Reference Quality VaporâLiquid Equilibrium Data for the Binary

Article pubs.acs.org/jced

Reference Quality Vapor−Liquid Equilibrium Data for the Binary Systems Methane + Ethane, + Propane, + Butane, and + 2‑Methylpropane, at Temperatures from (203 to 273) K and Pressures to 9 MPa Eric F. May,*,† Jerry Y. Guo,† Jordan H. Oakley,† Thomas J. Hughes,† Brendan F. Graham,† Kenneth N. Marsh,† and Stanley H. Huang‡ †

Centre for Energy, School of Mechanical & Chemical Engineering, University of Western Australia, Crawley, WA 6009, Australia Chevron Energy Technology Company, Houston Texas 77002, United States

‡

ABSTRACT: A specialized cell designed for vapor liquid equilibrium (VLE) measurements at cryogenic temperatures and high pressures was used to measure new (p,T,x,y) data for binary mixtures of methane + ethane, + propane, + 2-methylpropane (isobutane), and + butane from (203 to 273) K at pressures up to 9 MPa. A literature review of VLE data for these binary mixtures indicates that a significant number have large uncertainties; however, because estimates of uncertainties in measured phase compositions are often not quantified sufficiently, it can be difficult for equation of state (EOS) developers to identify which data sets are of poor quality. Robust quantitative uncertainties were estimated for the VLE data acquired in this work, which allowed the identification of literature data sets that should not be included in future EOS development. The new data were compared with the predictions of the Peng−Robinson (PR) EOS and the Groupe European de Recherche Gaziere (GERG-2008) multiparameter EOS. The former describes the new data measured at low pressures within experimental uncertainty but deviates systematically from the data as the bubble point pressure is increased; for the binary mixtures containing either of the butanes, the maximum relative deviation of the data from the PR EOS amounted to nearly 10 % of the methane liquid mole fraction. The GERG-2008 EOS was better able to describe the new high-pressure data for the CH4 + C3H8 system than the PR EOS. However, for both the CH4 + C4H10 mixtures, the GERG EOS deviated from these data by an amount twice as large as the PR EOS because of ambiguity about which VLE literature data sets should be used in model development. The new data resolve these ambiguities and should facilitate the development of improved EOS as needed, for example, in simulations of low temperature natural gas separation processes.

■

INTRODUCTION Significant capital expenditure and operating costs are involved in the production of liquefied natural gas (LNG). Simulations of these facilities have the potential to reduce the total cost of ownership if they are sufficiently optimized. A crucial operation within an LNG processing train is the cryogenic distillation column known as the scrub column, or demethanizer. The column’s functions are (i) to control the concentration of heavier hydrocarbons (propane and above) in the vapor overheads product, which goes on to the main cryogenic heat exchanger for conversion to LNG, and (ii) maximize the recovery of hydrocarbon liquids in the bottoms product, which can be an important source of revenue and/or the refrigerant used in the liquefaction process. The scrub column is one of the most difficult unit operations in an LNG plant to simulate accurately because it requires calculation of vapor−liquid equilibrium (VLE) for multicomponent mixtures at high pressures from about (4 to 6) MPa and over a wide range of temperatures from © 2015 American Chemical Society

(223 to 303) K. Furthermore, the equation of state (EOS) used to calculate this multicomponent VLE should be computationally efficient because scrub column simulations also require the iterative solution of nonlinear equations describing the material and energy balances on each of the trays within it. Currently, the thermodynamic model used most commonly for simulating processes such as LNG scrub columns is the Peng−Robinson equation of state (PR EOS).1 Its use is common for two reasons: it is cubic in the molar volume and can thus be solved without iteration, and its predictions of VLE for multicomponent mixtures are equivalent in accuracy to those of more complex EOS that require an iterative solution.2 However, cubic Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: July 17, 2015 Accepted: September 14, 2015 Published: September 29, 2015 3606

DOI: 10.1021/acs.jced.5b00610 J. Chem. Eng. Data 2015, 60, 3606−3620

Journal of Chemical & Engineering Data

Article

EOS have a well-known deficiency when it comes to the prediction of liquid volumes, which more complex models3 have been developed to address. The Groupe European de Recherche Gaziere 2008 (GERG-2008)4 multiparameter EOS is the reference model for the prediction of natural gas properties. For VLE predictions within its stated range of validity, the claimed relative uncertainties are generally between (1 and 5) %. Kunz and Wagner4 stated that the paucity of quality VLE data available for mixtures limited the accuracy achievable in the development of the GERG-2008 EOS, and that VLE data at low temperatures for mixtures of CH4 + C4H10 would be particularly useful for improving the description of richer natural gases. The first objective of this work was to review the available literature VLE data for the key binary mixtures relevant to LNG scrub column simulations, which are those involving methane (CH4) and one of [ethane (C2H6), propane (C3H8), isobutane (iC4H10), or butane (nC4H10)], and compare them with the predictions of the cubic EOS most commonly used in those simulations. As discussed below, the common feature of these comparisons is that the cubic EOS is tuned as well as it can be to the constituent binary systems given (a) the significant scatter present in the literature VLE data and (b) the decreasing ability of cubic EOS to describe VLE accurately as the mixture critical point is approached.5,6 In contrast, the more complex functional forms of multiparameter EOS means they are able to better capture the curvature of the phase envelope even quite close to the critical point. However, in some ways this additional flexibility means that identifying less accurate data sets is even more important for the development of multiparameter EOS. Given the significant scatter found in the literature VLE data, we report here the development of a specialized apparatus to produce reference quality VLE data at low temperature, high-pressure conditions spanning those found in LNG scrub columns. The analytic method was used to produce new VLE data including quantitative uncertainty estimates for each of the four key binary mixtures. The data are compared with the existing literature and clearly allow the identification of data sets that should not be included in EOS development, as well as suggesting those data sets that should receive an increased weighting. To compare the quality of many data sets acquired over a wide range of conditions, deviation plots are used with the baseline being the default PR EOS implemented in the software Aspen HYSYS7 because of its widespread use in the simulation of LNG scrub columns. Comparisons of the data with the GERG-2008 EOS are also made and reveal pathways for future improvements of this and similar models.

Figure 1. (a) Measured and predicted (curves) bubble-pressures for methane (1) + ethane (2) as a function of the measured liquid mole fraction of methane, x1: green +, Gupta et al.10 T = 270 K; red ○, Wei et al.11 T = 270 K; blue □, Raabe et al.12 T = 270 K; green △, Janisch et al.13 T = 270 K; ⧫, Davalos et al.14 T = 250 K; red ●, Wei et al.11 T = 250 K. (b) Deviations of the measured methane liquid mole fractions, x1, in panel (a) from the corresponding calculated methane liquid mole fraction, x1,calc, of the default HYSYS PR EOS as a function of x1.

better at one temperature or another. Figure 1b overcomes these limitations by showing the deviations of the measured (methane) liquid mole fraction, x1 from the EOS prediction, x1,calc: it is clear that the different data sets at both temperatures are generally consistent within a reasonable estimate of their uncertainties; that the EOS deviates systematically from the data with increasing methane liquid mole fraction, x1; and that the slope of this systematic deviation is larger at 270 K than at 250 K. The results of the comparisons between literature VLE data and the default HYSYS PR EOS predictions for the principal binary systems containing methane are presented in Figure 2 to Figure 5: these systems contain the information about the dominant binary interactions occurring in natural gas and LNG and, thus, are the most important for scrub column simulations. The focus here is on the bubble-point curve because for these systems it appears that the dominant deficiency in EOS predictions occurs for the liquid phase in terms of absolute mole fraction deviations. The deviations of EOS predictions for the vapor and liquid phases are similar on a relative basis but because the uncertainties of experimental composition measurements are often constrained to have a minimum absolute value (e.g., 0.001 mole fraction), the deviations of EOS predictions from the vapor phase data are usually closer to this minimum experimental uncertainty.

■

REVIEW OF LITERATURE VLE DATA The conventional and convenient way of presenting VLE data for binary mixtures and comparing them with EOS predictions is through a pressure−composition (p, x) plot. However, while (p, x) plots are helpful for providing a global overview of a binary system’s VLE and its description by a thermodynamic model, they are limited by the large scale of the pressure axis needed to represent the normally wide range of bubble-point conditions. An example of this is shown for the methane (1) + ethane (2) system in Figure 1a, which presents a (p, x) plot that contains several data sets measured at 250 and 270 K together with the corresponding predictions of the default PR EOS implemented in AspenTech HYSYS.7 While this (p, x) plot indicates a reasonable agreement between the measurements and the model predictions it is difficult to assess the consistency of the different data sets or whether the agreement of the model with the data is 3607



Article

Figure 2. Deviations of measured CH4 liquid mole fractions (x1) from the values calculated with the default HYSYS PR EOS (x1,calc) for CH4 (1) + C2H6 (2) as a function x1: red ◊, Wichterle15 190 < T/K < 200; blue ×, Wichterle and Kobayashi,8,9 130 < T/K < 213; green ○, Wilson16 T = 111 K; +, Davalos et al.14 T = 250 K; purple □, Miller et al.17 160 < T/K < 180; brown △, Gupta et al.10 260 < T/K < 280; orange ∗, Wei et al.11 210 < T/K < 270; red block cross, Raabe et al.12 240 < T/K < 270; ▽, Janisch et al.13 140 < T/K < 270.

