Experimental Measurements and Thermodynamic Modeling of VLE for

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Thermodynamics, Transport, and Fluid Mechanics

Experimental measurements and thermodynamic modeling of VLE for strong-zeotropic ternary system of 2,3,3,3-tetrafluoroprop-1ene (R1234yf)+ ethane (R170)+ tetrafluoromethane (R14) Yanbin Qin, Hua Zhang, Baolin Liu, and Nanxi Li Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b04124 • Publication Date (Web): 29 Jan 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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Industrial & Engineering Chemistry Research

Experimental measurements and thermodynamic modeling of VLE for strong-zeotropic ternary system of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf)+ ethane (R170)+ tetrafluoromethane (R14) Yanbin Qina, Hua Zhanga, Baolin Liua, Nanxi Lib (a University of Shanghai for Science and Technology, Shanghai 200093; b Kansas State University, Manhattan, KS 66506) Abstract The isothermal experimental VLE data for the strong-zeotropic mixture of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) + ethane (R170) + tetrafluoromethane (R14) were measured using a circulation type apparatus at temperatures ranging from 253.15 K to 273.15 K. Based on the UNIFAC (Dortmund) method, the new group volume, the area parameters, and the six binary interaction parameters of C2H2F, CF4, CF3 and CH3 were obtained by fitting the experimental data. Two theoretical models, the NRTL-RK model and the PR-WS-MUNIFAC model were used to correlate the experimental data. The AARD of pressure and the AAD of vapor phase mass fraction are 0.28%, 0.0077, and 0.0277 using the NRTL-RK model, and 0.32%, 0.0098, and 0.0185 using the PR-WS-MUNIFAC model, respectively. The isobaric VLE properties for the mixture were predicted using PR-WS-MUNIFAC model at pressures ranging from 0.1 MPa to 2 MPa, and the three dimensional phase equilibrium diagrams were presented. It is concluded that the temperature glide phenomenon is the most obvious at the mass fraction ratio of 0.35/0.1/0.55, and the maximum temperature glide reaches 73.4 K at the pressure of 0.5 MPa. Key words: VLE; R1234yf; UNIFAC; temperature glide; zeotropic mixtures

1. Introduction The auto cascade refrigeration cycle (ARC) shows more advantages comparing with traditional cascade refrigeration systems in small-scale refrigeration equipment and the liquefaction of natural gas [1]. Ruhemann [2] successfully applied freon refrigerants in ARC system for the first time in 1946, and obtained a temperature as low as 200 K using the mixed refrigerant of chlorotrifluoromethane (R13) + chlorodifluoromethane (R22). In 1959, Kleemenko [3] utilized a mixture of methane, ethane and n-butane with mole fraction of 65/20/15 and managed to liquefy the natural gas using single-stage compression and two-stage separation. In 1965, a low 

Corresponding author:

E-mail address: [email protected] Institute of Refrigeration and Cryogenic Engineering University of Shanghai for Science and Technology, Shanghai 200093, China Tel: +86 18817582733, Fax: +86-21-55275542 1 / 20

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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temperature of 117 K was successfully obtained using the mixed refrigerant of methane (R50) + dichlorodifluoromethane (R12) with mass fraction of 20/80 [4]. Since then, many researchers continued to improve the ARC system, and their contributions improved the efficiency of refrigeration and the cooling temperature became lower and lower [5], [6], [7], [8]. Du et al. [9] experimentally studied the cycle characteristics of an auto-cascade refrigeration system. The coefficient of performance, cooling capacity, evaporation temperature, pressures, and temperatures of refrigerant at the inlet and outlet were measured. Zhang et al. [10] carried out experimental and theoretical investigations on the performance of CO2 + propane auto-cascade refrigerator with a fractionation heat exchanger and concluded that the cycle performance could be improved by increasing the CO2 mass fraction or by decreasing the cooling water temperature. Wu et al. [11] calculated and analyzed the thermodynamic properties of the auto-cascade refrigeration system with 2-methylpropane (R600a) + trifluoromethane (R23) + tetrafluoromethane (R14). With an increasing concern on global environmental problems such as global warming, greenhouse effect, ozone layer destruction, there is a greater need for replacing traditional refrigerants with better alternatives in the refrigeration industry. Refrigerants with high GWP (Global Warming Potential) and ODP (Ozone Depression Potential) values will phase out, and new types of environmental-friendly refrigerants will gradually appear. The synthesis and design of the separation processes requires a deep understanding of the phase behavior of the system. It directly affects the reliability and efficiency of the whole system. However, most of the studies in the literature focus on near-azeotropic refrigerants, while little research concentrates on the VLE of strong-zeotropic refrigerants which are suitable for multi-stage auto cascade systems. Hu et al. studied the VLE properties of a series of mixtures including R1234yf + R600a [12], R1234yf + R152a [13], 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) + fluoroethane (R161) [14], R134a + R600a + R1234yf [15], 1,1,1,2-tetrafluoroethane (R134a) + 1,1,1,2,3,3,3-heptafluoropropane

and

1,1,1-trifluoroethane

(R143a)

+

2,3,3,3-tetrafluoroprop-1-ene (R1234yf) [16], and accumulated a large amount of experimental data. In a recent study, the binary interaction coefficient 𝑘𝑖𝑗, which is an important parameter in the VLE calculation was summarized based upon the aforementioned experimental data and theoretical model [17]. Li et al. [18] adopted the equation of state (EoS) to simulate the VLE properties of pentafluoroethane (R125) + 1,1,1,2-tetrafluoroethane (R134a) + 1,1,1-trifluoroethane (R143a) system and concluded that the EoS method could predict the VLE characteristics of mixtures well. Gong et al. [19], [20], Lim et al. [21] and Ju et al. [22] conducted both theoretical and experimental studies on the mixtures containing hydrocarbon R290. Budinsky et al. [23] utilized the Gibbs ensemble Monte Carlo (GEMC) simulation to calculate the VLE data of 2 / 20


