Prediction of ternary azeotropic refrigerants with a simple method

Accepted Manuscript Prediction of ternary azeotropic refrigerants with a simple method Yanxing Zhao, Maoqiong Gong, Xueqiang Dong, Haiyang Zhang, Hao Guo, Jianfeng Wu PII:

S0378-3812(16)30235-7

DOI:

10.1016/j.fluid.2016.05.010

Reference:

FLUID 11095

To appear in:

Fluid Phase Equilibria

Received Date: 15 December 2015 Revised Date:

19 April 2016

Accepted Date: 2 May 2016

Please cite this article as: Y. Zhao, M. Gong, X. Dong, H. Zhang, H. Guo, J. Wu, Prediction of ternary azeotropic refrigerants with a simple method, Fluid Phase Equilibria (2016), doi: 10.1016/ j.fluid.2016.05.010. 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 Prediction of Ternary Azeotropic Refrigerants with a Simple Method Yanxing

Zhaoa,b,

Maoqiong

Gonga,*,

([email protected]),

Xueqiang

Donga,*

([email protected]), Haiyang Zhanga,b, Hao Guoa, Jianfeng Wua a

Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese

b

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Academy of Sciences, P. O. Box 2711, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100039, China

* Corresponding authors. el. /fax: +86 10 82543728 (M. Gong), tel. /fax: +86 10 82543736 (X.

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Dong)

ACCEPTED MANUSCRIPT Abstract Refrigeration systems with azeotropic mixtures can achieve lower energy consumption, higher refrigeration capacity and coefficient of performance than both individual fluids and zeotropic refrigerants. In this paper, a simple method for predicting homogenous ternary

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azeotropic refrigerants was presented. The Peng-Robinson equation of state combined the Van der Waals mixing rule was proved successfully to represent the vapor + liquid equilibrium behavior of binary system and was employed to describe the ternary mixture phase equilibrium property. One hundred and seventy-one ternary systems were tested and eight

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azeotropes with six saddle-point azeotropes and two maximum-point azeotropes were found. The Antoine equation was used to correlate the azeotropic pressures and the temperatures,

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which showed the similar behavior to pure fluids and revealed the reliability of the calculated value. It can be concluded that to form ternary azeotropes in refrigerant mixtures at least two subsystems are azeotropic and if all subsystems are azeotropic, the ternary system is more likely to form ternary azeotrope.

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Keywords

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Ternary azeotropic; Refrigerant; Prediction; Saddle point; Maximum point

ACCEPTED MANUSCRIPT Nomenclature Abbreviations The average absolute deviation

AARD

The average absolute relative deviation

AZ

azeotropic

c 1, c 2

PR EoS parameter

EoS

equation of state

HC

hydrocarbon

HFC

fluorohydrocarbon

MIX

mixture

BAS

binary azeotropic subsystems

PR

Peng-Robinson

R170

ethane

R290

propane

R600

n-butane

R600a

isobutane

R23

triflurormethane

R32

difluoromethane

R116

hexafluoroethane

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pentafluoroethane 1, 1, 2, 2-tetrafluoroethane

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R134

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R125

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AAD

R134a

1, 1, 1, 2-tetrafluoroethane

R143a

1, 1, 1-trifluoroethane

R152a

1, 1-difluoroethane

R161

fluoroethane

RE170

methoxyethane

R227ea

1, 1, 1, 2, 3, 3, 3-heptafluoropropane

R236ea

1, 1, 1, 2, 3, 3-hexafluoropropane

R236fa

1, 1, 1, 3, 3, 3-hexafluoropropane

R245fa

1, 1, 1, 3, 3-pentafluoropropane

R1234yf

2, 3, 3, 3-tetrafluoroprop-1-ene

R1270

propylene

RC270

cyclopropane

R13I1

trifluoroiodomethane

R1216

1, 1, 2, 3, 3, 3-hexafluoro-1-propene

RK

Redlich-Kwong

TOTA

type of ternary azeotropy

VDW

Van der Waals

VLE

vapor liquid equilibrium

Z

zeotropic

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trans-1, 3, 3, 3-tetrafluoropropene

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R1234ze(E)

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Symbols

Antoine equation parameter

a

attractive parameter in the EoS

am

attractive parameter of the mixture

aij

cross parameter of an EoS

am'

the partial derivative of am with respect to xi

B

Antoine equation parameter

b

co-volume in the EoS

C

co-volume of the mixture

the partial derivative of bm with respect to xi

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bm'

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bm

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A

Antoine equation parameter

Kij

binary interaction parameter between components i and j

L

liquid phase

N

number of components

p

pressure, MPa

R

universal gas constant, J·mol-1·K-1

s

entropy, J·mol-1·K-1

T

temperature, K

ACCEPTED MANUSCRIPT x

liquid phase composition

y

vapor phase composition

Z

compressibility factor

Greek letters

µ

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chemical potential

Subscripts i, j

component index

m

mixture

vapor phase

L

liquid phase

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V

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Superscripts

ACCEPTED MANUSCRIPT 1. Introduction Since the halogenated refrigerants are restrictedly used in the vapor compression refrigeration system for its high ozone depleting potential, it is necessary to look for long-term alternatives to satisfy the objectives of international protocols. However, the single

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refrigerants including fluorohydrocarbons, hydrocarbons and other natural refrigerants have all kind of drawbacks such as inflammability (HCs), incompatibility with the mineral lubricating oils (HFCs), toxicity (ammonia), etc. These limitations shifted the focus on the mixed refrigerant alternatives, which are obtained as a mixture of two or more components.

