Experimental Solubility Data for Binary Mixtures of Ethane and 2,2,4

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Experimental Solubility Data for Binary Mixtures of Ethane and 2,2,4-Trimethylpentane at Pressures up to 6 MPa Using a New Variable-Volume Sapphire Cell Wayne Michael Nelson* and Deresh Ramjugernath Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa ABSTRACT: A variable volume apparatus of low cell volume (approximately 10 cm3) was designed and commissioned for measuring phase equilibrium and thermodynamic property data. The experimental procedure and equipment capability for phase equilibrium measurements were validated by measuring isothermal phase equilibrium (T−P−x) data for binary mixtures involving carbon dioxide + n-hexane and ethane + n-octane. There is good agreement between data measurement using the new equilibrium cell and previous measurements reported in the literature. New T−P−x data were also measured for the binary mixture of ethane + 2,2,4trimethylpentane. The data were correlated using the Peng− Robinson equation of state and the van der Waals mixing rule. The expanded uncertainties in the measurements were evaluated as 0.07 K, 0.02 MPa, and 0.008 for the temperature, pressure, and liquid mole fraction, respectively.

1. INTRODUCTION An equilibrium cell with a variable internal volume enables the acquisition of accurate and reliable thermodynamic data, for example, vapor−liquid equilibrium (VLE), critical points, cloud points, P−V−T data, and so forth.1−3 Such data are required by the chemical industry for the design and optimization of numerous chemical operations. With regards to phase equilibrium data, direct measurement is the most reliable method for obtaining such information. High capital costs are associated with the construction and operation of multistage separation unit operations, and consequently designs of such units based on unreliable phase equilibrium data can be costly to companies.4 Accordingly, a new isothermal low-volume (10 cm3) variable volume cell based on the “static−synthetic” method was commissioned. The low volume of the apparatus is advantageous for measurements involving chemicals which are costly and/or difficult to synthesize at high purity. However, in retrospect, the low volume of the equilibrium cell exasperates gravimetric synthesis of mixtures within the dilute regions (99 99.9 Pexp = 2.699 Plit = 2.691 NA

Sigma-Aldrich ≥99 99.2 NA

Sigma-Aldrich >99 99.3 NA

Sigma-Aldrich ≥99 99.1 NA

liquid densityd (g·cm−3) (T = 293.15 K)

Afrox >99 99.95 Pexp = 3.962 Plit = 3.970 NA

refractive indexe (T = 293.15 K)

NA

NA

ρexp = 0.660 ρlit = 0.6595 nexp = 1.375 nlit = 1.375

ρexp = 0.692 ρlit = 0.6919 nexp = 1.391 nlit = 1.391

ρexp = 0.703 ρlit = 0.7026 nexp = 1.396 nlit = 1.397

supplier supplier grade/puritya (%) GC peak areab (%) vapor pressurec (MPa) (T = 278.15 K)

a

Gas purities on a volume basis, liquid purities on a mass basis. bArea percentage of component identified by gas chromatography using a thermal conductivity detector and 3 m Porapak column. cLiterature data for the saturated vapor pressures (P) from NIST TDE.11 U(T) = 0.07 K; U(P) = 0.02 MPa. dLiterature data for the liquid density (ρ) at barometric pressure from NIST TDE.11 U(T) = 0.05 K; U(ρ) = 0.001 g·cm−3; U(P) = 1 kPa eLiterature data for the refractive index (n) at barometric pressure from ref 23 or 24; U(T) = 0.05 K; U(n) = 0.001; U(P) = 1 kPa.

Figure 1. Schematic of the “static−synthetic” apparatus incorporating a variable-volume sapphire cell. IC: immersion circulator, LB: liquid bath, LP: loading port, PP: platinum resistance temperature probe, PT: pressure transducer, SM: stirrer motor, SP: syringe pump, TR: temperature regulation.

dioxide + n-hexane and ethane + n-octane. New binary isothermal VLE data were measured for the binary system of ethane + 2,2,4trimethylpentane (isooctane) in the 303−333 K range. The data for this binary system were modeled using the Peng−Robinson equation of state and the van der Waals mixing rule.

