Document Type: Original Article
Authors
^{1} MSc Islamic Azad University Sciences & Research Branch, Hesarak, Tehran, Iran
^{2} Assistant Professor Department of Mechanical Engineering, Bozorgmehr University of Qaenat, Qaen, Iran
^{3} Professor Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
^{4} PhD Candidate of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Abstract
Keywords
Main Subjects
1. Introduction
Waste heat, in the most general sense, is the energy associated with the waste streams of air, exhaust gases, and/or liquids that leave the boundaries of a plant or building and enter the environment. In a more restricted definition, waste heat is the energy which is rejected from a process at a temperature high enough above the ambient temperature to permit the economic recovery of some fraction of that energy for useful purposes (Doty & Turner, 2004). The strategy of how to recover this heat depends on the temperature of the waste heat and the economics involved (Thumann & Mehta, 2001).
The energy and global warming crises have drawn renewed interests to thermally driven cooling systems from the air conditioning and process cooling facilities. The lithium bromidewater absorption chiller is one of the favorites due to the following specific reasons: (i) it can be thermally driven by lowtemperature heat as well as waste heat, which substantially reduce carbon dioxide emission; (ii) its use of water as a refrigerant; (iii) it is quiet and cheap to maintain, being nearly void of high speed moving parts; (iv) its vacuumed operation renders to scale up applications (Wang & Chua, 2009).
Heat recovery systems in which absorption chillers have been used to produce cooling have been studied by many researchers. Khoshgoftarmanesh and babaelahi have a 160 MW combined cycle power plant from Exergetic, Economic, Environmental aspects simultaneously through MultiObjective Optimization (Khoshgoftar Manesh & Babaelahi, 2017). Golchoobian et al. studied three combined power and refrigeration cycles for a defined demand and same fuel consumption in a 24 hours period, thermodynamically. Power cycle was used for power generation and also ejector refrigeration cycle is used to produce cooling (Golchoobian, Amidpour, & Pourali, 2018). Jeong et al. carried out a numerical simulation to predict the transient operating characteristics and performance of an absorption heat pump recovering low grade waste heat (Jeong, Kang, & Karng, 1998). Ameri and Hejazi presented an overview of an intake air cooling system that uses a steam absorption chiller and an air cooler in order to increase the performance of a gas turbine (Ameri & Hejazi, 2004). Wu and Wang worked on combined cooling, heating and power (CCHP) systems (Wu & Wang, 2006). They studied the various options to produce cooling in CCHP systems including absorption cooling, adsorption cooling, and desiccant dehumidifiers Deng et al. discussed thermally activated cooling technologies for CCHP systems are presented here in detail, mainly including absorption and adsorption refrigeration, and desiccant cooling (Deng, Wang, & Han, 2011).
Absorption refrigeration technology is studied by many researchers. ShariatiNiasar et al. presented a novel mixed fluid cascade natural gas liquefaction process and analyzed it through exergy and exergoeconomic methods. They used a waterammonia absorption refrigeration cycle instead of one of the vapor compression cycles (Shariati Niasar et al., 2017). Xu et al. carried out a thermodynamic analysis to study the effect of design parameters on the performance of double effect absorption of the series flow type (Xu, Dai, Tou, & Tso, 1996). Arun et al. evaluated the equilibrium temperatures at the low pressure (LP) generator for double effect series flow lithium bromide–water vapor absorption chiller and the system performance at these temperatures (Arun, Maiya, & Murthy, 2000). Chua et al. presented a thermodynamically consistent set of specific enthalpy, entropy, and heat capacity fields for LiBrwater solution (Chua, Toh, Malek, Ng, & Srinivasan, 2000). Srikhirin et al. provided a literature review on absorption refrigeration technology (Srikhirin, Aphornratana, & Chungpaibulpatana, 2001). In 2003, Florides et al. presented a method to evaluate the characteristics and performance of a single stage