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Both zeotropic and azeotropic mixtures have been investigated. Due to the mass transfer resistance in nucleate boiling and high temperature glide, heat transfer coefficients of

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zeotropic mixtures are normally lower than the single refrigerants and the azeotropic mixtures[1]. Further, refrigeration systems with azeotropic mixtures can achieve lower energy consumption, higher refrigeration capacity and coefficient of performance than that with both individual and zeotropic refrigerants[2-7]. Besides, zeotropic refrigerant mixtures have a fractionation problem caused by a leak in the system, while azeotropic mixtures can

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overcome this difficulty[8].

The phase equilibrium properties of the mixed refrigerants can be decided by experimental or theoretical methods. Accurate phase equilibrium data can be obtained

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experimentally but it is too time consuming, especially for azeotropes. To solve this problem, many prediction methods have been developed. Wang and Whiting [9] designed a algorithm

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for azeotropic prediction by treating vapor liquid equilibrium for the azeotropic point of a mixture as similar to that for a pure compound. Their algorithm was useful for rapid detection of azeotropes and did not search in regions where vapor and liquid compositions are not identical, with which the problem of spurious roots was avoided. Harding [10] described a homotopy method which, together with an arc length continuation, gave an efficient and robust scheme for computing azeotropes in multicomponent mixtures. Artemenko and Mazur[11] developed an approach for the prediction of azeotrope formation in a mixture that does not require vapor liquid equilibrium calculations. The method employs neural networks and global phase diagram methodologies to correlate azeotropic data for binary mixtures based only on critical properties and acentric factor of the individual components in

ACCEPTED MANUSCRIPT refrigerant mixtures. Fedali et al.[12] predicted the azeotropic behavior of the mixtures using the mole fractions instead of pressure. Hu and Chen et al.[13] estimated the vapor–liquid equilibria properties of several HFC binary refrigerant mixtures with a corresponding equation. The equation only needed the vapor pressures, critical constants and dipole

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moments of pure components, without any adjustable parameters or interaction coefficients. Hou and Duan et al.[14] developed the group contribution model to describe the vapor-liquid equilibria of the refrigerant mixtures and a ternary system was accurately predicted. Barley et al.[15] studied the ternary mixture (R32+R125+R143a) with Wilson activity coefficient

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model combined RK equation of state and predicted a saddle point azeotrope based on the binary experimental data. Aslam and Sunol[16] proposed a method establishing the pressure

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dependency of azeotropic composition allowing prediction of bifurcation pressure where refrigerant azeotropes may appear or disappear, with which the ternary azeotropic system proposed by Barley et al was successfully predicted.

Most of those approaches are difficult to operate because of complicated mathematical computation, although they were proved successful to predict azeotropic behavior. In this

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paper, a simple method originally proposed by Dong et al.[17, 18] was extended to predict ternary systems. Based on the MATLAB procedure, one hundred and seventy-one interested ternary systems were investigated.

2.1. Azeotropy

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2. Method description

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In order to develop a method for finding all azeotropes of a mixture, it is essential to first determine the thermodynamic conditions for azeotropy. Homogeneous azeotropes occur in a boiling mixture of one liquid phase when the composition of the vapor phase is the same as the composition of the liquid phase. The thermodynamic condition was mentioned by Malesiński[19].

The Gibbs-Duhem relation gives

sdT − vdp + ∑ ni d µi = 0 .

(1)

i

The symbol s refers to the molar entropy, and v refers to the molar volume. The symbol µ refers to the chemical potential with the subscript i refers to the component i. For a ternary

ACCEPTED MANUSCRIPT system, the Gibbs-Duhem equation can be applied in the both vapor and liquid phases as

s V dT − v V dp + y1d µ1V + y2 d µ 2V + y3 d µ 3V = 0 ,

(2)

and

s L dT − v L dp + x1d µ1L + x2 d µ 2L + x3 d µ3L = 0 .

(3)

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At an equilibrium state, the chemical potentials of component i in vapor and liquid phases are equal, that is

s V dT − v V dp + y1d µ1 + y2 d µ 2 + y3 d µ 3 = 0 ,

(4)

s L dT − v L dp + x1d µ1 + x2 d µ 2 + x3 d µ 3 = 0 .

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and

(5)

∑x

i

= 1, ∑ yi = 1 ,

i

i

the following equation can be obtained

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Combine equation (4) with equation (5) and the normalization of the composition as (6)

( s V − s L ) dT − ( v V − v L ) dp + ( y1 − x1 )( d µ1 − d µ 3 ) + ( y2 − x2 )( d µ 2 − d µ 3 ) = 0 .

dp =

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At constant temperatures,

(7)

( y1 − x1 ) ( y − x2 ) ( d µ1 − d µ3 ) + V2 (d µ 2 − d µ3 ) , V L (v − v ) (v − v L )

(8)

then the necessary condition for ternary azeotropy was derived as (9)

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dp =0 .

