Research Article Prediction the Vapor-Liquid Equilibria of ...downloads.hindawi.com/archive/2013/930484.pdfPrediction the Vapor-Liquid Equilibria of CO 2-Containing Binary Refrigerant

Hindawi Publishing CorporationISRN Chemical EngineeringVolume 2013 Article ID 930484 11 pageshttpdxdoiorg1011552013930484

Research ArticlePrediction the Vapor-Liquid Equilibria of CO2-ContainingBinary Refrigerant Mixtures Using Artificial Neural Networks

Ahmad Azari1 Saeid Atashrouz2 and Hamed Mirshekar2

1 Chemical Engineering Department Gas and Petrochemical Engineering Faculty Persian Gulf University Bushehr 7516913817 Iran2Department of Petrochemical Engineering Amirkabir University of Technology (Tehran Polytechnic)Mahshahr Campus PO Box 415 Mahshahr Iran

Correspondence should be addressed to Saeid Atashrouz satashrouzgmailcom

Received 9 May 2013 Accepted 18 July 2013

Academic Editors J A A Gonzalez K Okumura and J E Ten Elshof

Copyright copy 2013 Ahmad Azari et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Artificial neural network (ANN) technique has been applied for estimation of vapor-liquid equilibria (VLE) for eight binaryrefrigerant systemsThe refrigerants include difluoromethane (R32) propane (R290) 11-difluoroethane (R152a) hexafluoroethane(R116) decafluorobutane (R610) 22-dichloro-111-trifluoroethane (R123) 1-chloro-1222-tetrafluoroethane (R124) and 1112-tetrafluoroethane (R134a) The related experimental data of open literature have been used to construct the model Furthermoresome new experimental data (not applied in ANN training) have been used to examine the reliability of the model The resultsconfirm that there is a reasonable conformity between the predicted values and the experimental data Additionally the abilityof the ANN model is examined by comparison with the conventional thermodynamic models Moreover the presented model iscapable of predicting the azeotropic condition

1 Introduction

For nearly 60 years chlorofluorocarbons (CFCs) have beenwidely used as solvents foam blowing agents aerosols andespecially refrigerants due to their stability nontoxicity non-flammability good thermodynamic properties and so onHowever they also have a harmful effect on the earthrsquos pro-tective ozone layer So they have been regulated interna-tionally by Montreal Protocol since 1987 Much effort hasbeen made to find the suitable replacement for CFCs InitialCFC alternatives included some hydrochlorofluorocarbons(HCFCs) but they will be also phased out internationallybecause their ozone depletion potentials (ODPs) and globalwarming potentials (GWPs) are significant though less thanthose of CFCs Hydrofluorocarbons (HFCs) synthetic refrig-erants which have zero ODPs were proposed as promisingreplacements for CFCs and HCFCs [1] The deadline forHCFCs which have low ozone depletion potential is 2030Also there is no report for another type of refrigerants suchas light hydrocarbons or perfluorocarbons as harmful refrig-erants In order to develop new refrigerants for replacementwith harmful refrigerants the mixtures of carbon dioxide

and clean refrigerants have been studied in the number ofresearches [2ndash8] that was reviewed in the present study

R134a is an environmentally acceptable refrigerant whichhas replaced the ozone-depleting CFC-12 (dichlorodifluo-romethane) in a wide range of applications especially in auto-motive air conditioning and domestic refrigeration Anothernatural refrigerant carbon dioxide (R744) has received newworldwide interest as a working fluid in automotive air con-ditioning To expand the range of possible replacement fluidwith desired properties phase behavior of R134a-R744 shouldbe studied This clean mixture can be formulated so as toobtain a similar vapor pressure to that of the original refriger-ant to suppress flammability or toxicity of one of the compo-nents that otherwise has excellent thermophysical properties[5]

R152a is used for refrigeration and as an aerosol propel-lant It is most commonly found in electronic cleaning prod-ucts and many consumer aerosol products that must meetstringent volatile organic compounds (VOC) requirements[8] Such as the mixture of R134a-R744 prediction of vapor-liquid equilibria (VLE) for the mixture of R152a-R744 is

2 ISRN Chemical Engineering

necessary for the development of new refrigerant mixtureswith minimal environmental impact

R116 and R744 (CO2) are two very interesting fluids

for industry Their common peculiarity is their low criticaltemperatures The critical temperature of CO

2is 30420K

while that of R116 is 29304K Moreover this system presentsazeotropic behavior indicating strong interaction betweenthe two species in particular a strong repulsive interactionAzeotropic and even quasiazeotropic behaviors are of utmostinterest not only to refrigeration industry but also to allindustries involved in supercritical fluid extraction Utiliza-tion of fluids with low critical points that are also safe forthe environment is generally highly preferred An azeotropicmixture of R116 and R744 could be very interesting for indus-try of refrigeration as the azeotrope position is at high R744composition [6] So it is useful to study theVLE of this type ofmixtures

The mixture of CO2-R610 (perfluorocarbons) is another

type of refrigerants In addition to the role of a refrigerant thismixture has another application This application is ability ofperfluorocarbons in dissolving refinery gases such as CO

2

and it is necessary to prediction of phase behavior for thismixture [7]

R123 and R124 are two new clean fire extinguishing agentsin comparison to other agents For the new total floodingclean agents that were being developed to replace certainHalon fire extinguishing agents the discharge time requiredto achieve 95 of the minimum design concentration shallnot exceed 10 s and the expellant gas is needed for its lack ofvapor pressure Generally nitrogen is used as an expellant gasbecause it does not need to be liquefied at high pressure butCO2has some merits to nitrogen such as price storage area

and supplementary extinguishing effect When CO2is used

as an expellant gas the knowledge of the phase behavior ofthe mixtures CO

2and fire extinguishing agents is essential

to design fire extinguishing processes and equipmentsMore-over phase equilibrium data are needed to calculate the fric-tion loss along with the working plans (from the storage tankto the discharge orifice) [2]

Hydrocarbons like propane butane and isobutane haveexcellent thermophysical properties and are compatible withmaterials normally used in refrigeration plants such as cop-per However the flammability of hydrocarbons limits theirapplication to specific systems Carbon dioxide has advan-tages of being nontoxic inflammable and high in volumetriccapacity of refrigeration However the refrigeration systemusing carbon dioxide is operated under a very high pressureHydrocarbons would reduce the problems occurring due tohigh pressure of carbon dioxide while carbon dioxide wouldreduce the flammability of hydrocarbons The mixtures ofcarbon dioxide and propane (R290) are proposed as promis-ing alternative refrigerantsTheVLEdata are essential to eval-uate the performance of the refrigeration or the heat pumpcycles using these refrigerant mixtures and to determine theoptimum composition for the best performance [3]

Information about the phase behavior of refrigerantmixtures can be obtained from direct measurement of phaseequilibrium data or by the use of equation of state andoractivity coefficient based on thermodynamic models Direct

measurement of precise experimental data is often difficultand expensive while the second method which includes alarge number of equations of states and excess Gibbs freeenergy models is tedious and involves a certain amount ofempiricism to determine mixture constants through fittingexperimental data and using various arbitrary mixing rulesmaking it difficult to select the appropriatemodel for a partic-ular case [9]Thus due to the difficulties of experimentalmea-surements and also their time-consuming and costly natureit is desirable to develop predictive methods for estimatingthe phase behavior of these kinds of systems

Artificial intelligence (AI) methods are advanced tech-niques with extreme flexibility ANN as a branch of AI is aflexible modeling method and has shown high performancesin many cases ANN is an empirical tool which can modelany kind of data sets even in the cases where relations arecomplex [10] Recently ANN has found extensive applicationin the field of thermodynamics and transport properties suchas the estimation of VLE viscosity density vapor pressurecompressibility factor and thermal conductivity [11ndash33]Thismethod provides nonlinear functionmapping of a set of inputvariables into the corresponding network output ANNs canbe applied for accurate VLE determination of polar and non-polar components [9 34ndash51] Basic theory and application tochemical problems of ANN with the back-propagation algo-rithm have been previously discussed in [48]