lithium bromidewater absorption machine (Florides, Kalogirou, Tassou, & Wrobel, 2003). Kilic and Kaynakli performed the first and second law thermodynamic analysis of a single effect absorption refrigeration cycle with LiBrwater as working fluid pair (Kilic & Kaynakli, 2007). Kaushik and Arora presented the energy and exergy of single effect and series flow double effect LiBrwater absorption systems (Kaushik & Arora, 2009). Misra et al. applied the thermoeconomic concept to the optimization of a double effect LiBrwater system, aimed at minimizing its overall product cost (Misra, Sahoo, & Gupta, 2005). They used a simplified cost minimization methodology based on the thermoeconomic concept to carry out the costs of all the internal flows and products of the system by formulating thermoeconomic cost balances. Bereche et al. carried out a thermoeconomic analysis of single effect and double effect LiBrwater absorption refrigeration system in which the methodology of functional analysis with negentropy is used (Bereche, Palomino, & Nebra, 2009).
The energy of absorption refrigeration systems is usually supplied from waste heat sources although some researchers recently studied the integration of solar energy and absorption chillers.
Winston et al. have built a solar thermal cooling system using nontracking External Compound Parabolic Concentrators for cooling seasons (Winston, Jiang, & Widyolar, 2014). The solar cooling is used to power a 23 kW double effect (LiBr) absorption chiller. Lu and Wang presented experimental performance investigation and economic analysis of three small solar cooling systems with these different kinds of collectors and chillers (Lu & Wang, 2014). Jayasekara and Halgamuge studied a combined effect absorption cycle that can utilize two energy sources at different temperature ranges or a single source at a wide temperature range (Jayasekara & Halgamuge, 2014).
In the present study, the hot flue gas from the furnace exhaust is used to generate steam in a Heat Recovery Steam Generator (HRSG). Then the produced steam is sent to a double effect absorption chiller in order to produce chilled water. The cost of produced cooling is evaluated by using thermoeconomic (exergoeconomic) method. In other words, the cost of the main product, the cooling cost, was calculated as a function of the exergy of the heat source. Finally, optimization is accomplished on the system by considering most of the operating parameters. The decision variables in optimization are chosen from both HRSG and the Chiller. It is the first study in which the HRSG and Double Effect Absorption Chiller is optimized simultaneously as an integrated system.
2. System Modeling
2.1. HRSG Modeling
Heat recovery steam generator (HRSG) is applied for recovering the heat potential of high temperature flue gas to produce the required steam of utilities. Physical properties and mole fraction of the flue gas are shown in Table 1.
Table 1. physical properties and mole fractions of furnace flue gas
property 
amount 
Temperature 
460(°C) 
pressure 
101.3 (kpa) 
mass flow rate 
162100 (kg/hr)=45(kg/s) 
Mole fraction of CO_{2} 
0.052749 
Mole fraction of H_{2}O 
0.105596 
Mole fraction of O_{2} 
0.093324 
Mole fraction of N_{2} 
0.748286 
The principles of heat recovery steam generators are investigated by many researchers. A comprehensive study is accomplished by reference (Ganapathy, 2003) in which methods for design, applications, and calculations of these heat exchangers are discussed. Hot flue gas condition and temperature have sensible effects on configuration of the HRSG. In this study, a singlepressure water tube boiler is chosen. The device includes three main sections:
(1) economizer (2) evaporator (3) super heater. This model generates single pressure steam at the exit of the super heater section that its schematic configuration is shown in Fig. 1.
In this model, hot flue gas enters the super heater at the temperature of T_{g1} and leaves the economizer at the temperature of T_{g4}. On the water/steam side, cool water enters the economizer at the temperature and the enthalpy of T_{1}, h_{1} respectively and superheated steam leaves the super heater at the temperature and enthalpy of T_{6}, h_{6} respectively. Energy balance equations in different parts of the HRSG can be written as follows:
(1) 