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Because of the pressure continuation with composition of the liquid phase, equation (9) can be rewritten as

 ∂p    =0 . ∂ x  i T,x j

(10)

For a ternary system, the second order partial derivative compose the Hessen matrix, which gives as

D 2 p( x1 , x2 ) =

∂2 p ∂x12

∂2 p ∂x1 x2

∂2 p ∂x2 x1

∂2 p ∂x22

.

(11)

ACCEPTED MANUSCRIPT The pressure will have extreme values if the matrix norm det( D 2 p ( x1 , x2 )) > 0 , and if

∂2 p < 0,(i = 1, 2) ，the pressure has a maximum point, else the pressure has a minimum point; ∂xi2 if det( D 2 p ( x1 , x2 )) < 0 ， the pressure has a saddle point; if det( D 2 p ( x1 , x2 )) = 0 ， the

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stagnated pressure cannot be verified only by second order partial derivative. 2.2. PR+VDW model

Chen and Hu et al.[20] correlated thirty-nine binary mixtures consisting of HFCs and

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HCs using the PR equation of state with the Van der Waals mixing rule and showed that the VLE properties can be well described by the PR+VDW model. This is due to the weak

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polarity of HC/HFC refrigerants. In order to accelerate the calculation speed as well as to satisfy the high accuracy, the PR+VDW model was employed in this work. Ninety-four binary systems were recorrelated using PR+VDW model and the results were in good agreement with the experimental data, as shown in Table 1.

The PR EoS can be expressed as the liquid phase mole fraction x variate function at a

p=

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constant temperature

RT am − = f [ am ( x1 , x2 ,L , xi , xN ), bm ( x1 , x2 ,L , xi , xN ) ] , (12) v − bm (v + c1bm )(v + c2bm )

2) is derived as

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for PR EoS, c1 = 1 − 2 , c2 = 1 + 2 , then the partial derivative of p with respect to xi (i=1,

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∂p ∂f ∂am ∂f ∂bm , = + ∂xi ∂am ∂xi ∂bm ∂xi

(13)

where

∂f 1 , =− ∂ am (v + c1bm )(v + c2bm )

(14)

  ∂f RT am c12 c22 , = + −  2 2 2  ∂bm (v − bm ) v (c1 − c2 )  (v + c1bm ) (v + c2bm ) 

(15)

∂am = am' , ∂xi

(16)

ACCEPTED MANUSCRIPT ∂bm = bm' , ∂xi

(17)

where am , bm and the partial derivative of them depend on the mixing rules selected, for Van der Waals mixing rule, which can be expressed as

am = ∑∑ xi x j aii a jj (1 − Kij ) ,

(18)

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i

j

bm = ∑ xi bi ,

(19)

i

am' = 2∑ x j aij ,

(20)

bm' = bi .

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The second order derivative is derived as

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j

∂2 p ∂ ∂f ∂am ∂f ∂ 2 am ∂ ∂f ∂bm ∂f ∂ 2bm , = ( ) + + ( ) + ∂xi2 ∂xi ∂am ∂xi ∂am ∂xi2 ∂xi ∂bm ∂xi ∂bm ∂xi2 where

(21)

(22)

(23)

∂ 2 am = aii = 0 , ∂xi2

(24)

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∂ ∂f 1 ∂b ( )= c (v + c2bm ) + c2 (v + c1bm )] m , 2 2 [ 1 ∂xi ∂am ∂xi (v + c1bm ) (v + c2bm )

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∂ 2bm = 0, ∂xi2

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  ∂am   ∂bm ∂ ∂f RT ∂bm 1 c12 c22 am c13 c23 + − + +2 ( )=2 ,   −2  3 2 2 3 ∂xi ∂bm (v − bm ) ∂xi v (c1 − c2 )  (v + c1bm ) (v + c2bm )  ∂xi v (c1 − c2 )  (v + c1bm ) (v + c2bm )3  ∂xi

(25) (26)

∂2 p ∂ ∂p ∂ ∂f ∂am ∂f ∂ 2 am ∂ ∂f ∂bm ∂f ∂ 2bm , = ( )= ( ) + + ( ) + ∂xi x j ∂x j ∂xi ∂x j ∂am ∂x j ∂am ∂xi x j ∂x j ∂bm ∂xi ∂bm ∂xi x j

(27)

∂ 2 am = 2aij , ∂xi x j

(28)

∂ 2bm = 0. ∂xi x j

(29)

It is noteworthy that this method can employ other phase equilibrium models by replacing the partial derivative of the attractive and co-volume parameters of the mixtures.

3. Results and discussion

ACCEPTED MANUSCRIPT The R32 + R125 + R143a and R600a + R134 + R152a ternary system were predicted firstly, and the results were in satisfactorily agreement with reference (15) and were shown in Figures 1 and 2. One hundred and seventy-one ternary systems (presented in Table 2) were tested and eight of them were predicted as azeotropes. The azeotropic loci of each system,

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including the subsystems, were plotted in Figures 1 to 8. An approximate linear azeotropic loci with the temperatures was exhibited in the ternary phase diagram in a large scale temperature range, which is similar to the binary azeotropes.

