Richter and McLinden27 to calculate the combined uncertainty in density. The uncertainty budget for the combined standard uncertainty in density is listed in Table 3, where the individual uncertainty contributions were assumed to be not correlated. The combined expanded uncertainties (k = 2) in density were

uncertainty contribution

std uncertainty

T 2.5 mK p 3.5 × 10−5p ρ 7.5 × 10−5ρ c M 0.0084 g·mol−1 reproducibilityd 3.0 × 10−4ρ relative combined expanded uncertainty (k = 2)

× × × × × ×

71.3532 56.5210 42.9575 31.0881 20.4494 9.74868

4.98489 4.05114 3.01670 1.99199 1.01460 0.50316

121.352 89.7154 61.5091 37.9543 18.2895 8.83486

5.99737 5.03044 4.02943 3.00975 2.03106 1.03812 0.54921

121.561 96.6051 73.5962 52.4905 34.0104 16.7369 8.70026

100(ρexp − ρGERG)/ρGERG 0.0624 0.0214 −0.0022 −0.0092 −0.0058 0.0001 −0.1710 −0.1482 −0.0985 −0.0686 −0.0239 −0.0008 −0.3915 −0.2862 −0.1975 −0.1236 −0.0835 −0.0394 −0.0161

The expanded uncertainties (k = 2) of measurements are 5 mK for temperature, 7 × 10−5p for pressure, and 1.5 × 10−4ρ for density. The mixture samples were prepared gravimetrically with the expanded uncertainty in composition 0.00040 mole fraction (k = 2).

3.2. Comparison to Equations of State. At first we investigated the extent of sorption effects by comparing the measured densities at T = 293.15 K with values calculated by the GERG-2008 EOS. The original experimental data are listed in Table 5, and the comparison with the GERG-2008 EOS is shown in Figure 4. Arrows in Figure 4 demonstrate the sequence of measurements. At p ≈ 5 MPa, which was a relatively high pressure and close to the dew line, measurements started with four immediate points showing a relative deviation of about −0.18%. The gas sample remained in the measuring cell overnight, and the relative deviations of the two overnight points became as large as approximately −0.20%. Then, after the measuring cell was flushed, the relative deviations in density of the two flushing points became smaller again (−0.16%). This observation implies that carbon dioxide

contribution to uC(ρ)/ρ 0.16 0.45 0.75 2.01 2.94 7.34

3.03596 2.53690 2.02237 1.52462 1.03957 0.51352

100Uc(ρexp)/ρexp T = 273.150 K 0.059 0.059 0.059 0.059 0.059 0.059 T = 293.150 K 0.074 0.074 0.073 0.073 0.073 0.073 T = 323.150 K 0.074 0.073 0.073 0.073 0.073 0.073 0.073

a

Table 3. Uncertainty Budget for the Relative Combined Standard Uncertainty in Density uC(ρ)/ρa b

ρexp/(kg·m−3)

10−4 10−4 10−4 10−4 10−4 10−4

a

As an example, the contributions to uC(ρ)/ρ were calculated for the binary (hydrogen + carbon dioxide) mixture with a hydrogen mole fraction of 0.05362 at a temperature of 323.15 K and a pressure of 5.03044 MPa. bT = temperature, p = pressure, ρ = density, and M = molar mass. cFrom gravimetric sample preparation. dIncluding sorption effects. 2976



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Table 5. Experimental Densities for the (0.05362 Hydrogen + 0.94638 Carbon Dioxide) Mixture at T = 293.15 K and Relative Deviations of the Experimental Densities ρexp from Densities Calculated with the GERG-2008 Equation of State21 ρGERG where p is the Pressurea p/MPa

ρexp/(kg·m−3)

100(ρexp − ρGERG)/ρGERG

typeb

day of measurement

5.02447 5.02513 5.02570 5.02620 5.02693 5.02715 4.99077 4.99075 4.05062 4.05114 3.02162 3.02246 3.02304 2.03865 2.03947 2.05638 2.05656 1.99173 1.99199 1.03389 1.03446 1.03503 0.52907 0.52952 0.53697 0.53728 0.50299 0.50316

122.879 122.900 122.916 122.936 122.939 122.947 121.587 121.584 89.7079 89.7235 61.6373 61.6579 61.6728 38.9693 38.9857 39.3687 39.3726 37.9553 37.9608 18.6628 18.6723 18.6827 9.30651 9.31437 9.45399 9.45972 8.83244 8.83557