Figure 2 shows a liquid phase deviation plot for the CH4 (1) + C2H6 (2) binary for 330 literature VLE data measured between 110 K and 280 K. The root mean square (rms) deviation for x1 in Figure 2 is 0.007, and the distribution of the deviations does not exhibit any clear trend with composition. These results suggest that the default PR EOS is adequate over this range of conditions. Potentially some improvement could be achieved by filtering out the 1972 data of Wichterle and Kobayashi,8,9 which exhibit significantly more scatter than the other data sets. Figure 3 shows a comparison of measured and predicted methane liquid mole fractions x1 for CH4 (1) + C3H8 (3): the deviation plot, Figure 3b, contains 429 literature data measured between 130 K and 344 K. The rms deviation for x1 in Figure 3b is 0.015, and the distribution of the deviations exhibits an increasing positive trend with increasing liquid methane mole fraction. Figure 4 shows a comparison of measured and predicted liquid compositions for CH4 (1) + iC4H10 (4): the deviation plot in Figure 4b contains 145 literature data measured between 110 K and 378 K. The majority (94 points) of the literature VLE data for this binary system at conditions relevant to LNG scrub columns comes from a single source,18 whose measurements range from (198 to 378) K. The only other two literature VLE data sets available for this system are of less relevance having been measured at high temperatures19 from (311 to 377) K or very low temperatures20 from (110 to 140) K. The rms deviation for x1 in Figure 4b is 0.025 and the distribution of the deviations also exhibits an increasing positive trend with increasing x1. Figure 5 shows a comparison of measured and predicted methane liquid mole fractions for CH4 (1) + nC4H10 (5): the deviation plot in Figure 5b contains 416 literature data measured between 138 K and 411 K. The rms deviation for x1 in Figure 5b is 0.031. The isothermal data shown in Figure 5a are a small subset of those in Figure 5b; they were selected because they illustrate key problems with data quality, with cubic EOS, and importantly, occur at temperatures near those used in LNG scrub columns. At 244 K there is a very large discrepancy between the data of Roberts et al.21 and Wang and McKetta22 and those of Elliot et al.23 The HYSYS default PR EOS appears to be tuned to the latter data set at lower pressures but transitions to the former data sets as the critical point is approached.

Figure 3. (a) Select bubble pressures for the methane (1) + propane (3) system as a function of the measured liquid mole fraction of methane x1: ◊, Wichterle and Kobayashi24 T = 192 K; ◊, Wichterle and Kobayashi24 T = 214 K; ∗, Kalra et al.25 T = 214 K; ○, Webster et al.26 T = 230 K; ×, Benham et al.27 T = 255 K; □, Price et al.28 T = 255 K; +, Reamer et al.29 T = 278 K; △, Wiese et al.30 T = 278 K; △, Wiese et al.30 T = 311 K; △, Wiese et al.30 T = 344 K. (b) Deviations of measured CH4 liquid mole fractions (x1) from values calculated with the default HYSYS PR EOS (x1,calc) for CH4 (1) + C3H8 (3) as a function of x1: red ◊, Reamer et al.29 278 < T/K < 294; blue ×, Akers et al.31 174 < T/K < 273; green ○, Benham and Katz27 200 < T/K < 255; +, Price et al.28 144 < T/K < 283; purple □, Wichterle15 130 < T/K < 213; brown △, Wiese and Kobayashi30 278 < T/K < 344; orange ∗, Wichterle and Kobayashi24 130 < T/K < 213; red ▷, Kalra and Robinson25 T = 214 K; ▽, Joffe32 277 < T/K < 344; green block x, Raimondi33 T = 244 K; black block cross, Webster and Kidnay26 230 < T/K < 270.

Figure 3 to Figure 5 highlight the commonality of both the limitations in the literature VLE data quality and the inability of the cubic PR EOS to represent these binary mixtures at high mole fractions of CH4, which, for a given temperature, correspond to higher pressures on the bubble point curve.

■

EXPERIMENTAL SECTION Specialized Cryogenic VLE Apparatus. An experimental schematic of the specialized cryogenic VLE apparatus is shown schematically in Figure 6. While similar in concept to the VLE apparatus used by Kandil et al.39 and by Hughes et al.,40,41 substantial improvements in the ability to control and manipulate both system temperature and the acquired samples were implemented to significantly reduce experimental uncertainty. An equilibrium cell (EC) machined from a single billet of stainless steel grade 316 served as the pressure vessel with a 3608



Article

Figure 4. (a) Bubble pressures for the methane (1) + isobutane (4) system as a function of the measured liquid mole fraction of methane, x1: × (all colors), Barsuk et al.18 (temperatures indicated on figure); ―, bubble curves calculated with the HYSYS PR EOS. (b) Deviations of measured CH4 mole fractions (x1) from the values calculated with the default HYSYS PR EOS (x1,calc) for the CH4 (1) + iC4H10 (4) binary as a function of x1: red ▲, Olds et al.19 311 < T/K < 378; blue ×, Barsuk et al.18 198 < T/K < 378; green □, Haynes20 110 < T/K < 140.

Figure 5. (a) Select bubble pressures for the methane (1) + butane (5) system as a function of the measured liquid mole fraction of methane, x1: ◊, Roberts et al.21 T = 211 K; +, Wang et al.22 T = 211 K; ∗, Kahre34 T = 211 K; ○, Elliot et al.23 T = 211 K; ◊, Roberts et al.21 T = 244 K; +, Wang et al.22 T = 244 K; ○, Elliot et al.23 T = 244 K; ◊, Roberts et al.21 T = 278 K; +, Wang et al.22 T = 278 K; ○, Elliot et al.23 T = 278 K; ―, bubble curves calculated with the HYSYS PR EOS. (b) Deviations of measured CH4 mole fractions (x1) from the values calculated with the default HYSYS PR EOS (x1,calc) for the CH4 (1) + nC4H10 (5) binary as a function of x1: red ◊, Nederbragt35 252 < T/K < 316; blue ×, Sage et al.36,37 294 < T/K < 394; green ○, Rigas et al.38 T = 311 K; +, Roberts et al.21 211 < T/K < 411; purple □, Wang et al.22 178 < T/K < 378; brown △, Elliot et al.23 144 < T/K < 278; orange ∗, Kahre34 166 < T/K < 283; ▽, Raimondi33 138 < T/K < 310.

maximum operating pressure of 30 MPa. The cell had an internal diameter of 3 cm and a volume of approximately 60 cm3. The outer surface of the cell was plated with 1 mm thick copper to improve heat transfer and temperature uniformity. A foil-type heating element was wrapped and glued to the outer surface of the cell using high thermal conductivity epoxy suitable for cryogenic operation. A 100 Ω platinum resistance thermometer (PRT) was glued to the cell’s external surface directly underneath the heating foil, and was used as the sensor for temperature control (TC). Wells were bored in the top and the bottom of the equilibrium cell to house two 100 Ω PRTs (T1) and (T2). All three PRTs were calibrated over the temperature range from (77 to 300) K with an uncertainty of u(T) = 0.02 K prior to mounting in the EC. However, when mounted in the cell the uncertainty of the temperature readings increased as discussed below. The normal operating temperature profile of the apparatus established during the acquisition of samples for a VLE measurement, as recorded by each thermometer shown in Figure 6 relative to the set point of the TC, is listed in Table 1. An attachment to the bottom of the cell was used to mount a cryogenically compatible, variable speed motor (stirrer motor). The motor was used to generate a rotating magnetic field, which in turn drove a Teflon-coated magnetic bar sitting inside the cell

on the bottom surface. In this way the stirrer motor was used to mix the sample fluid. The lid of the cell was machined carefully to fit a custom, cryogenically compatible fill valve (V1), with a nonrotating stem that was flush with the inner surface of the cell lid when closed. This minimized any dead volume associated with the fill valve. This fill valve was operated by a stepper motor (M2) (Phytron UHVC-80). A pressure transducer (P1) (Kulite model CT-190) was also housed in the lid to minimize associated dead volume. This transducer utilized a strain-gauge on a silicon diaphragm and was suitable for operation at temperatures from (77 to 393) K. It was calibrated in situ by comparison with a reference quartz-crystal pressure transducer (P2) (Paroscientific Digiquartz model 1002K-01), located outside the Dewar at ambient conditions, with a full scale of 14 MPa and a relative uncertainty of 0.01 % of full scale as stated by the manufacturer. The manufacturer stated the Kulite transducer could be used to determine pressure with a relative uncertainty of 0.5 % for 3609



Article

Figure 6. Schematic of the specialized cryogenic VLE apparatus, which had improved temperature control and sampling systems relative to the setup described by Kandil et al.39 Symbols are explained in the text and Table 1.

