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Phase equilibrium and critical point data for ethylene and chlorodifluoromethane binary mixtures using a new “static-analytic” apparatus
Accepted Manuscript Phase equilibrium and critical point data for ethylene and chlorodifluoromethane binary mixtures using a new “static-analytic” apparatus Wayne Michael Nelson, Rasoul Hassanalizadeh, Deresh Ramjugernath PII:
S0378-3812(17)30297-2
DOI:
10.1016/j.fluid.2017.08.005
Reference:
FLUID 11551
To appear in:
Fluid Phase Equilibria
Received Date: 30 May 2017 Revised Date:
28 July 2017
Accepted Date: 4 August 2017
Please cite this article as: W.M. Nelson, R. Hassanalizadeh, D. Ramjugernath, Phase equilibrium and critical point data for ethylene and chlorodifluoromethane binary mixtures using a new “static-analytic” apparatus, Fluid Phase Equilibria (2017), doi: 10.1016/j.fluid.2017.08.005. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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P (MPa)
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x1, y1
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Phase equilibrium and critical point data for ethylene and chlorodifluoromethane binary mixtures using a new “staticanalytic” apparatus
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Wayne Michael Nelson*, Rasoul Hassanalizadeh, and Deresh Ramjugernath
Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa
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*Corresponding author: E-mail: [email protected]; Tel.: +27 31 2603121
ACCEPTED MANUSCRIPT ABSTRACT
An apparatus based on the “static-analytic” method was designed and commissioned. The apparatus was tested by measuring vapour-liquid equilibrium data for the binary system of
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carbon dioxide + chlorodifluoromethane at 273.15 K. There is excellent agreement between the experimental data and previous measurements reported in literature. New experimental vapour-liquid equilibrium data were also measured for the binary systems of ethylene +
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chlorodifluoromethane at five temperatures, viz. (273.15, 293.15, 313.15, 333.15, and 353.15) K. At the same temperatures (excluding 273.15 K) the critical points of the binary
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mixtures were also experimentally determined. The experimental data for this binary system were accurately correlated using the Peng–Robinson Equation of State utilizing the Wong– Sandler mixing rule coupled with the Non-Random Two-Liquid (NRTL) activity coefficient
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model.
Keywords: VLE, Static-Analytic, Phase Equilibrium, Phase Equilibria, Ethylene, Carbon Dioxide, Chlorodifluoromethane
ACCEPTED MANUSCRIPT 1.
INTRODUCTION
The importance and necessity for accurate and reliable phase equilibrium data is well documented in literature. Due to the rapidity of measurement and potential for high accuracy,
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experimental methods following the “static-analytic” technique are widely used [1, 2]. Nowadays, many of the apparatuses following the “static-analytic” method are based upon the designs originating from Laugier and Richon [3] and Figurere et al. [4]. The originality of these setups being the sampling system, featuring the preliminary versions of the rapid on-
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line sampler injector (ROLSI) [5]. A few examples of modern designs utilizing the “static-
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analytic” method, comprising of mainly modifications to the equilibrium cell, include: (i) Zhang et al. developed an equilibrium cell (100 cm3) from a sapphire tube, the cell was specifically designed to enable sampling with two ROLSIs at equilibrium pressures below the gas chromatograph (GC) carrier gas line pressure [6]. (ii) Westman et al. designed a cell (100 cm3) featuring a sapphire tube with two ROLSIs, one of the features of the apparatus include
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a plate-bellow to allow for slight volume control (1 cm3) to ensure stable pressures when sampling [7]. (iii) Uusi-Kyyny et al. developed a cell (70 cm3) from a cylindrical billet with
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two sapphire viewing windows (gold-sealed) with capillary samplers, the cell was developed for use at high-temperatures (up to 673 K) [2]. The cell assembly was able to pivot to enable
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sampling at any position within the cell, similar to the designs of Horstmann et al. [8] and Frost et. al. [9]. Within our research group, two equilibrium cell designs based on the “staticanalytic” method have been the workhorses for the acquisition of phase equilibrium data. Firstly, a low-volume sapphire cell (capacity of approximately 17 cm3) has been utilized for measurement of phase equilibrium data involving high-value and hazardous components [1012]. Secondly, an equilibrium cell of moderate volume (60 cm3), limited to pressures of 200 bar, originating from the work of Muhlbauer and Raal [13] has also been extensively used for phase equilibrium measurement [14-18]. In this work, a new apparatus following the “static-
ACCEPTED MANUSCRIPT analytic” method utilizing a sapphire cell was designed and tested. The apparatus was commissioned to compliment the aforementioned design of Muhlbauer and Raal [13] and allow for operation at higher pressure. The apparatus was tested by measuring VLE data for the binary system of carbon dioxide + chlorodifluoromethane at 273.15 K. New VLE and
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critical point data were also measured for the binary system of ethylene + chlorodifluoromethane at five temperatures, viz. (273.15, 293.15, 313.15, 333.15, and 353.15) K. The data were modelled with the Peng-Robinson Equation of State using the
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Wong-Sandler mixing rule and the NRTL activity coefficient. The mixture critical points
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were also modelled by scaling laws.
ACCEPTED MANUSCRIPT 2. EXPERIMENTAL 2.1 Materials. Ethylene (C2H4; R1150; CAS Number 74-85-1), Carbon dioxide (CO2; R744; CAS Number
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124-38-9) and chlorodifluoromethane (CHClF3; R22; CAS Number 75-45-6) were purchased from Afrox (South Africa). The chemical properties and purities of the gases in this study are listed in table 1. The components were characterized and instrument accuracy checked by
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measurement of saturated vapour pressures. The purities of all components were checked using GC analysis. No significant impurities beyond the supplier specifications were
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identified. 2.2 Apparatus.
A schematic of the new experimental setup is displayed in figure 1. The equilibrium cell was comprised from a synthetic sapphire tube with the following dimensions: 55 mm outer
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diameter (OD), 32 mm inner diameter (ID), and a length of 70 mm. The sapphire tube was sealed with an O-ring at each end between two stainless steel (SS) 316L flanges using three 8 mm SS bolts (2 of which are only shown in the schematic; figure 1). For the systems
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involving CO2, R22 and ethylene, O-rings machined from polytetrafluoroethylene (PTFE)
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were utilized. The total capacity of the equilibrium chamber was approximately 50 cm3. Two inlet ports were machined into the top flange and one inlet port into the bottom flange; the ports were sealed by 1/8” Valco fittings. Two non-rotating stem needle valves (Parker: 10V series; 1/8”; 103.4 MPa) were used for the inlet ports; one valve was located at the bottom and top flange, respectively. The heavy-walled SS flanges, sapphire tube, the use of highpressure Valco fittings, and Parker valves will enable reliable operation at high pressure. Micro samples (250 to 500 µl vaporized samples) were removed from the equilibrium cell using a single movable ROLSI. The tip of the ROLSI capillary was positioned via a
ACCEPTED MANUSCRIPT differential screw from the top to the base (above mixer) of the equilibrium cell, allowing for sampling of the liquid and vapour phases. The ROLSI capillary (3 mm OD) was sealed via a PTFE gland packing. The homogenous vaporized samples were transferred to the GC within temperature-regulated 1/16” SS 316L line. Either a Rtx-1 or Rtx-5 capillary column at 313 K
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were used to separate the mixtures of CO2 + R22 or ethylene + R22, respectively. Good resolution and relatively short analysis times were achieved. The equilibrium cell was maintained isothermally by submersion into a thermostatic liquid solution, accommodated in
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a 30 dm3 SS 316L insulated bath containing two glass viewing windows (100 mm OD; 8 mm thick). The fluid within the bath was controlled by an immersion circulator (Grant: model TX
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150). The surface of the fluid can be insulated for temperatures far from ambient. For temperatures below ambient and to liquefy the gases the bath fluid was cooled via an immersion cooler (Polyscience: model IP-35). The contents of the equilibrium cell were agitated via an internal impellor. A Neodymium magnet (OD 28 mm; grade N40H; nickel-
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plated) driven by an overhead stirrer (Maxon: model A-max) external to the equilibrium cell rotates an internal Neodymium magnet (OD 28 mm; grade N40H; gold-plated). The internal magnet was attached to two SS ball bearings and impellor via a SS sheath (see figure 1);
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enabling smooth rotation of the internal mixer. The large internal magnet can easily be
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replaced with a smaller sized magnet and mixer for working with non-viscous fluids. A 10 MPa pressure transmitter (WIKA: model P-10) was connected via a 1/16” SS line to the top flange via a Valco fitting, the line was brazed (silver solder) to 1/8” at the inlet connection. The slight extension of 1/16” line above the bath fluid was temperature regulated. The temperature of the fluid within the cell was measured by two 100 Ω platinum resistance thermometer (Pt100) probes, the Pt100 probes were placed within wells drilled into the top and bottom flange. The signals from the temperature and pressure sensors were recorded by a
ACCEPTED MANUSCRIPT computer linked to a data acquisition unit (Agilent; HP34970A). A two-stage vacuum pump (Edwards; RV3) was used for evacuation of the cell and loading lines.