(2) 

(3) 
In these equations, T_{g1}, T_{g2}, T_{g3}, and T_{g4} are the hot gas temperature in different parts of HRSG and h_{1}, h_{2}… h_{6} are enthalpies of water or steam inside the heat exchanger tubes.
Figure 1. The schematic of the model of the HRSG
2.1.1. Pinch and approach temperatures
As it is shown in Fig. 2 the pinch point is the temperature difference between the saturation temperature and the HRSG evaporator enter temperature. It is desirable to make the pinch point as small as possible without making the cost of the HRSG astronomical.
Figure 2. pinch and approach points temperature
The approach point temperature is the difference between the economizer water outlet temperature and the Saturation temperature of the steam. This temperature will guarantee that no steaming will occur in the economizer section.
For solving energy balance equations (equations 1 to 3), the following assumptions are considered:
It should be noted that among proposed assumptions, there are the decision variables of the optimization process which presented in the next parts.
2.2. Double Effect Absorption Chiller
As shown in Fig. 3, a double effect absorption chiller consists of two generators, two solution heat exchangers, an evaporator, a condenser, and an absorber.
High temperature heat is supplied at High Pressure Generator (HPG) and the generated vapor in this section is used as a heat source at Low Pressure Generator (LPG), in which additional vapor is generated.
In a doubleeffect absorption chiller, the entire vapor generated at the HPG is fully condensed at the low pressure LPG(Arun et al., 2000). It involves three pressure levels, i.e. high, medium and low. The HPG functions at high pressure and temperature, the LPG and condenser operate at medium pressure, and the evaporator and the absorber work at a low pressure level. The weak solution leaving the absorber is pumped to the high temperature generator through solution heat exchangers (HX1 and HX2). A high temperature heat source adds heat to HPG to generate water vapor from a weak solution. The strong solution leaving the HPG enters to the LPG where the refrigerant (water) vapor coming from HPG is condensed due to the low temperature of the strong solution. Latent heat of the vapor is utilized in generating water vapor from the strong solution. The strong solution, therefore, becomes stronger (in LithiumBromide) and it is delivered to the absorber through the solution heat exchanger 2 (HX2). Thus in a double effect system, the second effect generator increases the quantity of water vapor generated for the same amount of heat input. This results in higher values of COP than those achieved in the single effect system(Kaushik & Arora, 2009).
Figure 3. schematic diagram of absorption cooling cycle
2.2.1. Mass and Energy Balance Equations
The energy analysis of absorption systems involves the application of principles of mass conservation, species conservation and the first law of thermodynamics. The general equations are given in  Table 2.
Table 2. Mass and energy balance equations (Bereche et al., 2009; Florides et al., 2003; Kaushik & Arora, 2009; Kilic & Kaynakli, 2007; Misra et al., 2005; Srikhirin et al., 2001)
Number 
Mass balance equations 
(4) 

(5) 

(6) 

(7) 

(8) 


energy balance equations 
(9) 

(10) 

(11) 

(12) 

(13) 

)14) 

(15) 

(16) 

(17) 
In the above table, ss, ws, r, HPG, and HX reference to a strong solution, weak solution, refrigerant, high pressure generator, and heat exchanger. The following assumptions are considered for solving eq.1 to 14 (Xu & Dai, 1997):
Many of the assumptions made above are involved in decision variables and at the end of optimization; the optimal values will be carried out and replaced with them. Having used these assumptions, enthalpy and entropy of the streams are calculated. For calculating enthalpy and entropy of the solution, data is taken from ref. (Chua et al., 2000)and for pure refrigerant streams is taken from water and steam standard tables.
By using these assumptions, there are 14 unknown parameters in mass and energy balance equations and heat exchangers effectiveness equations. The unknown parameters of equations (4) to (17) are as follows:
1. Mass flow rate of weak solution leaving the absorber:
2. Mass flow rate of refrigerant vapor leaving the HPG:
3. Mass flow rate of refrigerant vapor leaving the LPG:
4. Mass flow rate of refrigerant stream entering the evaporator:
5. Mass flow rate of strong solution stream leaving the HPG:
6. Mass flow rate of strong solution stream leaving the LPG:
7. Solution concentration of strong solution leaving the HPG:
8. Temperature of weak solution stream leaving HX2:
9. Temperature of weak solution stream leaving HX1:
10. Temperature of strong solution stream leaving HX1:
11. Temperature of strong solution stream leaving HX2:
12. Heat transfer rate in condenser:
13. Heat transfer rate in evaporator:
14. Heat transfer rate in absorber:
2.3. Heat Exchangers Sizing
In singlepass heat exchangers, the temperature difference ( ) between hot and cold fluids varies along with the heat exchanger. Hence, it is convenient to use a mean temperature ( ) between hot and cold fluids. So the total heat transfer rate ( ) between the fluids can be determined from the following equation:
(18) 
Where, A (m^{2}) is the total heat transfer area and U (W/m2°C) is the average overall heat transfer coefficient, based on that area. For Equation (22), can be calculated as follows:
(19) 
Also for equation (22) the overall heat transfer coefficient (U) is defined as(Ozisik, 1985):