(LC) was used to sample the liquid phase; it extended nearly to the bottom of the cell and had a total length of 20 cm (3.5 μL volume). Although it was not measured, the volume of the liquid phase inside the VLE cell was estimated from an EOS and ranged normally from a minimum of 1.5 cm3 up to about 20 cm3. The other end of each capillary sampling tube was located inside a specialized “Rapid On-Line Sampler Injector” (ROLSI) electromagnetic solenoid valve supplied by TransValor.42 The two ROLSI sampling valves (VV, VL) were mounted on the top side of a steel plate approximately 5 cm above the top of the VLE cell lid. Cartridge heaters were used to control the temperature of the ROLSI valves, and 2 PRTs (TRC and TRS) were used as control and reference sensors. The temperatures of the two capillaries were controlled independently; this was found to be essential for obtaining representative samples of the equilibrium phases in the VLE cell. The capillaries were mounted on custom built copper plates with grooves machined to seat the capillaries. A Peltier element was glued using epoxy to the side of each copper plate and could be used to heat or cool the capillaries as required. A 100 Ω PRT was attached to the surface of each capillary (TL, TV) and together with the Peltier elements they were used in a proportional-integral (PI) loop implemented in software to control the capillary temperatures. The vapor capillary was heated to a temperature of 5 K higher than the VLE cell, and the liquid capillary was cooled to a temperature of 5 K lower than the VLE cell. The cell and ROLSI sampling valves were enclosed inside a sealed copper can, which could be evacuated or filled with helium; the latter was most commonly employed because it assisted with achieving temperature uniformity across the EC. A foil-type heating element that could be driven with up to 150 W, was used to control the temperature of the copper can, which was monitored by a control PRT (TCu) as well as a sensing PRT

Table 1. Thermal Profile and Control of the Specialized Cryogenic VLE Apparatus Established During the Acquisition of Samples for a VLE Measurement, as Recorded by each Thermometer Relative to the Set Point of the TC PRT

control set point relative to TC

TC T1 T2 TL TV TRC TRS TCu TCuB TS1

not controlled not controlled −5 K +5 K 0K not controlled −2 K not controlled 0K

TS2

0K

TS3

0K

LN2 sensor

−2 K

functionality controls cell temperature monitors cell bottom temperature monitors cell top temperature controls liquid capillary temperature controls vapor capillary temperature controls temperature of ROLSI valves monitors temperature of ROLSI valves controls copper can temperature monitors copper can temperature controls temperature of GC transfer line: section 1 controls temperature of GC transfer line: section 2 controls temperature of GC transfer line: section 3 controls delivery of liquid nitrogen into the Dewar

the pressure range from (1 to 14) MPa. The transducer was, however, sensitive to its local temperature and its excitation voltage; accordingly the latter was held constant throughout the experiments and the temperature-dependent calibration function was checked regularly as described below. Two capillary tubes made from Monel 400 with internal diameters of less than 0.015 cm were also mounted in the cell lid. One of the capillaries (VC) was used to sample the vapor phase in the cell; it extended 1.5 cm below the bottom of the cell lid and had a total length of 13 cm (2.3 μL volume). The other capillary 3610



Article

opening time. The specific opening times used when acquiring samples varied slightly depending on the cell pressure and the phase being sampled but generally an opening time of 0.05 s was used to acquire a sufficient amount of sample that did not saturate the GC column or its detectors. The temperatures of the sampling valves and of the transfer lines were set using the ROLSI control box. To avoid inadvertent condensation of heavy components in the transfer lines, each of the three sections of the transfer lines were thermally controlled using 100 Ω PRTs (TS1, TS2, and TS3) and wire heaters. The GC used was a Varian model CP-3800 equipped with two capillary columns and two flame ionization detectors (FID): one (FID V) for samples from the vapor phase inside the EC and the other (FID L) for samples from the liquid phase inside the EC. Further details of the instrument and method used to analyze samples taken from the EC are listed in Table 2. Uncertainty Estimates. The VLE apparatus produces measurements of four quantities: temperature, pressure, and the liquid and vapor phase compositions. Thus, it is essential that the transducers used to determine these four quantities are calibrated reliably and that robust estimates of the uncertainties in these measured quantities are made. Each of the mixture VLE experiments lasted several weeks and involved multiple cycles of temperature and pressure, which can often cause inadvertent drifts in the calibrations of the thermometers and pressure gauge. Accordingly, before and after a set of mixture experiments made with the VLE cell, in situ calibrations (or validations) of the Kulite pressure transducer and the PRTs TC, T1 and T2 were conducted using pure fluids. When excited with a 12 V DC power source, the Kulite pressure transducer, P1, produced a voltage output that varied linearly with the system pressure. However, both the slope and offset of this linear function varied with temperature (as well as

(TCuB). The copper can was enclosed inside a reflective radiation shield, which separated it from a sealed stainless steel (SS) can. The inside of the SS can was evacuated to maximize the thermal isolation between the copper can and the inner wall of the SS can. The SS can was placed inside a cryogenic Dewar equipped with an automatic liquid nitrogen dosing pump that maintained a constant level of liquid N2 in the bottom of the Dewar; usually the outside of the SS can was only in contact with the N2 boil-off vapor. A helium carrier gas line (shown in red) was also connected to each of the ROLSI sampling valves, and helium (BOC, mole fraction purity 0.99999) flowed continuously through each of the valves and into their respective gas chromatograph (GC) columns. When the valves were actuated, the carrier gas would ensure that the samples from the vapor and liquid phases within the cell were swept along heated transfer lines into the GC columns. The ROLSI sampling valves were actuated using a control box (VSC), which allowed specification of the valve opening time with a resolution of 0.01 s. Thus, for a given pressure in the VLE cell, the amount of sample withdrawn by opening the valves could be adjusted by varying the specified Table 2. Details of the Varian CP-3800 Gas Chromatograph and Method Used for Sample Analysis column length and diameter column head pressure (constant) column packing injection temperature injection split ratio initial and final oven temperatures oven temperature ramp rate FID temperature

25 m, 0.53 mm 83 kPa PoroPlot Q 473 K 10:1 323 K, 473 K 20 K· min−1 473 K

Table 3. Details of the Mixtures Prepared Gravimetrically in This Work, Including the Purity of the Component Fluids and Standard Uncertainties in the Mixture Component Mole Fractionsa source grade mole fraction purity

CH4

C2H6

C3H8

iC4H10

nC4H10

BOC UHP 0.99999

Coregas 4.0 0.9999

Air Liquide N35 0.9995

Coregas N35 0.9995

Coregas N35 0.9995

Gravimetric Mixture 1: CH4 + C2H6 (Estimated Cricondentherm Temperature 265.7 K) masses added to evacuated cylinder/g 21.309 37.113 component mole fraction 0.5183 0.4817 component mole fraction uncertainty 0.0008 0.0008 Gravimetric Mixture 2: CH4 + C3H8 (Estimated Cricondentherm Temperature 287.6 K) masses added to evacuated cylinder/g 29.661 23.731 component mole fraction 0.7745 0.2255 component mole fraction uncertainty 0.0007 0.0007 Gravimetric Mixture 3: CH4 + iC4H10 (Estimated Cricondentherm Temperature 284.4 K) masses added to evacuated cylinder/g 46.744 15.851 component mole fraction 0.9144 0.0856 component mole fraction uncertainty 0.0007 0.0007 Gravimetric Mixture 4: CH4 +nC4H10 (Estimated Cricondentherm Temperature 287.5 K) masses added to evacuated cylinder/g 24.993 component mole fraction 0.9354 component mole fraction uncertainty 0.0012

6.259 0.0646 0.0012

a

Mixtures were prepared in high-pressure cylinders that had masses of about 1030 g when evacuated. A stainless steel ball from a ball bearing was placed inside the cylinder and used to ensure the sample was mixed. 3611



Article

the precise excitation voltage used). During mixture experiments with V1 closed, the cell pressure was determined from the Kulite transducers voltage output, V, and the measured temperature T, using

Table 4. Relative Response Factors of the Two Flame Ionization Detectors (FID) Used to Convert the Ratios of Integrated Detector Response Areas into Mole Fraction Compositions Using eq 3 for Components CH4 (1), C2H6 (2), C3H8 (3), iC4H10 (4), and nC4H10 (5) κ2/κ1 κ3/κ1 κ4/κ1 κ5/κ1

FID-L

FID-V

2.031 ± 0.035 2.957 ± 0.008 3.906 ± 0.078 3.879 ± 0.071

2.003 ± 0.033 2.975 ± 0.035 3.843 ± 0.023 3.870 ± 0.098

p = (w0 + w1·T ) ·(V + w2 + w3·T )

(1)

The parameters w0, w1, w2, and w3 were determined by calibration against the reference Paroscientific Digiquartz pressure transducer, P2, at the temperatures 203 K, 243 K and 303 K using methane or argon from vacuum to 13 MPa. The standard uncertainty of P2 over this range was u(P) = 2 kPa based on the manufacturer’s specifications. The rms deviation of the Kulite pressures calculated using eq 1 from the pressures recorded by P2 during the calibration was 12 kPa, and in subsequent checks of P1 against P2, the variation remained within this amount. The standard uncertainty of the pressures reported here is thus estimated to be 0.02 MPa. (Over the course of these measurements, which lasted about 9 months, the stability of the reference transducer P2 was checked by monitoring its reading when under vacuum. The vacuum reading obtained was always consistent within the specified uncertainty of P2.) The PRTs used in the VLE apparatus were all Class A and measured using the four-wire method. Prior to their installation in the apparatus, they were all compared against a reference PRT in a liquid bath from (245 to 323) K, and at 77 K using liquid nitrogen. The measured resistances of each PRT were converted to a temperature using a quadratic function, the parameters of which were determined for each PRT using this ex situ calibration. Once installed in the apparatus, the PRT temperature readings were checked for drift by filling the cell with pure ethane and varying the cell temperature between 203 K and 283 K. Pure ethane is two-phase at these temperatures and from measurements of its vapor pressure, the corresponding saturation temperatures could be calculated and compared with the temperatures readings from the PRTs. An initial in situ calibration with the cell heater switched off and only the copper can temperature

Figure 7. Isochoric and isothermal measurement pathways used for the acquisition of VLE data reported in this work, illustrated by the example of the experiment with the binary system CH4 + iC4H10: □, isochoric pathway (including the initial single-phase condition at which the cell was loaded); ■, isothermal pathway. The solid curve represents the predicted phase envelope for the gravimetric composition. The dashed curve represents the predicted phase envelope for the leanest composition. The bubble point curves are shown in blue and the dew point curves are shown in red.