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1,1,1,2-tetrafluoroethane (R134a) + pentafluoroethane (R125) and 1,1,1,2-tetrafluoroethane (R134a) + difluoromethane (R32). The calculated results were highly consistent with data found in the literature, and it was revealed that the GEMC had the same accuracy of prediction with those of the Wilson and UNIFAC methods, which are based on thermodynamics. Ho et al. [24], [25]

experimentally

investigated

the

VLE

properties

of

propene

(R1270)

+

1,1,1,2-tetrafluoroethane (R134a) binary system and the hydrocarbon mixture propene (R1270) + propane (R290). Qin et al. [26] also investigated the VLE behavior of R1234yf + R23 + R14 system theoretically. It was found that the experimental data demonstrated a good agreement with the predicted results using the Peng–Robinson EoS [27] combined with the Wong–Sandler (WS) [28] mixing rule. R1234yf has excellent environment parameters with the a low GWP value of four, and zero ODP value, also an atmospheric lifetime as short as 0.029 years. It is recognized as the best alternative to R134a at present. R170 is a hydrocarbon refrigerant. As a natural working fluid, it has advantages such as energy saving and environmental friendly. Although R14 has a relatively high GWP value, its ODP is 0, and there is no restriction on the production and sale of R14. At the same time, it is difficult to find another alternative refrigerant for the corresponding temperature range (around 150K) in the current study. Therefore, R14 is the most suitable refrigerant for the three-stage ARC system. Zhao et al. [29] carried out studies on 48 pure substances and 58 binary systems composed of CxHy and CxHyFz, in which both Peng–Robinson (PR) and perturbed-chain SAFT (PCSAFT) were investigated. Hou et al. [30] used modified Soave-Redlich-Kwong EoS combined with zero reference pressure GE-EoS mixing rules and the UNIFAC group contribution model to predict the VLE behavior for the mixtures containing alkanes, alkenes, CO2, dimethyl ether, hydrofluorocarbons, and perfluoroalkanes. To the best of the authors’ knowledge, there is still no experimental VLE data of R1234yf + R170 + R14 system. Therefore, this study measured the isothermal VLE data for the strong-zeotropic system of R1234yf + R170 + R14, which is applicable for the three-stage ARC device, by synthetically considering the physical parameters of refrigerants with the characteristics and the temperature range of a three-stage ARC system. The measurements were taken using a circulation type apparatus coupled with a six-way valve sampler and two gas chromatographs to analyze the phases. The well-known NRTL (non-random two liquid) [31] method is one of the most widely adopted activity coefficient models. The excess Gibbs free energy-equation of states (𝐺EEoS) model could perform a good extrapolation at high temperatures and pressures because it encompasses the advantages of the activity coefficient method and the EoS method.. Moreover, it can also describe the supercritical and subcritical components continuously and accurately [32]. Thus, the experimental VLE data of 3 / 20



Page 4 of 20

R1234yf+R170+R14 in this work were correlated using the NRTL-RK model and the PR-WS combined with the group contribution method of modified UNIFAC(Dortmund) [33], [34] (PR-WS-MUNIFAC model). By fitting the experimental data, the new area parameters, group volume, and the six binary interaction parameters of C2H2F, CF4, CF3 and CH3 were acquired. The isobaric VLE properties of R1234yf+R170+R14 were predicted using PR-WS-MUNIFAC model with the pressure range of 0.1 MPa to 2 MPa, and the relevant three-dimensional phase equilibrium diagrams were drawn.

2. Experiment 2.1 Materials All chemicals were purchased from commercial sources and used without any further purification. A gas chromatographic analysis indicated that the compounds had purity close to 99.9%. The purities and suppliers of the chemicals used in these measurements are summarized in Table 1. The critical properties and acentric factors of R1234yf, R170, and R14 are shown in Table 2. Table. 1. Sample information. Component

Supplier

Purity/mass(%)

Analysis method (peak area fraction)

R1234yf

Honeywell Co., Ltd

99.9

GC (99.8724)

R170

Wei chuang Co., Ltd.

99.99

GC (99.9210)

R14

Wei chuang Co., Ltd

99.995

GC (99.9185)

Table. 2 Critical properties, normal boiling point, and acentric factors of pure components a. Component

M/(kg/kmol)

Tc/K

pc/MPa

Vc/(m3•kg)

ω

Tb/K

R1234yf

114.04

367.85

3.382

0.002220

0.2760

243.70

R170

30.07

305.32

4.872

0.004493

0.0995

184.57

R14

88.01

227.51

3.750

0.002125

0.1785

145.10

a

Obtained from REFPROP 9.0 software with corresponding references for R1234yf [35], R170 [36], and R14

[37], respectively.

2.2. Experimental apparatus and procedure Fig. 1 illustrates schematically the design of the static-analytic experimental apparatus used in this study.

