Optimization of geothermal energy aided absorption refrigeration system—GAARS: A novel ANN-based approach

Geothermics 65 (2017) 210–221

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Optimization of geothermal energy aided absorption refrigeration system—GAARS: A novel ANN-based approach Abtullah Tugcu a , Oguz Arslan b,∗ a b

Tavsanlı Vocational School, Dumlupinar University, 43300 Kutahya, Turkey Mechanical Engineering Department, Engineering Faculty, Dumlupinar University, 43270 Kutahya, Turkey

a r t i c l e

i n f o

Article history: Received 3 August 2016 Received in revised form 6 October 2016 Accepted 11 October 2016 Keywords: Absorption refrigeration system Ammonia-Water ANN Geothermal energy

a b s t r a c t The aim of this study is to optimize the geothermal energy aided absorption refrigeration system using NH3 –H2 O as the working fluid. A total of 3660 different designs, with different solution fractions and working parameters, were analyzed by means of energy-exergy and net present value (NPV) analysis. The obtained data was modeled by a novel two stage artificial neural network (ANN) with 14650 data points. Of this, 10248 points were used for training, and the remaining used for testing. The best topology of ANN were performed by using the back-propagation learning algorithm with three different variants such as Levenberg-Marquardt (LM), Pola-Ribiere Conjugate Gradient (CGP), and Scaled Conjugate Gradient (SCG). According to ANN results, the error rates were determined in an acceptable range change between 0.07% and 6% for the engineering applications. The R2 values of best network structures were calculated in higher acceptable range change between 0.9958 and 1.000 for LM. The optimum designs were determined using the obtained weights and biases of the best ANN topology, yielding a coefficient of performance (COP) and exergy efficiency (␧) of 0.5722 and 0.6201, respectively. NPV values were respectively calculated as 1.778 million US$, 6.328 million US$ and 27.183 million US$ for quince, apple and grape. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Refrigeration technologies are among the main technologies frequently needed in forming comfortable living environment and preserving food as well as in other living environments. This is why studies to improve refrigeration technologies increase day by day. There are numerous studies on absorption refrigeration systems. In these studies, it is aimed to investigate the performance of the system with different fluid couples by using thermodynamic laws (Talbi and Agnew, 2000; Lee and Sherif, 2001; Pilatowsky et al., 2001; De Lucas et al., 2004; Adewusi and Zubair, 2004; Kizilkan et al., 2007; Kaushik and Arora, 2009; Yılmazoglu, 2010; Gong and Boulama, 2014; Tugcu et al., 2016). From engineering point of view, it is more important to applicate the most optimum system design taking the thermodynamic and economic parameters into account. At this point, it is very hard to get a quick and acceptable solution. By this way, artificial neural networks (ANNs) are an alternative method. ANNs

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (O. Arslan). http://dx.doi.org/10.1016/j.geothermics.2016.10.004 0375-6505/© 2016 Elsevier Ltd. All rights reserved.

were used in various studies for different purposes and also for refrigeration applications (Mohanraj et al., 2012). Ertunc and Hosoz (2006) conducted an application of ANN to predict the performance of a refrigeration system with an evaporative condenser. Hosoz and Ertunc (2006) performed the applicability of ANN to predict the performance of automotive air conditioning systems. Tahavvor and Yaghoubi (2011) studied on ANN to predict frost thickness and density around a cooled horizontal circular cylinder. Antonio and Afonso (2011) used ANN method with supervised learning performed using a Genetic Algorithm for the prediction of temperatures of a commercial household refrigerator. Sahin (2011) handled ANN for the performance analysis of single-stage vapor compression refrigeration system with internal heat exchanger. Kumlutas et al. (2012) presented an application of ANN to predict the design parameter’s values of the static type domestic refrigerator. Chiang Ng et al. (2014), in their study, implemented a Model Predictive Controller (MPC) using an online trained ANN for an automotive air conditioning system. Mora et al. (2014), in their study, used ANN for prediction of thermodynamic properties of refrigerants in vapor-liquid equilibrium. Belman-Flores and Ledesma (2015), studied on the application of ANN to carry out a statistical analysis of the energy performance for a compression vapor system. Deng et al. (2016) used ANN based on genetic algorithm to pre-

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Nomenclature Bt b C E˙ ˙ Ex fr h ˙ m P Q˙ r s t T ˙ W X ε 



Cumulative cash flow (US$) Bias Cost (US$) Energy (kWh) Exergy (kW) Circulation rate Specific enthalpy (kJ kg−1 ) Mass flow (kg s−1 ) Pressure (kPa) Heat energy (kW) Discount rate (%) Entropy (kJ kg−1 K−1 ) Time (year) Temperature (◦ C) Work energy (kW) NH3 ratio (%) Energy efficiency (%) Exergy efficiency (%) Specific volume (m3 kg−1 ) Specific exergy (kJ kg−1 )