In this research a comprehensive model based onmultilayer feed forward back-propagation artificial neuralnetwork (FFBP-ANN) was developed to estimate VLE datafor eight refrigerant mixtures containing CO

2 The refriger-

ants include difluoromethane (R32) propane (R290) 11-difluoroethane (R152a) hexafluoroethane (R116) decafluor-obutane (R610) 22-dichloro-111-trifluoroethane (R123) 1-chloro-1222-tetrafluoroethane (R124) and 1112-tetraflu-oroethane (R134a) The developed model was trained andevaluated by using the experimental data for eight binaryrefrigerant mixtures reported by [2ndash8] and pure componentproperties for eight refrigerants reported by [2ndash8 52 53] Apart of experimental data was used to train the networks andthe rest was used to evaluate the performance of the networksFinally for the model validation the prediction of the ANNmodel (CO

2mole fraction in the vapor phase) was compared

with the thermodynamic model from different literatures [46 8] and also with the experimental data Furthermore theability of the ANN model for the prediction of VLE data forbinary mixture in azeotropic condition was examined

2 Artificial Neural Network

Neural networks consist of arrays of simple active units linkedby weighted connections ANN consists of multiple layers ofneurons arranged in such a way that each neuron in one layeris connected with each neuron in the next layer The networkused in this study is a multilayer feed forward neural networkwith a learning scheme of the back propagation (BP) of errorsand the Levenberg-Marquardt algorithm for the adjustmentof the connecting weights Neurons are the fundamentalprocessing element of an ANN which are arranged in layersthat make up the global architecture [48]

ISRN Chemical Engineering 3

The main advantage of using ANNs to predict the VLEdata lies in their ability to learn the relationship between thecomplex VLE data for different binary mixtures The ANNinput is the first layer in the network throughwhich the infor-mation is supplied The number of neurons in the input layerdepends on the network input parameters Hidden layersconnect the input and output layers Hidden layers enrich thenetwork for learning the relation between input and outputdata In theory ANN with only one hidden layer and enoughneurons in the hidden layer has the ability to learn anyrelation between the input and output data Transfer functionis the mathematic function that determines the relationbetween neuron output and the network In other wordstransfer function indicates the degree of nonlinearity in thenetwork Practically in the feed forward BP-ANN modelsome limited functions are used as transfer functions [54]Normally the transfer functions of all neurons in the hiddenlayers are similar Also for all neurons in the output layer thesame transfer function is used For the prediction of phenom-ena logistic transfer function is the most conventional trans-fer function that is used in the hidden layers because it is veryeasy to differentiate the sigmoid transfer function used in theBP algorithm [55 56] The sigmoid transfer function is asfollows

119874119875119895(net) = 1

1 + 119890minusnet (1a)

net =119899minus1

sum

119894=0

119908119894119909119894 (1b)

where ldquo119899rdquo in (1b) is the number of inputs to the neuronldquo119908119894rdquo is the weight coefficient corresponding to the input ldquo119909

119894rdquo

and ldquo119874119875119895rdquo is the output corresponding to the ldquo119895rdquo neuron For

completion of this section we illustrate the learning BP algo-rithm

21 ANN Training Algorithm The back-propagation algo-rithm is one of the least mean square methods which is nor-mally used in engineering In a multilayer perceptron eachneuron of a layer is linked to all neurons of the previous layerFigure 1 shows a perceptron with a hidden layer

Each layer output acts as the input to the next neurons Inorder to train multilayer feed forward neural network back-propagation law is used In the first stage all weights andbiases are selected according to small random numbers Inthe second stage input vector 119883

119875= 1199090 1199091 119909

119899minus1and the

target exit 119879119875= 1199050 1199051 119905

119898minus1are given to the network

where the subscripts 119899 and 119898 are the numbers of input andoutput vectors respectively In the third stage the followingquantitative values are calculated and transferred to thesubsequent layer until it eventually reaches the exit layer [57]

119874119875119895= 119891[

119899minus1

sum

119894=0

119908119894119909119894] (2)

The fourth stage begins from the exit layer during which theweight coefficients are corrected

119908119894119895(119905 + 1) = 119908

119894119895(119905) + 120578120575

119875119895119874119875119895 (3)

Input layer

Hidden layer

Output layer

Figure 1 Perceptron structure with a hidden layer

where ldquo119908119894119895(119905)rdquo stands for theweight coefficients fromnode ldquo119894rdquo

to node ldquo119895rdquo in time ldquo119905rdquo ldquo120578rdquo is the rate coefficient ldquo120575119875119895rdquo refers to

the corresponding error of input pattern ldquo119875rdquo to the node ldquo119895rdquoand ldquo119874

119875119895rdquo is the output corresponding to the ldquo119895rdquo neuron ldquo120575

119875119895rdquo

is calculated by the following equations for exit layer and hid-den layer respectively

120575119875119895= 119874119875119895(1 minus 119874

119875119895) (119905119875119895minus 119874119875119895)

120575119875119895= 119874119875119895(1 minus 119874

119875119895)sum

119896

120575119875119896119908119895119896

(4)

Here the sum acts for ldquokrdquo nodes on the subsequent layer afterthe node ldquo119895rdquo [57] In the learning process there are severalparameters that have influence on the ANN training Theseparameters are the number of iterations number of hiddenlayers and the number of hidden neurons To find the bestarchitecture of the model the best set of the aforementionedparameters based on minimizing the network output errorshould be chosen

3 Experimental Data

The first step in an ANNmodeling is compiling the databaseto train the network and to evaluate network ability for gen-eralization In the present study the experimental VLE datafor eight binary mixtures reported by [2ndash8 52 53] have beenused for training and validation of theANNmodelThe rangeof the intensive state variables (temperature (T) pressure (P)and CO

2mole fraction in the vapor (Y

1) and liquid (X

1)

phases for each binary) and the number of data points (N) forthe ANN training were listed in Table 1 Also the pure com-ponent properties (normal boiling point (T

119887) critical temper-

ature (T119888) critical pressure (P

119888) and acentric factor 120596) of the

eight refrigerants used in this work were collected from dif-ferent literatures [2ndash8 52 53] and the collection was listed inTable 2


Table 1 Experimental data range used for development of the ANN model

Mixture 119879 (K) 119875 (MPa) 1198831

1198841

119873 Reference

R744 (1)-R32 (2)

28312 1106ndash4508 0-1 0-1

56 [4]

29311 1472ndash5738 0-1 0-130313 1911ndash7208 0-1 0-130515 2032ndash6905 0ndash0928 0ndash09053133 2486ndash7318 0ndash0822 0ndash078832334 3157ndash7464 0ndash0656 0ndash062533333 3954ndash7191 0ndash0465 0ndash043334323 4879ndash6589 0ndash0228 0ndash0217

R744 (1)-R152a (2)

25844 0144ndash2294 0-1 0-1

67 [8]

27825 0311ndash3977 0-1 0-12988 0604ndash6502 0-1 0-130837 0812ndash7200 0ndash0959 0ndash093553233 1185ndash7648 0ndash08522 0ndash08083432 1891ndash741 0ndash06710 0ndash0594125315 0244ndash1964 0-1 0-1

R744 (1)-R290 (2)

26315 0344ndash2641 0-1 0-1

124 [3]

27315 0473ndash3478 0-1 0-128315 0636ndash4497 0-1 0-129315 0836ndash5723 0-1 0-130315 1079ndash7206 0-1 0-131315 1369ndash3650 0ndash0584 0ndash028632315 1714ndash6281 0ndash0636 0ndash0559

R744 (1)-R116 (2)

25329 2043-1051 00505ndash1 00284ndash1

75 [6]

27327 3576-1843 00385ndash1 00281ndash128324 4677-2382 00685ndash1 00592ndash129122 5550-2906 00244ndash1 00212ndash129422 5923ndash6155 00145ndash01152 00132ndash0115429672 6621-6448 00096ndash00717 00090ndash00705

R744 (1)-R610 (2)

26315 01832ndash23997 05736ndash09830 00300ndash08900

83 [7]

283 04589ndash39901 06253ndash09755 00636ndash0988030312 06544ndash66165 04800ndash09695 00593ndash0947330819 05021ndash68628 02418ndash09395 00218ndash091193232 09625ndash67376 03719ndash08323 00565ndash077373382 13940ndash63710 03448ndash07049 00713ndash0663335298 17097ndash55339 02492ndash05614 00638ndash05145