The purpose of the experimental apparatus is to obtain the data of T-p-x-y. The

measurement of VLE was carried out using the recirculation-type method. The experimental apparatus includes six major parts, namely, a sampling circulation and analysis system, an equilibrium cell, a thermostat liquid bath, a temperature measurement and control system, a pressure sensor, and a high-vacuum system. The experimental apparatus was designed and fabricated to withstand temperatures from 150 K to 350 K under absolute pressures from 0 MPa to 6.3 MPa. The equilibrium cell had an inner volume of 280 mL and was made of 316 stainless-steel. The liquid level and sample circulation was observed through a pair of 15mm-thick quartz glass windows mounted on the cell. An optical window was also installed in the 4 / 20


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thermostatic bath in which the cell was immersed. The thermostatic bath was located in a vacuum tank with all visualizing windows highly aligned in a central line. The cooling source for thermostatic bath was supplied by a liquid nitrogen dewar. T

6

5

P

3

7 4 8

P

carrier gas

to PC 6

14

5

1 2

4

18

3

P

10 13

19

15 12

17

2

9 to PID

16 11

1

Fig. 1. Schematic diagram of the static-analytic apparatus: 1.vacuum pump 3.gas chromatograph 3.data acquisition system 4.sample storage tank 5.flowmeter 6.magnetic pump 7.PID temperature controller 8.electromagnetic stirrer 9.thermostat 10.cooling coiled 11.vacuum cover 12.equilibria cell 13.precooling coiled 14.countercurrent heat exchanger 15.view windows 16.electric heater 17.liquid nitrogen dewar 18.six-way valve 19.nitrogen cylinder

Two high-precision platinum resistance thermometer probes (Pt100) (TC Inc., model RT47-ACF55SS, calibrated by the manufacturer) were used to measure temperatures of the equilibrium cell and the thermostatic bath. The uncertainty of the Pt100 was ±30 mK. A data acquisition/switch unit (Agilent 34972A) transferred the signal to a PC. The maximum estimated resulting uncertainty in the temperature measurement was 40 mK. The equilibrium cell pressure was monitored by an absolute pressure sensor (A and B, GE., Models PTX5072, calibrated by the manufacturer). The measuring range of the pressure sensor is 0-7 MPa with an accuracy of 0.04% of full scale. The premium accuracy performance is ±1.5% FS TEB (Temperature Error Band) at the temperature from 233.15 K to 353.15 K. The pressure uncertainty caused by the

temperature-induced errors is 0.03 kPa which is negligible when the temperature fluctuation was only at 40 mK. The pressure signal was sent to the PC using the data acquisition unit (Agilent 34972A). The total maximum uncertainty in pressure measurement was calculated to be 3 kPa. Both the vapor and the liquid phase mass fraction was obtained using a gas chromatograph (GC) (Model GC112A, Shanghai Precision and Scientific Instrument Ltd., China). The GC was equipped with a porapak-Q packed column (80/100 mesh, 2 m long, 3 mm diameter) and a flame ionization detector (FID). Multipoint correction method was utilized to calibrate the GC in 5 / 20



Page 6 of 20

advance using a digital balance (METTLER TOLEDO Inc., Model ME204E) with an accuracy of ±0.0001 g. For each sample, at least three analyses were conducted to ensure the deviations among them were less than ± 0.001. Considering the margin of error and reproducibility of GC, the combined standard uncertainty of the composition measurements is estimated to be within 0.002 in mass fraction. Prior to the experiment, the equilibrium cell and the circulation loop were cleaned and evacuated to 4×10-2 Pa to ensure no residual gas existed. A lesser component of the mixture with high boiling temperature was then used to purge the VLE cell before the cell was evacuated again. This procedure was repeated for three times. While the cell was being purged, the refrigeration system was turned on to cool the thermostatic bath, which reduces the pressure of equilibrium cell and the inflator time. After that, refrigerants were filled into the equilibrium cell in a proper sequence. A magnetic pump circulated the vapor in the cell from the top to bottom via the external circulation pipe. When the desired temperature was attained and remained constant for more than an hour, the vapor pressure of the mixture was measured. Samples of liquid and vapor phase were also extracted for composition analysis using GC. The average values of three measured mass fractions were considered as the results. Then the filling amount of different components and the temperature of thermostat bath were changed step by step to obtain a whole set of VLE data. Before the formal test, the thermodynamic consistency of the experimental apparatus was checked according to the above methods. 2.3 Results and correlation The compositions of the mixture were analyzed using the GC112A gas chromatograph with FID detector. The temperature of the column box, the injector, and the detector were set at 90 ℃, 120 ℃, 120 ℃ respectively. The injection volume was 15 𝜇L. The isothermal (p-x-y) VLE data of the strong-zeotropic ternary mixture of R1234yf+R170+R14 measured at three temperatures (253.15K, 263.15K, 273.15K) using the circulation-type apparatus are presented in table 3 with their uncertainties. Table. 3 Experimental VLE data for the ternary system of R1234yf(1) + R170(2) + R14(3)a. T/K

p/kPa

x1

x2

y1

y2

253.15

1168.09

0.5793

0.4184

0.2381

0.7581

253.15

1481.90

0.5400

0.3799

0.1694

0.5123

253.15

1633.35

0.5200

0.3599

0.1270

0.4170

253.15

1713.30

0.5048

0.3517

0.1161

0.3833

253.15

1836.62

0.4905

0.3298

0.1078

0.3258

253.15

1913.24

0.4801

0.3297

0.0997

0.2970

253.15

1964.56

0.4601

0.3397

0.0945

0.2943

253.15

2131.50

0.4402

0.3196

0.0818

0.2544

6 / 20


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263.15

1414.19

0.6783

0.3179

0.3073

0.6887

263.15

1747.19

0.6403

0.2897

0.2133

0.4718

263.15

2009.18

0.6008

0.2802

0.1721

0.3491

263.15

2020.81

0.6016

0.2707

0.1678

0.3317

263.15

2164.09

0.5807

0.2701

0.1550

0.3061

263.15

2210.21

0.5808

0.2602

0.1514

0.2891

263.15

2295.38

0.5815

0.2405

0.1450

0.2678

263.15

2332.47

0.5204

0.2997

0.1340

0.2994

273.15

1551.03

0.8007

0.1993

0.4284

0.5662

273.15

1839.02

0.8076

0.1407

0.3200

0.3178

273.15

2140.24

0.7863

0.1204

0.2611

0.2290

273.15

2185.74

0.7871

0.1104

0.2518

0.1979

273.15

2242.86

0.7877

0.1003

0.2428

0.1756

273.15

2319.52

0.7455

0.1406

0.2385

0.2262

273.15

2342.80

0.7251

0.1608

0.2357

0.2491

273.15

2388.74

0.6845

0.2011

0.2283

0.2870

a

Uncertainties u are u(T) = ±0.04K, u(p) =±3 kPa, and u(x) = u(y) =± 0.002.