−0.1742 −0.1773 −0.1826 −0.1824 −0.2028 −0.2031 −0.1641 −0.1654 −0.1393 −0.1392 −0.0893 −0.0895 −0.0888 −0.0316 −0.0343 0.0132 0.0133 −0.0513 −0.0516 0.0092 0.0018 −0.0009 0.0500 0.0473 0.0993 0.1002 0.0067 0.0073

IP IP IP IP OP OP FP FP IP IP IP IP IP IP IP OP OP FP FP IP IP IP IP IP OP OP FP FP

Thursday Thursday Thursday Thursday Friday Friday Friday Friday Friday Friday Friday Friday Friday Friday Friday Monday Monday Monday Monday Monday Monday Monday Monday Monday Tuesday Tuesday Tuesday Tuesday

a

In this table, all measurements along a typical isotherm are listed including all check values as an example. The purpose is explained in section 3.2 and Figure 4. bFP, flushing point (after flushing the measuring cell with fresh gas sample); IP, immediate point (no special preparation, e.g., cell only filled or pressure reduced + equilibration time); OP, overnight point (time of waiting at least 14 h).

absorbed overnight on the surface of the measuring cell meaning that the mixture became leaner. At reduced pressures of p ≈ (3 and 1) MPa, the relative deviations in density reveal the inverse behavior; i.e., the density increased overnight or over the weekend and decreased after the measuring cell was flushed with fresh sample gas. It is very likely that carbon dioxide desorbed back into the bulk gas phase at low pressures. According to Table 5 and Figure 4, the impact of sorption effects on the reproducibility of the density measurements was as large as approximately 6 × 10−4ρ (k = 2). The selected experimental (p, ρ, T, x) data for all studied (T, p) state points are listed in Table 4, with flushing points having the highest priority followed by selected immediate points (where no flushing points were measured); overnight points were not taken into account because these values were distorted by sorption effects (see above). Relative deviations of the isothermal experimental data from values calculated with the GERG-2008 EOS21 are shown in Figure 5. No experimental data for this binary system at similar composition and (T, p) state points are available from literature (see Table 1). As shown in Figure 5, relative deviations of our data generally decrease with decreasing pressure along each isotherm and, as expected from theory, converge to zero when approaching the ideal gas limit (at very low pressure). Besides, relative deviations increase with increasing temperature, reaching the largest deviation of −0.39% at T = 323.15 K and p =

Figure 4. Relative deviations of the experimental densities ρexp for the (0.05362 hydrogen + 0.94638 carbon dioxide) mixture from densities ρGERG calculated with the GERG-2008 EOS21 (zero line) at T = 293.15 K. This figure illustrates the influence of adsorption and desorption on the measurements along a typical isotherm. The measurement procedure is explained in section 2.3, and the measurement values are listed in Table 5. □, immediate point (no special preparation, e.g., cell only filled or pressure reduced + equilibration time); ◊, overnight point (time of waiting at least 14 h); ○, flushing point (after flushing the measuring cell with fresh gas sample). Arrows indicate the sequence of measurements.

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mol−1 is the molar gas constant, and B(T) and C(T) are the second and third virial coefficients, respectively. All data were weighted equally, and the results are given in Table 6. Including the fourth virial coefficient did not substantially improve the quality of the fitting. In the first step, B(T) and C(T) in eq 2 were fitted together with the molar mass M of the mixture. Excellent correlations were achieved. The root-mean-squares (RMSVE) of the relative deviations in pressure of the experimental data from values calculated with the fitted virial equation were smaller than 0.0051% for all isotherms (see Table 6). Relative deviations of all correlated molar masses MVE from the gravimetrically determined one (Mgrav = 41.7580 g·mol−1) were within 0.012%, which was smaller than the standard uncertainty of Mgrav, being 2 × 10−4Mgrav. In the second step, B(T) and C(T) in eq 2 were fitted with the molar mass being a constant; i.e., M = Mgrav. Thereby, the root-mean-squares (RMSgrav) of the relative deviations in pressure became slightly larger than that in the first step but were still within 0.0063% for all isotherms (see Table 6). The correlated results for B(T) and C(T) are listed in Table 6 together with the second interaction viral coefficient B12(T), which is defined by

Figure 5. Relative deviations of the experimental densities ρexp for the (0.05362 hydrogen + 0.94638 carbon dioxide) mixture from densities ρGERG calculated with the GERG-2008 EOS21 (zero line). ○, T = 273.15 K; ◊, T = 293.15 K; ▽, T = 323.15 K. Error bars for the relative combined standard uncertainty in density are illustrated for the measurement at T = 323.15 K as an example.