(20) 
Where and are the inside and the outside diameters of the tubes, and are the heat transfer coefficient inside and outside the tubes, , are the fouling factors of the tubes and k is the thermal conductivity of the material of the tubes. The method of calculating h_{i} and h_{o} could be found in Appendix I.
3. Exergy and Thermodynamic Analysis
3.1 Exergy Analysis
Eq. (21) is used to evaluate the physical exergy of different streams in the system.
(21) 
Where is the mass flow rate of the stream, h and s is the enthalpy and entropy of the stream per kg, T_{0} is the environmental temperature and h_{0} and s_{0} are the enthalpy and entropy values of the fluid at the environmental temperature T_{0} respectively (Bejan, Tsatsaronis, Moran, & Moran, 1996). The rate of exergy for each stream is calculated while the environment temperature and pressure are assumed as 25˚C and 1 bar respectively.
Considering the fuel and product principles in each component, the exergy destruction and exergy efficiency in each component of HRSG and absorption chiller are calculated as follows (Bejan et al., 1996):
(22) 

(23) 
In order to calculate the exergy efficiency as well as the exergy destruction for each component, it is necessary to first identify the fuel and product. For this purpose, the basic relations of the understudy component is presented in Table 3.
Table 3. The definition of fuel and product exergy for different component of the under study system
Exergy rate of fuel 
Exergy rate of product 
Schematic figure 
component 
اHeat exchanger 

Mixing chamber 

Boiler 
3.2. Thermoeconomic Analysis
The Thermoeconomic analysis is applied to calculate the expenditure cost and the system product cost. Thermoeconomic analysis requires solving energy, exergy, and cost balance equations of the considered HRSG as well as the components of the absorption chiller. The governing equation of thermoeconomic model for the cost balancing of an energy system is written as:
(24) 
By defining exergy cost of each stream, c, Eq. (37) could be changed to
(25) 
The above relations are global cost balance equation, which should be applied for a different component. Here, for each component of the combined system, the cost balance equation is taken into account as presented in Table 4.
For solving equations (26) to (33), the auxiliary equations (equations (34) to (46)) have been used according to the principles of thermoeconomic analysis.
4. Optimization Approach
In order to achieve the optimal parameters, an optimization algorithm tool can be used. Although gradient descent methods are the most elegant and precise numerical methods to solve optimization problems, however, they have the possibility of being trapped at local optimum depending on the initial guess of solution. In order to achieve a good result, these methods require very good initial guesses for parameters. Stochastic optimization method such as genetic algorithm (GA) that has been applied for this study seems to be a promising alternative for solving this problem. In general, it is robust search and optimization techniques, able to cope with illdefined problem domain such as multimodality, discontinuity, and timevariance. GA is a populationbased optimization technique that searches the best solution for a given problem based on the concepts of natural selection, genetics, and evolution(Holland, 1992).
Table 4. the thermoeconomic equations of the system
equation 
equipment 
No. 
HRSG 
(26) 

HPG 
(27) 

LPG 
(28) 

Condenser 
(29) 

Evaporator 
(30) 

Absorber 
(31) 

Heat Exchanger 1 
(32) 

Heat Exchanger 2 
(33) 


(34) 


(35) 


(36) 


(37) 


(38) 


(39) 


(40) 


(41) 


(42) 


(43) 


(44) 


(45) 