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2.3 Procedure. Following the sensor calibration (discussed below), the vapour pressures of all components were checked to validate the accuracy of the pressure and temperature readings. To measure the saturated vapour pressures, the equilibrium cell and loading lines were evacuated
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thoroughly and the respective component liquefied into the equilibrium cell. The temperature
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of the bath fluid and thus equilibrium cell was controlled and the respective pressure recorded over pre-defined temperature interval. The pure-components were degassed during vapour pressure measurement to check for consistency; if degassing was necessary this same technique was utilized for VLE measurements (it was only necessary to degas R22). R22 was degassed via periodic vapour withdrawal. For VLE measurements, the heavier component
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R22 was liquefied into the equilibrium cell and degassed. At a predefined temperature, a mixture was then prepared within the cell by introducing the lighter component (either CO2
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or ethylene). The mixture was thoroughly mixed until the pressure stabilized to a constant average value (generally, five to ten minutes), the mixture was then turned off. To allow for
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potential separation of phases and to prevent splashing when sampling the vapour phase. Multiple samples for each phase (at least six consistent samples) were withdrawn (gas volume roughly 500 µl) and the composition of the phase determined from the peak areas and calibrated GC detector response ratio. During sampling, the pressure and temperature values were recorded and averaged. At this point, the concentration of lighter component was increased and equilibrium was re-established and the T, P, x1 and y1 values were measured; this procedure was repeated to trace the entire phase envelope. For temperatures above 273.15 K the critical points of the mixtures were also experimentally determined via the
ACCEPTED MANUSCRIPT “static-analytic” method. As the critical point of the mixture was approached following the aforementioned technique, the pressure inside the cell was finely-tuned to a value slightly higher than the critical point. At this point, the mixture colour would appear brown due to critical opalescence [19]. The mixture composition (z1) and T as well as P values were
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recorded. The pressure within the cell was then slightly decreased either by venting to a regulated outlet pressure or by taking relatively large samples with the ROLSI. With each reduction in pressure, the z1, T and P values were continually recorded. In this manner the
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location between the critical point and divergence to the bubble and dew-point curves could be identified. At each temperature this procedure was repeated to reliably measure the
2.4 Calibrations and uncertainty.
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transition from the critical to bi-phasic mixture.
The Pt100 probes and pressure transmitter were calibrated using in-house standards, a WIKA
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CTH 6500 and Mensor CPC 8000 (25 MPa), respectively. For phase equilibrium measurements involving mixtures of gases, it is common to calibrate the GC detector by injection of known volumes (direct injection method). Although, the basis of the method is
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trivial, it can be potentially inaccurate unless meticulous practices are followed; albeit this is more important for calibration involving mixtures comprised of both a liquid and a gas. A
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small modification to the standard direct injection method was used in previous work to calibrate a mixture which exhibited a linear response over the working composition range [20]. The gravimetric method (preparation mixtures of known composition by mass) is commonly used for calibration the GC detector when working with liquid mixtures [21]. However, the same method can be utilized for gaseous mixtures. Bobbo et al. gravimetrically prepared gaseous mixtures for the calibration across the working composition range using a thin-walled (0.5 mm) 240 cm3 pressure vessel and a 240 g mass balance with a 1x10-4 g resolution [22]. In this work, the GC detector (thermal conductivity detector) was calibrated
ACCEPTED MANUSCRIPT using the gravimetric method for the binary systems of CO2 + R22 and Ethylene + R22 using an internally electro-polished pressure vessel with a capacity of 1000 cm3 featuring an internal mixer to ensure sample homogeneity. The vessel has a maximum operating pressure of 5 MPa and has a pressure-regulated sample port. Mixtures were prepared over the
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composition range using a mass balance (Ohaus Explorer; maximum capacity of 6100 g; resolution of 0.01 g) and the response ratio was obtained (1.414:1 for CO2:R22 and 1.438:1 for ethlyene:R22). The calibration covered ranges from (250 to 500) µl in volume. The
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maximum errors (difference between experimental value to correlated value) across the composition range for the binary system of CO2 + R22 and ethylene + R22 were 0.003 and
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0.002 respectively. The expanded uncertainties (U) were estimated following the guidelines supplied by NIST (National Institute of Standards and Technology) [23]. The standard uncertainties used for the estimation are listed in table 2.
As discussed in the NIST
guidelines, the combined uncertainty can be calculated through the law of propagation of
=
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uncertainty [23].
+2
,
(1)
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The expanded uncertainty (k = 2) for composition can then be estimated from: =2
+
+
!"
(2)
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Where ucal is the maximum error in the calibration polynomial (given in table 2), urep is the absolute difference between the magnitudes of the samples withdrawn at equilibrium (average given in table 2), and umix is the uncertainty in the molar composition from gravimetrically preparing gaseous mixtures used in the calibration, given by: =
#
$ $
+
$ $
(3)
Where u(m1) = u(m2) and is the standard uncertainty of the mass balance (given in table 2), and m1 and m2 are the masses of component 1 and 2, respectively, used to prepare the
ACCEPTED MANUSCRIPT calibration standards. The expanded uncertainties (using a coverage factor of k = 2) on average for temperature and pressure are U(T) = 0.07 K and U(P) = 0.002 MPa, respectively. The expanded uncertainty for composition for both binary systems are U(x1) = 0.005 and
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U(y1) = 0.004.
ACCEPTED MANUSCRIPT 3. DATA TREATMENT The VLE data were regressed using the Peng-Robinson (PR) Equation of State (EoS) [24] following the phi-phi approach utilizing Aspen Plus V8.0 [25]. The pure-component
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parameters of the PR EoS were extended to mixtures via either the van der Waals (vdW) or the Wong-Sandler (WS) mixing rules [26]. The Non-Random Two-Liquid (NRTL) activity coefficient model [27] was utilized to represent the excess Gibbs energy necessary for the WS mixing rule. The maximum-likelihood objective function (T, P, x1 and y1) was minimized
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by adjusting the binary interaction parameters using the Britt-Luecke algorithm [28]. The
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quality of the data-fit was assessed statistically using the average absolute deviation (AAD and the average absolute relative deviation (AARD) using a bubble-point calculation. The AAD and AARD are defined as:
1 %%& '̅ = *"
and '̅
-
+'!̅
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"
+'!̅
"
− '̅
− '̅ '!̅ "
+
"
+
(4)
(5)
are the experimental and calculated values of a measurand '̅ (P and y1),
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where '!̅
1 %%.& '̅ = *"
-
and Np is the total number of data points. The mixture critical co-ordinates (z1,c and Pc) were
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also estimated using the following scaling law [7, 29, 30]: / =/
,
+ 0 +1
0 2
2 −2 +ε
4 2 −2 2
5
(6)
Where ε = 1 for bubble point and ε = −1 for dew point, z1 is the bubble point (z1 = x1) or the dew point (z1 = y1) at a pressure, P. z1 and Pc are the critical co-ordinates for the mixture composition and pressure respectively, 0 , 0 , 4 are adjustable parameters fitted using the ordinary least squares method to VLE data close to the critical point, 7 is a universal scaling component and was fixed to 0.325 [31].
ACCEPTED MANUSCRIPT 4. RESULTS AND DISCUSSION The apparatus and experimental method were tested by measuring VLE data for the binary system of CO2 + R22 at 273.15 K. The experimental data were compared to previous
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measurements available in literature. The phase equilibria of this system are almost ideal below the critical points of each pure component. The experimental data for this system are listed in table 3 and displayed in figure 2. The experimental data compare well to the literature data of both Roth et al. at 273.14 K [32] and Nohka et al. at 273.1 K [33] and to
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data predicted at 273.15 K using the Reference Fluid Thermodynamic and Transport
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Properties (REFPROP) model [34] (see figure 2). The experimental and literature data were modelled using the PR EoS and vdW mixing rule. The modelling results and comparison are presented in table 4. A low AARD, of less than 0.5% for pressure, is noted between our experimental data and the data predicted by REPROP and modelled data of Roth et al. [32]. The vapour pressure data are listed in table 5; the data compare well to data predicted by
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REFPROP. New isothermal VLE data were experimental measured for the binary system of ethylene + chlorodifluoromethane at five temperatures, viz. (273.15, 293.15, 313.15, 333.15,
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and 353.15) K. The binary system exhibits a low positive deviation from Raoult’s law. The critical point co-ordinates (P and z1) for the mixtures were also experimentally measured at
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four temperatures, viz. (293.15, 313.15, 333.15, and 353.15) K. The experimental data were modelled using the PR EoS coupled with the WS mixing rule and NRTL activity coefficient model. Each isotherm was modelled independently to obtain the best possible representation close to the critical region. The experimental and modelled data are displayed in figures 3 and 4, and are listed in tables 6 and 7. Low deviations between the experimental and modelled data are evident across the entire temperature range. The deviations and model parameters are listed in table 8. An AARD for pressure of less than 0.5% is evident for all temperatures. The highest AAD for the vapour phase composition is 0.005. The critical points were also
ACCEPTED MANUSCRIPT calculated using the model and scaling laws, the data are listed in table 7. In all instances, the model cannot predict the experimental critical point to within the experimental uncertainty.