Table 5. Measured (p,T,x,y) Data for the CH4 (1) + C2H6 (2) Binary Mixturea T/K

p/kPa

x1

243.58 203.22 213.39 223.50 233.56

3949 2124 2517 2945 3417

0.3099 0.3653 0.3464 0.3315 0.3188

243.60 243.60 243.60 243.61 243.61 243.61 243.60 243.60 243.60 243.60 243.61 243.60

3942 4831 5395 6080 6469 6691 6885 6487 5564 5094 3718 3675

0.3082 0.3973 0.4553 0.5273 0.5673 0.5957 0.6218 0.5754 0.4741 0.4255 0.2865 0.2812

u(x1)

uc(x1)

Isochoric Path 0.0028 0.0037 0.0048 0.0064 0.0039 0.0052 0.0034 0.0045 0.0030 0.0039 Isothermal Path 0.0028 0.0037 0.0031 0.0039 0.0031 0.0040 0.0033 0.0042 0.0040 0.0049 0.0044 0.0055 0.0126 0.0133 0.0039 0.0049 0.0034 0.0042 0.0032 0.0040 0.0025 0.0034 0.0032 0.0040

y2

u(y2)

uc(y2)

0.3336 0.1333 0.1711 0.2195 0.2755

0.0033 0.0017 0.0020 0.0022 0.0018

0.0038 0.0023 0.0025 0.0028 0.0025

0.3340 0.2954 0.2788 0.2778 0.2731 0.2812 0.2877 0.2801 0.2745 0.2856 0.3421 0.3490

0.0026 0.0022 0.0036 0.0021 0.0029 0.0027 0.0024 0.0022 0.0013 0.0024 0.0021 0.0040

0.0031 0.0032 0.0038 0.0024 0.0031 0.0029 0.0028 0.0025 0.0018 0.0028 0.0028 0.0045

a The uncertainties, u, for the measured mole fractions refer to the Type A standard uncertainties associated with sampling and detector calibration. The uncertainties of the temperature and pressure measurements were 0.15 K and 20 kPa, respectively. These were combined in quadrature with the sampling and detector uncertainties to calculate a combined standard uncertainty, uc.

3612



Article

controlled resulted in the cell temperature readings from T1 and T2 being consistent with the calculated ethane saturation temperatures to within 0.1 K. However, when the cell heater was used to control TC the difference in the values of T1 and T2 was observed to increase. The standard deviations of the T1 and T2 readings from the ethane saturation temperature when the copper can temperature was controlled were both less than 0.12 K. The temperature of the VLE measurements reported here corresponds to the average of the T1 and T2 readings and the corresponding temperature uncertainty was estimated to be 0.15 K. The uncertainty in the flame ionization detector (FID) responses dominates the uncertainty of phase equilibrium measurements and, accordingly, significant efforts were made to calibrate and reduce the uncertainty associated with the relative response factors of the two FIDs. Mole fraction compositions were determined from ratio measurements of the FID’s responses to each component. Within the linear range of the detector, the integrated detector response, Ai, of an FID to component i is proportional to the number of moles of that component ni at the detector. Ai = κini

(2) 39

Kandil et al. determined that the linear range of the FID detectors used in this work corresponded to the equivalent of A1 < 1.5 × 108 counts, and that κ1 ≈ 3.6 × 1013 counts per mole. These values are useful for estimating whether a given sample was, in absolute terms, too small (e.g., only representative of fluid trapped in the sampling capillary rather than from the mixed region of the EC), or too large (exceeding the linearity range of the FID). However, assuming these constraints are satisfied, the mole fraction composition, zi, of a given N component mixture analyzed with the FID can be determined without reference to the ni from the measured ratios (Ai/Aj) by solving the system of equations:

(3b)

Figure 8. VLE data measured in this work, with selected literature data, for CH4 (1) + C2H6 (2). (a) Deviations of CH4 liquid mole fractions (x1) from values calculated with the PR EOS (x1, calc PR) as a function of x1. (b) Deviations of the C2H6 vapor mole fractions (y2) from values calculated with the PR EOS (y2, calc PR) as a function of the y2. The values of x1, calc PR and y2, calc PR were calculated at the experimental (p, T). Symbols: blue ⧫, 244 K, this work; blue ◊, isochore (203 K to 244 K), this work; ∗, 250 K, Davalos et al.;14 ○, 270 K, Gupta et al.;10 △, 250 K, Wei et al.;11 □, 270 K, Wei et al.;11 red ◊, 270 K, Raabe et al.;12 ×, 270 K, Janisch et al.13 Curves: − − − , GERG-2008 EOS at (p,T) measured in this work on the 244 K isotherm; ― GERG-2008 EOS at (p,T) measured in this work along the isochore for (203 to 244) K.

where i = 1 would normally be taken as the mixture component with the largest integrated detector response (methane in this work). The relative response factors of the FIDs, (κi /κ1), and their uncertainties can be determined using a standard gas mixture with known mole fractions, usually from gravimetric preparation. The mole fraction uncertainties for the measured phase compositions can then be estimated by propagating through eq 3 the uncertainties in the (κi /κ1) arising from the FID calibration together with the statistical uncertainty arising from repeat measurements of the area ratios (Ai/A1). Gravimetric Preparation of Gas Mixtures. Single-phase gas mixtures were prepared gravimetrically for two reasons: as part of the determination of the FID relative response factors, and to facilitate the initial loading of the equilibrium cell with a mixture of known composition. To prepare a mixture gravimetrically, a 300 cm3 cylinder was evacuated, and then the components were added into the cylinder in the order of increasing vapor pressure. With each step, the total mass was determined with an electronic balance with a resolution and standard uncertainty of 0.001 g and a full scale of 1100 g. Table 3 lists the

purities of the component fluids as well as the details of the gravimetric mixtures prepared in this work. There were three main contributions to the mole fraction uncertainties of the gravimetric mixtures: weighing, pure component impurities, and valve dead volume. The combination of these uncertainties in quadrature was used to estimate the uncertainties of the gravimetric mixture mole fractions which are reported in Table 3. The relative response factors, (κi /κ1), for each of the FIDs are listed together with their uncertainties in Table 4; as described in the following section, these response factors and their uncertainties were determined first by sampling gravimetric mixtures 1 to 4 while in a single-phase condition at a (p,T) far from the mixture’s dew point, and then at a (p,T) condition inside the two-phase region where the detector’s sensitivity was a maximum. Method. For each experiment, a gravimetric mixture was prepared and loaded into the cell and controlled at 298 K or 303 K, at least 10 K above the mixture’s estimated cricondentherm. This was done to obtain (1) an estimate of the single-phase fluid density using the GERG EOS,3 and (2) composition measurements

⎛ zi ⎞ ⎛ Ai ⎞⎛ κ1 ⎞ ⎜ ⎟ = ⎜ ⎟⎜ ⎟ ⎝ z1 ⎠ ⎝ A1 ⎠⎝ κi ⎠ ⎛ z1 = ⎜⎜1 + ⎝

−1 ⎛ Ai ⎞⎛ κ1 ⎞⎞ ∑ ⎜ ⎟⎜ ⎟⎟⎟ ⎝ A1 ⎠⎝ κi ⎠⎠ i=2

(3a)

N

3613



Article

Table 6. Measured (p,T,x,y) Data for the CH4 (1) + C3H8 (3) Binary Mixturea T/K

p/kPa

x1

283.38 273.48 263.51 263.56 253.59 243.61 243.64

7630 7102 6597 6560 6100 5611 5635

0.4586 0.4589 0.4623 0.4601 0.4708 0.4857 0.4907

243.62 233.67 233.61 223.54 223.36 213.38 203.40 243.62 243.62 243.63 243.61 243.62 243.63 243.62 243.62

5544 5119 5077 4622 4628 4108 3576 891 3909 5500 5544 6402 6989 7530 7943

0.4832 0.5077 0.5037 0.5333 0.5331 0.5614 0.5952 0.0710 0.3442 0.4788 0.4764 0.5565 0.6082 0.6572 0.6961

u(x1)

uc(x1)

Isochoric Path 0.0010 0.0018 0.0010 0.0018 0.0007 0.0018 0.0013 0.0021 0.0011 0.0021 0.0015 0.0024 0.0010 0.0022 Isothermal Path 0.0014 0.0024 0.0012 0.0026 0.0021 0.0031 0.0006 0.0027 0.0012 0.0030 0.0005 0.0033 0.0014 0.0044 0.0005 0.0019 0.0003 0.0019 0.0014 0.0024 0.0015 0.0025 0.0006 0.0022 0.0015 0.0026 0.0010 0.0025 0.0013 0.0027

y3

u(y3)

uc(y3)

0.2045 0.1614 0.1197 0.1174 0.0947 0.0715 0.0719

0.0006 0.0003 0.0012 0.0018 0.0004 0.0001 0.0001

0.0009 0.0007 0.0013 0.0019 0.0006 0.0004 0.0004

0.0715 0.0518 0.0520 0.0368 0.0366 0.0245 0.0162 0.2076 0.0743 0.0704 0.0734 0.0726 0.0768 0.0779 0.0855

0.0002 0.0003 0.0003 0.0005 0.0002 0.0003 0.0005 0.0003 0.0004 0.0002 0.0002 0.0006 0.0005 0.0016 0.0005

0.0004 0.0004 0.0004 0.0005 0.0003 0.0003 0.0005 0.0041 0.0006 0.0004 0.0004 0.0007 0.0006 0.0016 0.0007

a

The uncertainties, u, for the measured mole fractions refer to the Type A standard uncertainties associated with sampling and detector calibration. The uncertainties of the temperature and pressure measurements were 0.15 K and 20 kPa, respectively. These were combined in quadrature with the sampling and detector uncertainties to calculate a combined standard uncertainty, uc.