3.1. Azeotropic pressure and temperature

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There is only one degree of freedom for an azeotropic state, in other words, all the azeotropes of a system fall on a curve [9]. This uniform-composition curve can be plotted on

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a pressure-temperature diagram regardless of the number of components, and the reduction of the p–T data combined in one set can estimate the reliability of the measured or calculated quantities [119, 120]. The Antoine equation was employed:

log( p / kPa) = A −

B . T + C − 273.15

(30)

In this work, the parameters of equation (30) for the eight ternary azeotropic systems

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were regressed by the calculated azeotropic pressure and temperature, and shown in Table 3. All of the ternary azeotropic points can be well represented by the Antoine equation, and the regressed parameters agreed with that of pure fluids, which indicates the reliability of the

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calculated values. Figure 9 gives the variation of the azeotropic pressure with temperature for the ternary systems and the corresponding single fluids. The pressures of pure compounds

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were taken from REFPROP 9.1[121]. It can be showed that the system does not have to be a maximum-point azeotropic mixture even if the azeotropic pressure is higher than any of the pressures of the single fluids.

3.2. The type of ternary azeotropes The vapor + liquid equilibrium of the interested ternary systems was calculated near the azeotropic point at 253.15 K, and plotted in Figure 10. The azeotropic behavior of these systems was confirmed again, and six saddle-point azeotropic mixtures and two maximum-point azeotropic mixtures were found. In MIX 1 to 6 ternary systems, two subsystems show positive deviations from ideality while the other subsystem shows negative

ACCEPTED MANUSCRIPT deviations (R125 + R143a, R134 + R152a and R134a + RE170). This makes the ternary mixtures of great possibility to form saddle-point azeotropes. Not surprisingly, the ternary azeotrope with all subsystems show positive deviations from ideality will well be maximum-point azeotropes.

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4. Conclusions A simple method for predicting homogenous ternary azeotropic was presented in this paper. The PR + VDW model was proved effectively to represent the binary system VLE behavior and was employed to describe the ternary mixture phase equilibrium properties. One

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hundred and seventy-one ternary systems were tested, and eight azeotropes with six saddle-point azeotropic mixtures and two maximum-point azeotropic mixtures were found.

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The Antoine equation was used to correlate the azeotropic pressures and the temperatures. The results showed the similar behavior to pure fluids and revealed the reliability of the calculated value. It can be concluded that to form ternary azeotropes in refrigerant mixtures at least two subsystems are azeotropic and if one of the subsystems shows negative deviations from ideality the ternary system is more likely to be saddle-point azeotrope. Besides, the

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ternary system is easier to form ternary azeotrope if all subsystems are azeotropic. The predicted azeotropic mixtures may provide a direction for search multi-component azeotropic refrigerants.

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Acknowledgement

This work is financially supported by the National Natural Sciences Foundation of China

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under the contract number of 51376188 and 51322605.

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TE D

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AC C

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55

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ACCEPTED MANUSCRIPT [103]

X. Dong, M. Gong, Y. Zhang, et al, Vapor− Liquid Equilibria of the Fluoroethane +

1, 1, 1, 2-Tetrafluoroethane System at Various Temperatures from (253.15 to 292.92) K, J. Chem. Eng. Data [104]

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S. Koo, J. Chang, H. Kim, et al, Vapor–Liquid Equilibrium Measurements for

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J. Y. Park, J. S. Lim, B. G. Lee, et al, Phase Equilibria of CFC Alternative

Refrigerant Mixtures: 1, 1, 1, 2, 3, 3, 3-Heptafluoropropane + Difluoromethane,+ 1, 1, 1,

[106]

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2-Tetrafluoroethane, and+ 1, 1-Difluoroethane, Int. J. Thermophys. 22 (2001) 901-917.

M. Kleiber, Vapor-liquid equilibria of binary refrigerant mixtures containing

[107]

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propylene or R134a, Fluid Phase Equilib. 92 (1994) 149-194.

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1, 2 tetrafluoroethane + dimethyl ether system at temperatures from 293.18 to 358.15 K and pressures up to about 3MPa, Fluid Phase Equilib. 230 (2005) 184-191. [109]

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the Binary Mixture Trifluoroethane + Ethyl Fluoride over the Temperature Range (253.15 to 303.15) K, J. Chem. Eng. Data 55 (2010) 2990-2993. S. Bobbo, R. Camporese, C. Zilio, Isothermal Vapor-Liquid Equilibria for the

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[110]

Binary System 1, 1, 1-Trifluoroethane + 1, 1, 1, 3, 3, 3-Hexafluoropropane at 283.11, 298.16, and 313.21 K, J. Chem. Eng. Data 45 (2000) 276-279. [111]

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Z. Yang, M. Gong, H. Guo, et al, Phase equilibrium for the binary mixture of {1,