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However, the scaling law provides an excellent representation of the mixture critical point.
ACCEPTED MANUSCRIPT 5. CONCLUSIONS A new apparatus based on the “static-analytic” method was designed and commissioned. The apparatus and experimental procedure were tested by measuring VLE data for the binary
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system of carbon dioxide + chlorodifluoromethane. The experimental data match well with data available in literature. New VLE data and mixture critical point data were measured for the binary system of ethylene + chlorodifluoromethane. The data were correlated with the PR EoS, WS mixing rule, and NRTL activity coefficient model. The model provided a good
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representation of the experimental data below the critical region. However, the model was
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unable to estimate the mixture critical point to within the experimental uncertainty.
ACCEPTED MANUSCRIPT ACKNOWLEDGEMENTS 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
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Technology and the National Research Foundation Thuthuka Programme.
ACCEPTED MANUSCRIPT REFERENCES
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[1] J.M.S. Fonseca, R. Dohrn, S. Peper, Fluid Phase Equilibr. 300 (2011) 1-69. [2] P. Uusi-Kyyny, S. Ionita, M.S. Qureshi, V. Alopaeus, D. Richon, J. Chem. Eng. Data 61 (2016) 2700-2711. [3] S. Laugier, D. Richon, Rev. Sci. Instrum. 57 (1986) 469-472. [4] P. Figuiere, J.F. Hom, S. Laugier, H. Renon, R. D, H. Szwarc, AlChE J. 26 (1980) 872875. [5] P. Guilbot, A. Valtz, H. Legendre, D. Richon, Analusis 28 (2000) 426-431. [6] F. Zhang, P. Theveneau, E.E. Ahmar, X. Canet, C.-B. Soo, C. Coquelet, Fluid Phase Equilibr. 409 (2016) 425-433. [7] S.F. Westman, H.G.J. Stang, S.W. Løvseth, A. Austegar, I. Snustad, S.Ø. Størset, I.S. Ertesvåg, Fluid Phase Equilibr. 409 (2016) 207-241. [8] S. Horstmann, G. Birke, K. Fischer, J. Chem. Eng. Data, 49 (2004) 38-42. [9] M. Frost, N.v. Solms, D. Richon, G.M. Kontogeorgis, Fluid Phase Equilibr. 405 (2015) 88-95. [10] C.N. Narasigadu, P.; Coquelet, C.; Richon, D.; Ramjugernath, D., Fluid Phase Equilibr. 338 (2013) 188-196. [11] W.M. Nelson, P. Naidoo, D. Ramjugernath, J. Chem. Thermodyn. 91 (2015) 420-426. [12] W.M. Nelson, Z. Tebbal, P. Naidoo, L. Negadi, D. Ramjugernath, Fluid Phase Equilibr. 408 (2016) 33-37. [13] A.L. Muhlbauer, J.D. Raal, fluid Phase Equilibr. 64 (1991) 213-236. [14] P. Naidoo, D. Ramjugernath, J.D. Raal, Fluid Phase Equilibr, 269 (2008) 104-112. [15] F.J. Conradie, P.L. Crouse, X. Courtial, I.J. van der Walt, D. Ramjugernath, J. Chem. Eng. Data 57 (2012) 1978-1983. [16] F.J. Conradie, P.L. Crouse, X. Courtial, W.M. Nelson, I.J. van der Walt, D. Ramjugernath, J. Chem. Eng. Data 59 (2014) 82-88. [17] S.C. Subramoney, X. Courtial, P. Naidoo, C. Coquelet, D. Richon, D. Ramjugernath, Fluid Phase Equilibr. 353 (2013) 7-14. [18] S.C. Subramoney, W.M. Nelson, X. Courtial, P. Naidoo, C. Coquelet, D. Richon, D. Ramjugernath, J. Chem. Thermodyn. 90 (2015) 100-105. [19] E.S.R. Gopal, Resonance, Bangalore, India, Springer, 5 (2000) 37-45. [20] W.M. Nelson, M. Williams-Wynn, S.C. Subramoney, D. Ramjugernath, J. Chem. Eng. Data 90 (2015) 100-105. [21] J.D. Raal, A.L. Mühlbauer, Phase Equilibria: Measurement and Computation, Taylor and Francious, Washington, D.C., 1998. [22] S. Bobbo, R. Camporese, R. Stryjek, J. Chem. Thermodyn. 30 (1998) 1041-1046. [23] B.N. Taylor, C.E. Kuyatt, NIST Technical Note 1297: Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, National Institute of Standards and Technology, Gaithersburg, 1994. [24] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59-64. [25] AspenTech. Aspen Technology, Massachusetts, USA., 2010. [26] D.S.H. Wong, S.I. Sandler, AIChE J. 38 (1992) 671-680. [27] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135-144. [28] H.I. Britt, R.H. Luecke, Technometrics 15 (1973) 233 - 238. [29] P. Ungerer, B. Tavitian, A. Boutin, Editions Technip, Paris, (2005). [30] V. Lachet, T.d. Bruin, P. Ungerer, C. Coquelet, A. Valtz, V. Hasanov, F. Lockwood, D. Richon, Energy Procedia 1 (2009) 1641-1647. [31] J.V. Sengers, J.M.H. Levelt Sengers, Int. J. Thermophys. 5 (1984) 195-208.
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[32] H. Roth, P. Peters-Gerth, K. Lucas, Fluid Phase Equilibr. 73 (1992) 147-166 [33] J. Nohka, E. Sarashina, Y. Arai, S. Saito, J. Chem. Eng. Jpn. 6 (1973) 10. [34] E.W. Lemmon, M.L. Huber, M.O. McLinden, Reference Fluid Thermodynamic and Transport Properties (REFPROP), NIST Standard Reference Database 23: Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, 2007.
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Fig. 1. Schematic of the “static-analytic” apparatus. C: Gas cylinder, IC: immersion circulator, LB: liquid bath, LP: liquid venting port, GC: Gas chromatograph, PP: platinum resistance temperature probe, PT: pressure transmitter, OS: overhead stirrer, R: ROLSI, TR: temperature regulation, VP: vacuum pump.
ACCEPTED MANUSCRIPT 4
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2
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P (MPa)
3
0 0
0.2
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1
0.4
0.6
0.8
1
x1, y1
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Fig. 2. Experimental, literature and predicted (REFPROP – represented by the solid black line at 273.15 K) VLE data for the binary system of CO2 (1) + R22 (2): experimental data at 273.15 K (); Roth et al. at 273.14 K [32] (▲) and Nohka et al. at 273.1 K [33] ( ) (data
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point x1 = 0.554 of Nohka et al. not included on the figure).
ACCEPTED MANUSCRIPT 6
5
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P (MPa)
4
3
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2
0 0
0.2
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1
0.4
0.6
0.8
1
x1, y1
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Fig. 3. Experimental VLE data for the binary system ethylene (1) + R22 (2) at 273.15 K (○), 293.15 K (●), 313.15 K ( ), 333.15 K (▲), and 353.15 K ( ), as well as the experimental critical points (
). The solid black line depicts the modelled data using the PR EoS with the
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WS mixing rule and NRTL activity coefficient model.
ACCEPTED MANUSCRIPT
5.4
5.7
5.8
b)
5.5
c)
d)
x1, y1
0.91
5.4 0.63
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5.1 0.86
EP
P (MPa)
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P (MPa)
P (MPa)
P (MPa)
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a)
x1, y1
0.73
5.6 0.42
x1, y1
0.51
5.2 0.18
x1, y1
0.25
Fig. 4. Expanded view of the critical region for the binary system of ethylene (1) + R22 (2) at (a) 293.15 K, (b) 313.15 K, (c) 333.15 K, and (d) 353.15 K. Experimental critical points (
), solid lines depicts the PR EoS, WS mixing rule and NRTL activity coefficient model ( ), and
scaling laws represented by dashed black line ( ).
ACCEPTED MANUSCRIPT Table 1 Pure-component parameters and properties for carbon dioxide (CO2), ethylene and chlorodifluoromethane (R22). CO2
Ethylene
R22
Component characterization Afrox
Afrox
Afrox
Supplier purity wt.%
99.0
>99.9
>99.5
Purification
none
none
GC Area
>99.95
>99.9 b
Critical properties and acentric factor Tc (K)
304.13
282.35
Pc (MPa)
7.3773
5.0418
ω
0.22394
0.0866
a
degassed
>99.9
369.3
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a
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Supplier
4.99
0.22082
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Area percentage of the component identified by gas chromatography using a thermal conductivity detector and either a Rtx-1 or Rtx-5 RESTEK capillary column. b Critical properties and acentric factor from REFPROP [34].