Subscripts abs Absorber ch Chemical property Construction cns con Condenser c,w Cooling water d Destruction Electric e evap Evaporator Geothermal fluid gf h Heater hex Solution heat exchanger hg Heater group i Inlet Installation ins inv Initial investment m Maintenance and repair Outlet o O&M Operating and maintenance p Pump ph Physical property Profit pr rv Refrigeration expansion valve sal Salvage sv Solution expansion valve Staff stf val Valves Total tot 0 Dead state

dict the normal boiling point of refrigerants. Saleh and Aly (2016), improved a new technique using ANN to predict the mass flow rates in the electronic expansion valves. Sozen et al. (2003) determined thermodynamic characteristics of methanol/LiBr solution, an alternative fluid couple for absorption systems, using ANN method. Sencan (2007) developed a new formulation based on ANN model for the analysis of absorption refrigeration system with NH3 -H2 O fluid couple and they obtained optimum results using ANN model. COP and fr (circulation rate) were predicted upon temperature of system components and concentration values. As seen from given summary of the literature, ANN is a useful tool for prediction of

211

Table 1 Characteristics of the wells in Simav geothermal field (Anonymous, 2014; Pinar, 2014). Well

Depth (m)

Mass rate (kg s−1 )

Temperaturea (◦ C)

EJ-1 EJ-3 EJ-4 EJ-5 E-6 E-8 E-9 E-10 E-11 E-12

725 424 588 603 169.6 205 208 288 502 241

72 50 65 60 50 80 60 Re-injection well 35 35

162 93 152 152 157 92 98

a

99 150

Well bottom temperature, x: positive, o: negative.

some parameters of the systems. ANN is also useful for the optimization of the systems. Arslan (2011) used ANN to make a decision for the optimum working conditions of Kalina cycle system. Arslan and Yetik (2011) performed ANN to optimize the system parameters of supercritical ORC-Binary geothermal power plant. In another study, Arslan and Yetik (2014) performed ANN to optimize the system parameters of supercritical ORC-Binary geothermal power plant. Arslan (2014), in his study, determined the optimum working conditions of combustion chambers using ANN tool. Arat and Arslan (2017), in their study, determined the optimum system of geothermal aided heat pump system using a multistage and multilevel ANN model. In this study, the design data of geothermal energy aided singlestage absorption food refrigerator system using NH3 -H2 O solution compiled through energy, exergy and cost analyses to evaluate the geothermal sources in Simav district of the city of Kutahya were modelled with ANN. In this aim, a novel approach was conducted including two different stages in ANN. Finally, using bias and weights of the most appropriate composite model, the handled system was optimized. 2. Material and methods In the study, geothermal resources of Simav region were taken into account for the design of absorption refrigeration system. Simav geothermal field, being one of Turkey’s most important 15 geothermal fields, has 10 wells either in use or ready to use. Table 1 shows characteristic values of these wells. 2.1. Design of GAARS Formed through mixture of Simav geothermal wells, the geothermal fluid has a high level energy potential with 133.5 ◦ C temperature and 462 kg s−1 flow. To harness this potential, taking the target production group planned to be cooled and the system conditions into account, a single-stage absorption refrigeration system was dealt with in the study, which allows applications below 0 ◦ C, eliminates crystallization risk by using NH3 -H2 O fluid couple. The flow diagram of the system is shown in Fig. 1. By changing entrance and exit temperatures of geothermal fluid, 3660 designs were achieved according to different solution concentrations and different temperature parameters. These designs were evaluated with energy and exergy analysis. The governing equations used for designing of GAARS are given in Table 2. In the analysis, considering the worst case (uninsulated case) in the interaction of the heater group with the environment, a 5% loss was assumed. Since the average heat in other heat exchangers is an aim, this rate isn’t included into computations. Pump efficiencies were included into computations as 60% and surface heat loss is neglected. The detailed information can be achieved from the previous study of authors (Tugcu et al., 2016). Thermodynamic values

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Fig. 1. Single stage NH3 –H2 O mixed absorption refrigeration system. Table 2 Energy and exergy balances (Tugcu, 2015; Tugcu et al., 2016). Component

Energy balances

Eq.