5.99737 MPa. Comparing our new experimental densities with the GERG-2008 EOS, the relative deviations were less than 0.4%, which is clearly within the uncertainty of the GERG-2008 EOS in calculating gas-phase densities of the binary (hydrogen + carbon dioxide) mixture. The selected experimental data were also compared to three equations of state commonly used in industry. Relative deviations of the experimental data for all studied state points from values calculated with the Peng−Robinson (PR) EOS37 and the Lee−Kesler−Ploecker (LKP) EOS38 ranged from (−0.39 to −2.63) % and from (0.07 to 1.53) %, respectively, and the average relative deviations were 1.17 % and 0.47 %, respectively. The Soave−Redlich−Kwong (SRK) EOS39 showed better performance. The relative deviations of the experimental data from values calculated with the SRK EOS ranged from (0.00 to −0.41) %, and the average relative deviation was 0.10 %. For all three equations, relative deviations decrease with decreasing pressure. The calculations of the densities from the three equations of state were carried out with the software Trend 3.0.40 3.3. Virial Coefficients. As done in our previous work about thermal properties of binary mixtures,13,14,27 the isothermal data were correlated to the third-order virial equation p=

ρR mT ⎛ ⎛ ρ ⎞2 ⎞ ρ ⎜1 + B(T ) + C(T )⎜ ⎟ ⎟ ⎝M⎠ ⎠ M ⎝ M

B12 (T ) =

B(T ) − x12B11(T ) − x 2 2B22 (T ) 2x1x 2

(3)

where xi is the mole fraction of component i, Bii(T) is the second virial coefficient of the pure gas i, and the subscripts 1 and 2 represent carbon dioxide and hydrogen, respectively. [Please note: There is a typographical error in eq 3 of our recently published work.13 B11(T) and B22(T) are not supposed to be squared.] The values for Bii(T) were computed from the reference equations of state (hydrogen41 and carbon dioxide42). The uncertainties of the virial coefficients were also calculated and are listed in Table 6. As reported in our previous works about the determination of virial coefficients for the binary (argon + carbon dioxide) system,13,14 the main contributions to the uncertainty of B(T) and C(T) were the statistical uncertainties in fitting the virial equation, the uncertainty of measurements, and the uncertainty of Mgrav. The uncertainty of B12(T) was determined by applying the error propagation principle to eq 3. As can be seen in Table 6, both B(T) and B12(T) increase with increasing temperature while C(T) decreases with increasing temperature, which is a plausible result. The relative deviations of the experimental densities from densities calculated with the virial equation using the

(2)

where p is the pressure, ρ is the density, T is the temperature, M is the molar mass of the gas mixture, Rm = 8.314472 J·K−1·

Table 6. Summary of the Virial Analysis for the (0.05362 Hydrogen + 0.94638 Carbon Dioxide) Systema M taken as a fitted parameter

M = Mgrav

RMSVE/

MVE/

ΔMVE/

x(CO2)/

RMSgrav/

B/

U(B)/

C/

U(C)/

B12/

U(B12)/

T/K

%

(g·mol−1)

(g·mol−1)

(mol fraction)

%

(cm3·mol−1)

(cm3·mol−1)

(cm3·mol−1)

(cm3·mol−1)

(cm3·mol−1)

(cm3·mol−1)

273.150 293.150 323.150

0.0009 0.0042 0.0030

41.7631 41.7629 41.7581

0.0051 0.0048 0.0001

0.94650 0.94649 0.94638

0.0036 0.0063 0.0030

−135.62 −115.13 −91.45

0.37 0.22 0.23

4818 4541 3895

186 68 70

−10.68 −6.66 −1.43

4.43 3.04 2.83

a

M is the molar mass; RMS is the root-mean-square of the relative deviations in pressure of the experimental data from values calculated with the fitted virial equation (eq 2); MVE is the molar mass determined by the virial analysis (eq 2); ΔMVE is the absolute difference of the fitted molar mass MVE from the gravimetrically determined one Mgrav = 41.7580 g·mol−1; x(CO2) is the mole fraction of carbon dioxide determined by the fitted molar mass MVE; B and U(B) are the second virial coefficient and its expanded uncertainty (k = 2), respectively; C and U(C) are the third virial coefficient and its expanded uncertainty (k = 2), respectively; B12 and U(B12) are the second interaction virial coefficient calculated by eq 3 and its expanded uncertainty (k = 2), respectively. 2978