of the single-phase fluid to ensure consistency between the samples taken from the top and bottom of the cell, and between the GC-derived composition and the known gravimetric composition. The experiment then proceeded along an isochoric pathway (as shown, for example, in Figure 7) with cell temperatures controlled between 203 K and 273 K or 283 K (depending on the mixture’s phase envelope) in increments of 10 K. During the isochoric phase of the experiment, repeat measurements at several conditions were conducted to provide a consistency check; this usually included another single-phase measurement which allowed the total change in mass and overall composition caused by sampling to be estimated. Usually, after about 10 measurements along the isochore (which lasted about 10 days and about the removal of about 1000 samples, including flushing), upon returning to the initial single-phase temperature, the total cell pressure was about 2 % lower, while the overall mixture composition had not varied significantly from its original value. At the conclusion of the isochoric experiment, measurements were conducted along an isothermal pathway with the apparatus cooled to approximately 244 K. The system pressure was first raised, in increments of about 1 MPa, through the addition of methane to the mixture. Material balance was used to estimate the change in the overall composition of the mixture so that the cell pressure was not increased such that the fluid became single-phase. Once the maximum pressure along the isothermal pathway had been reached, the vapor phase of the mixture in the cell was vented in steps of about 1 MPa to complete the isotherm experiment. At each measurement condition at least 12 h were allowed to reach temperature and pressure equilibrium and then no less than 2 h of mixing was applied after the temperature stabilized. Prior to capturing samples for analysis, the capillaries were

flushed with the mixture multiple times to sweep the entire capillary volume. A typical procedure consisted of directing the GC carrier gas into a vented waste stream instead of onto the GC column using rotating valve RV1 in Figure 6. The vapor capillary was then flushed three times with an opening time of 0.25 s (sweeping a total amount of material about 15 times that which would be contained in the vapor capillary). The liquid capillary was flushed three times but with an opening time of 1 s (sweeping about 60 times the amount of material that would be contained in the liquid capillary). Then, the GC carrier gas was redirected back onto the column before two samples from each phase were taken (opening times about 0.05 s) and analyzed. The carrier gas lines were returned to the vent position and each of the capillaries was flushed three more times with an opening of 0.25 s. Then two further samples from each phase were taken, analyzed, and compared with the two samples acquired after the first set of flushes. This procedure was repeated until the samples taken between the flush runs gave consistent results. Once consistent readings had been achieved between flushing, all further samples (usually a minimum of six per measurement) were analyzed using the GC FIDs. The ratios of the areas from the integrated FID responses to each of the sample’s component species were calculated and used to determine its mole fraction composition. A criterion of achieving a relative standard deviation of less than 1 % in each of the measured area ratios (Ai/A1) over four consecutive runs was set for the measurement to be considered successful. Often, relative standard deviations of 0.5 % or better were achieved, which for an equimolar binary mixture, corresponds to a mole fraction variation for the four samples of about 0.0025. The magnitude of the (κi /κ1) uncertainties for each FID and their effect on the measured mole fraction compositions were 3614



Article

minimized through the use of a rotating valve RV2 shown in Figure 6, which could direct samples acquired from the top and bottom of the cell to either of the two detectors, FID-V or FID-L. In the normal detector configuration, vapor samples were analyzed with FID-V and liquid samples with FID-L, while in the alternate detector configuration liquid samples were analyzed with FID-V and vapor samples with FID-L. Once a successful measurement had been made in one detector configuration, the position of valve RV2 was switched and the measurement was repeated in the other configuration. (This occurred immediately following the first measurement so no additional flushing procedure was required.) Any difference in the composition measurements made using the two different detector configurations was then attributable to uncertainty in the values of (κi /κ1) being used for each FID, with the average of the compositions derived using the two configurations having a reduced uncertainty. This technique of measuring the same sample using two different detectors allowed for the values of the (κi /κ1) for each FID to be fine-tuned and their uncertainties reduced. As discussed by Kandil et al.,39 the sensitivity of FIDs is a maximum for equimolar mixtures; however, calibrations of FIDs cannot usually be performed at this most sensitive condition. This is because to prepare mixtures with accurately known compositions gravimetrically usually requires that the heavier components are present only in low concentrations to ensure the mixture is single phase at ambient temperature. The ability to measure the same sample with two different detectors allows the operator to apply the following constraint to improve each detector’s calibration: the composition measured by the two FIDs must be the same even if the exact composition of the sample is unknown. Thus, after performing the first order calibration using a single-phase, lean binary mixture prepared gravimetrically, a second order tuning of the calibration was performed by cooling the cell into the two phase region to a condition at which the liquid phase was approximately equimolar. Then the precise values of (κi /κ1) for each FID could be adjusted sensitively by forcing the two liquid phase compositions measured with the detectors to agree. The fine-tuned values of the (κi /κ1) with reduced uncertainties are listed in Table 4; these values were always consistent with the values determined during the first order calibration using the gravimetrically prepared mixtures, and this procedure had the effect of reducing the uncertainty of the (κi /κ1) by at least a factor of 2. As a final check, following the completion of the phase composition measurements with the FIDs in the alternate configuration, the sample in the cell was remixed with the magnetically driven stirrer for 30 min and allowed to stabilize for another 2 h. The flushing and sampling process was then repeated including the use of the two configurations of the FIDs. The experimental mole fraction compositions reported here correspond to the average of these four measurements (before and after the mixing at constant temperature and pressure in two detector configurations), with each measurement representing the average of at least four samples. The uncertainties in the mole fraction compositions listed here correspond to the standard deviation of these four measurements. These standard uncertainty estimates represent a conservative assessment of the contributions of sampling and FID calibration to the uncertainty of the measured composition. The uncertainties of the measured temperature and pressure of the mixture also propagate into the composition uncertainty; the magnitude of these propagated contributions can be estimated

Figure 9. VLE data measured in this work, with selected literature data, for the CH4 (1) + C3H8 (3) system. (a) Deviations of CH4 liquid mole fractions (x1) from values calculated with the PR EOS (x1, calc PR) as a function of the measured CH4 liquid mole fraction (x1). (b) Deviations of the C3H8 vapor mole fractions (y3) from values calculated with the PR EOS (y3, calc PR) as a function of the y3. The values of x1,calc PR and y3, calc PR were calculated at the experimental (p,T). Symbols: ⧫, 244 K, this work; ◊, isochore (203 K to 283 K), this work; □, 241 K, Akers et al.;31 △, 273 K, Akers et al.;31 ×, 255 K, Price and Kobayashi;28 ○, 230 K, Webster et al..26 Curves: , GERG-2008 EOS at (p,T) measured in this work on the 244 K isotherm; − − − , GERG-2008 EOS at (p,T) measured in this work along the isochore from (203 to 283) K.

using an EOS. The total combined standard uncertainty in the measured compositions may be calculated by combining in quadrature the sampling uncertainties with the propagated temperature and pressure uncertainty. Averaged across all of the measurements reported here made using the specialized cryogenic VLE apparatus, the estimated combined standard uncertainties in the mole fraction compositions were 0.0015 for the vapor phase and 0.0031 for the liquid phase.

■

RESULTS AND DISCUSSION The measured VLE phase compositions and estimated uncertainties at each temperature and pressure are tabulated in Tables 5 to 8. The tables also list the combined measurement uncertainties, u c , which include the GC measurement uncertainties, u(xi) and u(yi), together with the propagated uncertainties of the temperature and pressure measurements. The differences in the liquid and vapor compositions reported here from values calculated with the PR EOS implemented in Aspen HYSYS are shown in Figures 8 to 11, together with the 3615



Article

Table 7. Measured (p,T,x,y) Data for the CH4 (1) + iC4H10 (4) Binary Mixturea T/K

p/kPa

x1

273.47 263.56 253.60 243.61 243.60 243.58 233.57 223.49 213.39 203.25

8329 7819 7306 6785 6735 6824 6251 5714 5118 4503

0.5160 0.5237 0.5371 0.5561 0.5523 0.5607 0.5817 0.6151 0.6565 0.7133

243.60 243.60 243.60 243.59 243.60 243.60 243.60 243.60

8684 8280 7854 7847 6735 6041 4418 2642

0.7043 0.6749 0.6345 0.6386 0.5523 0.4971 0.3734 0.2300

u(x1)

uc(x1)

Isochoric Pathway 0.0027 0.0030 0.0025 0.0029 0.0017 0.0023 0.0010 0.0020 0.0020 0.0027 0.0019 0.0026 0.0037 0.0042 0.0009 0.0026 0.0027 0.0041 0.0002 0.0043 Isothermal Pathway 0.0015 0.0024 0.0021 0.0028 0.0024 0.0030 0.0016 0.0024 0.0020 0.0027 0.0006 0.0018 0.0009 0.0020 0.0011 0.0021

y4

u(y4)

uc(y4)

0.0753 0.0572 0.0420 0.0302 0.0308 0.0313 0.0204 0.0155 0.0097 0.0059

0.0008 0.0006 0.0007 0.0006 0.0005 0.0006 0.0008 0.0005 0.0002 0.0004

0.0009 0.0007 0.0007 0.0006 0.0005 0.0006 0.0008 0.0005 0.0002 0.0004

0.0506 0.0431 0.0394 0.0381 0.0308 0.0287 0.0263 0.0305

0.0009 0.0007 0.0008 0.0004 0.0005 0.0005 0.0004 0.0004

0.0011 0.0008 0.0009 0.0005 0.0005 0.0005 0.0004 0.0005

a

The uncertainties, u, for the measured mole fractions refer to the Type A standard uncertainties associated with sampling and detector calibration. The uncertainties of the temperature and pressure measurements were 0.15 K and 20 kPa, respectively. These were combined in quadrature with the sampling and detector uncertainties to calculate a combined standard uncertainty, uc.