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M. Gong, K. Cheng, X. Dong, et a, Measurements of isothermal (vapor+ liquid)

phase equilibrium for {trifluoroiodomethane [R13I1]+ 1, 1-difluoroethane [R152a]} from

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Q. Wang, Y. J. Xu, Z. J. Gao, et al, Isothermal vapor–liquid equilibrium data for the

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[115]

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H. Guo, M. Gong, X. Dong, et al, (Vapour+ liquid) equilibrium data for the binary

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system of {trifluoroiodomethane + trans-1, 3, 3, 3-tetrafluoropropene} at various temperatures from (258.150 to 298.150) K, J. Chem. Thermodyn. 47 (2012) 397-401. S. Bobbo, R. Camporese, R. Stryjek, (Vapour+ liquid) equilibrium measurements

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and correlations of the refrigerant mixture {dimethyl ether (RE170)+ 1, 1, 1, 3, 3, 3-hexafluoropropane (R236fa)} at the temperatures (303.68 and 323.75) K, J. Chem. Thermodyn. 30 (1998) 1041-1046. [118]

Y. Zhao, M. Gong, X. Dong, et al, The investigation on the vapor+ liquid

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equilibrium for the ternary mixture isobutene (R600a)+ 1, 1-difluoroethane (R152a)+ 1, 1, 2, 2-tetrafluoroethane (R134) at temperatures from 253.150 to 273.150 K, Fluid Phase Equilib. 408 (2016) 72-78.

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[119]

measurements and correlation for {1, 1, 2, 2-tetrafluoroethane (R134)+ isobutane (R600a)}

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system, J. Chem. Thermodyn. 78 (2014) 182-188. [120]

X. Dong, Y. Zhao, M. Gong, et al, (Vapour+ liquid+ liquid) equilibrium

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E. W. Lemmon, M. L. Huber, M. O. McLinden, NIST Standard Reference Database

23. Reference Fluid Thermodynamic and Transport Properties (REFPROP), 2012.

ACCEPTED MANUSCRIPT Table 1. Results of the recorrelated data with PR + VDW model for binary systems. AARDpa AADyb Kij

Com.1

Com.2

type

[21]

R170

R23

azeotropic 0.9526

0.0077

0.1874

[22]

R170

R116

azeotropic 0.6298

0.0051

0.1308

[23, 24]

R290

R600

zeotropic

0.4466

0.0178

0.0039

[24, 25]

R290

R600a

zeotropic

0.4090

0.0094

-2.50E-04

[26]

R290

R23

azeotropic 1.9843

0.0114

0.1994

[27-30]

R290

R32

azeotropic 1.7100

0.0104

0.1893

[31]

R290

R116

azeotropic 1.1735

0.0114

0.1583

[28, 32-35]

R290

R125

azeotropic 0.7182

0.0053

0.1490

[36]

R290

R134

azeotropic 0.6329

0.0099

0.1775

[37,38]

R290

R134a

azeotropic 0.7935

0.0051

0.1648

[38-40]

R290

R143a

azeotropic 0.4814

0.0036

0.1245

[41, 42]

R290

R152a

azeotropic 1.0890

0.0114

0.1346

[43-45]

R290

R227ea

azeotropic 0.9623

0.0057

0.1353

[46, 47]

R290

R236fa

azeotropic 0.8178

0.0046

0.1525

[47]

R290

R236ea

azeotropic 0.7117

0.0030

0.1546

[48]

R290

R1234ze[E] azeotropic 0.2969

0.0027

0.1089

[49]

R290

R13I1

zeotropic

0.3461

0.0022

0.0238

R600

R23

zeotropic

2.5950

0.0071

0.2046

R600

R32

azeotropic 4.5555

0.0120

0.1993

SC

M AN U

TE D

AC C

[50, 51]

EP

[26]

RI PT

Conference

[51, 52]

R600

R125

azeotropic 1.1403

0.0066

0.1584

[51, 53]

R600

R134a

azeotropic 1.3468

0.0117

0.1676

[54, 55]

R600

R143a

zeotropic

1.2326

0.0118

0.1318

[56, 57]

R600

R152a

azeotropic 0.9483

0.0064

0.1300

[58]

R600

R227ea

azeotropic 0.6188

0.0138

0.1400

[59]

R600a

R23

zeotropic

2.2983

0.0146

0.2171

[60]

R600a

R32

azeotropic 2.8500

0.0071

0.1910

[61]

R600a

R125

azeotropic 3.1621

N/A

0.1466

ACCEPTED MANUSCRIPT R600a

R134

azeotropic 0.8964

0.0076

0.1641

[60, 62]

R600a

R134a

azeotropic 1.2891

0.0076

0.1556

[59]

R600a

R143a

azeotropic 1.0830

0.0138

0.1364

[60]

R600a

R152a

azeotropic 0.7273

0.0154

0.1168

[62]

R600a

R236fa

azeotropic 0.2313

0.0029

0.1482

[63, 64]

R600a

R245fa

azeotropic 0.6620

0.0054

0.1570

[65]

R600a

R1234ze[E] azeotropic 0.3891

0.0020

0.1058

[66]

