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Prediction of Liquid and VaporEnthalpies of Ammonia-water MixtureA. encan a , S. Gk a & E. Dikmen aa Department of Mechanical Education, Technical EducationFaculty , Sleyman Demirel University , Isparta, TurkeyPublished online: 19 May 2011.

To cite this article: A. encan , S. Gk & E. Dikmen (2011) Prediction of Liquid and Vapor Enthalpiesof Ammonia-water Mixture, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects,33:15, 1463-1473, DOI: 10.1080/15567030903397891

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Energy Sources, Part A, 33:14631473, 2011

Copyright Taylor & Francis Group, LLC

ISSN: 1556-7036 print/1556-7230 online

DOI: 10.1080/15567030903397891

Prediction of Liquid and Vapor Enthalpies

of Ammonia-water Mixture

A. SENCAN,1 S. GK,1 and E. DIKMEN1

1Department of Mechanical Education, Technical Education Faculty,

Sleyman Demirel University, Isparta, Turkey

Abstract The ammonia-water mixture may be commonly employed as a work-ing fluid in the absorption chiller, especially because both ammonia and water are

natural substances and are harmless. In addition, these substances have excellentthermodynamic properties. In this study, an alternative method using the artificial

neural network (ANN) to determine liquid and vapor enthalpies of ammonia-watermixture is presented. The training and validation was performed with good accuracy.

The correlation coefficient obtained when unknown data were used to the networkswas 0.975 for the liquid enthalpy and 0.887 for the vapor enthalpy. Using the

weights obtained from the trained network, a new formulation is presented for thedetermination of the vapor and liquid enthalpies of ammonia-water mixture. The

results of the study show that the ANN is a perfect alternative method for thecalculation of thermodynamic properties of ammonia-water mixture. The faster and

simpler solutions with equations derived from the ANN can be carried out.

Keywords ammonia-water, liquid enthalpy, neural network, thermodynamic proper-ties, vapor enthalpy

1. Introduction

The ammonia-water mixture can be used as a working fluid in the absorption chillers. In

the absorption chillers operating with ammonia-water solution, water is the absorbent and

ammonia is the refrigerant. Since the 1970s, they are under consideration for residential

and commercial heating and cooling (Herold et al., 1996; ASHRAE, 1997; Darwish et al.,

2008).

Thermodynamic properties of fluid couples are very important parameters affecting

the performance of absorption systems. The engineering calculation and simulation of

absorption systems require the availability of simple and efficient mathematical formu-

lations for the determination of thermodynamic properties of fluid couples. Vapor and

liquid enthalpies of ammonia-water mixture were presented in the literature as limited

data (Yamankaradeniz et al., 2002). In this study, in order to determine liquid and vapor

enthalpies of this mixture, artificial neural networks (ANNs) were used. Vapor and liquid

enthalpies of ammonia-water mixture with new formulations obtained from an ANN

can be easily estimated. The method proposed offers more flexibility and, therefore,

thermodynamic simulation of absorption systems is fairly simplified.

Address correspondence to Dr. Arzu Sencan, Department of Mechanial Education, TechnicalEducation Faculty, Sleyman Demirel University, Isparta 32260, Turkey. E-mail: sencan@tef.sdu.edu.tr

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1464 A. Sencan et al.

Figure 1. Neural network process.

2. ANNs

ANN is an information processing paradigm that is inspired by the way biological nervous

systems, such as the brain, process information. The key element of this paradigm is the

novel structure of the information processing system. It is composed of a large number of

highly interconnected processing elements (neurons) working in unison to solve specific

problems. ANNs, like people, learn by example. An ANN is configured for a specific

application, such as pattern recognition or data classification, through a learning process.

Learning in biological systems involves adjustments to the synaptic connections that

exist between the neurons (Haykin, 1999; Fu, 1994; Tsoukalas and Uhrig, 1997; Lin and

Lee, 1996). The neural network process is described in Figure 1. Neural networks have

been used in the estimate of thermodynamic properties and analysis of energy systems

(Kalogirou, 2000a, b; Chouai et al., 2002; Pacheco-Vega et al., 2001; Bechtler et al.,

2001; Szen et al., 2004a, b; Szen and Akayol, 2004; Lazzs, 2009; Eslamloueyan

and Khademi, 2009).

ANN with a back-propagation algorithm learns by changing the connection weights,

and these changes are stored as knowledge. Some statistical methods, such as the root-

mean-squared (RMS), the coefficient of multiple determination (R2), and the coefficient

of variation (cov) may be used to compare predicted and actual values. These formulations

have been given in Bechtler et al. (2001).