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gravimetrically determined molar mass Mgrav and the fitted virial coefficients B(T) and C(T) are shown in Figure 6. According to

EOS, the values for B12(T) calculated with this model change with composition as discussed and demonstrated in ref 27. Therefore, the value range of B12(T) calculated using the GERG-2008 EOS is shown in Figure 7, with the upper and lower bounds calculated at 0.99 and 0.01 mole fraction hydrogen, respectively. As shown in the figure, there exists large scatter among the available data. Values from Mallu and Viswanath16 are significantly higher compared to the majority of values, while the relevant value from Edwards and Roseveare43 is much lower. Our data, together with those from Cottrell et al.,44 Boerboom and colleagues,45,46 and Abadio and McElroy17 agree within their mutual uncertainties and lie within the value range of the GERG-2008 EOS. This is good agreement despite the difficulty in acquiring good accuracy for B12(T) with a 95/5 composition ratio, as described by Eubank and Hall.47

Figure 6. Relative deviations of experimental densities ρexp for the (0.05362 hydrogen + 0.94638 carbon dioxide) mixture from densities ρvirial calculated using the virial equation (zero line), as given in eq 2, with the gravimetrically determined molar mass Mgrav = 41.7580 g· mol−1. ○, ◊, and ▽, measurements at T = (273.15, 293.15, and 323.15) K, respectively. For the experimental data, the combined expanded uncertainty (k = 2) in density was estimated to be less than or equal to 7.4 × 10−4ρ (see Table 4).

4. CONCLUSIONS Accurate density data of a binary (hydrogen + carbon dioxide) mixture with a hydrogen mole fraction of 0.05362 were measured at T = (273.15, 293.15, and 323.15) K with pressures up to the dew-point pressure or 6.0 MPa, whichever was lower. The mixture was prepared gravimetrically with an expanded uncertainty (k = 2) in composition of 0.00040 mole fraction. The measurements were carried out with a two-sinker magnetic suspension densimeter. To avoid condensation of the gas during the filling process, a new gas preheating device was specially designed and installed. The combined expanded uncertainty (k = 2) in density was estimated to be less than or equal to 7.4 × 10−4ρ. Sorption effects of the gas on the inner surfaces of the densimeter were carefully investigated, and their influence on the density measurements was taken into account by the estimation of the reproducibility. Relative deviations of the new experimental data from values calculated with the GERG-2008 EOS were less than 0.4%, which is within the uncertainty of the GERG-2008 EOS, 0.01ρ or more, for the present binary system over the investigated temperature range. The third-order virial equation was fitted to our isothermal data to determine the second and third virial coefficients. The second interaction virial coefficients were calculated as well. In summary, taking into account our careful uncertainty analysis, the new experimental data together with the virial coefficients can be considered accurate and could be used to further improve the performance of multiparameter equations of state for mixtures.

this figure, the virial equation with the fitted B(T) and C(T) represents the experimental densities, except one value, within 1.4 × 10−4ρ, which is considerably less than the standard uncertainty of the measured densities, being about 3.7 × 10−4ρ or less. Comparisons of experimental values of B12(T) from this work and values from literature are shown in Figure 7. Theoretically, B12(T) for a binary mixture is independent of composition. However, due to the structure of the GERG-2008

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Figure 7. Second interaction viral coefficient B12(T) for binary (hydrogen + carbon dioxide) mixtures versus temperature as determined at different compositions. ●, this work, mole fraction of hydrogen, xH2 = 0.05362; Δ, Edwards and Roseveare,43 xH2 = 0.5187; ▽,

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +49-234−32-26395.