R744 (1)-R123 (2)31315 0873ndash7189 08258ndash09788 01408ndash09209

18 [2]32315 2094ndash8074 08975ndash09611 03073ndash0901533315 1083ndash7904 07352ndash09426 01219ndash08146



R744 (1)-R134a (2)


29 [5]

27275 0288ndash2033 0ndash0916 0ndash060629295 0566ndash2048 0ndash0755 0ndash03543296 1991ndash7369 02412ndash07640 00821ndash074503391 2305ndash7098 01781ndash06612 00666ndash06266354 3250ndash6043 01733ndash04560 00826ndash03920


Tansig

OutputPurelin

Input7lowast1

10lowast7

+

10lowast1

1

n1

10lowast1

a1

10lowast1

1lowast10

+

1lowast1

1

n2

1lowast1

a2

1lowast1

wih

who

bo

bh

Figure 2 The feed forward back-propagation network used in the study

Table 2 Pure component properties used in this work

Component 119879119887(K) 119879

119888(K) 119875

119888(MPa) 120596

R32 22150 35155 5831 0271R290 23107 36982 4242 0149R116 19490 29304 3042 0245R152a 24815 38635 4499 0256R610 27120 38584 2289 0374R134a 24693 37425 4064 0326R123 30076 45683 3662 0282R124 26104 39543 3624 02881

4 Development of the ANN Model

An ANN model was considered for the prediction of CO2

mole fraction in the vapor phase In order to describe thephase behavior of the eight R744 (1)-refrigerants (2) binariesby one ANN model a total of eight variables have beenselected in this work four intensive state variables (equi-librium temperature equilibrium pressure and equilibriumCO2mole fractions in the liquid and vapor phases) and four

pure component properties of the refrigerant (normal boilingpoint critical temperature critical pressure and acentricfactor) The choice of the input and output variables wasbased on the phase rule practical considerations (bubble ordew point computation) and the need to describe the eightbinaries by only one ANNmodel Therefore the equilibriumtemperature and pressure and the R744 mole fraction in theliquid phase together with the pure component properties ofthe refrigerant have been selected as input variables and theR744 mole fraction in the vapor phase as output variable

As shown in Figure 2 a multilayer feed forward neuralnetwork structure with a hidden layer was used in this studyANN modeling for the VLE of eight CO

2(1)-refrigerant

(2) binaries was carried out in MATLAB ver 790 programInitially the program starts with the default FFBP-ANN type(newff MATLAB function) the Levenberg-Marquardt BPtraining algorithm (trainlmMATLAB training function) andone hidden layer Once the topology is specified the startingand ending number(s) of neurons in the hidden layer(s) haveto be specified The number of neurons in a hidden layer is

then modified by adding neurons one at a time The proce-dure begins with the logarithmic sigmoid activation functionthen the hyperbolic tangent sigmoid activation function forthe hidden layers and the linear activation function for theoutput layer The results of different runs of the programshow that the bayesian regularization back propagation(BRBP) using Levenberg-Marquardt optimization modelstrain more successfully than models using attenuated train-ing Table 3 shows the structure of the optimizedANNmodelThe weight matrices and bias vectors of the optimized ANNmodel were listed in Table 4 where 119908ih is the input-hiddenlayer connection weight matrix (10 rows and 7 columns)119908hois the hidden layer-output connection weight matrix (1 rowsand 10 columns) 119887h is the hidden neurons bias column vector(10 rows) and 119887o is the output neurons bias column vector (1row and 1 column)

5 Results and Discussion

Using the random selection method 60 of all data wereassigned to the training set 20 of all data were assigned tothe validation set and the rest of the data were used as the testset In the training phase the number of neurons in the hid-den layer was important for the network optimization How-ever decision on the number of hidden layer neurons is diffi-cult because it depends on the specific problem being solvedusing ANN With too few neurons the network may not bepowerful enough for a given learning taskWith a large num-ber of neurons the ANN may memorize the input trainingdata very well so that the network tends to perform poorly onnew test data and is called ldquooverfittingrdquo To prevent the over-fitting issue we should evaluate average absolute deviation(AAD) for train set validation set and test set and they mustbe in the same order of magnitude Absolute deviation (AD)and AAD were calculated from the following relations

AD = 10038161003816100381610038161003816119884Exp1minus 119884

Calc1

10038161003816100381610038161003816

AAD = 1119899

119899

sum

119894=1

10038161003816100381610038161003816119884Exp1119894minus 119884

Calc1119894

10038161003816100381610038161003816

(5)


Table 3 Architecture of the optimized ANN

Network type Training algorithmInput layer Hidden layer Output layerNo ofneurons

No ofneurons Activation function No of

neurons Activation function

FFBP-ANN(newff MATLABfunction)

BRBP usingLevenberg-Marquardtoptimization (trainbrMATLAB function)

7 10Logarithmicsigmoid (logsig

MATLAB function)1 Linear (purelin

MATLAB function)

Table 4 Weights and Bias for the optimized ANNmodel

Input-hidden layer connections Hidden layer-output connectionsWeights Bias Weights Bias

119908ih1198951

119908ih1198952

119908ih1198953

119908ih1198954

119908ih1198955

119908ih1198956

119908ih1198957

119887h119895

119908ho1119895

119887o

minus06056 minus09887 minus07923 minus06751 minus04102 minus15259 minus30024 minus02282 08706

minus46281

minus0134 01773 07049 minus08568 09083 minus00939 03924 02957 minus2764301781 minus00542 minus01658 3473 minus43534 07277 minus09445 minus06808 46201minus15473 minus05041 minus06426 minus06926 2273 03274 06674 21058 06233minus01471 minus169 minus46153 minus37246 40597 minus1133 04642 minus78154 minus48468minus05177 minus08163 minus07417 00359 minus0395 minus10492 minus2267 minus03021 minus12227minus03352 02159 03334 minus31563 34222 minus07444 0625 02541 5043900599 minus10839 24576 minus2211 10885 minus00151 minus08366 28284 minus0692304007 minus04818 10288 47919 minus30998 10456 01107 11395 12612minus01696 00643 10752 minus04978 15478 01578 minus00002 15111 17854

where ldquo119899rdquo is the number of data points and ldquoExprdquo andldquoCalcrdquo superscripts stand for the experimental and calculatedCO2mole fraction respectively In the training process

different hidden layers and neurons were tried and finally theoptimized ANN obtained for this study was a network witha hidden layer containing 10 neurons In an optimized ANNthe AAD values for the train validation and test data sets arein the sameorder ofmagnitude In this research theAADval-ues for the train validation and test sets of datawere obtained2851119890 minus 3 2384119890 minus 3 and 2731119890 minus 3 respectively and thenetwork performance (MSE) was achieved 13412119890 minus 5 Theability of themodel for the prediction of CO

2mole fraction in

the vapor phase is shown in Figure 3 As shown good agree-ment for the prediction of ANNmodel and the experimentaldata are observed So the developed ANNmodel can be usedfor the prediction of the new set of VLE data for the eightaforementioned binary mixtures

To validate the ANN model prediction the ability of theANN model for the prediction of CO

2mole fraction in the

vapor phase of CO2(1) R152a (2) binary mixture at 3083 K

was investigated Then the results were compared with Mad-ani model [8] The results were shown in Figure 4 and ADvalues for the ANN and Madani models were reported inTable 5 As shown the maximum of the AD values for theANN and Madani models were obtained 00124 and 00149respectively Also AAD for the ANN and Madani modelswere calculated 0002969 and 0002477 respectively ThusAAD results for the ANN and Madani models are very closetogether

0 01 02 03 04 05 06 07 08 09 10

01

02

03

04

05

06

07

08

09

1

Y1

ANN = Y1exp

Experimental data Y1

AN

N m

odel

Y1

Train data R = 099989

Test data R = 099993

Validation data R = 099994

Figure 3 Comparison of the experimental and ANN modelprediction for the mole fraction of CO