R600a

R1234yf

azeotropic 0.5722

0.0034

0.0948

[67]

R600a

RE170

azeotropic 0.5428

0.0031

0.0401

[68]

R600a

R13I1

zeotropic

0.2487

0.0045

0.0248

[69]

R23

R32

zeotropic

0.3616

0.0035

-0.0130

[70]

R23

R116

azeotropic 1.1521

0.0143

0.1106

[69]

R23

R125

zeotropic

0.5000

0.0044

0.0032

[71, 72]

R23

R134a

zeotropic

1.1200

0.0064

0.0081

[73]

R23

R143a

zeotropic

0.8600

0.0051

-0.0022

[73]

R23

R152a

zeotropic

1.2500

0.0066

-0.0190

[72]

R23

R227ea

zeotropic

1.8304

0.0083

0.0221

[74-77]

R32

R125

zeotropic

0.8700

0.0055

0.0033

[78-80]

R32

R134a

zeotropic

0.7515

0.0043

-0.0022

R32

R143a

azeotropic 0.4517

0.0046

0.0141

R32

R152a

zeotropic

1.6100

0.0073

0.0166

SC

M AN U

TE D

AC C

[81]

EP

[81, 82]

RI PT

[36]

[83]

R32

R161

zeotropic

0.9383

0.0129

0.0128

[84]

R32

R227ea

zeotropic

0.7868

0.0057

0.0058

[85]

R32

R236fa

zeotropic

0.5039

0.0039

-0.0042

[86]

R32

R236ea

zeotropic

0.6021

0.0033

-0.0153

[87, 88]

R32

R1234yf

zeotropic

0.5695

0.0102

0.0391

[89-91]

R32

RE170

zeotropic

0.7981

0.0046

-0.0077

[92]

R116

R134a

zeotropic

1.8869

0.0121

0.1157

[93]

R116

R143a

zeotropic

1.0935

N/A

0.1014

R125

R134a

zeotropic

[15]

R125

R143a

[69]

R125

[94]

0.0017

azeotropic 0.7966

N/A

-0.0101

R152a

zeotropic

0.5577

0.0063

-0.0205

R125

R161

zeotropic

1.4348

0.0141

-0.0023

[32]

R125

R227ea

zeotropic

1.1612

0.0054

0.0021

[85]

R125

R236fa

zeotropic

0.1603

0.0013

0.0020

[86]

R125

R236ea

zeotropic

0.2218

0.0016

0.0064

[88]

R125

R1234yf

zeotropic

1.2011

0.009

0.0031

[95]

R125

R1270

azeotropic 0.4692

0.0042

0.1005

[96]

R125

RC270

azeotropic 0.6583

0.0031

0.1034

[35]

R125

RE170

zeotropic

0.0191

-0.1186

[97]

R134

R152a

azeotropic 0.1600

0.0014

-0.0198

[98]

R134

R161

zeotropic

0.7032

0.0039

-0.0373

[99]

R134

R1234ze[E] azeotropic 0.1502

0.0027

0.0106

[100]

R134

R13I1

azeotropic 0.6022

0.0061

0.0965

[101, 102]

R134a

R143a

zeotropic

0.6559

0.0049

-0.0036

[103]

R134a

R161

zeotropic

0.4766

0.0044

-0.0116

[104, 105]

R134a

R227ea

zeotropic

0.6137

0.0059

0.0085

[62]

R134a

R236fa

zeotropic

0.1076

0.0016

-0.0020

[63]

R134a

R245fa

zeotropic

0.2263

0.0018

0.0013

R134a

R1234yf

azeotropic 0.3586

0.0024

0.0185

1.6244

M AN U

TE D

AC C

[88]

0.4300

SC

[78]

RI PT

0.0044

EP

ACCEPTED MANUSCRIPT

[106, 107]

R134a

R1270

azeotropic 0.5759

0.0042

0.1203

[96]

R134a

RC270

azeotropic 0.5759

0.0042

0.1203

[91, 108]

R134a

RE170

azeotropic 0.5662

0.0044

-0.0364

[101]

R143a

R152a

zeotropic

0.5867

0.0075

0.0096

[109]

R143a

R161

zeotropic

0.5363

0.0131

-0.0046

[110]

R143a

R236fa

zeotropic

0.3031

0.0030

-0.0130

[111]

R143a

RE170

zeotropic

2.6641

0.0112

-0.0062

[105]

R152a

R227ea

zeotropic

0.6946

0.0060

-0.0111

ACCEPTED MANUSCRIPT R152a

R1234ze[E] zeotropic

0.1753

0.0014

0.0026

[106]

R152a

R1270

zeotropic

0.8373

0.0044

0.0854

[113]

R152a

R13I1

azeotropic 0.3526

0.0026

0.0527

[114]

R161

R227ea

zeotropic

2.8922

0.0148

-0.0663

[115]

R1216

R1270

azeotropic 1.3860

0.0053

0.0858

[116]

R13I1

R1234ze[E] azeotropic 0.1655

0.0024

0.0510

[43]

RE170

R227ea

azeotropic 2.1361

0.0153

-0.1492

[47, 117]