3. Modeling of the Thermodynamic Properties Using ANN

In order to analyze and evaluate the performance of absorption systems, reliable thermo-

dynamic property models to predict enthalpy values depending on temperature, pressure,

and concentration values are required. These relationships have been provided using

ANN. In order to train the network, limited data reported by Yamankaradeniz et al.

(2002) were used. The inputs of the network are temperature, pressure, and concentration

of NH3-water mixture, whereas output is the liquid and vapor enthalpies. For this purpose,

neural networks were trained. There are different algorithms that can be applied to train a

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Enthalpies of Ammonia-water Mixture 1465

neural network. The most popular of them is the back propagation algorithm, which has

different variants. Standard back propagation is a gradient descent algorithm. It is very

difficult to know which training algorithm will be the fastest for a given problem, and the

best one is usually chosen by trial and error. In this study, LevenbergMarquardt (LM)

back-propagation training in a feed forward, single hidden layer network was repeatedly

applied until satisfactory training was achieved. Trainlm is a network training function

that updates weight and bias values according to LevenbergMarquardt optimization.

Inputs and outputs are normalized. Tan-sig activation function has been used for both the

hidden layer and the output layer. The function used is given by:

F.z/ D2

1C e2z 1; (1)

where z is the weighted sum of the input. The computer program was performed under

MATLAB environment using the neural network toolbox. In the training, we used a

variable number of neurons (from 3 to 12) in the hidden layer to define the output

accurately. The dataset for the liquid and vapor enthalpies of NH3-water mixture available

included 1,048 data patterns. Data patterns were collected from Yamankaradeniz et al.

(2002). From these, 838 data patterns were used for the training of the network and the

remaining 210 patterns were randomly selected and used as a test dataset. Figure 2 shows

the architecture of the ANN used for predicting the liquid and vapor enthalpies of NH3-

water mixture. In this figure, the temperature, pressure, liquid, and vapor concentration are

the input data and liquid enthalpy of the mixture is the actual output. The configuration

4-9-2 appeared to be the most optimal topology for liquid enthalpy. The configuration

4-10-2 appeared to be the most optimal topology for vapor enthalpy.

Training results based on the 4-9-2 configuration for liquid enthalpy is shown in

Figure 3. Training results based on the 4-10-2 configuration for liquid enthalpy is shown

in Figure 4.

Figure 2. ANN topology used for liquid enthalpy and vapor enthalpy prediction.

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1466 A. Sencan et al.

Figure 3. Training results based on the 4-9-2 configuration.

In order to achieve the optimal result, different numbers of hidden neurons were

used. Statistical values, such as RMS, R2, and cov, are given in Tables 1 and 2 for liquid

and vapor enthalpy for LM algorithm and 312 neurons in the hidden layer.

From the data presented in Table 1, it is shown that liquid enthalpy of NH3-water

mixture LM algorithm with nine neurons in the hidden layer (LM-9) appeared to be

the most optimal topology. From the data presented in Table 2, it is shown that vapor

enthalpy of NH3-water mixture LM algorithm with ten neurons in the hidden layer (LM-

10) appeared to be most optimal topology.

Figure 4. Training results based on the 4-10-2 configuration.

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Enthalpies of Ammonia-water Mixture 1467

Table 1

Statistical values of liquid enthalpy for

NH3-water mixture

Algorithm neurons RMS Cov R2

LM-3 40.218 0.580 0.968

LM-4 37.108 0.535 0.972

LM-5 36.804 0.531 0.973

LM-6 35.517 0.512 0.975

LM-7 35.538 0.513 0.975

LM-8 35.480 0.512 0.975

LM-9 35.314 0.509 0.975

LM-10 37.020 0.534 0.972

LM-11 35.901 0.518 0.974

LM-12 35.890 0.518 0.974

The regression curve of the output variable (liquid enthalpy) for the test data set is

shown in Figure 5. The correlation coefficient obtained in this case is 0.975, which is

very satisfactory.

Figure 6 shows the regression curve of the output variable (vapor enthalpy) for the

test data set. The correlation coefficient obtained in this case is 0.887, which is very

satisfactory.

4. Results and Discussion

Mathematical formulations derived from the ANN model are presented here. The best

approach, which has minimum errors, is performed by the LM algorithm with 9 neurons

for liquid enthalpy and the LM algorithm with 10 neurons for vapor enthalpy. In order

to calculate the liquid enthalpy and vapor enthalpy values of NH3-water mixture, the

Table 2

Statistical values of vapor enthalpy for

NH3-water mixture

Algorithm neurons RMS Cov R2

LM-3 88.846 0.061 0.870

LM-4 86.130 0.059 0.878

LM-5 84.435 0.058 0.883

LM-6 83.958 0.057 0.884

LM-7 83.795 0.057 0.884

LM-8 84.421 0.058 0.883

LM-9 84.057 0.058 0.884

LM-10 82.935 0.057 0.887

LM-11 89.085 0.061 0.870

LM-12 83.033 0.057 0.887

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1468 A. Sencan et al.