Cottrell et al.,44 xH2 = 0.5; ◊, Michels and Boerboom,45,46 xH2 not

ORCID

given; + , Brewer,48 xH2 not given; ×, Abadio and McElroy,17 xH2 = 0.3816−0.4903, and with an impurity xN2 = 0.0002; □, Mallu and Viswanath,16 xH2 = 0.2341. The B12(T) values calculated by the GERG2008 EOS depend on composition, and the dashed lines show B12(T) at xH2 = 0.99 and 0.01 for the upper and lower lines, respectively. Error bars for the combined expanded uncertainty (k = 2) of B12(T) of our work and of Cottrell et al.44 are illustrated, while those of Mallu and Viswanath16 are within the symbol size. The uncertainty of B12(T) of Edwards and Roseveare,43 Michels and Boerboom,45,46 Brewer,48 and Abadio and McElroy17 was not reported.

Markus Richter: 0000-0001-8120-5646 Funding

We are grateful to Deutsche Forschungsgemeinschaft (DFG) for funding the ongoing research within the Emmy Noether Programme under Grant No. RI 2482/2-1. Furthermore, this work is supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the DFG. Notes

The authors declare no competing financial interest. 2979



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(17) Abadio, B. D.; McElroy, P. J. Pressure, amount-of-substance density, temperature) of {(1-x)CO2+xH2} using a direct method. J. Chem. Thermodyn. 1993, 25, 1495−1501. (18) Jaeschke, M.; Hinze, H.-M.; Humphreys, A. E. Supplement to the GERG databank of high-accuracy compression factor measurements, GERG Technical Monograph 7 (TM7); VDI Verlag: Düsseldorf, Germany. 1996; Fortschritt-Berichte VDI Series 6: Energy Technology, No. 355. (19) Bezanehtak, K.; Combes, G.; Dehghani, F.; Foster, N.; Tomasko, D. Vapor-liquid equilibrium for binary systems of carbon dioxide+ methanol, hydrogen+ methanol, and hydrogen+ carbon dioxide at high pressures. J. Chem. Eng. Data 2002, 47, 161−168. (20) Cipollina, A.; Anselmo, R.; Scialdone, O.; Filardo, G.; Galia, A. Experimental P-T-ρ Measurements of Supercritical Mixtures of Carbon Dioxide, Carbon Monoxide, and Hydrogen and Semiquantitative Estimation of Their Solvent Power Using the Solubility Parameter Concept. J. Chem. Eng. Data 2007, 52, 2291−2297. (21) 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, 57, 3032−3091. (22) International Organization for Standardization 2015. Natural gas - Calculation of thermodynamic properties - Part 2: Single-phase properties (gas, liquid, and dense fluid) for extended ranges of application, ISO 20765-2:2015(E); International Organization for Standardization: Geneva, 2015. (23) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1; National Institute of Standards and Technology: Boulder, CO, USA, 2013. (24) Kunz, O.; Klimeck, R.; Wagner, W.; Jaeschke, M. The GERG2004 wide-range equation of state for natural gases and other mixtures, GERG Technical Monograph 15 (TM15); VDI Verlag: Düsseldorf, Germany, 2007; Fortschritt-Berichte VDI Series 6: Energie Technology, No. 557, http://www.gerg.eu/public/uploads/files/publications/ technical_monographs/tm15_04.pdf (accessed Feb. 23, 2017). (25) Gernert, J.; Span, R. EOS-CG: A Helmholtz energy mixture model for humid gases and CCS mixtures. J. Chem. Thermodyn. 2016, 93, 274−293. (26) Richter, M.; Kleinrahm, R. Influence of adsorption and desorption on accurate density measurements of gas mixtures. J. Chem. Thermodyn. 2014, 74, 58−66. (27) Richter, M.; McLinden, M. O. Vapor-Phase (p,ρ,T,x) Behavior and Virial Coefficients for the (Methane + Propane) System. J. Chem. Eng. Data 2014, 59, 4151−4164. (28) Kleinrahm, R.; Wagner, W. Measurement and correlation of the equilibrium liquid and vapour densities and the vapour pressure along the coexistence curve of methane. J. Chem. Thermodyn. 1986, 18, 739− 760. (29) Wagner, W.; Kleinrahm, R.; Pieperbeck, N.; Jaeschke, M. A new apparatus for high-precision gas-density measurements to calibrate gasdensity transducers, Proceedings of the International Gas Research Conference, Tokyo, Nov. 6−9, 1989; Government Institutes: Rockville, MD, USA, 1990; pp 462−471, http://www.thermo.rub.de/en/ research/72-forschung/339-literature.html (accessed Feb. 23, 2017). (30) Pieperbeck, N.; Kleinrahm, R.; Wagner, W.; Jaeschke, M. Results of (pressure, density, temperature) measurements on methane and on nitrogen in the temperature range from 273.15 to 323.15 K at pressures up to 12 MPa using a new apparatus for accurate gas-density measurements. J. Chem. Thermodyn. 1991, 23, 175−194. (31) Wagner, W.; Kleinrahm, R. Densimeters for very accurate density measurements of fluids over large ranges of temperature, pressure, and density. Metrologia 2004, 41, S24−S39. (32) McLinden, M. O.; Lösch-Will, C. Apparatus for wide-ranging, high-accuracy fluid (p, ρ, T) measurements based on a compact twosinker densimeter. J. Chem. Thermodyn. 2007, 39, 507−530. (33) McLinden, M.; Kleinrahm, R.; Wagner, W. Force transmission errors in magnetic suspension densimeters. Int. J. Thermophys. 2007, 28, 429−448.