2in eight binary mixtures

In addition Figure 5 compares the ANN results withthermodynamic model from the literature [6] and with theexperimental results for R116-R744 binarymixtureThefigureshows good agreement of the results with the experimentaldata Also Figure 5 shows that this comprehensive ANN


Table 5 Absolute deviation (AD) result for the ANN and Madani models for R744 (1)-R152a (2) mixture

1198831

1198841

1198841

1198841

AD ADexperiment [8] Madani model [8] ANN model Madani model [8] ANN model

0 0 0 0 0 000722 03157 03306 03281 00149 0012401419 0493 04969 04898 00039 0003202148 06097 06079 06041 00019 000560295 06937 06897 06939 00041 0000204194 07783 07756 07826 00028 0004305197 08239 08239 08273 0 0003406201 08621 08609 08621 00012 007176 08922 08921 08937 00001 0001507994 09179 09174 09198 00006 0001908755 09387 09391 09405 00004 0001809152 09507 09525 09506 00018 0000109355 09594 096 09552 00005 00042

0 02 04 06 08 10

02

04

06

08

1

Experimental dataANN modelMadani model

X1

Y1

Y1 = X1

Figure 4 R744 mole fraction in vapor phase for binary systemof R744 (1)-R152a (2) at 3083 K (experimental data [8] MadaniModel [8] and ANNmodel this work)

model can predict the azeotropic condition Since the ther-modynamicmodels are used for an especially binarymixturewhile the developed ANN model is applicable for the eightaforementioned binary refrigerant mixtures so this makestheANNmodel an interesting predictive tool in respect to thethermodynamic models

Figures 6 7 8 and 9 show the 1198841-1198831curves for the

binary mixtures of R610 R32 R134a and R152a with CO2

They include a comparison between experimental data andANN results at different temperatures As shown the figuresshow excellent agreement between experimental data andthe prediction of the ANN model In addition the AAD ofthe ANN model with the experimental data for the eightaforementioned binary mixtures at different temperatures

0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Experimental dataANN modelValtz model

X1

Y1

Y1 = X1

Figure 5 R744 mole fraction in vapor phase for binary system ofR744 (1)-R116 (2) at 2533 K (experimental data [6] Valtz Model[6] and ANNmodel this work)

were reported in Table 6 These results also indicate thepredictability of the ANNmodel in the prediction of the CO

2

mole fraction in the vapor phase for the binary refrigerantmixtures

6 Conclusions

In this work a comprehensive FFBP-ANN model wasdeveloped for the prediction of VLE data The model wasconstructed for eight conventional CO

2-containing binary

refrigerant mixtures at different temperatures ranges Binaryrefrigerants are CO

2-R32 mixture (28315ndash34323 K) CO

2-

R290 (25315ndash32315 K) CO2-R152a (258ndash343K) CO

2-R116

(25329ndash29672K) CO2-R610 (26315ndash35298K) CO

2-R123

(31315ndash33315 K) CO2-R124 (31315ndash33315 K) and CO

2-

R134a mixture (25295ndash354K) The optimized ANN modelwas obtained with a hidden layer and 10 neurons in thehidden layer The input layer contains three intensive state


Table 6 AAD values for the ANNmodel in prediction of CO2 molefraction in different binary mixtures

Mixture 119879 (K) AAD

R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031

variables (equilibrium temperature equilibrium pressureand equilibrium CO

2mole fraction in the liquid and vapour

0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Exp 263kANN 263kExp 283 kANN 283 kExp 303kANN 303kExp 308k

ANN 308kExp 323kANN 323kExp 338kANN 338kExp 353kANN 353k

X1

Y1

Y1 = X1

Figure 6 1198841-1198831curve for the R744 (1)-R610 (2) binary mixture at

different temperatures (Exp [7] and ANN this work)

0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Exp 283 kANN 283 kExp 293kANN 293kExp 303kANN 303kExp 305kANN 305k

Exp 313kANN 313kExp 323kANN 323kExp 333kANN 333kExp 343kANN 343k

X1

Y1

Y1 = X1



phases) and four pure component properties of the refrig-erant (normal boiling point critical temperature criticalpressure and acentric factor)The output layer includes equi-librium CO

2mole fraction in the vapor phase In the ANN

training procedure the AAD for the sets of train validationand test data were obtained 2851119890minus3 2384119890minus3 and 2731119890minus3 respectively and the network performance (MSE) wasachieved 13412119890 minus 5 It was shown that excellent agreementbetween themodel predictions and the experimental datawas


0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Exp 253kANN 253kExp 272kANN 272kExp 293kANN 293k


X1

Y1

Y1 = X1

Figure 8 1198841-1198831curve for the R744 (1)-R134a (2) binary mixture at


0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



achieved Also the ability of the ANN model was examinedin comparison with the different thermodynamic models forCO2-R152a mixture at 3083 K CO

2-R32 at 343K and CO

2-

R116 binary mixture at 2533 K The AAD results show thatANN model results are very close to the thermodynamicmodels Also ANN model can predict azeotropic conditionfor the CO

2-R116 binarymixture Finally the advantage of the

ANN model is its applicability for the eight CO2-containing

binary mixtures while the thermodynamic models are usedfor an especially binary mixture

References

[1] J S Lim J M Jin and K-P Yoo ldquoVLEmeasurement for binarysystems of CO

2+ 1112-tetrafluoroethane (HFC-134a) at high

pressuresrdquoThe Journal of Supercritical Fluids vol 44 no 3 pp279ndash283 2008

[2] K Jeong J Im G Lee Y-J Lee and H Kim ldquoVapor-liquidequilibria of the carbon dioxide (CO

2) + 22-dichloro-111-

trifluoroethane (R123) system and carbon dioxide (CO2) +

1-chloro-1222-tetrafluoroethane (R124) systemrdquo Fluid PhaseEquilibria vol 251 no 1 pp 63ndash67 2007

[3] J H Kim andM S Kim ldquoVapor-liquid equilibria for the carbondioxide + propane system over a temperature range from 25315to 32315 Krdquo Fluid Phase Equilibria vol 238 no 1 pp 13ndash192005

[4] F Rivollet A Chapoy C Coquelet and D Richon ldquoVapor-liquid equilibrium data for the carbon dioxide (CO

2) + difluo-

romethane (R32) system at temperatures from 28312 to 34325K and pressures up to 746MPardquo Fluid Phase Equilibria vol 218no 1 pp 95ndash101 2004

[5] G Silva-Oliver and L A Galicia-Luna ldquoVapor-liquid equilibriafor carbon dioxide + 1112-tetrafluoroethane (R-134a) systemsat temperatures from 329 to 354 K and pressures upto 737MPardquoFluid Phase Equilibria vol 199 no 1-2 pp 213ndash222 2002

[6] A Valtz C Coquelet andD Richon ldquoVapor-liquid equilibriumdata for the hexafluoroethane + carbon dioxide system at tem-peratures from 253 to 297 K and pressures up to 65 MPardquo FluidPhase Equilibria vol 258 no 2 pp 179ndash185 2007

[7] A Valtz X Courtial E Johansson C Coquelet and D Ram-jugernath ldquoIsothermal vapor-liquid equilibrium data for thecarbon dioxide (R744) + decafluorobutane (R610) system attemperatures from263 to 353Krdquo Fluid Phase Equilibria vol 304no 1-2 pp 44ndash51 2011

[8] H Madani A Valtz C Coquelet A H Meniai and D Richonldquo(Vapor + liquid) equilibrium data for (carbon dioxide + 11-difluoroethane) system at temperatures from (258 to 343) K andpressures up to about 8 MPardquoThe Journal of Chemical Thermo-dynamics vol 40 no 10 pp 1490ndash1494 2008

[9] C Si-Moussa S Hanini R Derriche M Bouhedda and ABouzidi ldquoPrediction of high-pressure vapor liquid equilibriumof six binary systems carbon dioxide with six esters using anartificial neural network modelrdquo Brazilian Journal of ChemicalEngineering vol 25 no 1 pp 183ndash199 2008

[10] M N Safamirzaei H Modarress and M Mohsen-Nia ldquoMod-eling the hydrogen solubility in methanol ethanol 1-propanoland 1-butanolrdquo Fluid Phase Equilibria vol 289 no 1 pp 32ndash392010