tube is identical to those used in previous experimental setups;5,6 in fact the new apparatus is a reconstruction of a previous apparatus.6 The maximum capacity of the equilibrium chamber is approximately 10 cm3 when accounting for the displaced volumes (piston and mixer). The variation of the internal volume in the equilibrium chamber is accomplished via a hydraulically driven SS 316L piston. A single O-ring positioned centrally on the piston provides a seal between the hydraulic fluid (upper chamber) and equilibrium fluid (lower chamber). The piston is stabilized using Teflon guide rings and is precisely driven by a hydraulic fluid pressurized with a highpressure syringe pump (Teledyne ISCO; 100DM). If necessary the exact volume displaced by the piston can be calculated by correcting the thermal expansion and compressibility of the hydraulic fluid as discussed by Meskel-Lesavre et al.1 The syringe pump is jacketed, and thus, the temperature of the fluid within the pump can be controlled. The cell was originally designed to allow for a ram-type piston to be driven by an overhead screw, similar to the cell of Schwan et al.7 With this envisioned arrangement, it was necessary to support the cell and overhead piston using two heavy wall rods, 20 mm outer diameter (OD), to support the assembly under torque loading. However, the piston seals (Teesele) used in this project proved

2. EXPERIMENTAL SECTION 2.1. Materials. The chemical properties and purities of the components used in this study are listed in Table 2. Where applicable, the components (either gaseous or liquid) were characterized through the measurement of density (Anton Paar; DMA 5000; expanded uncertainty of 0.001 g/cm−3), refractive index (Bellingham & Stanley; Abbe 60LR; expanded uncertainty of 0.001), and the saturated vapor pressure (expanded uncertainty for pressure of 0.02 MPa). The purities of all components were checked using gas chromatographic analysis. No significant impurities beyond the supplier specifications were identified. 2.2. Apparatus. A schematic of the experimental setup is displayed in Figure 1. The core of the setup, the equilibrium cell, consists of a sapphire tube sealed with O-rings between two stainless steel (SS) 316L flanges using 3 SS bolts (2 of which are only shown in the schematic; Figure 1). The sapphire B

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component into the liquid phase. At this point the total composition of the mixture loaded into equilibrium cell was reliably known. The cell was submerged into the thermo-regulated liquid solution and the necessary auxiliary equipment connected. The mixture within the equilibrium cell was compressed close to the bubble point and agitated at isothermal conditions for at least 20 min. The two-phase binary mixture was then slowly compressed (at a rate of approximately ∼5−10 μL/min) under rapid mixing to obtain the bubble point. The bubble point could be obtained using two complementary techniques; the methods always lead to concordant results. The two-phase mixture was carefully observed visually until the transition to single-phase mixture (or vice versa) or the transition from the two-phase to single-phase region is easily determined by a sudden increase (break point) in the pressure of the fluid within the equilibrium chamber as the fluid is slowly compressed. The break point may be difficult to identify when the densities of two phases are similar (close to the critical region). The temperature of the mixture was then adjusted to a higher value and the bubble point measured as aforementioned. 2.4. Calibrations and Uncertainty. The two Pt100 probes were calibrated against a standard temperature probe (WIKA Instruments; model CTH 6500). Within the working temperature range, the standard temperature probe was stated by WIKA Instruments to have a maximum uncertainty of 0.02 K. The 12 MPa gauge pressure transmitter (linearity of ≤0.05% of the span) was calibrated against a standard pressure transmitter (Mensor CPC 8000; 25 MPa gauge). The mass balance was calibrated using standardized masses and was reported to have an estimated uncertainty of 0.03 g. The expanded uncertainties were estimated following the guidelines documented by the National Institute of Standards and Technology (NIST).8 In this work a coverage factor of k = 2 was used. The standard uncertainties used for the estimation are listed in Table 3.

