Prediction the Vapor-Liquid Equilibria of CO<sub><b>2</b></sub>-Containing Binary Refrigerant Mixtures Using Artificial Neural Networks

Azari, Ahmad; Atashrouz, Saeid; Mirshekar, Hamed

doi:https://doi.org/10.1155/2013/930484

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Research Article | Open Access

Volume 2013 | Article ID 930484 | https://doi.org/10.1155/2013/930484

Prediction the Vapor-Liquid Equilibria of CO₂-Containing Binary Refrigerant Mixtures Using Artificial Neural Networks

Ahmad Azari,¹Saeid Atashrouz,²and Hamed Mirshekar²

Academic Editor: J. E. Ten Elshof, J. A. A. González, K. Okumura

Received09 May 2013

Accepted18 Jul 2013

Published10 Sept 2013

Abstract

Artificial neural network (ANN) technique has been applied for estimation of vapor-liquid equilibria (VLE) for eight binary refrigerant systems. The refrigerants include difluoromethane (R32), propane (R290), 1,1-difluoroethane (R152a), hexafluoroethane (R116), decafluorobutane (R610), 2,2-dichloro-1,1,1-trifluoroethane (R123), 1-chloro-1,2,2,2-tetrafluoroethane (R124), and 1,1,1,2-tetrafluoroethane (R134a). The related experimental data of open literature have been used to construct the model. Furthermore, some new experimental data (not applied in ANN training) have been used to examine the reliability of the model. The results confirm that there is a reasonable conformity between the predicted values and the experimental data. Additionally, the ability of the ANN model is examined by comparison with the conventional thermodynamic models. Moreover, the presented model is capable of predicting the azeotropic condition.

1. Introduction

For nearly 60 years, chlorofluorocarbons (CFCs) have been widely used as solvents, foam blowing agents, aerosols, and especially refrigerants due to their stability, nontoxicity, nonflammability, good thermodynamic properties, and so on. However, they also have a harmful effect on the earth’s protective ozone layer. So, they have been regulated internationally by Montreal Protocol since 1987. Much effort has been made to find the suitable replacement for CFCs. Initial CFC alternatives included some hydrochlorofluorocarbons (HCFCs), but they will be also phased out internationally because their ozone depletion potentials (ODPs) and global warming potentials (GWPs) are significant though less than those of CFCs. Hydrofluorocarbons (HFCs) synthetic refrigerants which have zero ODPs were proposed as promising replacements for CFCs and HCFCs [1]. The deadline for HCFCs which have low ozone depletion potential is 2030. Also there is no report for another type of refrigerants such as light hydrocarbons or perfluorocarbons as harmful refrigerants. In order to develop new refrigerants for replacement with harmful refrigerants, the mixtures of carbon dioxide and clean refrigerants have been studied in the number of researches [2–8] that was reviewed in the present study.

R134a is an environmentally acceptable refrigerant, which has replaced the ozone-depleting CFC-12 (dichlorodifluoromethane) in a wide range of applications especially in automotive air conditioning and domestic refrigeration. Another natural refrigerant, carbon dioxide (R744), has received new worldwide interest as a working fluid in automotive air conditioning. To expand the range of possible replacement fluid with desired properties, phase behavior of R134a-R744 should be studied. This clean mixture can be formulated so as to obtain a similar vapor pressure to that of the original refrigerant, to suppress flammability or toxicity of one of the components that otherwise has excellent thermophysical properties [5].

R152a is used for refrigeration and as an aerosol propellant. It is most commonly found in electronic cleaning products and many consumer aerosol products that must meet stringent 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 necessary for the development of new refrigerant mixtures with minimal environmental impact.

R116 and R744 (CO₂) are two very interesting fluids for industry. Their common peculiarity is their low critical temperatures. The critical temperature of CO₂ is 304.20 K, while that of R116 is 293.04 K. Moreover, this system presents azeotropic behavior, indicating strong interaction between the two species, in particular a strong repulsive interaction. Azeotropic and even quasiazeotropic behaviors are of utmost interest not only to refrigeration industry but also to all industries involved in supercritical fluid extraction. Utilization of fluids with low critical points that are also safe for the environment is generally highly preferred. An azeotropic mixture of R116 and R744 could be very interesting for industry of refrigeration as the azeotrope position is at high R744 composition [6]. So it is useful to study the VLE of this type of mixtures.

The mixture of CO₂-R610 (perfluorocarbons) is another type of refrigerants. In addition to the role of a refrigerant, this mixture has another application. This application is ability of perfluorocarbons in dissolving refinery gases such as CO₂, and it is necessary to prediction of phase behavior for this mixture [7].