Heater Group

(1)

Solution Pump

˙ = (m ˙ 6 h6 − m ˙ 1 h1 − m ˙ 9 h9 ) + (m ˙ 14 h14 ) · 0.95 ˙ 13 h13 − m Q˙ hg − W ˙ p = (P6 −P5 ) · 6 · fr W

Evaporator Condenser Absorber

˙ =m ˙ 3 h3 − m ˙ 4 h4 Q˙ evap − W ˙ =m ˙ 1 h1 + m ˙ 15 h15 − m ˙ 2 h2 − m ˙ 16 h16 Q˙ con − W ˙ =m ˙ 4 h4 + m ˙ 10 h10 + m ˙ 11 h11 − m ˙ 5 h5 − m ˙ 12 h12 Q˙ abs − W

(3) (4) (5)

COP

COP =

Component

Exergy balances ˙ d,hg = m ˙ 6 6 +m ˙ 13 Ex

Heater Group

Q˙ evap Q˙ h +Wp

(6)

Evaporator Condenser

˙ d,con = m ˙1 Ex

Absorber

˙ d,abs = m ˙4 Ex ˙ d,sv = m ˙9 Ex ˙ d,r v = m ˙2 Ex

Solution Expansion Valve Refrigerant Expansion Valve ε

ε=

4

14

˙1 −m



+ Q˙ evap 1 − ·

1

˙ 15 +m

15

4

˙ 10 +m

10

˙ 11 +m

11

˙9 −m

1

T0 T

˙ p,d − m2 + ˙W

˙ 10 −m ˙3 2 −m

9

˙ 14 −m ˙ p + ˙W 13

˙ d,p = m ˙ 5 5 −m ˙6 6 Ex ˙ d,evap = m ˙ 3 3 −m ˙4 Ex

Solution Pump

(2)

p

9

+ Q˙ hg

 2



1−

T0 T



Eq. ˙ p − ˙W

(7) (8)

˙ 14 −m



14

˙ p,d − m ˙5 + ˙W

5

− Q˙ con 1 − ˙ 12 −m

12

T0 T



(9)



− Q˙ abs 1 −

T0 T



(10) (11) (12) (13) (14)

10 3

COP COPCarnot

of NH3 -H2 O solution were determined using engineering software called REFPROP (REFPROP, 2010).

ment is not feasible. This reduced cash flow value can be expressed mathematically as follows.

2.2. Economic analysis of GAARS

NPV =

The objective function required for optimum solution in the system is composed of net present value (NPV) acquired through evaluation of the system in economic aspects. NPV of the system is the difference between the sum of reduced cost according to a certain discount rate and the sum of reduced net income and current value of scrap. If this difference is positive, the project is acceptable (NPV > 0). If NPV = 0, then it is understood that annual returns can barely meet the operating costs and annual investment costs. At this point, the investor decides on investment according to the other advantages of the investment. If NPV < 0, then invest-

n  t=0

Bt (1 + r)t

(15)

where NPV is net current value,n is profitable life of the project, Bt is the cash flow in t year, r denotes discount rate. In this study, profitable life of the project and discount rate were included as 20 years and 7.4% respectively. Cash flow was determined considering the initial investment cost of the system (Cinv ), operating and maintenance cost (CO&M ), salvage cost (Csal ) and profit (Cpr ) from the system. Bt = Cpr + Csal − CO&M − Cinv

(16)

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The initial investment cost of the system was comprised of heater (Ch ), condenser (Ccon ), evaporator (Cevap ), absorber (Cabs ), solution heat exchanger (Chex ), expansion valves (Cval ), pumps used in the system (Cp ), installation cost (Cins ) and construction cost (Ccns ). Cinv = Ch + Ccon + Cevap + Cabs + Chex + Cval + Cp + Cins + Ccns

(17)

In this context, heat exchanger cost was determined by choosing the suitable heat exchangers from the 2014 unit price list of Ministry of Environment and Urbanization depending on the required heat loads and taking unit price and installation cost into account. The cost of expansion valves to be used in NH3 and NH3 -H2 O solution lines of the system, also taking the market conditions into account, was determined according to manufacturer price lists and catalogues. The cost of pumps for NH3 -H2 O solution, cooling water in absorber and condenser, and geothermal fluid, taking the system parameters and fluid conditions into account, were determined according to manufacturer price lists and catalogues. The spare pumps also were taken into account in the study. Installation cost was taken as 10% of the total cost. Construction cost of the geothermal aided absorption refrigeration facility was computed according to the facility layout plan including the product capacity to be cold stored. During construction cost computations, unit cost was taken 222.727 US$ m−2 as determined by Ministry of Environment and Urbanization for cold storage facilities (Tugcu, 2015; Tugcu et al., 2016). Electric cost of the pumps (Ce ), staff cost (Cstf ), cost of pure NH3 (CNH3 ) and pure H2 O (CH2O ) used in the system, cooling water cost (Cc,w ), geothermal fluid cost (Cgf ) and maintenance and repair cost (Cm ) constituted the operating and maintenance cost. CO&M = Ce + Cstf + CNH3 + CH2O + Cc,w + Cgf + Cm

(18)