ACKNOWLEDGMENTS We thank Vanessa Kaub, who carried out part of the measurements within her Bachelors thesis, and our colleague Dr. Allan Harvey of NIST, who provided us with literature references for the second interaction virial coefficient of the binary (hydrogen + carbon dioxide) system.

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REFERENCES

(1) Beckman, E. J. Supercritical and near-critical CO2 in green chemical synthesis and processing. J. Supercrit. Fluids 2004, 28, 121− 191. (2) Pearson, A. Carbon dioxide−new uses for an old refrigerant. Int. J. Refrig. 2005, 28, 1140−1148. (3) Gozalpour, F.; Ren, S. R.; Tohidi, B. Récupération assistée du pétrole (EOR) et stockage du CO2 dans des réservoirs pétroliers. Oil Gas Sci. Technol. 2005, 60, 537−546. (4) De Visser, E.; Hendriks, C.; Barrio, M.; Molnvik, M. J.; De Koeijer, G.; Liljemark, S.; Le Gallo, Y. Dynamis CO2 quality recommendations. Int. J. Greenhouse Gas Control 2008, 2, 478−484. (5) Metz, B., Davidson, O., De Coninck, H., Loos, M., Meyer, L., Eds. Carbon dioxide capture and storage; Intergovernmental Panel on Climate Change (IPCC): Geneva, 2005. (6) Banu, L. A.; Wang, D.; Baltus, R. E. Effect of Ionic Liquid Confinement on Gas Separation Characteristics. Energy Fuels 2013, 27, 4161−4166. (7) Ivanova, M.; Kareth, S.; Spielberg, E. T.; Mudring, A. V.; Petermann, M. Silica ionogels synthesized with imidazolium based ionic liquids in presence of supercritical CO2. J. Supercrit. Fluids 2015, 105, 60−65. (8) Moya, C.; Alonso-Morales, N.; Gilarranz, M. A.; Rodriguez, J. J.; Palomar, J. Encapsulated Ionic Liquids for CO2 Capture: Using 1Butyl-methylimidazolium Acetate for Quick and Reversible CO2 Chemical Absorption. ChemPhysChem 2016, 17, 3891−3899. (9) Mantovani, M.; Chiesa, P.; Valenti, G.; Gatti, M.; Consonni, S. Supercritical pressure−density−temperature measurements on CO2− N2, CO2−O2 and CO2−Ar binary mixtures. J. Supercrit. Fluids 2012, 61, 34−43. (10) Yang, X.; Wang, Z.; Li, Z. Accurate Density Measurements on Ternary Mixtures (Carbon Dioxide + Nitrogen + Argon) at Temperatures from (323.15 to 423.15) K with Pressures from (3 to 31) MPa using a Single-Sinker Densimeter. J. Chem. Eng. Data 2015, 60, 3353−3357. (11) Yang, X.; Wang, Z.; Li, Z. Accurate density measurements on a binary mixture (carbon dioxide + methane) at the vicinity of the critical point in the supercritical state by a single-sinker densimeter. Fluid Phase Equilib. 2016, 418, 94−99. (12) Sanchez-Vicente, Y.; Drage, T. C.; Poliakoff, M.; Ke, J.; George, M. W. Densities of the carbon dioxide + hydrogen, a system of relevance to carbon capture and storage. Int. J. Greenhouse Gas Control 2013, 13, 78−86. (13) Ben Souissi, M. A.; Richter, M.; Yang, X.; Kleinrahm, R.; Span, R. Vapor-Phase (p, ρ, T, x) Behavior and Virial Coefficients for the (Argon + Carbon Dioxide) System. J. Chem. Eng. Data 2017, 62, 362− 369. (14) Yang, X.; Richter, M.; Ben Souissi, M. A.; Kleinrahm, R.; Span, R. Vapor-Phase (p, ρ, T, x) Behavior and Virial Coefficients for the Binary Mixture (0.05 Argon + 0.95 Carbon Dioxide) over the Temperature Range from (273.15 to 323.15) K with Pressures up to 9 MPa. J. Chem. Eng. Data 2016, 61, 2676−2681. (15) Kritschewsky, I. R.; Markov, V. P. The compressibility of gas mixtures. I. The P-V-T data for binary and ternary mixtures of hydrogen, nitrogen and carbon dioxide. Acta Physicochim. URSS 1940, 12, 59−66. (16) Mallu, B. V.; Viswanath, D. S. Compression factors and second virial coefficients of H2, CH4, {xCO2 + (1 − x)H2}, and {xCO2 + (1 − x)CH4}. J. Chem. Thermodyn. 1990, 22, 997−1006. 2980