The measured data were correlated with two types of models, the activity coefficient method (NRTL-RK model), and the GE-EoS method (PR-WS-MUNIFAC model). The cubic equation of state (CEoS) with two parameters is widely used because it has a simple form, is easy to solve, and its calculation accuracy can meet the general engineering requirements. NRTL model is a typical three-parameter equation with strong computational power and is suitable for partially miscible solutions. PR-WS-MUNIFAC model is a new method to calculate and predict phase equilibrium. It combines the advantages of the equation of state method and activity coefficient method. The CEoS with two parameters has a unified expression: 𝑝=

R𝑇 𝑣

𝑎

(1)

― 𝑣2 + 𝜇𝑏𝑣 + 𝛿𝑏2

where 𝑎 and 𝑏 are the equation constants. The expressions of 𝑎 and 𝑏 and the values of 𝜇 and 𝛿 in the Redlich-Kwong (RK) equation and Peng-Robinson (PR) equation are as follows. RK equation: 𝑎=

0.42748R2T2.5 C pc𝑇0.5

2 [1 + 𝑘(1 ― 𝑇0.5 𝑟 )] ,

𝑏=

2 [1 + 𝑘(1 ― 𝑇0.5 𝑟 )] ,

𝑏=

0.8664RTc pc

, 𝜇 = 1, 𝛿 = 0

(2)

PR equation: 𝑎=

0.457235R2T2C pc

0.077796RTc pc

, 𝜇 = 2, 𝛿 = ―1

(3)

𝑘 = 0.37464 + 1.54226𝜔 ― 0.26992𝜔2 (4) where R is the universal gas constant, Tc is the critical temperature, and pc is the critical 𝑇

pressure. 𝑇𝑟 = Tc is the reduced temperature, and 𝑘 is the function of the acentric factor 𝜔 of pure refrigerants. The excess free enthalpy of the NRTL equation is expressed as: 7 / 20



𝐺E R𝑇

∑𝑗(𝜏𝑗𝑖𝐺𝑗𝑖𝑥𝑗)

[

= ∑ 𝑖 𝑥 𝑖 ∑ (𝐺

𝑘𝑖𝑥𝑘)

𝑘

]

Page 8 of 20

(5)

The equation of activity coefficient is obtained: ln𝛾𝑖 = 𝜏𝑖𝑗 =

∑𝑗(𝜏𝑗𝑖𝐺𝑗𝑖𝑥𝑗) ∑𝑘(𝐺𝑘𝑖𝑥𝑘)

𝐺𝑖𝑗𝑥𝑗

∑𝑖(𝜏𝑖𝑗𝐺𝑖𝑗𝑥𝑖)

[

+ ∑𝑗𝐺𝑘𝑗𝑥𝑘 𝜏𝑗𝑖 ―

∑𝑘(𝐺𝑘𝑗𝑥𝑘)

]

(6)

𝑔𝑖𝑗 ― 𝑔𝑖𝑖 R𝑇

, 𝐺𝑖𝑗 = exp ( ― 𝛼𝑖𝑗𝜏𝑖𝑗)

(7)

𝛼𝑖𝑗 = 𝛼𝑗𝑖, 𝑔𝑖𝑗 = 𝑔𝑗𝑖, 𝜏𝑖𝑖 = 𝜏𝑗𝑗 = 0

(8)

𝑔𝑖𝑗 represents the energy parameter between two different molecules (i-j), which is regressed by experimental VLE data. 𝛼𝑖𝑗 is a characteristic function of solution type independent temperature and pressure, whose value is generally between 0.2 and 0.47. To apply PR EoS to a mixture, mixing rules are necessary to calculate the values of 𝑎 and 𝑏 of the mixture. The basic form of the WS mixing rule is: R𝑇QD

1

{

𝑎𝑚 = 1 ― D ；𝑏𝑚 = 1 ― 𝐷 ∑𝑖∑𝑗𝑥𝑖𝑥𝑗

[

𝑏𝑖 + 𝑏𝑗 2

―

(𝑎𝑖𝑎𝑗)1/2 R𝑇

(1 ― 𝑘𝑖𝑗)

]}

(9)

and (10)

𝑘𝑖𝑗 = 𝑘𝑗𝑖,𝑘𝑖𝑖 = 0； 𝐺E𝛾

( ), Q = ∑ ∑ x x [

D = C𝑇 + ∑𝑖𝑥𝑖

𝑎𝑖

bi + bj

i j i j

𝑏𝑖R𝑇

2

-

(aiaj)1/2 RT

(1 - kij)]

(11)

where 𝑎𝑚 and 𝑏𝑚 represent the gravitational parameters and the oblique volume parameters of mixtures, respectively. 𝑘𝑖𝑗 is the binary interaction coefficient, and 𝑥𝑖 is the liquid phase mass fraction of component 𝑖. C is a constant in the PR equation, with C = ln ( 2 - 1)/ 2. 𝐺E𝛾 is the excess Gibbs free energy of the activity coefficient method, and it is calculated as 𝐺E𝛾 = R𝑇∑𝑖𝑥𝑖 ln 𝛾𝑖. The activity coefficient 𝛾𝑖 is obtained with the modified UNIFAC (MUNIFAC model) in the improved PSRK EoS [38], [39]. It supplemented the group parameters and omitted the Flory-Huggins part of UNIFAC combined term. The remainder term still takes the form of the original UNIFAC model. There is: ln γi = ln γiC + ln γiR

(12 )