Taking the temperature decennial data per hour for Simav district obtained from Ministry of Forestry and Water Affairs, General Directorate of Meteorology into account, operation time of the refrigeration system was determined 4500 h annually. Unit cost of electricity was included into the computations as average 0.1318 US$ per kWh. Cooling water cost in the refrigeration system was composed of cooling water amount used in absorber and condenser. Cooling water unit cost was taken as 0.0372 US$ m−3 . Unit cost of geothermal fluid was taken from as 0.05954 US$ m−3 . Pure H2 O unit cost was included as 625 US$ per ton while pure NH3 unit cost was taken as 731.6 US$ per ton. Workforce requirement for the cooling system to execute the system operations was included in the computations as 1 director, 1 engineer, 1 technician and 40 qualified workers. Maintenance and repair cost of the cooling system was determined to be the 2% of the initial investment cost. Salvage cost of the cooling system was taken as 10% of the initial investment cost. For profit, 90.909 US$ per ton was included in the cooling gain account as unit cooling cost for grape and 68,181 US$ per ton was included for apple and quince (Tugcu, 2015; Tugcu et al., 2016).

Fig. 2. Artificial neural cell (Fu,1994).

be trained. ANN learns from examples and it can answer nonlinear problems. Compared with the conventional methods, some of ANN’s advantages are speed, simplicity and learning from examples. Its unit component is neuron. ANN is composed of input layer, hidden layers and output layer, all of which contain numerous neurons. An artificial neural cell is shown in Fig. 2 (Fu, 1994). As seen in Fig. 2, each artificial neural cell is composed of five main parts: input (Xn ), weight (Wn ), total function (˙), activation function f (˙) and output (y). Each input value was multiplied with connection weights. Later, these multiplications and bias values are added. Output was gained by passing the total result from transfer function (Fu, 1994; Oztemel 2012). When bias is used, the relation between input and output is understood more easily. In general, transfer function composed of algebraic equations might be linear or nonlinear. Function preference depends on the problem to be solved (Kalogirou, 2004). An important stage in neural network is training stage. The input is given into the network with the desired output and weights are arranged to obtain the desired output value. Before training, weights are chosen randomly and are meaningless, but after training, they contain very meaningful information. There are different learning algorithms to obtain the relation between input and output. The most common learning algorithm is backpropagation algorithm. The most common algorithms in energy are Levenberg-Marquardt (LM), Pola-Ribiere Conjugate Gradient (CGP) and Scaled Conjugate Gradient (SCG). LM algorithm is regarded as the fastest method for back-propagation neural networks. CGP and SCG algorithms are versions of conjugate algorithm. ANN with back-propagation algorithm learns by changing weights and this change is stored as information. In the study, performance of the structured model was determined using such statistical methods as root mean squared error (RMSE), coefficient of variation (cov), absolute proportion of variance (R2 ) and mean percentage error (MPE) whose equations are presented between 19 and 22.

RMSE =

 

2  n y −yactual  m=1 output youtput 

cov =



nm = 1 youtput − y¯ output (yactual − y¯ actual ) n

2.3. ANN modelling of GAARS ANN is a system based on the operating principles of the neurons in human brain. ANN seeks to solve the problems that cannot be solved with conventional methods with methods similar to the operating system of human brain. ANN gives rather good results in subjects involving deficient and fuzzy information or in problems that are ill-defined or complex. ANN has been used in various fields like mathematics, engineering, medicine, economy, meteorology, psychology and neurology (Sencan and Kalogirou, 2005). ANN works in two ways: one is training (learning) and the other is test (operating) stage. In order to use an ANN, it should first

(19)

n

⎡



· 100

(20)

⎤2



nm = 1 youtput − y¯ output (yactual − y¯ actual )

R2 = ⎣

nm



= 1 youtput − y¯ output

2

nm

= 1(yactual − y¯ actual )

⎦ 2

(21)

n MPE =

m=1



youtput − yactual



n.|yactual,max − yactual,min |

· 100

(22)

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Fig. 3. The first network architecture for ANN.

 These  statistical parameters can be expressed as output value

youtput , average output value y¯ output , actual value (yactual ), average actual value (y¯ actual ) and number of data (n). In this study, various algorithms were tried and CGP, LM and SCG algorithms were chosen because they gave the best results. Inputs and outputs were normalized between 0 and 1. Non-linear algorithmic sigmoid (logsig) transfer function was used. Logsig function is defined as below (Fu, 1994; Oztemel 2012):

f (ze) =

1 1 + e−ze

(23)

where ze is defined in terms of bias (b), weight (w) and output (y): zej =

n 

wij yi + bj

(24)