R123 and R124 are two new clean fire extinguishing agents in comparison to other agents. For the new total flooding clean agents that were being developed to replace certain Halon fire extinguishing agents, the discharge time required to achieve 95% of the minimum design concentration shall not exceed 10 s, and the expellant gas is needed for its lack of vapor pressure. Generally, nitrogen is used as an expellant gas because it does not need to be liquefied at high pressure, but CO₂ has some merits to nitrogen such as price, storage area, and supplementary extinguishing effect. When CO₂ is used as an expellant gas, the knowledge of the phase behavior of the mixtures, CO₂ and fire extinguishing agents, is essential to design fire extinguishing processes and equipments. Moreover, phase equilibrium data are needed to calculate the friction loss along with the working plans (from the storage tank to the discharge orifice) [2].

Hydrocarbons like propane, butane, and isobutane have excellent thermophysical properties and are compatible with materials normally used in refrigeration plants such as copper. However, the flammability of hydrocarbons limits their application to specific systems. Carbon dioxide has advantages of being nontoxic, inflammable, and high in volumetric capacity of refrigeration. However, the refrigeration system using carbon dioxide is operated under a very high pressure. Hydrocarbons would reduce the problems occurring due to high pressure of carbon dioxide while carbon dioxide would reduce the flammability of hydrocarbons. The mixtures of carbon dioxide and propane (R290) are proposed as promising alternative refrigerants. The VLE data are essential to evaluate the performance of the refrigeration or the heat pump cycles using these refrigerant mixtures and to determine the optimum composition for the best performance [3].

Information about the phase behavior of refrigerant mixtures can be obtained from direct measurement of phase equilibrium data or by the use of equation of state and/or activity coefficient based on thermodynamic models. Direct measurement of precise experimental data is often difficult and expensive, while the second method, which includes a large number of equations of states and excess Gibbs free energy models, is tedious and involves a certain amount of empiricism to determine mixture constants, through fitting experimental data and using various arbitrary mixing rules, making it difficult to select the appropriate model for a particular case [9]. Thus due to the difficulties of experimental measurements and also their time-consuming and costly nature, it is desirable to develop predictive methods for estimating the phase behavior of these kinds of systems.

Artificial intelligence (AI) methods are advanced techniques, with extreme flexibility. ANN, as a branch of AI, is a flexible modeling method and has shown high performances in many cases. ANN is an empirical tool which can model any kind of data sets even in the cases where relations are complex [10]. Recently, ANN has found extensive application in the field of thermodynamics and transport properties such as the estimation of VLE, viscosity, density, vapor pressure, compressibility factor, and thermal conductivity [11–33]. This method provides nonlinear function mapping of a set of input variables into the corresponding network output. ANNs can be applied for accurate VLE determination of polar and nonpolar components [9, 34–51]. Basic theory and application to chemical problems of ANN with the back-propagation algorithm have been previously discussed in [48].

In this research, a comprehensive model based on multilayer feed forward back-propagation artificial neural network (FFBP-ANN) was developed to estimate VLE data for eight refrigerant mixtures containing CO₂. The refrigerants include difluoromethane (R32), propane (R290), 1,1-difluoroethane (R152a), hexafluoroethane (R116), decafluorobutane (R610), 2,2-dichloro-1,1,1-trifluoroethane (R123), 1-chloro-1,2,2,2-tetrafluoroethane (R124), and 1,1,1,2-tetrafluoroethane (R134a). The developed model was trained and evaluated by using the experimental data for eight binary refrigerant mixtures reported by [2–8] and pure component properties for eight refrigerants reported by [2–8, 52, 53]. A part of experimental data was used to train the networks, and the rest was used to evaluate the performance of the networks. Finally, for the model validation, the prediction of the ANN model (CO₂ mole fraction in the vapor phase) was compared with the thermodynamic model from different literatures [4, 6, 8] and also with the experimental data. Furthermore, the ability of the ANN model for the prediction of VLE data for binary mixture in azeotropic condition was examined.

2. Artificial Neural Network

Neural networks consist of arrays of simple active units linked by weighted connections. ANN consists of multiple layers of neurons arranged in such a way that each neuron in one layer is connected with each neuron in the next layer. The network used in this study is a multilayer feed forward neural network with a learning scheme of the back propagation (BP) of errors and the Levenberg-Marquardt algorithm for the adjustment of the connecting weights. Neurons are the fundamental processing element of an ANN, which are arranged in layers that make up the global architecture [48].