(46) 
4.1. Decision Variables
In thermal system design and optimization, it is convenient to identify two types of independent variables. These variables are decision variables and parameters. The decision variables may be varied in the optimization process. However, the parameters remain fixed in a given application. All other variables are dependent variables. Their values are calculated from independent variables using thermodynamic relations.
5. Results and Discussion
The results of the thermodynamic simulation are shown in tables 5 and 6. Table 5 shows the thermodynamic properties of streams of chiller and Table 6 shows heat transfer rates of the components.
Table 5. Thermodynamic properties of chiller streams
Current No. 
mass flow rate (kg/s) 
temperature (˚C) 
pressure (bars) 
concentration (percent) 
enthalpy (kJ/kg) 
entropy (kJ/kg.K) 
1 
3.73 
153 
0.93 
0 
2671 
7.3832 
2 
3.59 
82.6 
0.0779 
0 
2654 
8.4740 
3 
3.73 
97.6 
0.93 
0 
409 
1.2797 
4 
3.73 
97.6 
0.93 
0 
409 
0.5858 
5 
7.32 
41 
0.0779 
0 
172 
0.5858 
6 
7.32 
5 
0.0087 
0 
21 
0.0763 
7 
7.32 
5 
0.0087 
0 
2510 
9.0249 
8 
87.86 
38.4 
0.0087 
57.75 
102 
0.2171 
9 
87.86 
38.4 
0.93 
57.75 
102 
0.2171 
10 
87.86 
54.62 
0.93 
57.75 
154 
0.3770 
11 
87.86 
121.67 
0.93 
57.75 
267 
0.6886 
12 
84.13 
153 
0.93 
60.31 
335 
0.8082 
13 
84.13 
91.14 
0.93 
60.31 
215 
0.5026 
14 
84.13 
91.14 
0.93 
60.31 
215 
0.5026 
15 
80.54 
82.6 
0.0779 
63 
211 
0.4378 
16 
80.54 
51.65 
0.0779 
63 
154 
0.2722 
17 
80.54 
51.65 
0.0779 
63 
154 
0.2722 
18 
5.48 
450 
10 
0 
3371 
0.6198 
19 
5.48 
168 
10 
0 
710 
2.0219 
20 
1380 
32 
1 
0 
134 
0.4642 
21 
1380 
35.8 
1 
0 
150 
0.5160 
22 
1380 
35.8 
1 
0 
150 
0.5160 
23 
1380 
37.51 
1 
0 
156.61 
0.5391 
24 
868 
12 
1 
0 
50 
0.1806 
25 
868 
7 
1 
0 
29 
0.1064 
Table 6. Temperature, pressure and heat transfer load in each component
Component 
Temperature 
Pressure 
Heat transfer rate (kJ) 
HPG 
153 
0.93 
14603 
LPG 
93 
0.0779 
 
Condenser 
41 
0.0779 
9803 
Evaporator 
5 
0.0087 
18225 
Absorber 
38.4 
0.0087 
21921 
As can be seen in the table, the cooling capacity of the refrigeration cycle (attainable cooling in the evaporator) is 18225 kW (5182 tons of refrigeration). The Coefficient of Performance (COP) of the chiller which is defined as the ratio of cooling capacity to the heat input the HPG can be calculated as follows:

Table 7 shows the results of solving heat exchangers sizing for HRSG and the absorption chiller components. According to the table, overall exergy destruction rate before the optimization is 11089 kJ/s and highest exergy efficiency (88.78%) is related to LPG.
By using heat transfer surface areas, the weight of heat exchangers of HRSG and chiller are calculated and the prices are evaluated as shown in Table 9.
Table 7. Heat exchangers calculations results
Component 
LMTD (°C) 
Overall heat transfer coefficient (W/(m^{2}.K)) 
Heat transfer rate (kW) 
Required heat transfer area (m^{2}) 
HRSG 

economizer 
61.48 
86 
3249 
515 
Evaporator 
76.27 
93 
11056 
1562 
Super heater 
67.88 
99 
3260 
487 
Double effect absorption chiller 

Absorber 
4.21 
2912 
21921 
1784 
HX1 
28.85 
478 
10004 
439 
HPG 
94.45 
2702 
14602 
57 
HX2 
15.49 
705 
4796 
705 
LPG 
35.83 
2568 
8440 
91 
Condenser 
4.28 
3473 
9803 
658 
Evaporator 
3.99 
1803 
18224 
2533 
Table 8. exergy destruction rate and exergy efficiency in each component
Component 
Exergy destruction rate (kJ/s) 
Exergy efficiency ( ) 
Heat Recovery Steam Generator 