for CH4 (1) + C2H6 (2) are presented as deviation plots in the mole fraction of methane x1 showing the difference between the measurements and the PR EOS predicted compositions in Figure 8. The deviations of the measurements made here along both the isothermal and isochoric pathways are consistent within experimental uncertainty at the same liquid mole fractions. The rms deviation of the measured methane liquid mole fractions (Figure 8a) from the PR EOS is 0.0090, while the rms deviations of the bubble point data from the GERG-2008 EOS is 0.0097 mole fraction, although the average deviations for the two EOS are −0.0033 and +0.0018, respectively. Given that across all the CH4 (1) + C2H6 (2) bubble point data, the average combined standard uncertainty in x1 ranges from 0.0026 to 0.0072, it is apparent that both EOS do a reasonable job predicting the new bubble point data. The new bubble point data are also consistent with the data of Davalos et al.14 and Wei et al.11 measured at similar temperatures, and the increased negative deviation of the literature data from the PR EOS measured at 270 K around x1 = 0.3, is similar in nature to the increased deviation in the new 244 K isothermal data from the PR EOS as the critical point is approached. The vapor phase ethane mole fractions y2 of the measured data shown in Figure 8b have an rms and average deviation from the PR EOS of 0.0040 and −0.0004, respectively, both of which are comparable with the average combined standard uncertainty in y2 ranging from 0.0023 to 0.0035. Some temperature dependence in the y2 deviations is apparent: the most positive occurs at the lowest temperature 203 K, and the deviations become increasingly negative as temperature increases. The measured vapor phase ethane mole fractions have an rms and average deviation from the GERG-2008 EOS of 0.0081 and −0.0051, respectively. As the mixture’s critical point at 243 K is approached (e.g., at 6885 kPa, x1 ≈ 0.62 and y1 ≈ 0.71) the GERG EOS vapor predictions oscillate slightly, perhaps for reasons of numerical stability.

corresponding deviations of selected literature VLE data. Differences between the phase compositions predicted at the experimental conditions with the GERG-2008 EOS from those predicted with the PR EOS are also shown. The GERG-2008 EOS was implemented in a dynamic linked library supplied by Kunz and Wagner43 and accessed through either Microsoft Excel or a stand-alone executable. In all cases, the calculated values were determined by first estimating the overall composition of the mixture, and then performing a flash calculation at the experimental pressure and temperature to produce both xi,calc and yi,calc. For the isochoric measurements, the mixture’s overall composition was taken to be that of the corresponding singlephase mixture that was prepared gravimetrically (Table 3) and loaded into the cell at ambient temperatures, prior to commencement of the isochore. For the isothermal measurements, the experimentally measured liquid and vapor phase compositions were combined using an assumed value for the vapor-phase mole fraction, β, to give an overall mixture composition. The assumed value of β was set either to an average of the values estimated by the flash calculations done for the isochoric measurements (β ≈ 0.8), or it was set to a particular value (usually around 0.5) to ensure that the flash calculation did not return a single-phase condition at the experimental pressure and temperature. Formally, the values of xi,calc and yi,calc calculated at a given (T, p, zi) with zi = β yi + (1 − β) xi are independent of the value of β chosen, as long as the experimental (T, p) is within the two-phase envelope predicted using the EOS with the resulting zi. In practice, the numerical solution of the flash algorithm does lead to small differences in the values of xi,calc and yi,calc obtained if different values of β are assumed; however, these differences were much smaller (typically ≤10−8 mole fraction) than the experimental uncertainty. The CH4 (1) + C2H6 (2) measurements are tabulated in Table 5. Five data were measured along the isochoric pathway at temperatures between 203 K and 244 K and twelve data were measured along the isothermal pathway at 243.6 K. The data 3616



Article

The results of the CH4 (1) + C3H8 (3) measurements are tabulated in Table 6. They include 14 isochoric values, measured at temperatures between 203 K and 283 K and 10 isothermal values measured at 243.6 K. The isochoric and isothermal measurements are consistent with each other within experimental uncertainty. The rms deviation of the measured methane liquid mole fractions x1 (Figure 9a) from the PR EOS was 0.0085. The new data exhibit the same trend in their deviations from the PR EOS as the literature data, and particularly those of Price and Kobayashi28 and Webster and Kidnay26 as the bubble point pressure increases toward the mixture critical pressure. (In all of the mixtures considered here, as x1 increases along the bubble point curve so does pressure). The data of Akers et al.31 are somewhat inconsistent with the other measurements, having a more negative deviation from the PR EOS at low values of x1 and either more positive (273 K) or more negative (241 K) deviations from the PR EOS at high values of x1. The GERG2008 predictions show the same positive divergence from the PR EOS as the critical point is approached, indicating that the equation’s more complex functional form is better able to emulate the physical dependence of pressure on composition in this region. However, the rms deviation of the new x1 data from the GERG-2008 EOS is still 0.0083 because it underpredicts the present data as well as those of Price and Kobayashi28 and Webster and Kidnay26 at lower pressures. The rms deviation of the measured propane vapor mole fractions y3 (Figure 9b) from the PR EOS is 0.0042, whereas the rms deviation of the y3 data from the GERG-2008 EOS is 0.0032. The data deviate negatively from the predictions of both models, with the magnitude of the deviations from the PR EOS being largest for data measured at pressures around 6500 kPa (y3 ≈ 0.12). The GERG-2008 EOS was better able to describe the relationship between y3 and pressure, exhibiting a shallow minimum in its deviations from the PR EOS at this condition near y3 = 0.12. Table 7 lists the results of the CH4 (1) + iC4H10 (4) measurements, ten of which were obtained along an isochoric pathway at temperatures between 203 and 273 K and eight of which were obtained along the 243.6 K isotherm. The rms deviation of the measured liquid methane mole fractions x1 shown in Figure 10a from the PR EOS is 0.0088. Notably, the deviations of x1 measured along the isothermal and isochoric pathways from the PR EOS are identical within experimental uncertainty at the same liquid methane mole fractions, which indicates that the temperature dependence of these data are well-described by the cubic model, and it is only at high pressures that the PR EOS does not describe the new data well, reflecting the cubic’s limited functional form. In contrast the x1 deviations of Barsuk et al.18 measured at 273 K are significantly offset from the deviations of their x1 data obtained along the 233 K and 253 K isotherms; the latter two isothermal data sets are only consistent with the new data at the two lowest pressures measured here. In the development of the GERG EOS no other thermodynamic data in the range 198 K to 278 K of any kind were identif ied for the CH4 (1) + iC4H10 (4) binary system3 (our emphasis) and so it was necessary to use the data of Barsuk et al.18 in the model’s regression. Consequently, the rms deviation of the new data from the GERG EOS is 0.0151, nearly twice that of the PR EOS because the GERG model has an offset from the present data. This is even though the GERG model correctly captures the temperature dependence in the data (as evidenced by the coincidence of the GERG EOS predictions for the isothermal

Figure 10. VLE data measured in this work, with selected literature data, for the CH4 (1) + iC4H10 (4) system. (a) Deviations of the CH4 liquid mole fractions (x1) from values calculated with the PR EOS (x1,calc PR) as a function of x1. (b) Deviations of the iC4H10 vapor mole fractions (y4) from values calculated with the PR EOS (y4 calc PR) as a function of the y4. The values of x1,calc PR and y4, calc PR were calculated at the experimental (p, T). Symbols: blue ◆, 244 K, this work; blue ◇, isochore (203 K to 273 K), this work; red ○, 233 K, Barsuk et al.;18 red □, 253 K, Barsuk et al.;18 ×, Barsuk et al.18 Curves: , GERG-2008 EOS at (p,T) measured in this work on the 244 K isotherm; − − − , GERG-2008 EOS at (p,T) measured in this work along the isochore (203 K to 273 K).

and isochoric pathways) and better captures the pressure dependence of the x1 data than the PR EOS. The deviations of the measured vapor phase isobutane mole fractions y4 from the PR EOS (Figure 10b) have an rms value of 0.0018, which is comparable with the combined experimental standard uncertainty. The y4 deviations from the PR EOS predictions increase with pressure along the 244 K isotherm, which is the first clear reflection in the vapor phase of the same trend that is apparent in the liquid phase. The rms deviation of the y4 data from the GERG EOS is 0.0037, reflecting that the deviations of the GERG EOS y4 predictions exhibit a negative slope with increasing y4. The CH4 (1) + nC4H10 (5) measurements are tabulated in Table 8. Ten isochoric values were measured at temperatures between 203 K, and 273 K and ten isothermal values were measured at 244.5 K. The rms deviation of the measured methane liquid mole fractions from the PR EOS shown in Figure 11a was 0.0184. The deviations of the isothermal and isochoric measurements were consistent within experimental uncertainty at the same methane liquid mole fraction except for one point at x1 ≈ 0.62; 3617



Article

Table 8. Measured (p,T,x,y) Data for the CH4 (1) + nC4H10 (5) Binary Mixturea T/K

p/kPa

x1

273.42 263.48 253.52 244.52 243.52 233.50 233.49 223.44 213.36 203.25

7249 6842 6431 6005 6010 5593 5604 5163 4702 4224

0.4246 0.4331 0.4480 0.4601 0.4646 0.4880 0.4882 0.5201 0.5615 0.6217

244.52 244.53 244.48 244.52 244.52 244.51 244.52 244.52 244.52 244.48

1311 3318 5058 6005 6593 8016 8238 9161 9913 10132

0.1071 0.2669 0.3950 0.4601 0.5008 0.6002 0.6180 0.6869 0.7522 0.7764

u(x1)

uc(x1)