i=1

3. Results and discussion In the study, different mixture rates of NH3 -H2 O solution (% 46 NH3 -% 54 H2 O, % 40 NH3 -% 60 H2 O, % 30 NH3 -% 70 H2 O, % 20 NH3 -% 80 H2 O) were taken into account and input temperature of the geothermal fluid (gf) was taken 110 ◦ C. Output temperatures were changed and 3660 designs were built for different temperature values of the system components. COP and ε of the designs were computed using energy and exergy analysis methods. Using these data, absorption refrigeration system was modelled with artificial neural network. ANN models were prepared using MATLAB (MATLAB, 2007). There are 14640 data of 3660 designs in the models used for predicting cooling effect coefficient (COP), exergy efficiency (ε) and net present value (NPV) of the absorption refrigeration system and while 10248 of these data were used for training, the remaining 4392 data were used for test. In the study, a dual-stage network model was used in which output of the first network were used as input of the second network. In Fig. 3, network architecture of the first network which was used for predicting vaporizer capacity, initial investment cost, total operating cost and scrap cost values

is shown. To obtain the sensitive results during training in the first network of ANN modelling of absorption refrigeration system, neuron numbers in the single hidden layer were raised from 8 to 20. The 8 inputs in the first model are room capacity, heater output temperature (T1 ), condenser output temperature (T2 ), vaporizer output temperature (T4 ), absorber output temperature (T5 ), poor solution heater return temperature (T8 ), geothermal water output temperature (T14 ) and rich solution concentration (XZ ). The four parameters in the output layer of this network were evaporator capacity (Qevap ), initial investment cost (Cinv ), operating cost and maintenance (CO&M ), and salvage cost (Csal ), respectively. The network architecture was trained for 1000 iterations and it was determined that R2 value differentiated between 0.9945 and 1.000 for evaporator capacity at the training stage and between 0.9944 and 1.000 at the testing stage. These values were determined to differentiate for initial investment cost between 0.9983 and 0.9998 for the training and between 0.9984 and 0.9998 for the testing; for total operating cost between 0.9956 and 1.000 for the training and between 0.9955 and 0.9999 for the testing; and for salvage cost between 0.9983 and 0.9998 for the training and testing. In Table 3, statistical results of the best network outputs are shown. According to Table 3, it was determined that R2 value differentiated between 0.9990 and 1.000 for evaporator capacity at the training and the testing stage. These values were determined to differentiate for initial investment cost between 0.9991 and 0.9998 for the training and between 0.9990 and 0.9998 for the testing; for total operating cost between 0.9974 and 1.000 for the training and between 0.9974 and 0.9999 for the testing; and for salvage cost between 0.9991 and 0.9998 for the training and between 0.9990 and 0.9998 for the testing. Accordingly, the best network for Qevap was determined to be LM training algorithm with 20-neuron (LM20) for initial investment and scrap costs and LM training algorithm with 16-neuron (LM-16) for total operating cost. The second network model shown in Fig. 4 was designed separately for cold storage products like grape, apple and quince raised in the area. The second network architecture was composed of single hidden layer and neuron number of the layer was raised from

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215

Table 3 Statistical evaluation results of the first network. Algorithm

Training

Test

cov

RMSE

MPE

R2

cov

RMSE

MPE

R2

Q evap LM-20 CGP-20 SCG-12

0.1314 1.4394 1.3122

33.0305 361.7927 329.8081

0.0649 0.7288 0.6578

1.0000 0.9990 0.9992

0.1298 1.4498 1.2954

0.0643 0.7394 0.6491

32.7482 365.7909 326.8308

1.0000 0.9990 0.9992

C inv LM-20 CGP-20 SCG-12

0.5113 1.2491 1.0142

26725.8327 65286.4686 53008.8032

0.3405 0.8110 0.6884

0.9998 0.9991 0.9994

0.5123 1.2847 1.0179

0.3415 0.8357 0.6891

26897.5664 67450.4041 53441.4338

0.9998 0.9990 0.9994

C O&M LM-16 CGP-20 SCG-12

0.1947 1.3647 1.3800

11605.3461 81348.4735 82256.6006

0.1522 1.3329 1.3516

1.0000 0.9974 0.9974

0.2201 1.3546 1.3673

0.1555 1.3386 1.3452

13146.7325 80911.5787 81671.9612

0.9999 0.9975 0.9974

C sal LM-20 CGP-20 SCG-12

0.5113 1.2424 1.0100

2672.5833 6493.6103 5279.2969

0.3405 0.8087 0.6840

0.9998 0.9991 0.9994

0.5123 1.2755 1.0135

0.3415 0.8319 0.6851

2689.7566 6696.6084 5321.2184

0.9998 0.9990 0.9994

Fig. 4. The second network architecture for ANN.