[11] H Ghanadzadeh M Ganji and S Fallahi ldquoMathematicalmodel of liquid-liquid equilibrium for a ternary system usingthe GMDH-type neural network and genetic algorithmrdquoApplied Mathematical Modelling vol 36 no 9 pp 409ndash41052012

[12] V H Alvarez and M D A Saldana ldquoThermodynamic predic-tion of vapor-liquid equilibrium of supercritical CO

2or CHF

3+

ionic liquidsrdquoThe Journal of Supercritical Fluids vol 66 pp 29ndash35 2012

[13] F Gharagheizi A Eslamimanesh P Ilani-Kashkouli A HMohammadi and D Richon ldquoDetermination of vapor pressureof chemical compounds a group contribution model for anextremely large databaserdquo Industrial amp Engineering ChemistryResearch vol 51 pp 7119ndash7125 2012


[14] A Z Hezave M Lashkarbolooki and S Raeissi ldquoCorrelatingbubble points of ternary systems involving nine solvents andtwo ionic liquids using artificial neural networkrdquo Fluid PhaseEquilibria vol 352 pp 34ndash41 2013

[15] M Lashkarblooki A Z Hezave A M Al-Ajmi and S Ayatol-lahi ldquoViscosity prediction of ternary mixtures containing ILsusing multi-layer perceptron artificial neural networkrdquo FluidPhase Equilibria vol 326 pp 15ndash20 2012

[16] M Lashkarbolooki A Z Hezave and S Ayatollahi ldquoArtificialneural network as an applicable tool to predict the binary heatcapacity ofmixtures containing ionic liquidsrdquo Fluid Phase Equi-libria vol 324 pp 102ndash107 2012

[17] M Safamirzaei and H Modarress ldquoCorrelating and predictinglow pressure solubility of gases in [bmim][BF

4] by neural net-

work molecular modelingrdquo Thermochimica Acta vol 545 pp125ndash130 2012

[18] A Sencan Sahin and H Yazıcı ldquoThermodynamic evaluation ofthe Afyon geothermal district heating system by using neuralnetwork and neuro-fuzzyrdquo Journal of Volcanology and Geother-mal Research vol 233-234 pp 65ndash71 2012

[19] Y Sun G Bian W Tao C Zhai M Zhong and Z QiaoldquoThermodynamic optimization and calculation of the YCl

3-ACl

(A=LiNaK RbCs) phase diagramsrdquoCalphad vol 39 pp 1ndash102012

[20] X Xiao G Q Liu B F Hu et al ldquoA comparative study onArrhenius-type constitutive equations and artificial neural net-work model to predict high-temperature deformation behav-iour in 12Cr3WV steelrdquo Computational Materials Science vol62 pp 227ndash234 2012

[21] K M Yerramsetty B J Neely and K M Gasem ldquoA non-linear structure-property model for octanol-water partitioncoefficientrdquo Fluid Phase Equilibria vol 332 pp 85ndash93 2012

[22] F Yousefi and H Karimi ldquoP-V-T properties of polymer meltsbased on equation of state and neural networkrdquo European Poly-mer Journal vol 48 pp 1135ndash1143 2012

[23] F Yousefi H Karimi and M M Papari ldquoModeling viscosity ofnanofluids using diffusional neural networksrdquo Journal of Molec-ular Liquids vol 175 pp 85ndash90 2012

[24] M Safamirzaei and H Modarress ldquoApplication of neuralnetwork molecular modeling for correlating and predictingHenryrsquos law constants of gases in [bmim][PF

6] at low pressuresrdquo

Fluid Phase Equilibria vol 332 pp 165ndash172 2012[25] K Shahbaz S Baroutian F S Mjalli M A Hashim and I M

Alnashef ldquoDensities of ammonium and phosphonium baseddeep eutectic solvents prediction using artificial intelligenceand group contribution techniquesrdquo Thermochimica Acta vol527 pp 59ndash66 2012

[26] F Gharagheizi P Ilani-Kashkouli N Farahani and A HMohammadi ldquoGene expression programming strategy for esti-mation of flash point temperature of non-electrolyte organiccompoundsrdquo Fluid Phase Equilibria vol 329 pp 71ndash77 2012

[27] I P Koronaki E Rogdakis and T Kakatsiou ldquoThermodynamicanalysis of an open cycle solid desiccant cooling system usingartificial neural networkrdquo Energy Conversion and Managementvol 60 pp 152ndash160 2012

[28] T Hatami M Rahimi H Daraei E Heidaryan and A AAlsairafi ldquoPRSV equation of state parameter modeling throughartificial neural network and adaptive network-based fuzzyinference systemrdquo Korean Journal of Chemical Engineering vol29 no 5 pp 657ndash667 2012

[29] M Saber ldquoComparative analysis of hydrate formation pressureapplying cubic Equations of State (EoS) Artificial Neural

Network (ANN) and Adaptive Neuro-Fuzzy Inference System(ANFIS)rdquo International Journal of Thermodynamics vol 15 pp91ndash101 2012

[30] F Gharagheizi A Eslamimanesh P Ilani-Kashkouli A HMohammadi and D Richon ldquoQSPR molecular approach forrepresentationprediction of very large vapor pressure datasetrdquoChemical Engineering Science vol 76 pp 99ndash107 2012

[31] F Hajabdollahi Z Hajabdollahi and H Hajabdollahi ldquoSoftcomputing based multi-objective optimization of steam cyclepower plant usingNSGA-II and ANNrdquoApplied Soft Computingvol 12 no 11 pp 3648ndash3655 2012

[32] H Karimi and F Yousefi ldquoApplication of artificial neuralnetwork-genetic algorithm (ANN-GA) to correlation of densityin nanofluidsrdquo Fluid Phase Equilibria vol 336 pp 79ndash83 2012

[33] S Zendehboudi M A Ahmadi L James and I Chatzis ldquoPre-diction of condensate-to-gas ratio for retrograde gas condensatereservoirs using artificial neural network with particle swarmoptimizationrdquo Energy amp Fuels vol 26 pp 3432ndash3447 2012

[34] S Urata A Takada J Murata T Hiaki and A Sekiya ldquoPredic-tion of vapor-liquid equilibrium for binary systems containingHFEs by using artificial neural networkrdquo Fluid Phase Equilibriavol 199 no 1-2 pp 63ndash78 2002

[35] R Sharma D Singhal R Ghosh and A Dwivedi ldquoPotentialapplications of artificial neural networks to thermodynamicsvapormdashliquid equilibrium predictionsrdquo Computers amp ChemicalEngineering vol 23 no 3 pp 385ndash390 1999

[36] S Mohanty ldquoEstimation of vapour liquid equilibria of binarysystems carbon dioxide-ethyl caproate ethyl caprylate andethyl caprate using artificial neural networksrdquo Fluid Phase Equi-libria vol 235 no 1 pp 92ndash98 2005

[37] C A Faundez F A Quiero and J O Valderrama ldquoPhase equi-libriummodeling in ethanol + congener mixtures using an arti-ficial neural networkrdquo Fluid Phase Equilibria vol 292 no 1-2pp 29ndash35 2010

[38] M C Iliuta I Iliuta and F Larachi ldquoVapour-liquid equilibriumdata analysis for mixed solvent-electrolyte systems using neuralnetwork modelsrdquo Chemical Engineering Science vol 55 no 15pp 2813ndash2825 2000

[39] S Mohanty ldquoEstimation of vapour liquid equilibria for thesystem carbon dioxide-difluoromethane using artificial neuralnetworksrdquo International Journal of Refrigeration vol 29 no 2pp 243ndash249 2006

[40] A Mun A K Mutlag and M S Hameed ldquoVapor-liquid equi-librium prediction by PE andANN for the extraction of unsatu-rated fatty acid esters by supercritical CO

2rdquoNetwork vol 6 no

9 pp 122ndash134 2011[41] A Ghaemi S Shahhoseini M Ghannadi and M Farrokhi

ldquoPrediction of vapor-liquid equilibrium for aqueous solutions ofelectrolytes using artificial neural networksrdquo Journal of AppliedSciences vol 8 no 4 pp 615ndash621 2008