RE170

R236fa

zeotropic

1.1827

0.0069

-0.0922

[47]

RE170

R236ea

zeotropic

0.9236

0.0078

-0.1176

SC

RI PT

[112]

N/A The vapor phase compositions are not available in the original paper.

b

AARD p =

AAD y =

1 N

N

1 N

∑ abs( p

exp

− pcal ) / pexp × 100

i

N

∑ abs( y

exp

− y cal )

i

M AN U

a

Com.3

R23

R116

R600

R23/R32/R125/R134a/R143a/R152a/R227ea

R600a

R23/R32/R125/R134/R134a/R143a/R152a/R236fa/R1234ze(E)/R13I1

R23

R116/R125/R134a/R143a/R152a/R227ea

AC C

R170

Com.2

EP

Com.1

TE D

Table 2. The 171 ternary systems tested in present work.

R290

R32

R125/R134a/R143a/R152a/R227ea/R236fa/R236ea

R116

R134a/R143a

R125

R134a/R143a/R152a/R227ea/R236fa/R236ea

R134

R152a/R1234ze(E)/R13I1

R134a

R143a/R227ea/R236fa

R143a

R152a/R236fa

R152a

R227ea/R1234ze(E)/R13I1

R13I1

R1234ze(E)

ACCEPTED MANUSCRIPT R23

R32/R125/R134a/R143a/R152a

R32

R134a/R143a/R152a/R236fa/R1234yf/RE170

R125

R134a/R143a/R152a/R236fa/R1234yf/RE170

R134

R152a/R1234ze(E)/R13I1

R134a

R143a/R236fa/R245fa/R1234yf/RE170

R143a

R152a/R236fa/RE170

R23

R125/R134a/R143a/R152a/R227ea

R32

R125/R134a/R143a/R152a/R227ea

R125

R134a/R143a/R152a/R227ea

R134a

R143a/R227ea

R152a

R143a/R227ea

R32

R125/R134a/R143a/R152a/R227ea

R116

R134a/R143a

R125

R134a/R143a/R152a/R227ea

R134a

R143a/R227ea

R152a

R143a/ R227ea

R227ea

RE170

R125

R134a/R143a/R152a/R161/R227ea/R236fa/R236ea/R1234yf/RE170

R134a

R143a/R161/R227ea/R236fa/R1234yf/RE170

SC

EP

R143a

R152a/R161/R236fa/RE170

R227ea

R152a/R161

AC C

R32

TE D

R23

M AN U

R600

R116

RI PT

R600a

R236ea

RE170

R134a

R143a

R134a

R143a/R161/R227ea/R236fa/R1234yf/R1270/RC270/RE170

R143a

R152a/R161/R236fa/RE170

R152a

R227ea/R1270

RE170

R227ea/R236fa/R236ea

R152a

R1234ze(E)/R13I1

R13I1

R1234ze(E)

R125

R134

R143a

R161/R236fa/RE170

R161

R227ea

RE170

R236fa/R227ea

R143a

R236fa

RE170

R152a

R13I1

R1234ze(E)

R134a

RI PT

ACCEPTED MANUSCRIPT

Table 3. The azeotropic type and the parameters of Antoine equation of the predicted ternary azeotropic refrigerants. Com.1

Com.2

Com.3

BAS

TOTA

MIX1

R32

R125

R143a

3

saddle

MIX2

R600a

R134

R152a

3

saddle

MIX3

R134a

RE170

R600a

3

saddle

MIX4

R152a

R134

R1234ze(E)

2

MIX5

R13I1

R134

R152a

MIX6

RE170

R236fa

MIX7

R170

R23

MIX8

R13I1

R600a

A

B

C

4.754

1056.917

275.149

4.356

1020.966

263.299

4.380

1039.206

262.479

saddle

4.692

1193.517

275.863

3

saddle

4.357

1023.473

262.408

R600a

2

saddle

4.278

1038.311

262.026

R116

3

max

4.350

771.052

274.735

2

max

4.251

986.954

257.219

TE D

M AN U

SC

No.

EP

R1234ze(E)

0.00 1.00

0.25

0.50

25 R1

R1 43

a

AC C

0.75

0.50

0.75

0.25 T

1.00 0.00

0.25

0.50

0.75

0.00 1.00

R32

Figure 1. The azeotropic loci of R32 + R125+ R143a ternary system. (○): reference [13] at 221 K; (☆): reference [14] at 219.945 K; (●): this work at temperatures range from 223.15 K to 283.15 K.

ACCEPTED MANUSCRIPT 0.00 1.00

0.75 34 R1

0.50

0.50

0.75

0.25 T

1.00 0.00

0.25

0.50

0.00 1.00

0.75

R600a

RI PT

R1 52 a

0.25

Figure 2. The azeotropic loci of R600a + R134 + R152a ternary system. (○): reference [118]

SC

at temperatures range from 253.15 K to 273.15 K; (●): this work at temperatures range from

0.00 1.00

T

0.75 0 17 RE

R6 00 a

0.25

0.50

0.50

0.75

1.00 0.00

0.25

0.50 R134a

TE D

0.25

M AN U

243.15 K to 323.15 K.

0.00 1.00

0.75

Figure 3. The azeotropic loci of R134a + RE170 + R600a ternary system at temperatures

EP

range from 233.15 K to 323.15 K.