Economizer 
487 
55 
Evaporator 
1465 
72 
Super heater 
326 
82.75 
Double Effect Absorption Chiller 

HPG 
1276 
88.5 
LPG 
185 
88.78 
Condenser 
1082 
20.38 
Evaporator 
310 
76.1 
Absorber 
750 
46.3 
Solution heat exchanger 1 
4184 
78.7 
Solution heat exchanger 2 
1022 
65.77 
Table 9. price estimation and overall implementation expenditure of the chiller
Component 
Heat transfer area (m^{2}) 
Price (USD) 
Double effect absorption chiller 

Absorber 
1784 
1349246 
HX1 
439 
609864 
HPG 
57 
27307 
HX2 
705 
593346 
LPG 
91 
43781 
Condenser 
658 
520191 
Evaporator 
2533 
1915245 
The optimal values of decision variables, decision variables and thermoeconomic parameter values for the base case and optimal solution of GA are presented in Table 10.
The result indicates that by increasing the Pinch Point temperature and the steam pressure, the heat transfer area of HRSG will be decreased. Moreover, the mass flow rate of generated steam in the super heater is increased by producing steam with lower temperature in higher pressure than initial pressure.
According to the obtained results, the optimized values of temperatures of HPG and LPG are lower than the initial system, while the pressures of these components are higher after optimization. In general, it is obtainable that the optimized system works under lower temperature in comparison with the initial system.
With optimized decision variables, the COP of the absorption chiller is 1.45, the steam flow rate of HRSG is 6.87 kg/s, total heat transfer area is 7140 m^{2} for a capacity of 19790 kW of refrigeration. The changes in heat transfer areas are shown in fig. 2.
As can be seen in Fig. 4, in some components heat transfer area is increased by optimization, however, the total heat transfer area is reduced after optimization.
Generally, changes in the main parameters of the system can be summarised as follows:
Ö Cooling capacity of the system is increased from 18225 kW to 19790 kW by 8.5%.
Ö The COP of the system is changed by 16.9%. While the COP of initial system is 1.24, the COP of optimized system is 1.45.
Ö Exergy destruction rate is decreased by 33% after optimization.
Ö Due to optimization, total heat transfer area is decreased by 22.5%, from 9219 m^{2} to 7140 m^{2}.
Ö After optimization, capital investment of the proposed coupling is reduced by 555840 (USD).
Ö The price of the produced cooling is decreased by 7%. It decreased from 1.98×10^{6} (Dollar per second) to 1.84×10^{6} (Dollar per second).
Table 10. values of object function, decision variables and thermoeconomic parameter for base case and optimal solution
Parameters 
Unit 
Base case 
Optimal 
Objective function 

Total product cost 
$/TR 
0.0190 
0.0171

Decision variables 

Bar 
10 
5.97 

°C 
450 
230.43 

°C 
15 
35.87 

°C 
153 
151.02 

Bar 
0.93 
1.10 

°C 
41 
37.21 

°C 
38.4 
35.95 

°C 
32 
31.82 

°C 
35.8 
34.23 

% 
57.75 
55 

% 
63 
64.95 

HRSG thermodynamic parameters 

°C 
134.87 
135.57 

kg/s 
5.48 
6.38 

Chiller thermodynamic parameters 

kg/s 
3.73 
4.27 

kg/s 
3.59 
3.56 

kg/s 
7.32 
7.82 

kg/s 
60.31 
60.01 

kg/s 
80.54 
43.26 

kg/s 
87.86 
51.696 

High pressure 
Bar 
0.93 
1.09 
Medium pressure 
Bar 
0.0779 
0.0636 
Low pressure 
Bar 
0.0087 
0.0087 
Heat transfer rates in chiller components 

HPG 
kW 
14603 
14131 
Condenser 
kW 
9803 
10094 
Evaporator 
kW 
18225 
19486 
Absorber 
kW 
21921 
22468 
Other parameters 