ACCEPTED MANUSCRIPT Table 2 Standard uncertainty estimates and influences of the variables in this work. Source of uncertainty Pressure (P)
Estimate
Distribution
0.01%
normal
Correlation for P (MPa): (10 MPag)
0.001
rectangular
Temperature (T)
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P reference (MPa): Mensor CPC 8000 (25 MPag)
T reference (K): CTH 6500
0.02
rectangular
Correlation for T (K)
0.06
rectangular
0.03
rectangular
0.03
rectangular
0.001
rectangular
Composition (zi)
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Mass balance uncertainty (g) Repeatability of masses (g)
0.002
rectangular
Correlation for x1 and y1 [CO2 + R22]
0.003
rectangular
Correlation for x1 and y1 [C2H4 + R22]
0.002
rectangular
Range (average) of x: (xi,[max] – xi,[min]) [CO2 + R22]
0.003
rectangular
Range (average) of y: (yi,[max] – yi,[min]) [CO2 + R22]
0.001
rectangular
Range (average) of x: (xi,[max] – xi,[min]) [C2H4 + R22]
0.003
rectangular
0.002
rectangular
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Gravimetric x1 and y1 [C2H4 + R22]
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Gravimetric x1 and y1 [CO2 + R22]
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Range (average) of y: (yi,[max] – yi,[min]) [C2H4 + R22]
ACCEPTED MANUSCRIPT
x1
y1
0.498
0
0
0.546
0.020
0.090
0.615
0.049
0.201
0.712
0.090
0.327
0.905
0.168
0.488
1.040
0.222
0.577
1.254
0.306
1.414
0.362
1.565
0.419
0.724 0.766
0.486
0.808
0.573
0.852
0.612
0.870
0.682
0.899
0.722
0.915
2.645
0.769
0.931
3.008
0.872
0.963
3.143
0.912
0.975
3.314
0.955
0.988
3.487
1
1
2.012 2.141 2.347
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2.484
U(T) = 0.07 K; U(P) = 0.002 MPa; U(x1) = 0.005; U(y1) = 0.004
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a
0.673
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1.761
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P (MPa)
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Table 3 Experimental vapour-liquid equilibrium data for the binary system of carbon dioxide (1) + chlorodifluoromethane (2), including the measured temperature (T), pressure (P), and both the liquid and vapour phase compositions (x1, y1), including the expanded uncertaintiesa.
ACCEPTED MANUSCRIPT Table 4 Comparison of the experimental vapor-liquid equilibrium data for the binary system of carbon dioxide (1) + chlorodifluoromethane (2) at 273.15 K to data available in literature and modeled data. AAD(P)/MPa AARD(P) AAD(y1) AAD(y1) k12 -0.0010
0.005
0.24%
0.003
0.97%
Roth et. al. [32]a
0.0004
0.011
0.54%
0.002
0.35%
Nohka et al. [33] a
0.0107
0.024
1.71%
0.006
0.94%
-NA-
0.009
0.49%
0.003
0.86%
PR – Roth et. al. [32]b
0.0004
0.004
0.23%
0.003
1.12%
PR – Nohka et al. [33]b
0.0107
0.027
1.84%
0.007
2.31%
a
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REFPROP
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Experimentala
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Data modelled using PR EoS + WS mixing rule/NRTL model. Deviations calculated with respect to difference between data and modelled data. b Comparison between the modelled data and the experimental data. Deviations calculated with respect to difference between experimental data and modelled literature data.
ACCEPTED MANUSCRIPT Table 5 Experimental vapour pressure data for chlorodifluoromethane, carbon dioxide, and ethylene including the temperature (T), pressure (P), and the expanded uncertaintiesa. Texp (K)
Pref (MPa)b
Pexp (MPa)
Pexp-Pref (MPa)
Chlorodifluoromethane 0.498
0.4979
0.0001
293.15
0.911
0.9100
0.001
313.15
1.529
1.5336
333.15
2.426
2.4275
353.15
3.664
3.6638
273.15
3.487
3.4851 4.0990
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U(T) = 0.07 K; U(P) = 0.002 MPa Reference vapour pressure data predicted from REFPROP [34].
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b
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a
4.094
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Ethylene 273.15
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Carbon dioxide
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273.15
-0.005 -0.002
0.0002 0.002 -0.005
ACCEPTED MANUSCRIPT Table 6 Experimental vapour-liquid equilibrium data for the binary system of ethylene (1) + chlorodifluoromethane (2), including the measured temperature (T), pressure (P), and both the liquid and vapour phase compositions (x1, y1), including the expanded uncertaintiesa. P (MPa)
x1
y1
P (MPa)
x1 T = 293.15 K
0
0
0.911
0.597
0.029
0.171
0.945
0.747
0.072
0.337
1.021
0.842
0.100
0.419
1.231
1.270
0.228
0.631
1.597
1.623
0.337
0.728
1.945
0.436
0.786
2.357
0.560
0.838
2.633
0.643
0.868
2.990
0.742
0.903
3.382
0.845
0.938
3.765
0.935
0.970
3.845
0.951
0.978
4.015
0.984
4.094
1
0.007
0.035
0.023
0.103
0.067
0.258
0.146
0.440 0.587
2.628
0.369
0.681
3.034
0.457
0.733
3.423
0.539
0.775
3.694
0.594
0.800
4.376
0.728
0.854
4.920
0.822
0.890
5.167
0.863
0.902
0.992
5.266
0.882
0.906
1
5.308
0.891
0.906
5.318
0.893
0.905
5.326
0.896
0.904
5.329
0.898
0.902
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0.260
0
1.640
0.017
0.061
1.558
0.004
0.015
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0
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0
2.124
T = 313.15 K 1.529
0
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0.498
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T = 273.15 K
y1
T = 333.15 K
2.019
0.079
0.237
2.426
0
0
2.420
0.144
0.363
2.475
0.006
0.018
3.056
0.248
0.498
2.669
0.031
0.083
3.621
0.342
0.580
2.892
0.060
0.149
4.041
0.410
0.628
3.199
0.101
0.224
4.394
0.467
0.659
3.546
0.146
0.299
4.691
0.513
0.683
3.994
0.206
0.366
5.251
0.605
0.715
4.573
0.284
0.438
5.413
0.631
0.720
4.953
0.335
0.471
ACCEPTED MANUSCRIPT 0.658
0.723
5.016
0.344
0.478
5.654
0.678
0.719
5.502
0.416
0.504
5.689
0.691
0.714
5.629
0.434
0.508
5.696
0.694
0.710
5.674
0.445
0.506
5.697
0.697
0.707
5.698
0.450
0.503
5.722
0.456
0.500
5.733
0.460
0.499
0.466
0.497
0.478
0.481
T = 353.15 K 0
5.745
3.885
0.024
0.046
5.755
4.308
0.071
0.123
4.747
0.121
0.185
5.251
0.183
0.236
5.403
0.206
0.243
5.435
0.211
0.243
5.447
0.213
0.242
5.472
0.220
0.238
5.480
0.224
0.235
5.480
0.225
0.237
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0
EP
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U(T) = 0.07 K; U(P) = 0.002 MPa; U(x1) = 0.005; U(y1) = 0.004
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a
3.664
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5.561
ACCEPTED MANUSCRIPT Table 7 Experimental and modeled critical points for the binary mixture of ethylene (1) + chlorodifluoromethane (2). The mixture critical points were modeled using both a scaling law and the PR EoS with the WS mixing rule incorporating the NRTL activity coefficient model. Scaling law
Experimental Pc (MPa)
z1,c
Pc (MPa)
z1,c
Pc (MPa)
z1,c
293.15
5.330
0.899
5.329
0.900
5.313
0.905
313.15
5.698
0.701
5.698
0.703
333.15
5.755
0.479
5.755
0.481
353.15
5.482
0.230
5.482
0.231
5.689
0.712
5.797
0.496
5.497
0.238
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U(T) = 0.07 K; U(P) = 0.002 MPa; U(z1) = 0.005
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T (K)
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a
PR EoS/WS/NRTL
ACCEPTED MANUSCRIPT Table 8 Regressed binary interaction parameters (k12, b12 and b21) for the PR EoS with the WS mixing rules incorporating the NRTL activity coefficient model, and statistical analysis of the data-fit for the binary system of ethylene (1) + chlorodifluoromethane (2). T = 273.15 K
T = 293.15 K
T = 313.15 K
T = 333.15 K
T = 353.15 K
0.058
0.100
0.091
b12a
0.096
-222.7
-266.5
-160.1
b21a
-69.3
-99.6
-152.8
AAD(P)/MPa
0.008
0.012
0.015
AARD(P)
0.34%
0.36%
AAD(y1)
0.003
0.003
AARD(y1)
0.64%
0.67%
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k12
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Model parameters -159.2
282.5
-147.5
-216.6
0.010
0.008
0.34%
0.21%
0.16%
0.005
0.005
0.003
0.73%
1.34%
1.53%
Deviations
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NRTL binary interaction parameters are defined as 8 = 9⁄:; non-randomness parameter fixed at 0.3. a
0.108
S0378-3812(17)30297-2
DOI:
10.1016/j.fluid.2017.08.005
Reference:
FLUID 11551
To appear in:
Fluid Phase Equilibria
Received Date: 30 May 2017 Revised Date:
28 July 2017
Accepted Date: 4 August 2017
Please cite this article as: W.M. Nelson, R. Hassanalizadeh, D. Ramjugernath, Phase equilibrium and critical point data for ethylene and chlorodifluoromethane binary mixtures using a new “static-analytic” apparatus, Fluid Phase Equilibria (2017), doi: 10.1016/j.fluid.2017.08.005. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
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P (MPa)
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6
0 0
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EP
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x1, y1
1
ACCEPTED MANUSCRIPT
Phase equilibrium and critical point data for ethylene and chlorodifluoromethane binary mixtures using a new “staticanalytic” apparatus
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Wayne Michael Nelson*, Rasoul Hassanalizadeh, and Deresh Ramjugernath
Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa
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*Corresponding author: E-mail: [email protected]; Tel.: +27 31 2603121
ACCEPTED MANUSCRIPT ABSTRACT
An apparatus based on the “static-analytic” method was designed and commissioned. The apparatus was tested by measuring vapour-liquid equilibrium data for the binary system of
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carbon dioxide + chlorodifluoromethane at 273.15 K. There is excellent agreement between the experimental data and previous measurements reported in literature. New experimental vapour-liquid equilibrium data were also measured for the binary systems of ethylene +
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chlorodifluoromethane at five temperatures, viz. (273.15, 293.15, 313.15, 333.15, and 353.15) K. At the same temperatures (excluding 273.15 K) the critical points of the binary
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mixtures were also experimentally determined. The experimental data for this binary system were accurately correlated using the Peng–Robinson Equation of State utilizing the Wong– Sandler mixing rule coupled with the Non-Random Two-Liquid (NRTL) activity coefficient
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model.