8 to 24. The second network input was composed of the input and output of the first network. The three outputs in the output layer of the second network were COP, ε and NPV, respectively. The second network architecture was also trained for 1000 iterations. It was determined that for NPV, R2 value differentiated between 0.9595 and 0.9996 for the training and between 0.9597 and 0.9995 for testing. These values of COP were determined to differentiate between 0.9943 and 1.000 for the training and between 0.9944 and 1.000 for the testing while they differentiated for exergy efficiency (␧) between 0.9895 and 1.000 for the training and between 0.9899 and 1.000 for the testing. If the best solutions of the each training algorithms were taken into consideration, it was determined that R2 value differentiated between 0.9904 and 0.9997 for NPV at the training stage and between 0.9870 and 0.9993 at the testing stage. These values were

determined to differentiate for COP between 0.9989 and 1.000 at the stages of both training and testing; for exergy efficiency (␧) between 0.9943 and 1.000 at the training stage and between 0.9944 and 1.0000 at the testing stage. Depending on the statistical analysis results, the best model for grape in the second network was determined LM-20 for NPV and LM-24 for other outputs. Statistical results of the network outputs are shown in Table 4. Graphic display of comparison of ANN results of the best models with the analytic results for the cooled product group grape was given in Fig. 5 for training data and in Fig. 6 for test data. As seen in Fig. 5 and 6, it was determined that distributions of ANN predictions and analytic results are coherent. Accordingly, the ideal network architecture is suitable for optimization. The same operations were also done for the other product groups. So, for the product groups of apple, it was determined that for NPV, R2

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Fig. 5. Comparison of ANN estimation and analytic results at training stage; a) for NBD, b) for COP and c) for ε.

value differentiated between 0.9595 and 0.9996 for the training and between 0.9597 and 0.9995 for the testing. These values for COP were determined to differentiate between 0.9943 and 1.000 for the training and between 0.9944 and 1.000 for the testing while they differentiated for exergy efficiency (␧) between 0.9895 and 1.000

for the training and between 0.9899 and 1.000 for the testing. The results of best solutions for apple are given in Table 5. As seen in Table 5, it was determined that R2 value differentiated between 0.9808 and 0.9996 for NPV at the training stage and between 0.9805 and 0.9995 at the testing stage. These values were determined to differentiate for COP between 0.9988 and

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217

Fig. 6. Comparison of ANN estimation and analytic results at test stage; a) for NBD, b) for COP and c) for ε.

1.000 at the training stage and between 0.9989 and 1.000 at the testing stage; for exergy efficiency (␧) between 0.9976 and 1.000 at the training stage and between 0.9975 and 1.000 at the testing stage. Depending on the statistical analysis results, the best model

for apple in the second network was determined LM-20 for COP and LM-24 for other outputs. For the product groups of quince, it was determined that for NPV, R2 value differentiated between 0.9334 and 0.9993 during training and between 0.9068 and 0.9958 during test. These val-

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Fig. 7. NBD evaluation for optimum design a) for grape, b) for apple and c) for quince.

ues were determined to differentiate for COP between 0.9887 and 1.000 during training and between 0.9878 and 1.000 during test while they differentiated for exergy efficiency (␧) between 0.9907

and 1.000 during training and between 0.9894 and 1.000 during test. The results of best solutions for quince are given in Table 6. As seen in Table 6, it was determined that R2 value differentiated between 0.9629 and 0.9993 for NPV at the training stage

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219

Table 4 Statistical evaluation results of the second network for grape. Algorithm

Training

Test

cov

RMSE

MPE

R2

cov

RMSE

MPE

R2

NPV LM-20 CGP-16 SCG-24

6.9509 37.9673 36.5996

347804.2171 1899768.3924 1831331.8551

0.2488 1.7494 1.7261

0.9997 0.9904 0.9910

10.0157 43.1070 43.4130

507468.2766 2184125.6457 2199626.8792

0.2927 1.8690 1.8283

0.9993 0.9872 0.9870

COP LM-24 CGP-10 SCG-8

0.0128 0.1741 0.1796

0.0001 0.0009 0.0009

0.0358 0.5481 0.5425

1.0000 0.9990 0.9989

0.0139 0.1687 0.1808

0.0001 0.0009 0.0009

0.0366 0.5374 0.5365

1.0000 0.9990 0.9989

ε LM-24 CGP-8 SCG-24

0.0556 2.0321 1.2470

0.0003 0.0110 0.0067

0.0321 1.2097 0.7722

1.0000 0.9943 0.9979

0.0631 2.0209 1.3988

0.0003 0.0110 0.0076

0.0338 1.2116 0.8031

1.0000 0.9944 0.9973

Table 5 Statistical evaluation results of the second network for apple. Algorithm