COP 
 
1.25 
1.38 
Capital investment of HRSG 
$ 
1,326,833 
1,003,605 
Capital investment of Chiller 
$ 
5,058,984 
5,897,359 
Figure 5. comparison of heat transfer areas of the components before and after the optimization
6. Conclusion
In this paper, a combined system consisting of a double effect absorption chiller and an HRSG was coupled with a refinery furnace located in Tehran to provide chilled water from furnace exhaust gasses. At first, thermodynamic analysis was conducted to the system to calculate unknown thermodynamic parameters like mass flow rates and heat loads of heat exchangers. Afterward, by calculating heat transfer areas of the components and exergy of the streams and using Thermoeconomic approach, the price of the product (refrigeration) was calculated. Finally, the system was optimized by the means of the Genetic Algorithm (GA). The optimal solution of GA proposed a system with the lowest price of the product and the highest cooling capacity as well.
In fact, in comparison with the base case of HRSG and Absorption chiller, the optimal solution showed 33% increase in exergy efficiency and 7% decrease in the total cost of products. Moreover, compared with the base case, the optimal solution presented a system with lower heat transfer areas and therefore, lower total capital investment is needed. It is obtainable that thermoeconomic analysis of a system is able to provide suggestions about potential costeffective improvements achievable by the means of changes in the values of the internal operating parameters of the system.
The annual cost of producing 5672 tons of refrigeration is 3.28×10^{5} (USD). To produce the same amount of cooling with natural gas, 1.186×10^{7} cubic meter of natural gas with the price of 1.508×10^{6} (USD) is needed. Consequently, by using the integrated system, the price of the product is one fifth to produce cooling with natural gas. Besides, the use of waste heat in this plan has many environmental advantages that conserving natural resources can be considered as one of them.
Appendix I
For calculating , there are other factors that initially need to be evaluated:
(A1) 

(A2) 

(A3) 
Where, and . Accordingly can be calculated as follows:
(A4) 
Where, Nu is Nusselt Number and k is thermal conductivity of fluid.
Equations for calculating in HRSG are as follows (Ganapathy, 2003):
(A5) 
Where G is Gas mass velocity (lb/ft^{2} h).
(A6) 
k is gas thermal conductivity and the factor F has been computed for air and flue gases, and a good estimate is given in Table (5)(Winston et al., 2014).
Table A1. F Factor for air and flue gases
Temperature (°C) 
F 
93 
0.094 
204 
0.103 
315 
0.110 
426 
0.116 
537 
0.123 
648 
0.130 
The gas mass velocity G is given by
(A7) 
For Absorption chiller, the overall heat transfer in each component is given by equation 18. For this equation, the values of fouling factors ( , ) are considered as negligible. The thermal conductivity of copper tubes is calculated from the following equation:
(W/mK) 
(A8) 
Where, T is the temperature of the component.
The following equation is recommended in the case of condensation on a single horizontal tube which gives the average heat transfer coefficient (Florides et al., 2003):
(A9) 
Where k_{l} is the thermal conductivity of liquid (W/m K). For determining an overall heat transfer coefficient (U), physical properties in equation (A8) need to be calculated at the mean wall surface and vapor saturation temperature.
Nomenclature
A 
Area(m^{2}) 
C 
Cost ($/kJ) 
c 
Cost ($/sec) 
CCHP 
combined cooling, heating and power 
COP 
Performance operation coefficient (%) 
E 
Exergy (kW) 
e 
Exergy(kJ/kg) 
h 
Enthalpy(kJ/kg) 
HRSG 
Heat recovery steam generator 
HPG 
High pressure generator 
LPG 
Low pressure generator 
m 
Flow rate (kg/s) 
P 
Pressure (bar) 
Q 
Heat (kW) 
S 
Entropy (kJ/kg.K) 
T 
Temperature) °C( 
U 
Average overall transfer coefficient (W/m2.°C) 
X 
Mass fraction 
Z 
Equipment cost ($/sec) 
Subscript
D 
distraction 
p 
product 
f 
fuel 
g 
gas 
Hx 
Heat exchanger 
r 
Refrigerator 
ss 
Strong solution 
ws 
Weak solution 
Greek symbols
ε 
Exergy Efficiency (%) 
Δ 
Different 
η 
Efficiency (%) 