unreliable, and the ram-type piston was removed and replaced with the aforementioned floating piston design. The bottom flange and hence lower chamber within the equilibrium cell consists of two inlet ports (1/8″ Valco fittings) for the pressure transmitter and loading line, respectively. Two nonrotating stem needle valves (Parker; 10 V series; 1/8″) are used for the inlet ports. The flange and sapphire tube specifications, the arrangement of the tube and piston o-rings, as well as the Valco fittings and nonrotating stem needle valves enable easy operation at a high pressure (maximum tested pressure: 35 MPa). The fluid within the equilibrium chamber is agitated by an internal Teflon stirrer. This assembly involves a neodymium ring-magnet (10 mm OD) which is housed within the Teflon stirrer, which in turn is driven by an external rotating neodymium magnet (30 mm OD) connected with bevel gears to an overhead stirrer (Maxon; A-max). Isothermal conditions within the equilibrium chamber are achieved by submersion into a thermo-regulated liquid solution. The thermo-regulated solution is accommodated in a 30 dm3 SS 316 L bath containing two viewing windows (100 mm OD). The temperature of the solution is controlled by an immersion circulator (Grant; TX 150). It is convenient to use water as the bath fluid, as it is necessary to dry the cell externally between loadings. The pressure and temperature within the equilibrium cell are measured by two 100 Ω platinum resistance thermometer (Pt100) probes (WIKA; 1/10 DINN) and a single pressure transmitter (WIKA; P-10). The temperature probes are not in direct contact with the fluid within the cell but are positioned within the walls of the top and bottom flange of the equilibrium cell. The pressure transmitter is connected to the cell via the bottom flange and is easily interchangeable depending on the working pressure range. The signals from these sensors are recorded by a computer linked to a data acquisition unit (Agilent; HP34970A). A two-stage vacuum pump (Edwards; RV3) is used for the evacuation of the cell and loading lines. 2.3. Procedure. To prepare a mixture within the equilibrium cell, the cell must be disconnected from the syringe pump and removed from the thermo-regulated liquid solution. The chamber located above the upper end of the piston was loaded with a small amount hydraulic fluid (in this case water) and sealed (valve closed). This was to ensure that, when the equilibrium chamber (located below the piston) was pressurized, that an equal force was applied on either end of the piston O-ring, reducing the potential for leakage during the loading procedure. The equilibrium chamber was evacuated, and the mass of the apparatus was recorded using a mass balance (Ohaus Explorer; maximum capacity of 6100 g; readability of 0.01 g). A small amount (∼0.02 g) of the gaseous component was added to the cell to pressurize the vessel to a value higher than the barometric pressure, and the mass of gas loaded was recorded. This was found to be the optimal procedure to ensure that leakage did not occur under vacuum. Leakage under vacuum would consequently draw air into the cell and result in erroneous bubble point measurements. The liquid component was degassed in a Büchner flask connected to the vacuum pump. The liquid component was subsequently charged under pressure using a syringe into the equilibrium chamber. The loading valve of the equilibrium chamber was then dried, the cell weighed, and the mass of the liquid component charged into the cell was recorded. The sapphire cell was inverted, and the gaseous component was charged into the equilibrium chamber and the mass recorded; during this procedure the mixture was agitated to promote solubility of the gaseous

Table 3. Standard Uncertainty Estimates and Influences of the Variables in this Work source of uncertainty Pressure (P) P reference (MPa): Mensor CPC 8000 (25 MPag) accuracy for P (MPa) (12 MPag) repeatability (average) of bubble-point P (MPa) Temperature (T) T reference (K): CTH 6500 @ 230 K correlation for T (K) Composition (zi) mass balance uncertainty (g) repeatability of masses (g)

estimate

distribution

0.01% 0.05% 0.01

normal normal rectangular

0.02 0.06

rectangular rectangular

0.03 0.03

rectangular rectangular

The expanded uncertainties in the measurements were evaluated as 0.07 K, 0.02 MPa, and 0.008 for the temperature, pressure, and liquid mole fraction, respectively.

3. DATA TREATMENT The VLE data were regressed in Aspen Plus V8.0 following the phi−phi approach.9 The VLE data were modeled using the Peng−Robinson (PR) equation of state (EoS):10 P= C

a(T ) RT − Vm − b Vm(Vm + b) + b(Vm − b)

(1)

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different binary test systems, namely, carbon dioxide + n-hexane at 313 K and ethane + n-octane at 313 and 323 K. In total, for validation and testing, 20 binary mixtures were prepared and their respective bubble points measured (listed in Table 4). Multiple bubble points were tested to validate the experimental setup and also to develop and fine-tune the experimental procedure. The experimental data compared well with data available in the literature.14−16 Deviations between the experimental, modeled, and the literature data are shown in Figure 2 and Table 5. On average the AARD in pressure

where b is a function of Tc and Pc. a(T) is a function of Tc and Pc. The attractive (a) and covolume (b) parameters of the PR EoS were extended to mixtures via either the van der Waals (vdW) or the Wong−Sandler (WS) mixing rules.11 The nonrandom two-liquid (NRTL) activity coefficient model12 was used to represent the excess Gibbs energy for the WS mixing rule. The magnitude of the binary interaction parameters were determined by minimizing only pressure using the ordinary least-squares objective function using the Britt−Luecke algorithm.13 The quality of the data fit was assessed statistically using the average absolute deviation (AAD), the average absolute relative deviation (AARD), and the bias. The AAD is AAD(θ ̅ ) =

1 Np

Np

̅ | ∑ |θexp̅ − θcalc

(2)

1

where θ̅exp and θ̅calc are the experimental and calculated values of a measurand θ̅, and Np is the total number of data points. The AARD is defined as 1 AARD(θ ̅ ) = Np

Np

∑

|θexp ̅ − θcalc ̅ | θexp ̅

1

(3)