[42] M Bilgin ldquoIsobaric vapourmdashliquid equilibrium calculations ofbinary systems using a neural networkrdquo Journal of the SerbianChemical Society vol 69 no 8-9 pp 669ndash674 2004

[43] HYamamoto andKTochigi ldquoPrediction of vapormdashliquid equi-libria using reconstruction-learning neural network methodrdquoFluid Phase Equilibria vol 257 no 2 pp 169ndash172 2007

[44] B Zarenezhad and A Aminian ldquoPredicting the vapor-liquidequilibrium of carbon dioxide + alkanol systems by using anartificial neural networkrdquo Korean Journal of Chemical Engineer-ing vol 28 no 5 pp 1286ndash1292 2011


[45] R Abedini I Zanganeh and M Mohagheghian ldquoSimulationand estimation of vapor-liquid equilibrium for asymmetricbinary systems (CO

2-Alcohols) using artificial neural networkrdquo

Journal of Phase Equilibria and Diffusion vol 32 no 2 pp 105ndash114 2011

[46] S Ganguly ldquoPrediction of VLE data using radial basis functionnetworkrdquoComputers ampChemical Engineering vol 27 no 10 pp1445ndash1454 2003

[47] C A Faundez F A Quiero and J O Valderrama ldquoCorrelationand prediction of VLE of water + congener mixtures found inalcoholic beverages using an artificial neural networkrdquo Chem-ical Engineering Communications vol 198 no 1 pp 102ndash1192010

[48] H Karimi and F Yousefi ldquoCorrelation of vapour liquid equilib-ria of binary mixtures using artificial neural networksrdquo ChineseJournal of Chemical Engineering vol 15 no 5 pp 765ndash771 2007

[49] H Ghanadzadeh and H Ahmadifar ldquoEstimation of (vapour +liquid) equilibrium of binary systems (tert-butanol + 2-ethyl-1-hexanol) and (n-butanol + 2-ethyl-1-hexanol) using an artificialneural networkrdquoThe Journal of Chemical Thermodynamics vol40 no 7 pp 1152ndash1156 2008

[50] T Hiaki M Nanao S Urata and J Murata ldquoVapormdashliquidequilibria for 112333-hexafluoropropyl 222-trifluoroethylether with several organic solventsrdquo Fluid Phase Equilibria vol194ndash197 pp 969ndash979 2002

[51] S Ketabchi H Ghanadzadeh A Ghanadzadeh S Fallahi andM Ganji ldquoEstimation of VLE of binary systems (tert-butanol +2-ethyl-1-hexanol) and (n-butanol + 2-ethyl-1-hexanol) usingGMDH-type neural networkrdquoThe Journal of ChemicalThermo-dynamics vol 42 no 11 pp 1352ndash1355 2010

[52] AspenONE Aspen Hysys 2006 Software[53] M O McLinden ldquoThermodynamic properties of CFC alterna-

tives a survey of the available datardquo International Journal ofRefrigeration vol 13 no 3 pp 149ndash162 1990

[54] G Zhang B E Patuwo and M Y Hu ldquoForecasting with arti-ficial neural networks the state of the artrdquo International Jour-nal of Forecasting vol 14 no 1 pp 35ndash62 1998

[55] AMalallah and I S Nashawi ldquoEstimating the fracture gradientcoefficient using neural networks for a field in theMiddle EastrdquoJournal of PetroleumScience andEngineering vol 49 no 3-4 pp193ndash211 2005

[56] M Chakraborty C Bhattacharya and S Dutta ldquoStudies on theapplicability of Artificial Neural Network (ANN) in emulsionliquid membranesrdquo Journal of Membrane Science vol 220 no1-2 pp 155ndash164 2003

[57] R Beale and T Jackson Neural Computing An IntroductionInstitude of Physics London UK 1998

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



necessary for the development of new refrigerant mixtureswith minimal environmental impact

R116 and R744 (CO2) are two very interesting fluids

for industry Their common peculiarity is their low criticaltemperatures The critical temperature of CO

2is 30420K

while that of R116 is 29304K Moreover this system presentsazeotropic behavior indicating strong interaction betweenthe two species in particular a strong repulsive interactionAzeotropic and even quasiazeotropic behaviors are of utmostinterest not only to refrigeration industry but also to allindustries involved in supercritical fluid extraction Utiliza-tion of fluids with low critical points that are also safe forthe environment is generally highly preferred An azeotropicmixture of R116 and R744 could be very interesting for indus-try of refrigeration as the azeotrope position is at high R744composition [6] So it is useful to study theVLE of this type ofmixtures

The mixture of CO2-R610 (perfluorocarbons) is another

type of refrigerants In addition to the role of a refrigerant thismixture has another application This application is ability ofperfluorocarbons in dissolving refinery gases such as CO

2

and it is necessary to prediction of phase behavior for thismixture [7]

R123 and R124 are two new clean fire extinguishing agentsin comparison to other agents For the new total floodingclean agents that were being developed to replace certainHalon fire extinguishing agents the discharge time requiredto achieve 95 of the minimum design concentration shallnot exceed 10 s and the expellant gas is needed for its lack ofvapor pressure Generally nitrogen is used as an expellant gasbecause it does not need to be liquefied at high pressure butCO2has some merits to nitrogen such as price storage area

and supplementary extinguishing effect When CO2is used

as an expellant gas the knowledge of the phase behavior ofthe mixtures CO

2and fire extinguishing agents is essential

to design fire extinguishing processes and equipmentsMore-over phase equilibrium data are needed to calculate the fric-tion loss along with the working plans (from the storage tankto the discharge orifice) [2]

Hydrocarbons like propane butane and isobutane haveexcellent thermophysical properties and are compatible withmaterials normally used in refrigeration plants such as cop-per However the flammability of hydrocarbons limits theirapplication to specific systems Carbon dioxide has advan-tages of being nontoxic inflammable and high in volumetriccapacity of refrigeration However the refrigeration systemusing carbon dioxide is operated under a very high pressureHydrocarbons would reduce the problems occurring due tohigh pressure of carbon dioxide while carbon dioxide wouldreduce the flammability of hydrocarbons The mixtures ofcarbon dioxide and propane (R290) are proposed as promis-ing alternative refrigerantsTheVLEdata are essential to eval-uate the performance of the refrigeration or the heat pumpcycles using these refrigerant mixtures and to determine theoptimum composition for the best performance [3]

Information about the phase behavior of refrigerantmixtures can be obtained from direct measurement of phaseequilibrium data or by the use of equation of state andoractivity coefficient based on thermodynamic models Direct

measurement of precise experimental data is often difficultand expensive while the second method which includes alarge number of equations of states and excess Gibbs freeenergy models is tedious and involves a certain amount ofempiricism to determine mixture constants through fittingexperimental data and using various arbitrary mixing rulesmaking it difficult to select the appropriatemodel for a partic-ular case [9]Thus due to the difficulties of experimentalmea-surements and also their time-consuming and costly natureit is desirable to develop predictive methods for estimatingthe phase behavior of these kinds of systems

Artificial intelligence (AI) methods are advanced tech-niques with extreme flexibility ANN as a branch of AI is aflexible modeling method and has shown high performancesin many cases ANN is an empirical tool which can modelany kind of data sets even in the cases where relations arecomplex [10] Recently ANN has found extensive applicationin the field of thermodynamics and transport properties suchas the estimation of VLE viscosity density vapor pressurecompressibility factor and thermal conductivity [11ndash33]Thismethod provides nonlinear functionmapping of a set of inputvariables into the corresponding network output ANNs canbe applied for accurate VLE determination of polar and non-polar components [9 34ndash51] Basic theory and application tochemical problems of ANN with the back-propagation algo-rithm have been previously discussed in [48]

In this research a comprehensive model based onmultilayer feed forward back-propagation artificial neuralnetwork (FFBP-ANN) was developed to estimate VLE datafor eight refrigerant mixtures containing CO