Isochoric Path 0.0008 0.0014 0.0018 0.0022 0.0004 0.0014 0.0003 0.0015 0.0013 0.0020 0.0005 0.0019 0.0010 0.0021 0.0006 0.0024 0.0028 0.0042 0.0004 0.0052 Isothermal Path 0.0000 0.0016 0.0004 0.0014 0.0017 0.0022 0.0003 0.0015 0.0021 0.0026 0.0009 0.0021 0.0015 0.0025 0.0005 0.0024 0.0017 0.0034 0.0018 0.0037

y5

u(y5)

uc(y5)

0.0482 0.0357 0.0265 0.0197 0.0188 0.0126 0.0146 0.0075 0.0061 0.0036

0.0017 0.0016 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0015 0.0015

0.0017 0.0016 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0015 0.0015

0.0289 0.0175 0.0154 0.0197 0.0185 0.0274 0.0251 0.0399 0.0515 0.0594

0.0015 0.0015 0.0023 0.0015 0.0016 0.0015 0.0062 0.0015 0.0019 0.0016

0.0016 0.0015 0.0023 0.0015 0.0016 0.0015 0.0062 0.0017 0.0024 0.0024

a The uncertainties, u, for the measured mole fractions refer to the Type A standard uncertainties associated with sampling and detector calibration. The uncertainties of the temperature and pressure measurements were 0.15 K and 20 kPa, respectively. These were combined in quadrature with the sampling and detector uncertainties to calculate a combined standard uncertainty, uc.

improved by including the new data and those of Elliot et al.23 in a new fitting process. The rms deviation of the measured butane vapor mole fractions (Figure 11b) from the PR EOS is 0.0036, whereas the rms deviation of the y5 data from the GERG-2008 EOS is 0.0031. The measured y5 deviations from the PR EOS predictions increase with pressures along the 244 K isotherm even more strongly than was the case for y4 in the CH4 (1) + iC4H10 (4) system (Figure 10b). The values of y5 predicted with the GERG EOS at 244 K deviate slightly from those predicted using the PR EOS, with the deviations becoming more positive at higher pressures, partially reflecting the trend exhibited by the data albeit with a much smaller magnitude.

at this point, however, the temperature of the isochoric measurement was 203 K, some 40 K lower than the corresponding point on the isotherm, and thus this difference potentially reflects an effect of temperature dependence. The isothermal data set shows the most significant positive divergence from the PR EOS of all the binary systems considered here, as the bubble-point pressure is increased toward the mixture critical point. Importantly, the new data further validate the three isothermal data sets of Elliot et al.,23 the temperature dependence of which appears to be reasonably well-described by the PR EOS even though each isotherm exhibits a similar divergence from the PR EOS predictions as the critical point is approached. In contrast the new data are clearly inconsistent with the earlier data sets of Roberts et al.21 and Wang and McKetta,22 which appear to be erroneous. Kunz et al.3 stated that none of these literature data sets were used in the development of the GERG-2008 EOS for the CH4 (1) + nC4H10 (5) binary system; this may have been partly because of the inconsistency between the data of Elliot et al.23 and those of McKetta and co-workers.21,22 Given that the only binary VLE data used in the development of the GERG EOS for the CH4 (1) + nC4H10 (5) mixture were those of Weise et al.30 and Sage et al.37 measured at temperatures between (278 and 394) K, it is interesting that the GERG predictions at 244 K effectively split the literature data sets.21−23 As a consequence, the rms deviation of the new x1 data from the GERG EOS prediction is 0.0464, which is a factor of 2.5 times larger than the rms deviation of the PR EOS and more than 40 times larger than the average combined experimental standard uncertainty. This is despite the fact that the curvature of the GERG-2008 EOS deviations from the PR EOS predictions of x1 with increasing pressure match those of the new VLE data, and suggests that the performance of the GERG EOS for this binary could be

■

CONCLUSIONS A review was conducted of the available literature VLE data for the binary mixtures most relevant to the simulation of LNG scrub columns. Analysis of those data identified that EOS used to model such industrial operations are limited in their ability to describe those data by the presence of a large number of poor quality measurements. Accordingly, a specialized cryogenic VLE apparatus was developed and used to produce new, reference quality data for the methane binary systems of most importance to LNG scrub columns consisting of CH4, C2H6, C3H8, and iC4H10 or nC4H10. The term reference quality is used to indicate that (a) unlike many similar VLE data reported in the literature, robust quantitative uncertainty estimates have been made for the measured mole fraction compositions; and (b) the accuracy of the present data is equal to or better than other sources available for these systems over this range of temperature and pressure. As a result, the new measurements have enabled the identification of literature data sets that should receive an increased weighting as well as those that should not be included in future EOS development. This work has, therefore, contributed to the 3618



Article

For the liquid phase, the rms deviations in x1 from the PR EOS for the four binaries ranged from (0.008 to 0.018) mole fraction, which corresponds to (2 to 4) % of the average value of x1 ≈ 0.5 at the conditions studied. This is about two to six times the average combined experimental standard uncertainty of the x1 data; however the deviations in x1 from the PR EOS are systematic in nature, increasing with bubble point pressure as the mixture critical point is approached, and reaching up to 0.05 mol fraction in the case of the CH4 (1) + nC4H10 (5) data set. This systematic deficiency of the PR EOS is a consequence of its cubic form, which prevents it from describing simultaneously the shape of the phase envelope at both low and high pressure. The default PR EOS in Aspen HYSYS has been tuned to describe the VLE of these binary systems at low to medium pressures essentially within experimental standard uncertainty, and it would seem there is little prospect of further improving the performance of this cubic EOS at higher pressures, without sacrificing the lower pressure performance. The multiparameter nature of the GERG-2008 EOS means it has the capacity to describe accurately the VLE of these binary mixtures over a much wider range of pressure and temperature. However, with the exception of the CH4 (1) + C3H8 (3) mixture, the rms deviations of the measured x1 from the GERG EOS were larger than those for the PR EOS. This was particularly the case for the CH4 (1) + iC4H10 (4) and CH4 (1) + nC4H10 (5) mixtures, and is likely a consequence of the uncertainty regarding the literature data sets that should be used in the model’s development. Prior to these measurements, we are aware of only one other data set for any thermodynamic property of the CH4 (1) + iC4H10 (4) binary in the temperature range 198 K to 278 K, and accordingly the GERG EOS represents the average of the Barsuk et al.18 data, which have an anomalous temperature dependence. For the CH4 (1) + nC4H10 (5) binary at 244 K, two groups of inconsistent VLE data were available in the literature at the time of the GERG EOS development and so neither was used in its regression. The GERG EOS currently splits the difference between the erroneous data of McKetta and co-workers,21,22 and those of Elliot et al.,23 which are in excellent agreement with the new data presented here. The reference quality VLE data presented in this work for the binary systems of primary interest to LNG scrub columns should therefore contribute significantly to the improvement of the advanced EOS capable of describing rich natural gases over a wider range of temperatures and pressures.

Figure 11. VLE data measured in this work, with selected literature data, for the CH4 (1) + nC4H10 (5) system. (a) Deviations of CH4 liquid mole fractions (x1) from values calculated with the PR EOS (x1, calc PR,) as a function of the x1. (b) Deviations of the nC4H10 vapor mole fractions (y5) from values calculated with the PR EOS (y5, calc PR) as a function of y5. The values of x1,calc PR and y5, calc PR were calculated at the experimental (p, T). Symbols: blue ◆, 244 K, this work; blue ◇, isochore (203 K to 273 K), this work; red △, 244 K, Roberts et al.;21 ∗, 244 K, Wang and McKetta;22 red □, 244 K, Elliot et al.;23 ×, 255 K, Elliot et al.;23 red ○, 233 K, Elliot et al.23 Curves: , GERG-2008 EOS at (p,T) measured in this work on the 244 K isotherm; − − − , GERG2008 EOS at (p,T) measured in this work along the isochore (203 K to 273 K).