The BIAS is defined as ⎛ ⎞ 1 BIAS⎜⎜θ ⎟⎟ = Np ⎝ ⎠

Np

∑ 1

θexp − θcalc θexp

(4)

Figure 2. Experimental, literature, and predicted (PSRKrepresented by the solid black line) VLE data for the binary system of CO2 (1) + n-hexane (2): our experimental data at 313.15 K (red ▲); Li et al. at 313.14 K (black ▲);16 Wagner et al. at 313.14 K (△).15 Binary system of ethane (1) + n-octane (2): our experimental data at 323.00 K (red ■); Rodriguez et al. at 322.99 K (□);14 our experimental data at 313.00 K (red ●); Rodriguez et al. at 312.99 K (black ●).14 Only P−x data are displayed for the literature data.

4. RESULTS AND DISCUSSION The solubility of ethane in 2,2,4-trimethylpentane was measured using a new variable-volume “static−synthetic” apparatus of low total volume capacity. The apparatus was built to compliment measurements performed in our laboratories. As measurements performed via static−synthetic methods can be very reliable, provided that the apparatus is designed effectively and that the experimental procedure is thorough. The equipment and experimental technique were validated by measuring two

Table 5. Comparison of the Experimental Vapor−Liquid Equilibrium Data for the Binary Systems of Carbon Dioxide + n-Hexane at 313.15 K and Ethane + n-Octane at 313.00 and 323.00 K to Data Available in the Literature and Modeled Data

Table 4. Experimental Vapor−Liquid Equilibrium Data for the Binary Systems of Carbon Dioxide (1) + n-Hexane (2) and Ethane (1) + n-Octane (2), Including the Measured Temperature (T), Pressure (P), Liquid-Phase Composition (x1), and the Expanded Uncertainty (k = 2)a ethane + n-octane P (MPa) 0.67 1.77 2.72 3.87 4.43 1.57 2.24 2.49 3.22 3.98 5.07 a

x1 T = 313.00 K 0.149 0.383 0.565 0.766 0.855 T = 323.00 K 0.310 0.426 0.469 0.580 0.689 0.842

AAD(P) (MPa) C2H6 + C8H18a C2H6 + C8H18b14 C2H6 + C8H18c

carbon dioxide + n-hexane U(x1)

P (MPa)

0.021 0.016 0.010 0.006 0.005

2.81 3.58 3.74 4.56 5.22 6.37 6.51 6.85 7.25

0.015 0.012 0.010 0.008 0.006 0.005

x1 T = 313.15 K 0.295 0.384 0.405 0.513 0.609 0.778 0.803 0.855 0.891

C2H6 + C8H18a C2H6 + C8H18b,14 C2H6 + C8H18c

U(x1) 0.015 0.009 0.007 0.006 0.006 0.005 0.005 0.005 0.003

CO2 + C6H14a CO2 + C6H14b,16 CO2 + C6H14c

AARD(P)

T = 313.00 K 0.008 0.018 0.022 T = 323.00 K 0.021 0.021 0.028 T = 313.15 K 0.021 0.037 0.074

BIAS(P)

0.31% 0.76% 1.21%

0.24% 0.05% 0.68%

0.66% 0.96% 0.75%

0.16% −0.02% −0.75%

0.37% 0.95% 1.29%

0.03% −0.30% −1.00%

a

Experimental data modeled using the PR EoS + WS mixing rule/NRTL model. Deviations are calculated with respect to the difference between experimental data and modeled experimental data. b Literature data modeled using the PR EoS + WS mixing rule/NRTL model. Deviations are calculated with respect to the difference between literature data and modeled literature data. cLiterature data modeled using the PR EoS + WS mixing rule/NRTL model. Deviations are calculated with respect to the difference between experimental data and modeled literature data.

U(T) = 0.07 K; U(P) = 0.02 MPa. D

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the data fit are listed in Table 7. Future work and testing for this apparatus involves determining the maximum operating pressure of the apparatus, which may involve further modification. Furthermore, for dilute mixtures (high concentration of the least volatile component) an alternate method of synthesizing the mixture is recommended, for example, loading the liquid component gravimetrically and loading the gaseous component from a reservoir of known volume, temperature, and pressure.

between our experimental data and modeled literature data (PR EoS + WS mixing rule) is less than 1.5%. New T−P−x data were measured for the binary system of ethane + 2,2,4trimethylpentane at four temperatures, namely, 303.15, 313.15, 323.15, to 333.15 K. The data are presented in Figure 3 and

5. CONCLUSIONS A new variable-volume cell comprising a sapphire tube with a capacity of approximately 10 cm3 was commissioned to enable acquisition of phase equilibrium data using the “static− synthetic” technique. The apparatus was tested by reproducing measurements of data readily available in the literature, namely, the binary systems of carbon dioxide + n-hexane and ethane + n-octane. The experimental data were in good agreement with the data available in the literature. New isothermal phase equilibrium data were reported for the binary system of ethane + 2,2,4-trimethylpentane in the 303−333 K temperature range. The data were accurately correlated using the PR EoS and the van der Waals mixing rule.