The calculation formula of the modified combined term is written as: ln 𝛾𝑖C = 1 ― ∅´𝑖 + ln∅´𝑖 ―

𝑍°𝑞𝑖 2

∅𝑖

∅𝑖

(13)

(1 ― 𝜃𝑖 + ln𝜃𝑖)

𝑟3/4 𝑖

𝑟𝑖

𝑞𝑖

𝑗 𝑗 𝑗

𝑗 𝑗 𝑗

𝑗 𝑗 𝑗

∅´𝑖 = ∑ 𝑥 𝑟3/4, ∅𝑖 = ∑ 𝑥 𝑟 , 𝜃𝑖 = ∑ 𝑥 𝑞

(14)

rj = ∑kvjkRk, qj = ∑kvjkQk (15) The expression of remainder term is: 8 / 20


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ln γiR = ∑mvjk(ln Γk - ln Γik)

(16)

[

ln 𝛤𝑘 = 𝑄𝑘 1 ― ln (∑𝑚𝜃𝑚𝜏𝑚𝑘) ― ∑𝑚

(

𝜃𝑚𝜏𝑚𝑘

)]

(17)

∑𝑛𝜃𝑛𝜏𝑛𝑘

Rk and Qk respectively represent the volume parameter and the surface area parameter of group k in component j. vjk is the number of group k in component j. 𝜏𝑚𝑘 was considered as a function of temperature, and was introduced into the group interaction parameter. Its expression is as follows:

(

𝜏𝑚𝑘 = exp ―

𝐴𝑚𝑘 + 𝐵𝑚𝑘𝑇 + 𝐶𝑚𝑘𝑇2

)

𝑇

(18)

According to the group partition method of UNIFAC (Dortmund), we divide R1234yf into the (CH3 + CF=CH2) group, the R170 (CH3+CH3) group, and the R14 (CF4) group. This study minimized the following objective function (obj) to regress the group binary parameters 𝜏𝑚𝑘 and the binary interaction coefficient kij for PR-WS-MUNIFAC model. 1

𝑁

𝑜𝑏𝑗 = 𝑁∑𝑖 = 1[

(

𝑝𝑖,cal ― 𝑝𝑖,exp 2 𝑝𝑖,exp

)

0.5

+ (𝑦𝑖,cal ― 𝑦𝑖,exp)2]

(19)

The adjustable parameters of 𝜏12 and 𝜏21 for NRTL-RK model, the binary interaction parameters of kij, the surface area parameters of Rk, and the volume parameters of Qk for PR-WS-MUNIFAC model are listed in Table 4. The six group-binary-parameters of Amn, Bmn, Cmn, Anm, Bnm and Cnm for UNIFAC(Dortmund) model are presented in Table 5. Table 6 summarizes the deviation between the experimental data and the correlation results. Table. 4 Regressed parameters of NRTL-RK model and PR-WS-MUNIFAC model. Systems

R1234yf+R170

R1234yf+R14

R170+R14

PR-WS-MUNIFA

NRTL model 𝜏12 = 0.19395 ― 6.96404/𝑇 𝜏21 = ―19.7748 + 5567.44/𝑇 𝜏12 = 0.904112 ― 282.477/𝑇 𝜏21 = ―7.92835 + 2419.9/𝑇 𝜏12 = ―25.4442 + 7288.94/𝑇 𝜏21 = 22.2695 ― 5981.14/𝑇

-

Groups

Rk

Qk

0.3143

CH3

0.6297

1.0658

0.0605

C2H2F

1.2047

1.166

0.1204

CF4

1.063

1.032

-

CF3

1.6153

1.5156

C kij

-

Table. 5 Regressed results for the group interaction parameter of PR-WS-MUNIFAC model. Group m

C2H2F

C2H2F

C2H2F

CF3

CF3

Group n

CF3

CF4

CH3

CF4

CH3

Amn

1975.286

-1320.99

616.3457

255.64

261.2975

Anm

-1048.44

535.0559

767.4061

2168.354

1004.999

Bmn

18.69297

-0.9516

0.056552

-0.07695

1.515904

Bnm

-3.77399

51.49521

-0.15353

3.988983

-2.32731

Cmn

-0.09965

0.021489

-0.00799

-0.00354

-0.0134

Cnm

0.028918

0.192047

-0.00702

0.012987

-0.00576

9 / 20



Page 10 of 20

Table. 6 Deviation between the regressed results and the experimental data for R1234yf(1) + R170(2) + R14(3) system a. NRTL-RK

T/K

PR-WS-MUNIFAC

δp(%)

Δy1

Δy2

δp(%)