Keywords: VLE, Static-Analytic, Phase Equilibrium, Phase Equilibria, Ethylene, Carbon Dioxide, Chlorodifluoromethane
ACCEPTED MANUSCRIPT 1.
INTRODUCTION
The importance and necessity for accurate and reliable phase equilibrium data is well documented in literature. Due to the rapidity of measurement and potential for high accuracy,
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experimental methods following the “static-analytic” technique are widely used [1, 2]. Nowadays, many of the apparatuses following the “static-analytic” method are based upon the designs originating from Laugier and Richon [3] and Figurere et al. [4]. The originality of these setups being the sampling system, featuring the preliminary versions of the rapid on-
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line sampler injector (ROLSI) [5]. A few examples of modern designs utilizing the “static-
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analytic” method, comprising of mainly modifications to the equilibrium cell, include: (i) Zhang et al. developed an equilibrium cell (100 cm3) from a sapphire tube, the cell was specifically designed to enable sampling with two ROLSIs at equilibrium pressures below the gas chromatograph (GC) carrier gas line pressure [6]. (ii) Westman et al. designed a cell (100 cm3) featuring a sapphire tube with two ROLSIs, one of the features of the apparatus include
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a plate-bellow to allow for slight volume control (1 cm3) to ensure stable pressures when sampling [7]. (iii) Uusi-Kyyny et al. developed a cell (70 cm3) from a cylindrical billet with
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two sapphire viewing windows (gold-sealed) with capillary samplers, the cell was developed for use at high-temperatures (up to 673 K) [2]. The cell assembly was able to pivot to enable
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sampling at any position within the cell, similar to the designs of Horstmann et al. [8] and Frost et. al. [9]. Within our research group, two equilibrium cell designs based on the “staticanalytic” method have been the workhorses for the acquisition of phase equilibrium data. Firstly, a low-volume sapphire cell (capacity of approximately 17 cm3) has been utilized for measurement of phase equilibrium data involving high-value and hazardous components [1012]. Secondly, an equilibrium cell of moderate volume (60 cm3), limited to pressures of 200 bar, originating from the work of Muhlbauer and Raal [13] has also been extensively used for phase equilibrium measurement [14-18]. In this work, a new apparatus following the “static-
ACCEPTED MANUSCRIPT analytic” method utilizing a sapphire cell was designed and tested. The apparatus was commissioned to compliment the aforementioned design of Muhlbauer and Raal [13] and allow for operation at higher pressure. The apparatus was tested by measuring VLE data for the binary system of carbon dioxide + chlorodifluoromethane at 273.15 K. New VLE and
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critical point data were also measured for the binary system of ethylene + chlorodifluoromethane at five temperatures, viz. (273.15, 293.15, 313.15, 333.15, and 353.15) K. The data were modelled with the Peng-Robinson Equation of State using the
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Wong-Sandler mixing rule and the NRTL activity coefficient. The mixture critical points
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were also modelled by scaling laws.
ACCEPTED MANUSCRIPT 2. EXPERIMENTAL 2.1 Materials. Ethylene (C2H4; R1150; CAS Number 74-85-1), Carbon dioxide (CO2; R744; CAS Number
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124-38-9) and chlorodifluoromethane (CHClF3; R22; CAS Number 75-45-6) were purchased from Afrox (South Africa). The chemical properties and purities of the gases in this study are listed in table 1. The components were characterized and instrument accuracy checked by
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measurement of saturated vapour pressures. The purities of all components were checked using GC analysis. No significant impurities beyond the supplier specifications were
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identified. 2.2 Apparatus.
A schematic of the new experimental setup is displayed in figure 1. The equilibrium cell was comprised from a synthetic sapphire tube with the following dimensions: 55 mm outer
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diameter (OD), 32 mm inner diameter (ID), and a length of 70 mm. The sapphire tube was sealed with an O-ring at each end between two stainless steel (SS) 316L flanges using three 8 mm SS bolts (2 of which are only shown in the schematic; figure 1). For the systems
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involving CO2, R22 and ethylene, O-rings machined from polytetrafluoroethylene (PTFE)
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were utilized. The total capacity of the equilibrium chamber was approximately 50 cm3. Two inlet ports were machined into the top flange and one inlet port into the bottom flange; the ports were sealed by 1/8” Valco fittings. Two non-rotating stem needle valves (Parker: 10V series; 1/8”; 103.4 MPa) were used for the inlet ports; one valve was located at the bottom and top flange, respectively. The heavy-walled SS flanges, sapphire tube, the use of highpressure Valco fittings, and Parker valves will enable reliable operation at high pressure. Micro samples (250 to 500 µl vaporized samples) were removed from the equilibrium cell using a single movable ROLSI. The tip of the ROLSI capillary was positioned via a
ACCEPTED MANUSCRIPT differential screw from the top to the base (above mixer) of the equilibrium cell, allowing for sampling of the liquid and vapour phases. The ROLSI capillary (3 mm OD) was sealed via a PTFE gland packing. The homogenous vaporized samples were transferred to the GC within temperature-regulated 1/16” SS 316L line. Either a Rtx-1 or Rtx-5 capillary column at 313 K
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were used to separate the mixtures of CO2 + R22 or ethylene + R22, respectively. Good resolution and relatively short analysis times were achieved. The equilibrium cell was maintained isothermally by submersion into a thermostatic liquid solution, accommodated in
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a 30 dm3 SS 316L insulated bath containing two glass viewing windows (100 mm OD; 8 mm thick). The fluid within the bath was controlled by an immersion circulator (Grant: model TX
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150). The surface of the fluid can be insulated for temperatures far from ambient. For temperatures below ambient and to liquefy the gases the bath fluid was cooled via an immersion cooler (Polyscience: model IP-35). The contents of the equilibrium cell were agitated via an internal impellor. A Neodymium magnet (OD 28 mm; grade N40H; nickel-
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plated) driven by an overhead stirrer (Maxon: model A-max) external to the equilibrium cell rotates an internal Neodymium magnet (OD 28 mm; grade N40H; gold-plated). The internal magnet was attached to two SS ball bearings and impellor via a SS sheath (see figure 1);
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enabling smooth rotation of the internal mixer. The large internal magnet can easily be
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replaced with a smaller sized magnet and mixer for working with non-viscous fluids. A 10 MPa pressure transmitter (WIKA: model P-10) was connected via a 1/16” SS line to the top flange via a Valco fitting, the line was brazed (silver solder) to 1/8” at the inlet connection. The slight extension of 1/16” line above the bath fluid was temperature regulated. The temperature of the fluid within the cell was measured by two 100 Ω platinum resistance thermometer (Pt100) probes, the Pt100 probes were placed within wells drilled into the top and bottom flange. The signals from the temperature and pressure sensors were recorded by a
ACCEPTED MANUSCRIPT computer linked to a data acquisition unit (Agilent; HP34970A). A two-stage vacuum pump (Edwards; RV3) was used for evacuation of the cell and loading lines.