Training

Test 2

cov

RMSE

MPE

R

cov

RMSE

MPE

R2

NPV LM-24 CGP-16 SCG-16

0.9662 6.4182 4.9832

195941.8285 1301572.9530 1010571.2441

0.2561 2.0339 1.5738

0.9996 0.9808 0.9884

1.0737 6.5128 5.0083

217018.7090 1316375.3092 1012287.0415

0.2668 2.0792 1.5941

0.9995 0.9805 0.9885

COP LM-20 CGP-12 SCG-8

0.0145 0.1831 0.1836

0.0001 0.0009 0.0009

0.0430 0.5882 0.6002

1.0000 0.9988 0.9988

0.0147 0.1829 0.1817

0.0001 0.0009 0.0009

0.0434 0.5911 0.5949

1.0000 0.9989 0.9989

␧ LM-24 CGP-12 SCG-12

0.0620 1.3265 1.2029

0.0003 0.0072 0.0065

0.0382 0.7898 0.7012

1.0000 0.9976 0.9980

0.0619 1.3648 1.2177

0.0003 0.0074 0.0066

0.0383 0.8064 0.7158

1.0000 0.9975 0.9980

Table 6 Statistical evaluation results of the second network for quince. Algorithm

Training

Test

cov

RMSE

MPE

R

cov

RMSE

MPE

R2

NPV LM-20 CGP-20 SCG-24

0.7924 5.8117 5.5151

200426.6550 1469989.1471 1394971.1005

0.2769 2.5701 2.3748

0.9993 0.9629 0.9666

1.9530 7.9465 7.2454

494125.8013 2010519.7883 1833137.6083

0.3909 2.8276 2.6303

0.9958 0.9299 0.9416

COP LM-24 CGP-8 SCG-8

0.0242 0.3119 0.2017

0.0001 0.0016 0.0010

0.0772 0.9969 0.6370

1.0000 0.9967 0.9986

0.0239 0.3127 0.2081

0.0001 0.0016 0.0011

0.0775 1.0130 0.6615

1.0000 0.9966 0.9985

␧ LM-24 CGP-10 SCG-10

0.0772 1.3120 1.8353

0.0004 0.0071 0.0099

0.0450 0.7495 1.0761

1.0000 0.9976 0.9953

0.0796 1.4062 1.8566

0.0004 0.0077 0.0102

0.0472 0.7934 1.0774

1.0000 0.9973 0.9954

and between 0.9299 and 0.9958 at the testing stage. These values were determined to differentiate for COP between 0.9967 and 1.000 at the training stage and between 0.9966 and 1.000 at the testing stage; for exergy efficiency (␧) between 0.9953 and 1.000 at the training stage and between 0.9954 and 1.000 at the testing stage. Depending on the statistical analysis results, the best model for quince in the second network was determined LM-20 for NPV and LM-24 for other outputs. According to formed networks, the results showed that the increase in the number of neurons gives more sensitive outputs from the statistical point of view. However, at this time, the timing problem occurs for the solution of the outputs which result in much more. So, it is more appropriate to evaluate the best network according to the statistical results. The second problem is the

2

divergence problem which occurs by using more neurons. In the proposed ANN model, it was aimed to maximize the NPV. Therefore, the minimum and maximum values of the inputs belonging to the design parameters was considered as constraints and the optimization of GAARS was carried out taking the previous study of the author, in which the system was analytically optimized and investigated by means of energy and exergy analysis, into consideration (Tugcu et al., 2016). So, using the weights and bias values of the best network architectures, geothermal aided absorption refrigeration system was analyzed for different parameters and optimum system was obtained. These results show well-matched with analytical solutions. Accordingly, for 46% NH3 -% 54 H2 O solution, the exergy values acquired by considering that geothermal fluid entered the system at 110 ◦ C and thermodynamic character-

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A. Tugcu, O. Arslan / Geothermics 65 (2017) 210–221

Table 7 Thermodynamic characteristics and exergy values for optimum refrigeration system design. Point

Fluid

˙ (kg s−1 ) m

T (◦ C)

P (kPa)

X (%)

h (kJ kg−1 )

s (kJ kg−1 K−1 )

˙ ph (kW) Ex

˙ ch (kW) Ex

˙ tot (kW) Ex

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

NH3 NH3 NH3 NH3 NH3 -H2 O NH3 -H2 O NH3 -H2 O H2 O H2 O H2 O H2 O H2 O gf gf H2 O H2 O

40.76 40.76 40.76 40.76 88.57 88.57 88.57 47.81 47.81 47.81 1628.58 1628.58 462 462 1228.04 1228.04

70 30 −4 −4 30 30.06 48.54 70 32.06 32.23 25 35 110 70 25 35

1167.2 1167.2 368.8 368.8 368.8 1167.2 1167.2 1167.2 1167.2 368.8 101.325 101.325 300 300 101.325 101.325