253.15

-1.26

-0.0097

0.0069

-0.30

-0.0232

0.0172

253.15

0.17

-0.0047

0.0376

0.17

-0.0133

0.0228

253.15

-0.11

0.0104

0.0507

-0.11

0.0090

0.0346

253.15

-0.08

0.0071

0.0534

-0.17

0.0099

0.0285

253.15

-0.28

0.0044

0.0589

-0.39

0.0102

0.0333

253.15

-0.16

0.0009

0.0661

-0.38

0.0109

0.0316

253.15

-0.09

-0.0015

0.0616

-0.42

0.0109

0.0394

253.15

0.07

-0.0033

0.0586

-0.49

0.0144

0.0369

263.15

1.24

-0.0067

-0.0145

0.79

-0.0172

0.0127

263.15

0.36

0.0027

-0.0181

0.39

-0.0210

-0.0147

263.15

0.26

0.0066

0.0194

0.25

-0.0099

0.0218

263.15

0.35

0.0074

0.0236

0.36

-0.0081

0.0247

263.15

0.21

0.0081

0.0234

0.24

-0.0058

0.0227

263.15

0.21

0.0084

0.0245

0.25

-0.0045

0.0228

263.15

0.21

0.0095

0.0170

0.25

-0.0016

0.0137

263.15

0.50

0.0032

0.0190

0.42

-0.0059

0.0168

273.15

-0.61

0.0116

-0.0116

-0.67

-0.0102

0.0101

273.15

-0.32

0.0028

-0.0256

-0.33

-0.0077

-0.0137

273.15

-0.11

0.0100

-0.0227

-0.21

0.0051

-0.0125

273.15

-0.02

0.0130

-0.0123

-0.19

0.0100

-0.0033

273.15

0.02

0.0155

-0.0108

-0.22

0.0147

-0.0026

273.15

0.00

0.0131

-0.0113

0.06

0.0034

-0.0004

273.15

0.01

0.0125

-0.0106

0.18

-0.0008

0.0013

273.15

0.02

0.0118

-0.0061

0.35

-0.0070

0.0071

AARD/AAD

0.28

0.0077

0.0277

0.32

0.0098

0.0185

a AARD:

average absolute relative deviation and AARD(δ𝑝) =

[|

100 𝑁 (𝑝exp ― 𝑝cal) ∑ 𝑁 1 𝑝exp

Δy1

Δy2

| ]%

𝑁|𝑦exp ―𝑦cal| 𝑁

AAD: average absolute deviation and AAD( △ y) = ∑1 δp(%)=100*(pexp-pcal)/pexp, △y1=y1, exp-y1, cal

Fig. 2 compares experimental values at different temperatures using the two types of correlation models. The AARD of pressure is 0.28% for NRTL-RK model, which is slightly better than that for PR-WS-MUNIFAC model, which is 0.32%. The AAD of vapor phase mass fraction are 0.0077 and 0.0277 for NRTL-RK model, 0.0098 and 0.0185 for PR-WS-MUNIFAC model, respectively. The results show that both models can well express the VLE properties of R1234yf + R170 + R14 system. The accuracy of PR-WS-MUNIFAC model is better than that of NRTL-RK model. When 10 / 20


Page 11 of 20

the mass fraction of R14 is relatively small (around 0.1), there is an obvious increase in the deviations of NRTL-RK model at 273.15K. The main reason is that the calculation accuracy of the activity coefficient model decreases gradually at high temperature and pressure region. y2,exp 1.5

0.5

1.0

0.2

0.4

0.6

NRTL-RK PR-WS-MUNIFAC 0.02

0.0

0.2 -0.02

0.3

0.4

0.2

0.6

-0.5 -1.0 250

0.1

NRTL-RK PR-WS-MUNIFAC

255

260

T/K

265

270

275

1.0

y2,cal

0.5

0.8

y1 y 2

0.4

y1,cal

p%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0

-0.05

0.05

0.1

(A)

0.2

0.3

y1,exp

0.4

0.8 1.0 0.5

(B)

Fig. 2. Deviation between the experimental data and the calculated results for R1234yf(1) + R170(2) + R14(3) system. (A) Deviations of pressure; (B) Deviations of vapor mass fraction

3. Thermodynamic modeling 3.1 Model verification The essential VLE data can be achieved directly using the experimental method, but conducting experiments often costs a large amount of work and money, and the measured data is hardly enough to meet the needs of refrigeration applications and research. Sometimes we need to predict the VLE behavior of mixtures without experimental data. At this point, we can obtain the VLE characteristics of mixtures for a wider range of temperatures, pressures, and component concentrations by theoretical models. It is well known that the phase diagram can provide important and effective information for the thermodynamic analysis of refrigeration systems. Thus, we predicted the isobaric VLE behavior of R1234yf + R170 + R14 ternary system at pressures ranging from 0.1 MPa to 2 MPa using the PR-WS-MUNIFAC model which has prediction ability. In order to further verify the prediction accuracy and the reliability of PR-WS-MUNIFAC model, experimental data of R1234yf + R14 binary system from the literature were used for model verification. The experimental data are taken from Reference [40], and the calculated results are listed in Table 7. Fig. 3 shows the relationship between calculated results and experimental data of R14 + R234yf. Reference [40] did not include experimental data with the mass fraction from 0 to 1 of pure R14 and R1234yf due to the measured temperature went beyond the critical temperature or the solidification temperature. Accordingly, the bubble-point line and dew-point line did not form a closed loop. Due to the fact that R1234yf+R14 system is a strong-zeotropic mixture, there are 11 / 20



Page 12 of 20

three large deviations of pressure (3.76%, 4.08% and 4.30%), but they still meet the requirement of engineering applications (within 5%). The AARD of pressure and AAD of mass fraction are 1.38% and 0.0023, respectively. The calculation model also has a great prediction accuracy in low temperature range. The group contribution method of MUNIFAC (Dortmund) is mainly employed to calculate the fugacity of liquid phase, and the fugacity of vapor phase also depends on the EoS. It is difficult to calculate macromolecular compounds using the EoS, which leads to the larger deviation of vapor phase mass fraction. Therefore, the prediction accuracy and the applicability of the model could be improved using the EoS with a higher accuracy and by analyzing the parameters of MUNIFAC (Dortmund) group contribution method thoroughly and carefully. Table. 7 VLE data for the R14(1) + R1234yf(2) system at 153-273 K with combined standard uncertainties u(X) of the experimental values and deviations between experimental values and PR-WS-MUNIFAC calculations (X = {T; p; x1; y1}). Experimental data T/K

PR-WS-MUNIFAC model

pexp/kPa

x1,exp

y1,exp

u(T)/K

u(p)/kPa

u(x1)

u(y1)

pcal/kPa

y1,cal

δp(%)