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2.3 Procedure. Following the sensor calibration (discussed below), the vapour pressures of all components were checked to validate the accuracy of the pressure and temperature readings. To measure the saturated vapour pressures, the equilibrium cell and loading lines were evacuated
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thoroughly and the respective component liquefied into the equilibrium cell. The temperature
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of the bath fluid and thus equilibrium cell was controlled and the respective pressure recorded over pre-defined temperature interval. The pure-components were degassed during vapour pressure measurement to check for consistency; if degassing was necessary this same technique was utilized for VLE measurements (it was only necessary to degas R22). R22 was degassed via periodic vapour withdrawal. For VLE measurements, the heavier component
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R22 was liquefied into the equilibrium cell and degassed. At a predefined temperature, a mixture was then prepared within the cell by introducing the lighter component (either CO2
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or ethylene). The mixture was thoroughly mixed until the pressure stabilized to a constant average value (generally, five to ten minutes), the mixture was then turned off. To allow for
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potential separation of phases and to prevent splashing when sampling the vapour phase. Multiple samples for each phase (at least six consistent samples) were withdrawn (gas volume roughly 500 µl) and the composition of the phase determined from the peak areas and calibrated GC detector response ratio. During sampling, the pressure and temperature values were recorded and averaged. At this point, the concentration of lighter component was increased and equilibrium was re-established and the T, P, x1 and y1 values were measured; this procedure was repeated to trace the entire phase envelope. For temperatures above 273.15 K the critical points of the mixtures were also experimentally determined via the
ACCEPTED MANUSCRIPT “static-analytic” method. As the critical point of the mixture was approached following the aforementioned technique, the pressure inside the cell was finely-tuned to a value slightly higher than the critical point. At this point, the mixture colour would appear brown due to critical opalescence [19]. The mixture composition (z1) and T as well as P values were
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recorded. The pressure within the cell was then slightly decreased either by venting to a regulated outlet pressure or by taking relatively large samples with the ROLSI. With each reduction in pressure, the z1, T and P values were continually recorded. In this manner the
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location between the critical point and divergence to the bubble and dew-point curves could be identified. At each temperature this procedure was repeated to reliably measure the
2.4 Calibrations and uncertainty.
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transition from the critical to bi-phasic mixture.
The Pt100 probes and pressure transmitter were calibrated using in-house standards, a WIKA
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CTH 6500 and Mensor CPC 8000 (25 MPa), respectively. For phase equilibrium measurements involving mixtures of gases, it is common to calibrate the GC detector by injection of known volumes (direct injection method). Although, the basis of the method is
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trivial, it can be potentially inaccurate unless meticulous practices are followed; albeit this is more important for calibration involving mixtures comprised of both a liquid and a gas. A
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small modification to the standard direct injection method was used in previous work to calibrate a mixture which exhibited a linear response over the working composition range [20]. The gravimetric method (preparation mixtures of known composition by mass) is commonly used for calibration the GC detector when working with liquid mixtures [21]. However, the same method can be utilized for gaseous mixtures. Bobbo et al. gravimetrically prepared gaseous mixtures for the calibration across the working composition range using a thin-walled (0.5 mm) 240 cm3 pressure vessel and a 240 g mass balance with a 1x10-4 g resolution [22]. In this work, the GC detector (thermal conductivity detector) was calibrated
ACCEPTED MANUSCRIPT using the gravimetric method for the binary systems of CO2 + R22 and Ethylene + R22 using an internally electro-polished pressure vessel with a capacity of 1000 cm3 featuring an internal mixer to ensure sample homogeneity. The vessel has a maximum operating pressure of 5 MPa and has a pressure-regulated sample port. Mixtures were prepared over the
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composition range using a mass balance (Ohaus Explorer; maximum capacity of 6100 g; resolution of 0.01 g) and the response ratio was obtained (1.414:1 for CO2:R22 and 1.438:1 for ethlyene:R22). The calibration covered ranges from (250 to 500) µl in volume. The
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maximum errors (difference between experimental value to correlated value) across the composition range for the binary system of CO2 + R22 and ethylene + R22 were 0.003 and
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0.002 respectively. The expanded uncertainties (U) were estimated following the guidelines supplied by NIST (National Institute of Standards and Technology) [23]. The standard uncertainties used for the estimation are listed in table 2.
As discussed in the NIST
guidelines, the combined uncertainty can be calculated through the law of propagation of
=
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uncertainty [23].
+2
,
(1)
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The expanded uncertainty (k = 2) for composition can then be estimated from: =2
+
+
!"
(2)
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Where ucal is the maximum error in the calibration polynomial (given in table 2), urep is the absolute difference between the magnitudes of the samples withdrawn at equilibrium (average given in table 2), and umix is the uncertainty in the molar composition from gravimetrically preparing gaseous mixtures used in the calibration, given by: =
#
$ $
+
$ $
(3)
Where u(m1) = u(m2) and is the standard uncertainty of the mass balance (given in table 2), and m1 and m2 are the masses of component 1 and 2, respectively, used to prepare the
ACCEPTED MANUSCRIPT calibration standards. The expanded uncertainties (using a coverage factor of k = 2) on average for temperature and pressure are U(T) = 0.07 K and U(P) = 0.002 MPa, respectively. The expanded uncertainty for composition for both binary systems are U(x1) = 0.005 and
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U(y1) = 0.004.
ACCEPTED MANUSCRIPT 3. DATA TREATMENT The VLE data were regressed using the Peng-Robinson (PR) Equation of State (EoS) [24] following the phi-phi approach utilizing Aspen Plus V8.0 [25]. The pure-component
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parameters of the PR EoS were extended to mixtures via either the van der Waals (vdW) or the Wong-Sandler (WS) mixing rules [26]. The Non-Random Two-Liquid (NRTL) activity coefficient model [27] was utilized to represent the excess Gibbs energy necessary for the WS mixing rule. The maximum-likelihood objective function (T, P, x1 and y1) was minimized
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by adjusting the binary interaction parameters using the Britt-Luecke algorithm [28]. The
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quality of the data-fit was assessed statistically using the average absolute deviation (AAD and the average absolute relative deviation (AARD) using a bubble-point calculation. The AAD and AARD are defined as:
1 %%& '̅ = *"
and '̅
-
+'!̅
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"
+'!̅
"
− '̅
− '̅ '!̅ "
+
"
+
(4)
(5)
are the experimental and calculated values of a measurand '̅ (P and y1),
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where '!̅
1 %%.& '̅ = *"
-
and Np is the total number of data points. The mixture critical co-ordinates (z1,c and Pc) were
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also estimated using the following scaling law [7, 29, 30]: / =/
,
+ 0 +1
0 2
2 −2 +ε
4 2 −2 2
5
(6)
Where ε = 1 for bubble point and ε = −1 for dew point, z1 is the bubble point (z1 = x1) or the dew point (z1 = y1) at a pressure, P. z1 and Pc are the critical co-ordinates for the mixture composition and pressure respectively, 0 , 0 , 4 are adjustable parameters fitted using the ordinary least squares method to VLE data close to the critical point, 7 is a universal scaling component and was fixed to 0.325 [31].
ACCEPTED MANUSCRIPT 4. RESULTS AND DISCUSSION The apparatus and experimental method were tested by measuring VLE data for the binary system of CO2 + R22 at 273.15 K. The experimental data were compared to previous
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measurements available in literature. The phase equilibria of this system are almost ideal below the critical points of each pure component. The experimental data for this system are listed in table 3 and displayed in figure 2. The experimental data compare well to the literature data of both Roth et al. at 273.14 K [32] and Nohka et al. at 273.1 K [33] and to
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data predicted at 273.15 K using the Reference Fluid Thermodynamic and Transport
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Properties (REFPROP) model [34] (see figure 2). The experimental and literature data were modelled using the PR EoS and vdW mixing rule. The modelling results and comparison are presented in table 4. A low AARD, of less than 0.5% for pressure, is noted between our experimental data and the data predicted by REPROP and modelled data of Roth et al. [32]. The vapour pressure data are listed in table 5; the data compare well to data predicted by
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REFPROP. New isothermal VLE data were experimental measured for the binary system of ethylene + chlorodifluoromethane at five temperatures, viz. (273.15, 293.15, 313.15, 333.15,
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and 353.15) K. The binary system exhibits a low positive deviation from Raoult’s law. The critical point co-ordinates (P and z1) for the mixtures were also experimentally measured at
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four temperatures, viz. (293.15, 313.15, 333.15, and 353.15) K. The experimental data were modelled using the PR EoS coupled with the WS mixing rule and NRTL activity coefficient model. Each isotherm was modelled independently to obtain the best possible representation close to the critical region. The experimental and modelled data are displayed in figures 3 and 4, and are listed in tables 6 and 7. Low deviations between the experimental and modelled data are evident across the entire temperature range. The deviations and model parameters are listed in table 8. An AARD for pressure of less than 0.5% is evident for all temperatures. The highest AAD for the vapour phase composition is 0.005. The critical points were also
ACCEPTED MANUSCRIPT calculated using the model and scaling laws, the data are listed in table 7. In all instances, the model cannot predict the experimental critical point to within the experimental uncertainty.