2 The refriger-

ants include difluoromethane (R32) propane (R290) 11-difluoroethane (R152a) hexafluoroethane (R116) decafluor-obutane (R610) 22-dichloro-111-trifluoroethane (R123) 1-chloro-1222-tetrafluoroethane (R124) and 1112-tetraflu-oroethane (R134a) The developed model was trained andevaluated by using the experimental data for eight binaryrefrigerant mixtures reported by [2ndash8] and pure componentproperties for eight refrigerants reported by [2ndash8 52 53] Apart of experimental data was used to train the networks andthe rest was used to evaluate the performance of the networksFinally for the model validation the prediction of the ANNmodel (CO

2mole fraction in the vapor phase) was compared

with the thermodynamic model from different literatures [46 8] and also with the experimental data Furthermore theability of the ANN model for the prediction of VLE data forbinary mixture in azeotropic condition was examined

2 Artificial Neural Network

Neural networks consist of arrays of simple active units linkedby weighted connections ANN consists of multiple layers ofneurons arranged in such a way that each neuron in one layeris connected with each neuron in the next layer The networkused in this study is a multilayer feed forward neural networkwith a learning scheme of the back propagation (BP) of errorsand the Levenberg-Marquardt algorithm for the adjustmentof the connecting weights Neurons are the fundamentalprocessing element of an ANN which are arranged in layersthat make up the global architecture [48]



119874119875119895(net) = 1

1 + 119890minusnet (1a)

net =119899minus1

sum

119894=0

119908119894119909119894 (1b)


119894rdquo





119875= 1199090 1199091 119909

119899minus1and the

target exit 119879119875= 1199050 1199051 119905



119874119875119895= 119891[

119899minus1

sum

119894=0

119908119894119909119894] (2)


119908119894119895(119905 + 1) = 119908

119894119895(119905) + 120578120575

119875119895119874119875119895 (3)

Input layer

Hidden layer

Output layer






119875119895rdquo


120575119875119895= 119874119875119895(1 minus 119874

119875119895) (119905119875119895minus 119874119875119895)

120575119875119895= 119874119875119895(1 minus 119874

119875119895)sum

119896

120575119875119896119908119895119896

(4)


3 Experimental Data



1) and liquid (X

1)








Mixture 119879 (K) 119875 (MPa) 1198831

1198841

119873 Reference

R744 (1)-R32 (2)

28312 1106ndash4508 0-1 0-1

56 [4]


R744 (1)-R152a (2)

25844 0144ndash2294 0-1 0-1

67 [8]


R744 (1)-R290 (2)

26315 0344ndash2641 0-1 0-1

124 [3]


R744 (1)-R116 (2)

25329 2043-1051 00505ndash1 00284ndash1

75 [6]


R744 (1)-R610 (2)


83 [7]






R744 (1)-R134a (2)


29 [5]



Tansig

OutputPurelin

Input7lowast1

10lowast7

+

10lowast1

1

n1

10lowast1

a1

10lowast1

1lowast10

+

1lowast1

1

n2

1lowast1

a2

1lowast1

wih

who

bo

bh



Component 119879119887(K) 119879

119888(K) 119875

119888(MPa) 120596

R32 22150 35155 5831 0271R290 23107 36982 4242 0149R116 19490 29304 3042 0245R152a 24815 38635 4499 0256R610 27120 38584 2289 0374R134a 24693 37425 4064 0326R123 30076 45683 3662 0282R124 26104 39543 3624 02881






2(1)-refrigerant





AD = 10038161003816100381610038161003816119884Exp1minus 119884

Calc1

10038161003816100381610038161003816

AAD = 1119899

119899

sum

119894=1

10038161003816100381610038161003816119884Exp1119894minus 119884

Calc1119894

10038161003816100381610038161003816

(5)










MATLAB function)



119908ih1198951

119908ih1198952

119908ih1198953

119908ih1198954

119908ih1198955

119908ih1198956

119908ih1198957

119887h119895

119908ho1119895

119887o


minus46281




2mole fraction in






0 01 02 03 04 05 06 07 08 09 10

01

02

03

04

05

06

07

08

09

1

Y1

ANN = Y1exp


AN

N m

odel

Y1









1198831

1198841

1198841

1198841


0 0 0 0 0 000722 03157 03306 03281 00149 0012401419 0493 04969 04898 00039 0003202148 06097 06079 06041 00019 000560295 06937 06897 06939 00041 0000204194 07783 07756 07826 00028 0004305197 08239 08239 08273 0 0003406201 08621 08609 08621 00012 007176 08922 08921 08937 00001 0001507994 09179 09174 09198 00006 0001908755 09387 09391 09405 00004 0001809152 09507 09525 09506 00018 0000109355 09594 096 09552 00005 00042

0 02 04 06 08 10

02

04

06

08

1


X1

Y1

Y1 = X1






0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1


X1

Y1

Y1 = X1



2


6 Conclusions


2-containing binary



2-


2-R116


2-R123


2-





R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1







0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119874119875119895(net) = 1

1 + 119890minusnet (1a)

net =119899minus1

sum

119894=0

119908119894119909119894 (1b)


119894rdquo





119875= 1199090 1199091 119909

119899minus1and the

target exit 119879119875= 1199050 1199051 119905



119874119875119895= 119891[

119899minus1

sum

119894=0

119908119894119909119894] (2)


119908119894119895(119905 + 1) = 119908

119894119895(119905) + 120578120575

119875119895119874119875119895 (3)

Input layer

Hidden layer

Output layer






119875119895rdquo


120575119875119895= 119874119875119895(1 minus 119874

119875119895) (119905119875119895minus 119874119875119895)

120575119875119895= 119874119875119895(1 minus 119874

119875119895)sum

119896

120575119875119896119908119895119896

(4)


3 Experimental Data



1) and liquid (X

1)








Mixture 119879 (K) 119875 (MPa) 1198831

1198841

119873 Reference

R744 (1)-R32 (2)

28312 1106ndash4508 0-1 0-1

56 [4]


R744 (1)-R152a (2)

25844 0144ndash2294 0-1 0-1

67 [8]


R744 (1)-R290 (2)

26315 0344ndash2641 0-1 0-1

124 [3]


R744 (1)-R116 (2)

25329 2043-1051 00505ndash1 00284ndash1

75 [6]


R744 (1)-R610 (2)


83 [7]






R744 (1)-R134a (2)


29 [5]



Tansig

OutputPurelin

Input7lowast1

10lowast7

+

10lowast1

1

n1

10lowast1

a1

10lowast1

1lowast10

+

1lowast1

1

n2

1lowast1

a2

1lowast1

wih

who

bo

bh



Component 119879119887(K) 119879

119888(K) 119875

119888(MPa) 120596

R32 22150 35155 5831 0271R290 23107 36982 4242 0149R116 19490 29304 3042 0245R152a 24815 38635 4499 0256R610 27120 38584 2289 0374R134a 24693 37425 4064 0326R123 30076 45683 3662 0282R124 26104 39543 3624 02881






2(1)-refrigerant





AD = 10038161003816100381610038161003816119884Exp1minus 119884

Calc1

10038161003816100381610038161003816

AAD = 1119899

119899

sum

119894=1

10038161003816100381610038161003816119884Exp1119894minus 119884

Calc1119894

10038161003816100381610038161003816

(5)










MATLAB function)



119908ih1198951

119908ih1198952

119908ih1198953

119908ih1198954

119908ih1198955

119908ih1198956

119908ih1198957

119887h119895

119908ho1119895

119887o


minus46281




2mole fraction in






0 01 02 03 04 05 06 07 08 09 10

01

02

03

04

05

06

07

08

09

1

Y1

ANN = Y1exp


AN

N m

odel

Y1









1198831

1198841

1198841

1198841


0 0 0 0 0 000722 03157 03306 03281 00149 0012401419 0493 04969 04898 00039 0003202148 06097 06079 06041 00019 000560295 06937 06897 06939 00041 0000204194 07783 07756 07826 00028 0004305197 08239 08239 08273 0 0003406201 08621 08609 08621 00012 007176 08922 08921 08937 00001 0001507994 09179 09174 09198 00006 0001908755 09387 09391 09405 00004 0001809152 09507 09525 09506 00018 0000109355 09594 096 09552 00005 00042