The main advantage of using ANNs to predict the VLE data lies in their ability to learn the relationship between the complex VLE data for different binary mixtures. The ANN input is the first layer in the network through which the information is supplied. The number of neurons in the input layer depends on the network input parameters. Hidden layers connect the input and output layers. Hidden layers enrich the network for learning the relation between input and output data. In theory, ANN with only one hidden layer and enough neurons in the hidden layer has the ability to learn any relation between the input and output data. Transfer function is the mathematic function that determines the relation between neuron output and the network. In other words, transfer function indicates the degree of nonlinearity in the network. Practically, in the feed forward BP-ANN model some limited functions are used as transfer functions [54]. Normally, the transfer functions of all neurons in the hidden layers are similar. Also, for all neurons in the output layer, the same transfer function is used. For the prediction of phenomena, logistic transfer function is the most conventional transfer function that is used in the hidden layers, because it is very easy to differentiate the sigmoid transfer function used in the BP algorithm [55, 56]. The sigmoid transfer function is as follows:where “” in (1b) is the number of inputs to the neuron. “” is the weight coefficient corresponding to the input “” and “” is the output corresponding to the “” neuron. For completion of this section, we illustrate the learning BP algorithm.

2.1. ANN Training Algorithm

The back-propagation algorithm is one of the least mean square methods, which is normally used in engineering. In a multilayer perceptron, each neuron of a layer is linked to all neurons of the previous layer. Figure 1 shows a perceptron with a hidden layer.

Each layer output acts as the input to the next neurons. In order to train multilayer feed forward neural network, back-propagation law is used. In the first stage, all weights and biases are selected according to small random numbers. In the second stage, input vector and the target exit are given to the network, where the subscripts and are the numbers of input and output vectors, respectively. In the third stage, the following quantitative values are calculated and transferred to the subsequent layer until it eventually reaches the exit layer [57] The fourth stage begins from the exit layer, during which the weight coefficients are corrected where “” stands for the weight coefficients from node “” to node “” in time “”, “” is the rate coefficient, “” refers to the corresponding error of input pattern “” to the node “”, and “” is the output corresponding to the “” neuron. “” is calculated by the following equations for exit layer and hidden layer, respectively: Here, the acts for “” nodes on the subsequent layer after the node “” [57]. In the learning process, there are several parameters that have influence on the ANN training. These parameters are the number of iterations, number of hidden layers, and the number of hidden neurons. To find the best architecture of the model, the best set of the aforementioned parameters based on minimizing the network output error should be chosen.

3. Experimental Data

The first step in an ANN modeling is compiling the database to train the network and to evaluate network ability for generalization. In the present study, the experimental VLE data for eight binary mixtures reported by [2–8, 52, 53] have been used for training and validation of the ANN model. The range of the intensive state variables (temperature (), pressure (), and CO₂ mole fraction in the vapor () and liquid () phases for each binary) and the number of data points () for the ANN training were listed in Table 1. Also, the pure component properties (normal boiling point (), critical temperature (), critical pressure (), and acentric factor ) of the eight refrigerants used in this work were collected from different literatures [2–8, 52, 53], and the collection was listed in Table 2.

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 the phase behavior of the eight R744 (1)-refrigerants (2) binaries by one ANN model a total of eight variables have been selected in this work: four intensive state variables (equilibrium temperature, equilibrium pressure, and equilibrium CO₂ mole fractions in the liquid and vapor phases) and four pure component properties of the refrigerant (normal boiling point, critical temperature, critical pressure, and acentric factor). The choice of the input and output variables was based on the phase rule, practical considerations (bubble or dew point computation), and the need to describe the eight binaries by only one ANN model. Therefore, the equilibrium temperature and pressure and the R744 mole fraction in the liquid phase together with the pure component properties of the refrigerant have been selected as input variables and the R744 mole fraction in the vapor phase as output variable.

As shown in Figure 2, a multilayer feed forward neural network structure with a hidden layer was used in this study. ANN modeling for the VLE of eight CO₂ (1)-refrigerant (2) binaries was carried out in MATLAB ver. 7.9.0 program. Initially, the program starts with the default FFBP-ANN type (newff MATLAB function), the Levenberg-Marquardt BP training algorithm (trainlm MATLAB training function), and one hidden layer. Once the topology is specified, the starting and ending number(s) of neurons in the hidden layer(s) have to be specified. The number of neurons in a hidden layer is then modified by adding neurons one at a time. The procedure begins with the logarithmic sigmoid activation function, then the hyperbolic tangent sigmoid activation function for the hidden layers, and the linear activation function for the output layer. The results of different runs of the program show that the bayesian regularization back propagation (BRBP), using Levenberg-Marquardt optimization models, train, more successfully than models using attenuated training. Table 3 shows the structure of the optimized ANN model. The weight matrices and bias vectors of the optimized ANN model were listed in Table 4, where is the input-hidden layer connection weight matrix (10 rows and 7 columns), is the hidden layer-output connection weight matrix (1 rows and 10 columns), is the hidden neurons bias column vector (10 rows), and is the output neurons bias column vector (1 row and 1 column).