△y1

153.24

20.80

0.0469

0.9945

0.11

0.19

0.0297

0.0057

21.09

0.9945

-1.39

0.0000

153.25

44.46

0.1015

0.9987

0.11

0.15

0.0173

0.0013

43.84

0.9974

1.39

0.0013

153.24

66.76

0.1669

0.9992

0.11

0.15

0.0337

0.0009

66.89

0.9984

-0.19

0.0008

153.24

96.86

0.2751

0.9988

0.11

0.14

0.0103

0.0012

97.26

0.9989

-0.41

-0.0001

153.25

120.88

0.4051

0.9992

0.11

0.17

0.0110

0.0008

121.05

0.9992

-0.14

0.0000

153.25

139.08

0.5708

0.9994

0.11

0.17

0.0065

0.0006

139.15

0.9994

-0.05

0.0000

153.27

157.37

0.8508

0.9996

0.11

0.17

0.0057

0.0005

157.40

0.9996

-0.02

0.0000

153.23

171.92

1.0000

1.0000

0.11

0.17

-

-

176.20

1.0000

-2.49

0.0000

193.26

5.46

0.0000

0.0000

0.11

0.15

-

-

5.60

0.0000

-2.56

0.0000

193.25

29.52

0.0135

0.7968

0.11

0.15

0.0135

0.0298

30.12

0.7980

-2.03

-0.0012

193.25

55.97

0.0237

0.8978

0.11

0.15

0.0167

0.0145

55.20

0.8879

1.38

0.0099

193.25

81.99

0.0337

0.9314

0.11

0.14

0.0120

0.0090

79.84

0.9314

2.62

0.0000

193.27

343.72

0.1574

0.9834

0.11

0.17

0.0057

0.0021

334.91

0.9827

2.56

0.0007

193.33

492.54

0.2437

0.9885

0.11

0.20

0.0049

0.0015

486.53

0.9910

1.22

-0.0025

193.34

773.80

0.4719

0.9929

0.11

0.20

0.0030

0.0015

765.23

0.9929

1.11

0.0000

193.33

938.28

0.6815

0.9947

0.11

0.21

0.0206

0.0015

932.80

0.9948

0.58

-0.0001

193.43

1205.31

1.0000

1.0000

0.11

0.23

-

-

1214.03

1.0000

-0.72

0.0000

233.04

62.24

0.0000

0.0000

0.11

0.14

-

-

62.44

0.0000

-0.32

0.0000

233.18

164.21

0.0188

0.6048

0.11

0.17

0.0102

0.0181

165.23

0.6105

-0.62

-0.0057

233.20

483.87

0.0747

0.8616

0.11

0.18

0.0037

0.0017

465.69

0.8596

3.76

0.0020

233.20

815.00

0.1368

0.9143

0.11

0.20

0.0030

0.0016

799.74

0.9118

1.87

0.0025

233.21

1203.91

0.2140

0.9383

0.11

0.23

0.0036

0.0015

1184.69

0.9362

1.60

0.0021

233.23

1465.04

0.2711

0.9472

0.11

0.25

0.0027

0.0015

1439.53

0.9462

1.74

0.0010

233.25

1795.83

0.3471

0.9544

0.11

0.28

0.0043

0.0015

1765.77

0.9538

1.67

0.0006

272.69

310.80

0.0000

0.0000

0.11

0.17

-

-

310.30

0.0000

0.16

0.0000

272.78

311.18

0.0000

0.0000

0.11

0.15

-

-

310.95

0.0000

0.07

0.0000

272.81

399.98

0.0154

0.1953

0.11

0.15

0.0154

0.0011

416.28

0.2160

-4.08

-0.0207

12 / 20


Page 13 of 20

272.70

665.67

0.0377

0.4983

0.11

0.26

0.0033

0.0023

658.56

0.5087

1.07

-0.0104

272.71

862.15

0.0575

0.5969

0.11

0.65

0.0034

0.0095

852.70

0.6001

1.10

-0.0032

272.72

1171.59

0.0894

0.6947

0.11

0.25

0.0024

0.0021

1121.25

0.6869

4.30

0.0078

272.75

1566.35

0.1316

0.7597

0.11

0.30

0.0024

0.0019

1523.73

0.7551

2.72

0.0046

273.03

2497.85

0.2413

0.8246

0.11

0.39

0.0156

0.0011

2485.72

0.8264

0.49

-0.0018

272.84

3509.27

0.3614

0.8530

0.11

0.42

0.0140

0.0009

3489.96

0.8532

0.55

-0.0002

272.89

4500.73

0.4920

0.8586

0.11

0.46

0.0145

0.0009

4490.13

0.8589

0.24

-0.0003

AARD/AAD

-

-

-

-

-

-

-

-

-

1.39

0.0023

0.0 5000

5000

3000 2000

0.6

0.4

x1

0.6

0.8

0.2 0.4 0.6

2000

0

1.0

1.0 0.0

3%

-3%

3000

1000

0.2

0.8

△y δp(%)

-0.01

1000 0 0.0

0.4

4000

pcal/kPa

p /kPa

4000

0.2

y1,exp

y1,cal

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1000

2000

3000

0.01

4000

0.8 1.0 5000

pexp/kPa

(A)

(B)

Fig. 3. (A) Pressure-composition relationship of calculated results and experimental data diagrams for the R14(1) + R1234yf(2) system. (Black:T=153.2 K; Blue:T=193.2 K; Red:T=233.2 K; Violet:T=273.2 K); (B) Deviation between calculated results and experimental data diagrams for the R14(1) + R1234yf(2) system.