0 02 04 06 08 10

02

04

06

08

1


X1

Y1

Y1 = X1






0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1


X1

Y1

Y1 = X1



2


6 Conclusions


2-containing binary



2-


2-R116


2-R123


2-





R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1







0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Mixture 119879 (K) 119875 (MPa) 1198831

1198841

119873 Reference

R744 (1)-R32 (2)

28312 1106ndash4508 0-1 0-1

56 [4]


R744 (1)-R152a (2)

25844 0144ndash2294 0-1 0-1

67 [8]


R744 (1)-R290 (2)

26315 0344ndash2641 0-1 0-1

124 [3]


R744 (1)-R116 (2)

25329 2043-1051 00505ndash1 00284ndash1

75 [6]


R744 (1)-R610 (2)


83 [7]






R744 (1)-R134a (2)


29 [5]



Tansig

OutputPurelin

Input7lowast1

10lowast7

+

10lowast1

1

n1

10lowast1

a1

10lowast1

1lowast10

+

1lowast1

1

n2

1lowast1

a2

1lowast1

wih

who

bo

bh



Component 119879119887(K) 119879

119888(K) 119875

119888(MPa) 120596

R32 22150 35155 5831 0271R290 23107 36982 4242 0149R116 19490 29304 3042 0245R152a 24815 38635 4499 0256R610 27120 38584 2289 0374R134a 24693 37425 4064 0326R123 30076 45683 3662 0282R124 26104 39543 3624 02881






2(1)-refrigerant





AD = 10038161003816100381610038161003816119884Exp1minus 119884

Calc1

10038161003816100381610038161003816

AAD = 1119899

119899

sum

119894=1

10038161003816100381610038161003816119884Exp1119894minus 119884

Calc1119894

10038161003816100381610038161003816

(5)










MATLAB function)



119908ih1198951

119908ih1198952

119908ih1198953

119908ih1198954

119908ih1198955

119908ih1198956

119908ih1198957

119887h119895

119908ho1119895

119887o


minus46281




2mole fraction in






0 01 02 03 04 05 06 07 08 09 10

01

02

03

04

05

06

07

08

09

1

Y1

ANN = Y1exp


AN

N m

odel

Y1









1198831

1198841

1198841

1198841


0 0 0 0 0 000722 03157 03306 03281 00149 0012401419 0493 04969 04898 00039 0003202148 06097 06079 06041 00019 000560295 06937 06897 06939 00041 0000204194 07783 07756 07826 00028 0004305197 08239 08239 08273 0 0003406201 08621 08609 08621 00012 007176 08922 08921 08937 00001 0001507994 09179 09174 09198 00006 0001908755 09387 09391 09405 00004 0001809152 09507 09525 09506 00018 0000109355 09594 096 09552 00005 00042

0 02 04 06 08 10

02

04

06

08

1


X1

Y1

Y1 = X1






0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1


X1

Y1

Y1 = X1



2


6 Conclusions


2-containing binary



2-


2-R116


2-R123


2-





R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1







0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Tansig

OutputPurelin

Input7lowast1

10lowast7

+

10lowast1

1

n1

10lowast1

a1

10lowast1

1lowast10

+

1lowast1

1

n2

1lowast1

a2

1lowast1

wih

who

bo

bh



Component 119879119887(K) 119879

119888(K) 119875

119888(MPa) 120596

R32 22150 35155 5831 0271R290 23107 36982 4242 0149R116 19490 29304 3042 0245R152a 24815 38635 4499 0256R610 27120 38584 2289 0374R134a 24693 37425 4064 0326R123 30076 45683 3662 0282R124 26104 39543 3624 02881






2(1)-refrigerant





AD = 10038161003816100381610038161003816119884Exp1minus 119884

Calc1

10038161003816100381610038161003816

AAD = 1119899

119899

sum

119894=1

10038161003816100381610038161003816119884Exp1119894minus 119884

Calc1119894

10038161003816100381610038161003816

(5)










MATLAB function)



119908ih1198951

119908ih1198952

119908ih1198953

119908ih1198954

119908ih1198955

119908ih1198956

119908ih1198957

119887h119895

119908ho1119895

119887o


minus46281




2mole fraction in






0 01 02 03 04 05 06 07 08 09 10

01

02

03

04

05

06

07

08

09

1

Y1

ANN = Y1exp


AN

N m

odel

Y1









1198831

1198841

1198841

1198841


0 0 0 0 0 000722 03157 03306 03281 00149 0012401419 0493 04969 04898 00039 0003202148 06097 06079 06041 00019 000560295 06937 06897 06939 00041 0000204194 07783 07756 07826 00028 0004305197 08239 08239 08273 0 0003406201 08621 08609 08621 00012 007176 08922 08921 08937 00001 0001507994 09179 09174 09198 00006 0001908755 09387 09391 09405 00004 0001809152 09507 09525 09506 00018 0000109355 09594 096 09552 00005 00042

0 02 04 06 08 10

02

04

06

08

1


X1

Y1

Y1 = X1






0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1


X1

Y1

Y1 = X1



2


6 Conclusions


2-containing binary



2-


2-R116


2-R123


2-





R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1







0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















MATLAB function)



119908ih1198951

119908ih1198952

119908ih1198953

119908ih1198954

119908ih1198955

119908ih1198956

119908ih1198957

119887h119895

119908ho1119895

119887o


minus46281




2mole fraction in






0 01 02 03 04 05 06 07 08 09 10

01

02

03

04

05

06

07

08

09

1

Y1

ANN = Y1exp


AN

N m

odel

Y1









1198831

1198841

1198841

1198841


0 0 0 0 0 000722 03157 03306 03281 00149 0012401419 0493 04969 04898 00039 0003202148 06097 06079 06041 00019 000560295 06937 06897 06939 00041 0000204194 07783 07756 07826 00028 0004305197 08239 08239 08273 0 0003406201 08621 08609 08621 00012 007176 08922 08921 08937 00001 0001507994 09179 09174 09198 00006 0001908755 09387 09391 09405 00004 0001809152 09507 09525 09506 00018 0000109355 09594 096 09552 00005 00042

0 02 04 06 08 10

02

04

06

08

1


X1

Y1

Y1 = X1






0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1


X1

Y1

Y1 = X1



2


6 Conclusions


2-containing binary



2-


2-R116


2-R123


2-





R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1







0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1198831

1198841

1198841

1198841


0 0 0 0 0 000722 03157 03306 03281 00149 0012401419 0493 04969 04898 00039 0003202148 06097 06079 06041 00019 000560295 06937 06897 06939 00041 0000204194 07783 07756 07826 00028 0004305197 08239 08239 08273 0 0003406201 08621 08609 08621 00012 007176 08922 08921 08937 00001 0001507994 09179 09174 09198 00006 0001908755 09387 09391 09405 00004 0001809152 09507 09525 09506 00018 0000109355 09594 096 09552 00005 00042

0 02 04 06 08 10

02

04

06

08

1


X1

Y1

Y1 = X1






0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1


X1

Y1

Y1 = X1



2


6 Conclusions


2-containing binary



2-


2-R116


2-R123


2-





R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1







0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












R744 (1)-R134a (2)

253 00031272 00032293 00063330 00037339 00031354 00025

R744 (1)-R124 (2)313 00048323 00020333 00038

R744 (1)-R116 (2)

253 00066273 00043283 00049291 00023294 00007297 00005

R744 (1)-R290 (2)

253 00107263 00049273 00035283 00030293 00030303 00045313 00035323 00044

R744 (1)-R610 (2)

263 00163283 00025303 00025308 00018323 00035338 00036353 00024

R744 (1)-R32 (2)

283 00017293 00039303 00038305 00034313 00038323 00046333 00024343 00045

R744 (1)-R152a (2)

258 00021278 00040299 00047308 00030323 00035343 00025

R744 (1)-R123 (2)313 00103323 00047333 00031



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1







0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1



0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1



X1

Y1

Y1 = X1





2-





References





2) + 22-dichloro-111-





2) + difluo-










2or CHF

3+








4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














4] by neural net-




3-ACl


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Prediction the Vapor-Liquid Equilibria of ...downloads.hindawi.com/archive/2013/930484.pdfPrediction the Vapor-Liquid Equilibria of CO 2-Containing Binary Refrigerant