5. Results and Discussion

Using the random selection method, 60% of all data were assigned to the training set, 20% of all data were assigned to the validation set, and the rest of the data were used as the test set. In the training phase, the number of neurons in the hidden layer was important for the network optimization. However, decision on the number of hidden layer neurons is difficult because it depends on the specific problem being solved using ANN. With too few neurons, the network may not be powerful enough for a given learning task. With a large number of neurons, the ANN may memorize the input training data very well so that the network tends to perform poorly on new test data and is called “overfitting”. To prevent the over-fitting issue, we should evaluate average absolute deviation (AAD) for train set, validation set, and test set and they must be in the same order of magnitude. Absolute deviation (AD) and AAD were calculated from the following relations: where “” is the number of data points and “Exp” and “Calc” superscripts stand for the experimental and calculated CO₂ mole fraction, respectively. In the training process, different hidden layers and neurons were tried, and finally the optimized ANN obtained for this study was a network with a hidden layer containing 10 neurons. In an optimized ANN, the AAD values for the train, validation, and test data sets are in the same order of magnitude. In this research, the AAD values for the train, validation, and test sets of data were obtained , , and , respectively, and the network performance (MSE) was achieved . The ability of the model for the prediction of CO₂ mole fraction in the vapor phase is shown in Figure 3. As shown, good agreement for the prediction of ANN model and the experimental data are observed. So the developed ANN model can be used for the prediction of the new set of VLE data for the eight aforementioned binary mixtures.

To validate the ANN model prediction, the ability of the ANN model for the prediction of CO₂ mole fraction in the vapor phase of CO₂ (1) R152a (2) binary mixture at 308.3 K was investigated. Then the results were compared with Madani model [8]. The results were shown in Figure 4, and AD values for the ANN and Madani models were reported in Table 5. As shown, the maximum of the AD values for the ANN and Madani models were obtained 0.0124 and 0.0149, respectively. Also AAD for the ANN and Madani models were calculated 0.002969 and 0.002477, respectively. Thus AAD results for the ANN and Madani models are very close together.

In addition, Figure 5 compares the ANN results with thermodynamic model from the literature [6] and with the experimental results for R116-R744 binary mixture. The figure shows good agreement of the results with the experimental data. Also, Figure 5 shows that this comprehensive ANN model can predict the azeotropic condition. Since the thermodynamic models are used for an especially binary mixture, while the developed ANN model is applicable for the eight aforementioned binary refrigerant mixtures, so this makes the ANN model an interesting predictive tool in respect to the thermodynamic models.

Figures 6, 7, 8, and 9 show the curves for the binary mixtures of R610, R32, R134a, and R152a with CO₂. They include a comparison between experimental data and ANN results at different temperatures. As shown, the figures show excellent agreement between experimental data and the prediction of the ANN model. In addition, the AAD of the ANN model with the experimental data for the eight aforementioned binary mixtures at different temperatures were reported in Table 6. These results also indicate the predictability of the ANN model in the prediction of the CO₂ mole fraction in the vapor phase for the binary refrigerant mixtures.

6. Conclusions

In this work, a comprehensive FFBP-ANN model was developed for the prediction of VLE data. The model was constructed for eight conventional CO₂-containing binary refrigerant mixtures at different temperatures ranges. Binary refrigerants are CO₂-R32 mixture (283.15–343.23 K), CO₂-R290 (253.15–323.15 K), CO₂-R152a (258–343 K), CO₂-R116 (253.29–296.72 K), CO₂-R610 (263.15–352.98 K), CO₂-R123 (313.15–333.15 K), CO₂-R124 (313.15–333.15 K), and CO₂-R134a mixture (252.95–354 K). The optimized ANN model was obtained with a hidden layer and 10 neurons in the hidden layer. The input layer contains three intensive state variables (equilibrium temperature, equilibrium pressure, and equilibrium CO₂ mole fraction in the liquid and vapour phases) and four pure component properties of the refrigerant (normal boiling point, critical temperature, critical pressure, and acentric factor). The output layer includes equilibrium CO₂ mole fraction in the vapor phase. In the ANN training procedure, the AAD for the sets of train, validation, and test data were obtained , , and , respectively, and the network performance (MSE) was achieved . It was shown that excellent agreement between the model predictions and the experimental data was achieved. Also, the ability of the ANN model was examined in comparison with the different thermodynamic models for CO₂-R152a mixture at 308.3 K, CO₂-R32 at 343 K, and CO₂-R116 binary mixture at 253.3 K. The AAD results show that ANN model results are very close to the thermodynamic models. Also, ANN model can predict azeotropic condition for the CO₂-R116 binary mixture. Finally, the advantage of the ANN model is its applicability for the eight CO₂-containing binary mixtures, while the thermodynamic models are used for an especially binary mixture.

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

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