Article

(34) Schäfer, M. Improvements to two viscometers based on a magnetic suspension coupling and measurements on carbon dioxide. Ph.D. Dissertation, Ruhr-Universität Bochum, Bochum, Germany, 2015. http://hss-opus.ub.ruhr-uni-bochum.de/opus4/frontdoor/ index/index/docId/4542 (accessed Feb. 23, 2017). (35) Richter, M.; Ben Souissi, M. A.; Span, R.; Schley, P. Accurate (p,ρ,T,x) Measurements of Hydrogen-Enriched Natural-Gas Mixtures at T = (273.15, 283.15, and 293.15) K with Pressures up to 8 MPa. J. Chem. Eng. Data 2014, 59, 2021−2029. (36) International Organization for Standardization 2008. Uncertainty of measurement - Part 3: Guide to the expression of uncertainty in measurement (GUM:1995), ISO/IEC Guide 98-3:2008; International Organization for Standardization: Geneva, 2008. (37) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (38) Plocker, U.; Knapp, H.; Prausnitz, J. Calculation of highpressure vapor-liquid equilibria from a corresponding-states correlation with emphasis on asymmetric mixtures. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 324−332. (39) Soave, G. Equilibrium constants from a modified RedlichKwong equation of state. Chem. Eng. Sci. 1972, 27, 1197−1203. (40) Span, R.; Eckermann, T.; Herrig, S.; Hielscher, S.; Jäger, A.; Thol, M. TREND. Thermodynamic Reference and Engineering Data 3.0; Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum; Bochum, Germany, 2016. (41) Leachman, J. W.; Jacobsen, R. T.; Penoncello, S.; Lemmon, E. Fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen. J. Phys. Chem. Ref. Data 2009, 38, 721−748. (42) Span, R.; Wagner, W. A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple Point Temperature to 1100 K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 1509−1596. (43) Edwards, A.; Roseveare, W. The second virial coefficients of gaseous mixtures. J. Am. Chem. Soc. 1942, 64, 2816−2819. (44) Cottrell, T.; Hamilton, R.; Taubinger, R. The second virial coefficients of gases and mixtures. Part 2. - Mixtures of carbon dioxide with nitrogen, oxygen, carbon monoxide, argon and hydrogen. Trans. Faraday Soc. 1956, 52, 1310−1312. (45) Lunbeck, R.; Boerboom, A. On the second virial coefficient of gas mixtures. Physica 1951, 17, 76−80. (46) Michels, A.; Boerboom, A. The volume change on mixing two gases at constant pressure. Bull. Soc. Chim. Belg. 1953, 62, 119−124. (47) Eubank, P. T.; Hall, K. R. Optimum mixture compositions for measurement of cross virial coefficients. AIChE J. 1990, 36, 1661− 1668. (48) Brewer, J. Determination of Mixed Virial Coefficients, Report No. MRL-2915-C, AFOSR-67-2795; Midwest Research Institute: Kansas City, MO, USA, 1967.

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