Figure 3. Experimental VLE data and modeling results for the binary system of ethane (1) + 2,2,4-trimethylpentane (2) at 303.15 K (○), 313.15 K (●), 323.15 K (△), and 333.15 K (▲). Data modeled () with the PR-EoS and van der Waals mixing rule. Errors bars represent the uncertainty in the liquid phase composition.

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AUTHOR INFORMATION

Corresponding Author

Table 6. The data were modeled simultaneously using the PR EoS and the van der Waals mixing rule, resulting in a single binary interaction parameter capable of accurately predicting the experimental data at all temperatures. The regressed binary interaction parameters for the model and statistical analyses of

*E-mail: [email protected]; tel.: +27 31 2603121. ORCID

Wayne Michael Nelson: 0000-0003-0544-6530 Deresh Ramjugernath: 0000-0003-3447-7846

Table 6. Experimental Vapor−Liquid Equilibrium Data for the Binary System of Ethane (1) + 2,2,4-Trimethylpentane (2), Including the Measured Temperature (T), Pressure (P), Liquid-Phase Composition (x1), and the Expanded Uncertainty (k = 2)a P/MPa (bubble point)

composition

a

x1

U(x1)

T = 303.15 K

T = 313.15 K

T = 323.15 K

T = 333.15 K

0.157 0.218 0.319 0.392 0.504 0.519 0.558 0.567 0.683 0.752 0.907

0.014 0.013 0.010 0.009 0.007 0.007 0.006 0.006 0.005 0.004 0.002

0.58 0.75 1.14 1.43 1.88 1.94 2.14 2.16 2.71 3.10 3.92

0.66 0.87 1.32 1.67 2.20 2.26 2.49 2.54 3.18 3.66 4.66

0.76 0.99 1.51 1.92 2.53 2.60 2.87 2.92 3.69 4.25 5.44

0.85 1.13 1.72 2.17 2.88 2.97 3.28 3.34 4.22 4.87 6.23

U(T) = 0.07 K; U(P) = 0.02 MPa.

Table 7. Regressed Binary Interaction Parameters for the PR EoS and the Van Der Waals Mixing Rule and Statistical Analysis of the Data Fit for the Binary System of Ethane (1) + 2,2,4-Trimethylpentane (2) T = 303.15 K k12

0.005

AAD(P) (MPa) AARD(P) (%)

0.017 1.3

T = 313.15 K Model Parameters 0.005 Deviations 0.019 1.1 E

T = 323.15 K

T = 333.15 K

0.005

0.005

0.023 1.1

0.029 1.1 DOI: 10.1021/acs.jced.7b00613 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Funding

(19) Su, B.; Lv, X.; Yang, Y.; Ren, Q. Solubilities of Dodecylpolyoxyethylene Polyoxypropylene Ether in Supercritical Carbon Dioxide. J. Chem. Eng. Data 2006, 51, 542−544. (20) Elizalde-Solis, O.; Galicia-Luna, L. A. Solubilities and Densities of Capsaicin in Supercritical Carbon Dioxide at Temperatures from 313 to 333 K. Ind. Eng. Chem. Res. 2006, 45, 5404−5410. (21) Perez, E.; Cabanas, A.; Sanchez-Vicente, Y.; Renuncio, J. A. R.; Pando, C. High-pressure phase equilibria for the binary system carbon dioxide + dibenzofuran. J. Supercrit. Fluids 2008, 46, 238−244. (22) Jaubert, J. N.; Coniglio, L.; Denet, F. From the Correlation of Binary Systems Involving Supercritical CO2 and Fatty Acid Esters to the Prediction of (CO2−Fish Oils) Phase Behavior. Ind. Eng. Chem. Res. 1999, 38, 3162−3171. (23) Dean, J. A. Lange’s Handbook of Chemistry; McGraw-Hill: New York, 1998. (24) Wohlfarth, C. Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology; Vol. 47, Optical Constants; Springer: New York, 2008.

This work is based upon research supported by the National Research Foundation of South Africa under the South African Research Chair Initiative of the Department of Science and Technology and the National Research Foundation Thuthuka Programme. Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jced.7b00613 J. Chem. Eng. Data XXXX, XXX, XXX−XXX