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However, the scaling law provides an excellent representation of the mixture critical point.
ACCEPTED MANUSCRIPT 5. CONCLUSIONS A new apparatus based on the “static-analytic” method was designed and commissioned. The apparatus and experimental procedure were tested by measuring VLE data for the binary
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system of carbon dioxide + chlorodifluoromethane. The experimental data match well with data available in literature. New VLE data and mixture critical point data were measured for the binary system of ethylene + chlorodifluoromethane. The data were correlated with the PR EoS, WS mixing rule, and NRTL activity coefficient model. The model provided a good
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representation of the experimental data below the critical region. However, the model was
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unable to estimate the mixture critical point to within the experimental uncertainty.
ACCEPTED MANUSCRIPT ACKNOWLEDGEMENTS 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
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Technology and the National Research Foundation Thuthuka Programme.
ACCEPTED MANUSCRIPT REFERENCES
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[1] J.M.S. Fonseca, R. Dohrn, S. Peper, Fluid Phase Equilibr. 300 (2011) 1-69. [2] P. Uusi-Kyyny, S. Ionita, M.S. Qureshi, V. Alopaeus, D. Richon, J. Chem. Eng. Data 61 (2016) 2700-2711. [3] S. Laugier, D. Richon, Rev. Sci. Instrum. 57 (1986) 469-472. [4] P. Figuiere, J.F. Hom, S. Laugier, H. Renon, R. D, H. Szwarc, AlChE J. 26 (1980) 872875. [5] P. Guilbot, A. Valtz, H. Legendre, D. Richon, Analusis 28 (2000) 426-431. [6] F. Zhang, P. Theveneau, E.E. Ahmar, X. Canet, C.-B. Soo, C. Coquelet, Fluid Phase Equilibr. 409 (2016) 425-433. [7] S.F. Westman, H.G.J. Stang, S.W. Løvseth, A. Austegar, I. Snustad, S.Ø. Størset, I.S. Ertesvåg, Fluid Phase Equilibr. 409 (2016) 207-241. [8] S. Horstmann, G. Birke, K. Fischer, J. Chem. Eng. Data, 49 (2004) 38-42. [9] M. Frost, N.v. Solms, D. Richon, G.M. Kontogeorgis, Fluid Phase Equilibr. 405 (2015) 88-95. [10] C.N. Narasigadu, P.; Coquelet, C.; Richon, D.; Ramjugernath, D., Fluid Phase Equilibr. 338 (2013) 188-196. [11] W.M. Nelson, P. Naidoo, D. Ramjugernath, J. Chem. Thermodyn. 91 (2015) 420-426. [12] W.M. Nelson, Z. Tebbal, P. Naidoo, L. Negadi, D. Ramjugernath, Fluid Phase Equilibr. 408 (2016) 33-37. [13] A.L. Muhlbauer, J.D. Raal, fluid Phase Equilibr. 64 (1991) 213-236. [14] P. Naidoo, D. Ramjugernath, J.D. Raal, Fluid Phase Equilibr, 269 (2008) 104-112. [15] F.J. Conradie, P.L. Crouse, X. Courtial, I.J. van der Walt, D. Ramjugernath, J. Chem. Eng. Data 57 (2012) 1978-1983. [16] F.J. Conradie, P.L. Crouse, X. Courtial, W.M. Nelson, I.J. van der Walt, D. Ramjugernath, J. Chem. Eng. Data 59 (2014) 82-88. [17] S.C. Subramoney, X. Courtial, P. Naidoo, C. Coquelet, D. Richon, D. Ramjugernath, Fluid Phase Equilibr. 353 (2013) 7-14. [18] S.C. Subramoney, W.M. Nelson, X. Courtial, P. Naidoo, C. Coquelet, D. Richon, D. Ramjugernath, J. Chem. Thermodyn. 90 (2015) 100-105. [19] E.S.R. Gopal, Resonance, Bangalore, India, Springer, 5 (2000) 37-45. [20] W.M. Nelson, M. Williams-Wynn, S.C. Subramoney, D. Ramjugernath, J. Chem. Eng. Data 90 (2015) 100-105. [21] J.D. Raal, A.L. Mühlbauer, Phase Equilibria: Measurement and Computation, Taylor and Francious, Washington, D.C., 1998. [22] S. Bobbo, R. Camporese, R. Stryjek, J. Chem. Thermodyn. 30 (1998) 1041-1046. [23] B.N. Taylor, C.E. Kuyatt, NIST Technical Note 1297: Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, National Institute of Standards and Technology, Gaithersburg, 1994. [24] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59-64. [25] AspenTech. Aspen Technology, Massachusetts, USA., 2010. [26] D.S.H. Wong, S.I. Sandler, AIChE J. 38 (1992) 671-680. [27] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135-144. [28] H.I. Britt, R.H. Luecke, Technometrics 15 (1973) 233 - 238. [29] P. Ungerer, B. Tavitian, A. Boutin, Editions Technip, Paris, (2005). [30] V. Lachet, T.d. Bruin, P. Ungerer, C. Coquelet, A. Valtz, V. Hasanov, F. Lockwood, D. Richon, Energy Procedia 1 (2009) 1641-1647. [31] J.V. Sengers, J.M.H. Levelt Sengers, Int. J. Thermophys. 5 (1984) 195-208.
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[32] H. Roth, P. Peters-Gerth, K. Lucas, Fluid Phase Equilibr. 73 (1992) 147-166 [33] J. Nohka, E. Sarashina, Y. Arai, S. Saito, J. Chem. Eng. Jpn. 6 (1973) 10. [34] E.W. Lemmon, M.L. Huber, M.O. McLinden, Reference Fluid Thermodynamic and Transport Properties (REFPROP), NIST Standard Reference Database 23: Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, 2007.
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Fig. 1. Schematic of the “static-analytic” apparatus. C: Gas cylinder, IC: immersion circulator, LB: liquid bath, LP: liquid venting port, GC: Gas chromatograph, PP: platinum resistance temperature probe, PT: pressure transmitter, OS: overhead stirrer, R: ROLSI, TR: temperature regulation, VP: vacuum pump.
ACCEPTED MANUSCRIPT 4
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2
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P (MPa)
3
0 0
0.2
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1
0.4
0.6
0.8
1
x1, y1
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Fig. 2. Experimental, literature and predicted (REFPROP – represented by the solid black line at 273.15 K) VLE data for the binary system of CO2 (1) + R22 (2): experimental data at 273.15 K (); Roth et al. at 273.14 K [32] (▲) and Nohka et al. at 273.1 K [33] ( ) (data
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point x1 = 0.554 of Nohka et al. not included on the figure).
ACCEPTED MANUSCRIPT 6
5
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P (MPa)
4
3
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2
0 0
0.2
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1
0.4
0.6
0.8
1
x1, y1
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Fig. 3. Experimental VLE data for the binary system ethylene (1) + R22 (2) at 273.15 K (○), 293.15 K (●), 313.15 K ( ), 333.15 K (▲), and 353.15 K ( ), as well as the experimental critical points (
). The solid black line depicts the modelled data using the PR EoS with the
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WS mixing rule and NRTL activity coefficient model.
ACCEPTED MANUSCRIPT
5.4
5.7
5.8
b)
5.5
c)
d)
x1, y1
0.91
5.4 0.63
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5.1 0.86
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P (MPa)
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P (MPa)
P (MPa)
P (MPa)
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a)
x1, y1
0.73
5.6 0.42
x1, y1
0.51
5.2 0.18
x1, y1
0.25
Fig. 4. Expanded view of the critical region for the binary system of ethylene (1) + R22 (2) at (a) 293.15 K, (b) 313.15 K, (c) 333.15 K, and (d) 353.15 K. Experimental critical points (
), solid lines depicts the PR EoS, WS mixing rule and NRTL activity coefficient model ( ), and
scaling laws represented by dashed black line ( ).
ACCEPTED MANUSCRIPT Table 1 Pure-component parameters and properties for carbon dioxide (CO2), ethylene and chlorodifluoromethane (R22). CO2
Ethylene
R22
Component characterization Afrox
Afrox
Afrox
Supplier purity wt.%
99.0
>99.9
>99.5
Purification
none
none
GC Area
>99.95
>99.9 b
Critical properties and acentric factor Tc (K)
304.13
282.35
Pc (MPa)
7.3773
5.0418
ω
0.22394
0.0866
a
degassed
>99.9
369.3
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a
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Supplier
4.99
0.22082
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Area percentage of the component identified by gas chromatography using a thermal conductivity detector and either a Rtx-1 or Rtx-5 RESTEK capillary column. b Critical properties and acentric factor from REFPROP [34].