■

resolution of a problem articulated by Kunz and Wagner;4 namely that the paucity of quality VLE data available for mixtures limits the accuracy achievable in the further development of modern EOS, especially those aimed at describing richer natural gases at low temperatures. When comparing the new VLE data with the predictions of EOS it is important to consider both the absolute mole fraction deviations and the deviations relative to the amount of the minor component in the phase under consideration. For the vapor phase, the rms deviations of the heavy component, yi (i = 2, 3, 4, or 5), data from either the PR or GERG EOS had an average value across all systems of 0.004 mol fraction, and amounted to between (1 and 13) % of the average value of the yi at the conditions studied. These deviations are, however, closer in magnitude to the combined experimental standard uncertainty, which makes it more difficult to discern whether clear systematic trends are exhibited in the vapor phase predictions of either model.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The research was funded by Chevron Energy Technology Company and the Australian Research Council through LP0882519 and LP120200605. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank Craig Grimm for helping to construct the apparatus. The authors are also grateful to Mohammed Kandil and Andrew Vieler for their contributions to the project. 3619



■

Article

(23) Elliot, D. G.; Chen, R. J. J.; Chappelear, P. S.; Kobayashi, R. VaporLiquid Equilibrium of Methane-Butane System at Low Temperatures and High Pressures. J. Chem. Eng. Data 1974, 19, 71−77. (24) Wichterle, I.; Kobayashi, R. Vapor-Liquid Equilibrium of Methane-Propane System at Low Temperatures and High Pressures. J. Chem. Eng. Data 1972, 17, 4−9. (25) Kalra, H.; Robinson, D. B. An Apparatus for the Simultaneous Measurement of Equilibrium Phase Composition and Refractive Index Data at Low Temperatures and High Pressures. Cryogenics 1975, 15, 409−412. (26) Webster, L. A.; Kidnay, A. J. Vapor-Liquid Equilibria for the Methane-Propane-Carbon Dioxide Systems at 230 and 270 K. J. Chem. Eng. Data 2001, 46, 759−764. (27) Benham, A. I.; Katz, D. L. Vapor-Liquid Equilibria for Hydrogen Light Hydrocarbon Systems at Low Temperatures. AIChE J. 1957, 3, 33−36. (28) Price, A. R.; Kobayashi, R. Low Temperature Vapor-Liquid Equilibrium in Light Hydrocarbon Mixtures: Methane-Ethane-Propane System. J. Chem. Eng. Data 1959, 4, 40−52. (29) Reamer, H. H.; Sage, B. H.; Lacey, W. N. Phase Equilibria in Hydrocarbon Systems: Volumetric and Phase Behavior of the MethanePropane System. Ind. Eng. Chem. 1950, 42, 534−539. (30) Wiese, H. C.; Jacobs, J.; Sage, B. H. Phase Equilibria in the Hydrocarbon Systems. Phase Behavior in the Methane- Propane-nButane System. J. Chem. Eng. Data 1970, 15, 82−91. (31) Akers, W. W.; Burns, J. F.; Fairchild, W. R. Low-Temperature Phase Equilibria. Methane-Propane System. Ind. Eng. Chem. 1954, 46, 2531−2534. (32) Joffe, J. Vapor-Liquid Equilibria by the Pseudocritical Method. Ind. Eng. Chem. Fundam. 1976, 15, 298−304. (33) Raimondi, L. A Modified Redlich-Kwong Equation of State for Vapour-Liquid Equilibrium Calculations. Chem. Eng. Sci. 1980, 35, 1269−1275. (34) Kahre, L. C. Low-Temperature K Data for Methane-n-Butane. J. Chem. Eng. Data 1974, 19, 67−71. (35) Nederbragt, G. W. Gas-Liquid Equilibria for the System Methane - Butane. Ind. Eng. Chem. 1938, 30, 587−588. (36) Sage, B. H.; Budenholzer, R. A.; Lacey, W. N. Phase Equilibria in Hydrocarbon Systems: Methane - n-Butane System in the Gaseous and Liquid Regions. Ind. Eng. Chem. 1940, 32, 1262−1277. (37) Sage, B. H.; Hicks, B. L.; Lacey, W. N. Phase Equilibria in Hydrocarbon Systems: The Methane-n-Butane System in the TwoPhase Region. Ind. Eng. Chem. 1940, 32, 1085−1092. (38) Rigas, T. J.; Mason, D. F.; Thodos, G. Vapor-Liquid Equilibria Microsampling Technique Applied to a New Variable-Volume Cell. Ind. Eng. Chem. 1958, 50, 1297−1300. (39) Kandil, M. E.; Thoma, M. J.; Syed, T.; Guo, J.; Graham, B. F.; Marsh, K. N.; Huang, S. H.; May, E. F. Vapor-Liquid Equilibria Measurements of the Methane + Pentane and Methane + Hexane Systems at Temperatures from (173 to 330) K and Pressures to 14 MPa. J. Chem. Eng. Data 2011, 56, 4301−4309. (40) Hughes, T. J.; Kandil, M. E.; Graham, B. F.; May, E. F. Simulating the Capture of CO2 from Natural Gas: New Data and Improved Models for Methane + Carbon Dioxide + Methanol. Int. J. Greenhouse Gas Control 2014, 31, 121−127. (41) Hughes, T. J.; Kandil, M. E.; Graham, B. F.; Marsh, K. N.; Huang, S. H.; May, E. F. Phase Equilibrium Measurements of (Methane + Benzene) and (Methane + Methylbenzene) at Temperatures from (188 to 348) K and Pressures to 13 MPa. J. Chem. Thermodyn. 2015, 85, 141− 147. (42) TransValor. The ROLSI Evolution IV. http://www.rolsi.com/ English.htm (accessed February 2, 2011). (43) Kunz, O.; Wagner, W. Software for the Calculation of Thermodynamic Properties from the GERG-2004 XT08 Wide Range Equation of State for Natural Gases and Other Mixtures; Ruhr Universitat Bochum: 2009.

REFERENCES

(1) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (2) Assael, M. J.; Trusler, J. P. M.; Tsolakis, T. F. Thermophysical Properties of Fluids: An Introduction to Their Prediction; Imperial College Press: London, UK, 1996. (3) Kunz, O.; Klimeck, R.; Wagner, W.; Jaeschke, M. The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures, GERG Technical Monograph 15; Fortschr.-Ber. VDI Verlag: Düsseldorf, Germany, 2007. (4) 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. (5) Kiselev, S. B.; Friend, D. G. Cubic Crossover Equation of State for Mixtures. Fluid Phase Equilib. 1999, 162, 51−82. (6) Lafitte, T.; Apostolakou, A.; Avendaño, C.; Galindo, A.; Adjiman, C. S.; Müller, E. A.; Jackson, G. Accurate Statistical Associating Fluid Theory for Chain Molecules Formed from Mie Segments. J. Chem. Phys. 2013, 139, 154504. (7) Aspen HYSYS Process Simulator, v7.3; Aspen Technology, Inc: Cambridge, MA, 2011. (8) Wichterle, I.; Kobayashi, R. Vapor-Liquid Equilibrium of MethaneEthane System at Low Temperatures and High Pressures. J. Chem. Eng. Data 1972, 17, 9−12. (9) Wichterle, I.; Kobayashi, R. Vapor-Liquid Equilibrium of MethaneEthane-Propane System at Low Temperatures and High Pressures. J. Chem. Eng. Data 1972, 17, 13−18. (10) Gupta, M. K.; Gardner, G. C.; Hegarty, M. J.; Kidnay, A. J. LiquidVapor Equilibriums for the N2 + CH4 + C2H6 System from 260 to 280 K. J. Chem. Eng. Data 1980, 25, 313−318. (11) Wei, M. S. W.; Brown, T. S.; Kidnay, A. J.; Sloan, E. D. Vapor + Liquid Equilibria for the Ternary System Methane + Ethane + Carbon Dioxide at 230 K and Its Constituent Binaries at Temperatures from 207 to 270 K. J. Chem. Eng. Data 1995, 40, 726−731. (12) Raabe, G.; Janisch, J.; Köhler, J. Experimental Studies of Phase Equilibria in Mixtures Relevant for the Description of Natural Gases. Fluid Phase Equilib. 2001, 185, 199−208. (13) Janisch, J.; Raabe, G.; Köhler, J. Vapor-Liquid Equilibria and Saturated Liquid Densities in Binary Mixtures of Nitrogen, Methane, and Ethane and Their Correlation Using the VTPR and PSRK GCEOS. J. Chem. Eng. Data 2007, 52, 1897−1903. (14) Davalos, J.; Anderson, W. R.; Phelps, R. E.; Kidnay, A. J. LiquidVapor Equilibria at 250.00K for Systems Containing Methane, Ethane, and Carbon Dioxide. J. Chem. Eng. Data 1976, 21, 81−84. (15) Wichterle, I. Low Temperature Vapor−Liquid Equilibria in the Methane-Ethane-Propane Ternary and Associated Binary Methane Systems with Special Consideration of the Equilibria in the Vicinity of the Critical Temperature of Methane, A Monograph. Rice University: Houston TX, 1970. (16) Wilson, G. M. Vapor−Liquid Equilibria of Nitrogen, Methane, Ethane, and Propane Binary Mixtures at LNG Temperatures from Total Pressure Measurements. Adv. Cryog. Eng. 1975, 20, 164−171. (17) Miller, R. C.; Kidnay, A. J.; Hiza, M. J. Liquid + Vapor Equilibriums in Methane + Ethene and in Methane + Ethane from 150.00 to 190.00 K. J. Chem. Thermodyn. 1977, 9, 167−178. (18) Barsuk, S. D.; Skripka, V. G.; Ben’yaminovich, O. A. Liquid-Vapor Equilibriums in a Methane-Isobutane System at Low Temperatures. Gaz. Prom-st. 1970, 15, 38−41. (19) Olds, R. H.; Sage, B. H.; Lacey, W. N. Methane-Isobutane System. Ind. Eng. Chem. 1942, 34, 1008−1013. (20) Haynes, W. M. Orthobaric Liquid Densities and Dielectric Constants of (Methane + 2-Methylpropane) and (Methane + n-Butane) at Low Temperatures. J. Chem. Thermodyn. 1983, 15, 903−911. (21) Roberts, L. R.; Wang, R. H.; Azarnoosh, A.; McKetta, J. J. Methane-n-Butane System in the Two-Phase Region. J. Chem. Eng. Data 1962, 7, 484−485. (22) Wang, R. H.; McKetta, J. J. Vapor-Liquid Equilibrium of the Methane-n-Butane-Carbon Dioxide System at Low Temperatures and Elevated Pressures. J. Chem. Eng. Data 1964, 9, 30−35. 3620


Reference Quality VaporâLiquid Equilibrium Data for the Binary

Recommend Documents

Reference Quality VaporâLiquid Equilibrium Data for the Binary