R1

23 4ze (E )

0.25

0.50

T

0.75 34 R1

AC C

0.00 1.00

0.50

0.75

1.00 0.00

0.25

0.50

0.25

0.75

0.00 1.00

R152a

Figure 4. The azeotropic loci of R152a + R134 + R1234ze(E) ternary system at temperatures range from 253.15 K to 343.15 K.

ACCEPTED MANUSCRIPT 0.00 1.00

0.75 34 R1

0.50

0.50

0.75

0.25 T

1.00 0.00

0.25

0.50

0.00 1.00

0.75

R13I1

RI PT

R1 52 a

0.25

Figure 5. The azeotropic loci of R13I1 + R134 + R152a ternary system at temperatures range

SC

from 253.15 K to 323.15 K.

0.50

0.50

T

0.25

0.25

0.50 RE170

0.00 1.00

0.75

TE D

0.75

1.00 0.00

0.75 fa 36 R2

R6 00 a

0.25

M AN U

0.00 1.00

Figure 6. The azeotropic loci of RE170 + R236fa + R600a ternary system at temperatures range from 243.15 K to 333.15 K.

EP

0.00 1.00

AC C

0.75

3 R2

R1 16

0.25

0.50

0.50 T

0.75

1.00 0.00

0.25

0.50

0.25

0.75

0.00 1.00

R170

Figure 7. The azeotropic loci of R170 + R23 + R116 ternary system at temperatures range from 173.15 K to 253.15 K.

ACCEPTED MANUSCRIPT 0.00 1.00

0.25

R6

23 4ze (E )

0.75

0.75

0.25

RI PT

R1

0.50

00a

0.50

T 1.00 0.00

0.25

0.50

0.00 1.00

0.75

R13I1

Figure 8. The azeotropic loci of R13I1 + R600a + R1234ze(E) ternary system at temperatures

M AN U

R32 R125 R143a MIX1

1.0

SC

range from 233.15 K to 313.15 K.

R600a R134 R152a MIX2

1.2 1.0

p/MPa

p/MPa

0.8

0.5

0.6 0.4

0.0

240

TE D

0.2

260

0.0

280

260

280

(a) R32 + R125 + R143a system

R134a RE170 R600a MIX3

1.2

2.0

1.2 p/MPa

0.8

p/MPa

R152a R134 R1234ze(E) MIX4

1.6

AC C

1.0

320

(b) R600a + R134 + R152a system

EP

1.4

300

T/K

T/K

0.6

0.8

0.4

0.4

0.2 0.0

240

260

280

300

T/K

(c) R134a + RE170 + R600a system

320

0.0

260

280

300

320

340

T/K

(d) R152a + R134 + R1234ze(E) system

ACCEPTED MANUSCRIPT 1.2 1.0

1.2 1.0 p/MPa

0.8 p/MPa

RE170 R236fa R600a MIX6

1.4

R13I1 R134 R152a MIX5

0.6

0.8 0.6

0.4

0.0

0.2 240

260

280

300

0.0

320

260

T/K

320

0.8 0.7

p/MPa

0.8

R13I1 R600a R1234ze(E) MIX8

M AN U

0.6

1.2

SC

0.9

p/MPa

300

(f) RE170 + R236fa + R600a system

R170 R23 R116 MIX7

1.6

280

T/K

(e) R13I1 + R134 + R152a system

2.0

RI PT

0.4 0.2

0.5 0.4 0.3 0.2

0.4

0.1

0.0

0.0

180

200

220

240

TE D

T/K

(g) R170 + R23 + R116 system

240

260

280

300

T/K

(h) R13I1 + R600a + R1234ze(E) system

Figure 9. The azeotropic pressure of the ternary systems and the saturated vapor pressures of

AC C

EP

the single fluids.

(a) R32 + R125 + R143a system

(b) R600a + R134 + R152a system

(d) R152a + R134 + R1234ze(E) system

TE D

M AN U

SC

(c) R134a + RE170 + R600a system

RI PT

ACCEPTED MANUSCRIPT

(f) RE170 + R236fa + R600a system

AC C

EP

(e) R13I1 + R134 + R152a system

(g) R170 + R23 + R116 system

(h) R13I1 + R600a + R1234ze(E) system

Figure 10. The vapor + liquid phase equilibrium of the azeotropic ternary systems near the azeotropic point at 253.15 K.

ACCEPTED MANUSCRIPT ► A simple method for predicting homogenous ternary azeotropic refrigerants was presented. ► 171 systems were tested and eight azeotropes with six saddle-point azeotropes and two maximum-point azeotropes were found. Seven of them are proposed for the first time on the public publications.

RI PT

► It can be concluded that to form ternary azeotropes in refrigerant mixtures at least two subsystems are azeotropic and if all subsystems are azeotropic, the ternary system is more likely to

AC C

EP

TE D

M AN U

SC

form ternary azeotrope.