Comparison of the calculated results and the experimental data demonstrates a high consistency between the two based on the above study on the VLE properties for the binary mixture of R1234yf + R14 and the ternary mixture of R1234yf + R170+ R14, thereby the high prediction accuracy of the PR-WS-MUNIFAC model was proved. It fully indicates that the model can satisfactorily predict the VLE of binary and ternary mixtures. On this basis, the isobaric VLE properties of the strong-zeotropic mixture of R1234yf + R170 + R14 were calculated at pressures varying from 0.1 MPa to 2 MPa using the PR-WS-MUNIFAC model. 3.2 Prediction The images from top to bottom in Fig. 4 are the three-dimensional phase equilibrium diagrams of R1234yf + R170 + R14 ternary system at 0.1 MPa, 0.2 MPa, 0.5 MPa respectively, and the isothermal ternary diagrams at the temperature of 183.15 K. The three-dimensional phase equilibrium diagrams of system at 1 MPa, 1.5 MPa, 2.2 MPa, and the isothermal ternary diagrams at temperature of the 233.15 K are shown in Fig. 5. The upper surface in the three-dimensional phase equilibrium diagram is the dew-point surface, and the part above it is the vapor phase region. The lower surface is the bubble-point surface, and the part under it is the liquid phase region. The part between the dew-point surface and the bubble-point surface is the vapor - liquid 13 / 20



phase region (indicated as “L+V”). The relationship between the compositions, the temperature, the pressure and the bubble-dew point of the mixture is manifested directly in the figure. The wine colored lines in the ternary diagrams represent the dew-point lines, which are the intersect-lines of the dew-point surface and the isothermal surface (183.15 K and 233.15 K). Also, the olive colored lines stand for the bubble-point lines. The part on the left-hand side of the dew-point line is the vapor phase region, the part on the right-hand side of the bubble-point line is the liquid phase region, and the part between the bubble-point line and the dew-point line is the vapor - liquid phase region. R1234yf, R170, and R14 are strong-zeotropic with each other so that the vapor-liquid phase region is very large, indicating the mixtures have a large sliding temperature. The phenomenon of temperature gliding of the ternary system is the most conspicuous with the mass fraction of the mixture around 0.35/0.1/0.55, and the highest sliding temperature reaches 73.4K. Based on the comparison of Fig. 4 and Fig. 5, it can be found that the dew-point and bubble-point temperatures rise with an increase of the mass fraction of R1234yf. The difference between normal boiling temperatures of the two components is between 40 K and 80 K in a three-stage auto cascade refrigeration system. We are able to make an approximate determination for many practical engineering applications via the analysis of three-dimensional phase equilibrium diagrams of the R1234yf + R170 + R14 system. The proposed VLE properties have crucial referential significance in designing and improving refrigeration devices, choosing suitable operating temperature and pressure range, enabling optimal separation of mixtures and components ratio of mixtures. However, few literatures report about the experimental data of R1234yf + R170 + R14 could be found. It is strongly suggested that the results in this paper should be verified by experiments before applying to practical engineering applications. Therefore, it is necessary to investigate the VLE of R1234yf + R170 + R14 using experimental methods, and further research on the system will provide more accurate VLE data.

14 / 20


Page 14 of 20

Page 15 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 4. Three-dimensional phase equilibrium diagrams of R1234yf + R170 + R14 ternary system at 0.1 MPa, 0.2 MPa, 0.5 MPa, and isothermal ternary diagrams at the temperature of 183.15 K.

15 / 20



Fig. 5. Three-dimensional phase equilibrium diagrams of R1234yf (1)+ R170 (2) + R14 (3) ternary system at 1 MPa, 1.5 MPa, 2 MPa, and isothermal ternary diagrams at the temperature of 233.15 K.

4. Conclusion The isothermal VLE data for the strong-zeotropic mixture of R1234yf + R170 + R14 were measured using a circulation type apparatus at temperatures of 253.15 K, 263.15 K, and 273.15 K. Two theoretical models, the NRTL-RK model and PR-WS-MUNIFAC model, were used to correlate the experimental data. The AARD of pressure and the AAD of vapor phase mass fraction are 0.28%, 0.0077, and 0.0277 for the NRTL-RK model, and 0.32%, 0.0098, and 0.0185 for the PR-WS-MUNIFAC model, respectively. The calculated results show a good agreement with the measured values. Based on the UNIFAC (Dortmund) method, the new group volume and area parameters (Rk & Qk) and the six binary interaction parameters (Amn, Bmn, Cmn, Anm, Bnm and Cnm) of C2H2F, CF4, CF3 and CH3 were obtained by fitting the experimental data, which expands the application of group contribution method in fluorinated refrigerants. The isobaric VLE behavior of R1234yf + R170 + R14 system was presented using the PR-WS-MUNIFAC model, and corresponding three-dimensional phase equilibrium diagrams were constructed at pressures of 0.1 MPa, 0.2 MPa, 0.5 MPa, 1 MPa, 1.5 MPa, and 2 MPa for the first time. It was found that the phenomenon of temperature glide of the system was the most obvious with the mass fraction near 0.35/0.1/0.55, and the maximum sliding temperature reached 73.4 K. The dew-point and bubble-point temperatures rose with an increase of the mass fraction of R1234yf. The calculated results have certain significance in the design and optimization for the three-stage ARC system. The prediction accuracy of the prediction model can be further increased by using the EoS with multi parameters and improved activity coefficient model.

Acknowledgments This work was financially supported by Scientific research and innovation project of Shanghai education Commission (14ZZ133) and Shanghai alliance program project (LM2014191).

References [1] Rui S. J. Experimental study on three stage cascade refrigeration system with two bypass. Ph.D. Thesis, Shanghai: University of Shanghai for Science and Technology, 2014. [2] Ruhemann M. The separation of gases (2nd edition). London: Oxford University Press,1949. [3] Kleemenko A. P. One-flow cascade cycle. Proceedings of 10th International Congress of Refrigeration, Copenhagen, Denmark, 1959. [4] Fuderer A. Compression Process for refrigeration: US, 3203194[P]. 1965-08-31. [5] Little W. A. Sapozhnikov I. Low cost cryocoolers for cryoelectronics. Cryocooler. 1997, 9, 16 / 20


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Experimental Measurements and Thermodynamic Modeling of VLE for

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