Figure 5. Comparison of actual and ANN-predicted values of NH3-water mixture liquid enthalpyfor the test data set.

following equations are derived:

Ei D

4XnD1

Inwni C bn; (2)

Fi D2

1C e2Ei 1: (3)

In the above equations, for Ei the first two values are the multiplication of the input

parameters (In) with their weights at location n, and the last constant value (bn) represents

Figure 6. Comparison of actual and ANN-predicted values of NH3-water mixture vapor enthalpyfor the test data set.

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Enthalpies of Ammonia-water Mixture 1469

the bias term. The subscript i represents the number of hidden neuron. The four input

parameters are:

I1 D Pressure .P /; (4)

I2 D Temperature .T /; (5)

I3 D Liquid concentration .Xf /; (6)

I4 D Vapor concentration .Xv/: (7)

In the ANN, nine hidden neurons are used for liquid enthalpy; thus, nine pairs of

equations, i.e., E1 to E9 and F1 to F9 are required, which represent the summation and

activation functions of each neuron of the hidden layer, respectively. The coefficients of

Eq. (2) are given in Table 3.

In the ANN, ten hidden neurons are used for vapor enthalpy; thus, ten pairs of

equations, i.e., E1 to E10 and F1 to F10 are required, which represent the summation and

activation functions of each neuron of the hidden layer, respectively. The coefficients of

Eq. (2) are given in Table 4.

Additionally, the actual input data of the various parameters need to be normalized.

For this purpose, the actual values of each parameter are divided with the coefficients

shown in Table 5.

Finally, the liquid enthalpy .hf / of NH3-water mixture depending on temperature,

pressure, and concentration values can be computed from:

E10 D F1 .44:4563/C F2 .0:095365/C F3 .0:76719/C F4 .0:0055292/

C F5 .0:64566/C F6 .0:04226/C F7 .40:0133/C F8 .0:23058/ (8)

C F9 .0:75846/C 5:4231;

hf D

2

1C e2E10 1

:991: (9)

Table 3

Weight coefficients and bias values used for the determination of liquid enthalpy

Neuron

position (wni) I1 (P ) I2 (T ) I3 (Xf ) I4 (Xv) bn

1 0.113 0.206 1.573 0.424 2.432

2 10.791 8.848 3.333 20.526 0.361

3 0.423 0.015 1.125 0.523 0.526

4 49.229 4.814 2.330 16.648 26.587

5 0.016 0.017 2.606 0.476 0.231

6 16.804 0.028 3.527 14.241 1.401

7 16.519 0.920 0.577 0.035 2.690

8 4.510 0.467 0.370 0.912 1.121

9 16.825 2.030 15.251 5.760 24.384

Note: In weights, n represents the input number and i represents the hidden neuron number.

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Table 4

Weight coefficients and bias values used for the determination of vapor enthalpy

Neuron

position (wni ) I1 (P ) I2 (T ) I3 (Xf ) I4 (Xv) bn

1 3.831 2.016 2.918 7.828 15.779

2 5.275 0.88 16.090 17.312 1.196

3 3.446 1.270 26.761 24.422 7.158

4 0.105 0.803 1.703 2.580 1.084

5 18.061 19.350 14.800 14.410 29.720

6 0.093 0.034 0.366 0.225 0.973

7 5.229 0.592 0.209 0.568 1.743

8 4.239 8.328 26.906 25.099 5.319

9 0.252 6.855 3.450 15.297 1.594

10 0.117 0.844 1.667 2.656 1.198

Note: In weights, n represents the input number and i represents the hidden neuron number.

The coefficient shown in Eq. (5) is used to convert the normalized output to actual output

.hf / of NH3-water mixture.

Similarly, vapor enthalpy .hv/ of NH3-water depending on temperature, pressure,

and concentration values can be computed from:

E11 D F1 .2:3056/C F2 .0:76346/C F3 .0:095678/C F4 .0:99316/

C F5 .10:1107/C F6 .5:7407/C F7 .8:3/C F8 .0:67651/ (10)

C F9 .15:2952/C F10 .1:1989/C 5:0796;

hv D

2

1C e2E11 1

:2802: (11)

Table 5

Normalization coefficients for the input

and output parameters

Coefficient

Input parameter

Pressure (TG) 3,000

Temperature (T ) 232

Liquid concentration (Xf ) 102

Vapor concentration (Xv) 102

Output parameter

Liquid enthalpy (hf ) 991

Vapor enthalpy (hv) 2,802

Note: The actual values are divided with the abovecoefficients to obtain the normalized values.