100 100 100 100 46 46 46 0 0 0 0 0 0 0 0 0

1744.2 484.91 484.91 1601 41.333 42.29 127.88 293.99 135.42 135.42 104.92 146.72 461.5 293.29 104.92 146.72

6.0915 1.9597 1.9991 6.1457 0.91201 0.91201 1.186 0.95445 0.46476 0.46739 0.3672 0.5051 1.4187 0.95497 0.3672 0.5051

14142.49 13000.58 12521.98 7646.88 1487.55 1572.45 1922.17 672.72 68.23 30.76 44690.91 0 628836.03 150848.18 33699.26 0

808792.21 808792.21 808792.21 808792.21 810842.78 810842.78 810842.78 25221.52 2389.40 2389.40 81384.27 81384.27 23087.17 23087.17 61367.96 61367.96

822934.71 821792.79 821314.19 816439.10 812330.33 812415.24 812764.96 25894.25 2457.64 2420.17 126075.18 81384.27 651923.20 173935.35 95067.22 61367.96

Table 8 Energy analysis values of optimum design. Component

Ex˙ i (kW)

˙ o (kW) Ex

Q˙ (kW)

˙ (kW) W

COP

Heater Group Solution Pump Evaporator Condenser Absorber Solution Expansion Valve Refrigerant Expansion Valve Geothermal Pump Condenser Pump Absorber Pump The Overall System

3746.076866 3661.1715 19766.26252 71098.37926 71736.22083 6475.066607 19766.26252 – – –

77573.44587 3746.076866 65261.15422 19766.26252 3661.1715 6475.066607 19766.26252 – – –

73827.369 – 45494.8917 −51332.11674 −68075.04933 – – – – –

– 145 – – – – – 250 750 750

0.5722

Table 9 Exergy analysis values of optimum design. Q

W

Component

˙ mass.i (kW) Ex

˙ mass.o (kW) Ex

˙ (kW) Ex

˙ (kW) Ex

˙ d (kW) Ex

ε (%)

Heater Group Solution Pump Evaporator Condenser Absorber Solution Expansion Valve Refrigerant Expansion Valve Geothermal Pump Condenser Pump Absorber Pump The Overall System

812415.24 812330.33 821314.19 822934.71 818859.27 2457.64 821792.79 – – –

825392.35 812415.24 816439.10 821792.79 812330.33 2420.17 821314.19 – –

18296.74 – 676.12 −5079.87 −6736.76 – – – – –

– 145 –

5319.63 60.09 5551.22 6221.78 13265.70 37.47 478.60 250 750 750

0.6201

istics of absorption refrigeration system at 70 ◦ C and computing the physical and chemical exergy values of the fluid or solution couple are given in Table 7. While Table 8 shows energy analysis values of optimum design by computing heater group, condenser, vaporizer, absorber and pump capacities of optimum design given in Table 7 and COP value of the system, Table 9 shows exergy analysis results. COP value of the optimum system was computed 0.5722 and total exergy efficiency was found 0.6201. NPV values of grape, apple and quince obtained for 20 years of system life and 7.4% discount rate are given in Fig. 7. According to Fig. 7, payback time of the system for optimum design according to NPV analysis results was computed 7–8 years for grape, 13–14 years for apple and 18–19 years for quince. Table 10 shows the characteristic values of optimum design. As seen in Table 10, analytic design results are rather close to those obtained from ANN model. In terms of COP values, error rate is

– – – 250 750 750

computed almost 2% for all products. These values were also determined 2% for exergy efficiency (ε). In terms of NPV values, error rates were determined as follows: 0.07% for grape, 0.14% for apple and 6% for quince. Comparing the COP, ε and NPV values computed analytically in the study with those computed with ANN model, it was determined that they were statistically acceptable. 4. Conclusion In this study, an absorption refrigeration system designed using Simav geothermal resources was analyzed parametrically and modelling 14640 data of obtained 3660 designs with artificial neural networks, the best architectures and training algorithms were determined. In the study, a novel two-stage ANN model was built in which the outcome of the first network was comprised of the input of the second network and using the weights of the resultant networks and bias values, optimum system was determined.

A. Tugcu, O. Arslan / Geothermics 65 (2017) 210–221 Table 10 Characteristic values of optimum design. Wp (kW)

1895.00

Qhg (kW) Qcon (kW) Qevap (kW) Qabs (kW) Qhex (kW)

73827.37 51332.12 45494.89 68075.049 7581.98 Analytic

COP Grape Apple Quince ␧ (%) Grape Apple Quince NPV (million US$) Grape Apple Quince

ANN

0.5722

0.5846 0.5847 0.5846

0.6201

0.6341 0.6344 0.6342

27.183 6.328 1.778

27.164 6.337 1.662

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