ACCEPTED MANUSCRIPT Table 2 Standard uncertainty estimates and influences of the variables in this work. Source of uncertainty Pressure (P)
Estimate
Distribution
0.01%
normal
Correlation for P (MPa): (10 MPag)
0.001
rectangular
Temperature (T)
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P reference (MPa): Mensor CPC 8000 (25 MPag)
T reference (K): CTH 6500
0.02
rectangular
Correlation for T (K)
0.06
rectangular
0.03
rectangular
0.03
rectangular
0.001
rectangular
Composition (zi)
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Mass balance uncertainty (g) Repeatability of masses (g)
0.002
rectangular
Correlation for x1 and y1 [CO2 + R22]
0.003
rectangular
Correlation for x1 and y1 [C2H4 + R22]
0.002
rectangular
Range (average) of x: (xi,[max] – xi,[min]) [CO2 + R22]
0.003
rectangular
Range (average) of y: (yi,[max] – yi,[min]) [CO2 + R22]
0.001
rectangular
Range (average) of x: (xi,[max] – xi,[min]) [C2H4 + R22]
0.003
rectangular
0.002
rectangular
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Gravimetric x1 and y1 [C2H4 + R22]
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Gravimetric x1 and y1 [CO2 + R22]
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Range (average) of y: (yi,[max] – yi,[min]) [C2H4 + R22]
ACCEPTED MANUSCRIPT
x1
y1
0.498
0
0
0.546
0.020
0.090
0.615
0.049
0.201
0.712
0.090
0.327
0.905
0.168
0.488
1.040
0.222
0.577
1.254
0.306
1.414
0.362
1.565
0.419
0.724 0.766
0.486
0.808
0.573
0.852
0.612
0.870
0.682
0.899
0.722
0.915
2.645
0.769
0.931
3.008
0.872
0.963
3.143
0.912
0.975
3.314
0.955
0.988
3.487
1
1
2.012 2.141 2.347
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2.484
U(T) = 0.07 K; U(P) = 0.002 MPa; U(x1) = 0.005; U(y1) = 0.004
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a
0.673
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1.761
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P (MPa)
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Table 3 Experimental vapour-liquid equilibrium data for the binary system of carbon dioxide (1) + chlorodifluoromethane (2), including the measured temperature (T), pressure (P), and both the liquid and vapour phase compositions (x1, y1), including the expanded uncertaintiesa.
ACCEPTED MANUSCRIPT Table 4 Comparison of the experimental vapor-liquid equilibrium data for the binary system of carbon dioxide (1) + chlorodifluoromethane (2) at 273.15 K to data available in literature and modeled data. AAD(P)/MPa AARD(P) AAD(y1) AAD(y1) k12 -0.0010
0.005
0.24%
0.003
0.97%
Roth et. al. [32]a
0.0004
0.011
0.54%
0.002
0.35%
Nohka et al. [33] a
0.0107
0.024
1.71%
0.006
0.94%
-NA-
0.009
0.49%
0.003
0.86%
PR – Roth et. al. [32]b
0.0004
0.004
0.23%
0.003
1.12%
PR – Nohka et al. [33]b
0.0107
0.027
1.84%
0.007
2.31%
a
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REFPROP
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Experimentala
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Data modelled using PR EoS + WS mixing rule/NRTL model. Deviations calculated with respect to difference between data and modelled data. b Comparison between the modelled data and the experimental data. Deviations calculated with respect to difference between experimental data and modelled literature data.
ACCEPTED MANUSCRIPT Table 5 Experimental vapour pressure data for chlorodifluoromethane, carbon dioxide, and ethylene including the temperature (T), pressure (P), and the expanded uncertaintiesa. Texp (K)
Pref (MPa)b
Pexp (MPa)
Pexp-Pref (MPa)
Chlorodifluoromethane 0.498
0.4979
0.0001
293.15
0.911
0.9100
0.001
313.15
1.529
1.5336
333.15
2.426
2.4275
353.15
3.664
3.6638
273.15
3.487
3.4851 4.0990
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U(T) = 0.07 K; U(P) = 0.002 MPa Reference vapour pressure data predicted from REFPROP [34].
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b
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a
4.094
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Ethylene 273.15
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Carbon dioxide
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273.15
-0.005 -0.002
0.0002 0.002 -0.005
ACCEPTED MANUSCRIPT Table 6 Experimental vapour-liquid equilibrium data for the binary system of ethylene (1) + chlorodifluoromethane (2), including the measured temperature (T), pressure (P), and both the liquid and vapour phase compositions (x1, y1), including the expanded uncertaintiesa. P (MPa)
x1
y1
P (MPa)
x1 T = 293.15 K
0
0
0.911
0.597
0.029
0.171
0.945
0.747
0.072
0.337
1.021
0.842
0.100
0.419
1.231
1.270
0.228
0.631
1.597
1.623
0.337
0.728
1.945
0.436
0.786
2.357
0.560
0.838
2.633
0.643
0.868
2.990
0.742
0.903
3.382
0.845
0.938
3.765
0.935
0.970
3.845
0.951
0.978
4.015
0.984
4.094
1
0.007
0.035
0.023
0.103
0.067
0.258
0.146
0.440 0.587
2.628
0.369
0.681
3.034
0.457
0.733
3.423
0.539
0.775
3.694
0.594
0.800
4.376
0.728
0.854
4.920
0.822
0.890
5.167
0.863
0.902
0.992
5.266
0.882
0.906
1
5.308
0.891
0.906
5.318
0.893
0.905
5.326
0.896
0.904
5.329
0.898
0.902
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0.260
0
1.640
0.017
0.061
1.558
0.004
0.015
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0
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0
2.124
T = 313.15 K 1.529
0
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0.498
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T = 273.15 K
y1
T = 333.15 K
2.019
0.079
0.237
2.426
0
0
2.420
0.144
0.363
2.475
0.006
0.018
3.056
0.248
0.498
2.669
0.031
0.083
3.621
0.342
0.580
2.892
0.060
0.149
4.041
0.410
0.628
3.199
0.101
0.224
4.394
0.467
0.659
3.546
0.146
0.299
4.691
0.513
0.683
3.994
0.206
0.366
5.251
0.605
0.715
4.573
0.284
0.438
5.413
0.631
0.720
4.953
0.335
0.471
ACCEPTED MANUSCRIPT 0.658
0.723
5.016
0.344
0.478
5.654
0.678
0.719
5.502
0.416
0.504
5.689
0.691
0.714
5.629
0.434
0.508
5.696
0.694
0.710
5.674
0.445
0.506
5.697
0.697
0.707
5.698
0.450
0.503
5.722
0.456
0.500
5.733
0.460
0.499
0.466
0.497
0.478
0.481
T = 353.15 K 0
5.745
3.885
0.024
0.046
5.755
4.308
0.071
0.123
4.747
0.121
0.185
5.251
0.183
0.236
5.403
0.206
0.243
5.435
0.211
0.243
5.447
0.213
0.242
5.472
0.220
0.238
5.480
0.224
0.235
5.480
0.225
0.237
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0
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U(T) = 0.07 K; U(P) = 0.002 MPa; U(x1) = 0.005; U(y1) = 0.004
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3.664
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5.561
ACCEPTED MANUSCRIPT Table 7 Experimental and modeled critical points for the binary mixture of ethylene (1) + chlorodifluoromethane (2). The mixture critical points were modeled using both a scaling law and the PR EoS with the WS mixing rule incorporating the NRTL activity coefficient model. Scaling law
Experimental Pc (MPa)
z1,c
Pc (MPa)
z1,c
Pc (MPa)
z1,c
293.15
5.330
0.899
5.329
0.900
5.313
0.905
313.15
5.698
0.701
5.698
0.703
333.15
5.755
0.479
5.755
0.481
353.15
5.482
0.230
5.482
0.231
5.689
0.712
5.797
0.496
5.497
0.238
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U(T) = 0.07 K; U(P) = 0.002 MPa; U(z1) = 0.005
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T (K)
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PR EoS/WS/NRTL
ACCEPTED MANUSCRIPT Table 8 Regressed binary interaction parameters (k12, b12 and b21) for the PR EoS with the WS mixing rules incorporating the NRTL activity coefficient model, and statistical analysis of the data-fit for the binary system of ethylene (1) + chlorodifluoromethane (2). T = 273.15 K
T = 293.15 K
T = 313.15 K
T = 333.15 K
T = 353.15 K
0.058
0.100
0.091
b12a
0.096
-222.7
-266.5
-160.1
b21a
-69.3
-99.6
-152.8
AAD(P)/MPa
0.008
0.012
0.015
AARD(P)
0.34%
0.36%
AAD(y1)
0.003
0.003
AARD(y1)
0.64%
0.67%
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k12
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Model parameters -159.2
282.5
-147.5
-216.6
0.010
0.008
0.34%
0.21%
0.16%
0.005
0.005
0.003
0.73%
1.34%
1.53%
Deviations
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NRTL binary interaction parameters are defined as 8 = 9⁄:; non-randomness parameter fixed at 0.3. a
0.108