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Table 6

Comparison between actual liquid enthalpy and liquid enthalpy obtained

with equations derived from ANN for NH3-water mixture

P ,

kPa T , C Xf , % Xv , %

Actual

hf , kJ/kg

Predicted

hf , kJ/kg Error

Percentage

difference,

%a

60 55.4 10 74.9 155.4 155.32 0.08 0.050

140 56 20 90.47 87.3 86.95 0.35 0.406

480 78.2 28 93.77 136.6 136.99 0.39 0.284

520 76.8 30 94.4 125 124.70 0.30 0.241

560 79.4 30 94.14 138.4 138.32 0.08 0.057

600 84.2 28 92.44 177 178.33 1.33 0.752

640 97.5 24 88.41 247.2 247.22 0.02 0.01

680 99.7 24 88.05 261.1 259.89 1.21 0.463

720 80.7 34 95.33 131 130.97 0.03 0.024

800 92.7 30 92.59 202.7 202.26 0.44 0.216

840 172.4 0 0 729.3 729.68 0.38 0.051

920 107.1 26 88.42 284.9 286.18 1.28 0.449

1,000 89.2 36 95.08 164.7 165.43 0.73 0.443

1,200 70 50 98.36 66.3 66.41 0.11 0.161

1,400 68.3 55 98.74 68.7 68.60 0.10 0.148

1,600 112.7 34 92.04 281.8 281.58 0.22 0.076

1,800 47.5 94 99.95 182.8 183.556 0.756 0.413

2,000 59.4 80 99.79 142 143.180 1.180 0.831

2,400 58 96 99.99 250.2 251.224 1.024 0.409

aPercentage difference (%) D (error/actual vapor pressure) 100.

The coefficient shown in Eq. (7) is used to convert the normalized output to actual output

.hv/ of NH3-water mixture.

In Table 6, a comparison is presented between the actual liquid enthalpy and liquid

enthalpy predicted with the equations derived from ANN for NH3-water mixture. In

Table 7, a comparison is presented between the actual vapor enthalpy and vapor enthalpy

predicted with the equations derived from ANN for NH3-water mixture. As can be seen,

the error in both cases is very small.

5. Conclusions

A new methodology for forecasting NH3-water mixture enthalpies is presented. This

methodology, based on ANN, is successfully applied to determine NH3-water mixture

enthalpies. In order to calculate NH3-water mixture enthalpies, mathematical formulations

were derived from the ANN model. Mathematical formulations have been obtained from

formulations of the summation and activation functions used in the ANN model and

weights of neurons. This approach is valid for estimating liquid and vapor enthalpies of

NH3-water mixture at any temperature, pressure, and concentration. This formulation

can especially help manufacturers and engineers with thermodynamic simulation of

absorption systems.

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1472 A. Sencan et al.

Table 7

Comparison between actual vapor enthalpy and vapor enthalpy obtained with equations

derived from ANN for NH3-water mixture

P ,

kPa T , C Xf , % Xv , %

Actual

hf , kJ/kg

Predicted

hf , kJ/kg Error

Percentage

difference,

%a

140 56 20 90.47 1,527.6 1,531.10 3.50 0.229

320 17.7 55 99.87 1,318.2 1,326.80 8.60 0.652

480 78.2 28 93.77 1,535.9 1,544.20 8.30 0.540

520 153.3 0 0 2,747.4 2,752.90 5.50 0.200

560 79.4 30 94.14 1,523.5 1,532.00 8.50 0.557

600 84.2 28 92.44 1,558.2 1,572.50 14.30 0.917

680 99.7 24 88.05 1,639.8 1,646.30 6.50 0.396

720 106.1 22 85.23 1,686.3 1,693.90 7.60 0.450

760 82.7 34 95.13 1,508.8 1,516.40 7.60 0.503

800 92.7 30 92.59 1,563.3 1,576.60 13.30 0.850

880 20.8 100 100 1,280.9 1,292.00 11.10 0.866

920 111.7 24 86.16 1,683 1,685.30 2.30 0.136

1,000 89.2 36 95.08 1,520.1 1,520.00 0.10 0.006

1,100 85.2 40 96.28 1,491.6 1,491.50 0.10 0.006

1,400 120.8 28 88.1 1,669.2 1,666.60 2.60 0.155

1,600 50.3 80 99.82 1,324.5 1,325 0.5 0.037

1,800 55 80 99.81 1,328 1,325.7 2.3 0.173

2,000 59.4 80 99.79 1,331.6 1,328.8 2.8 0.210

2,400 58 96 99.99 1,300.3 1,306.7 6.4 0.492

aPercentage difference (%) D (error/actual vapor pressure) 100.

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