Abstract
This paper proposes a systematic approach for energy integration involving waste heat recovery through an organic Rankine cycle (ORC). The proposed approach is based on a twostage procedure. In the first stage, heating and cooling targets are determined through heat integration. This enables the identification of the excess process heat available for use in the ORC. The optimization of the operating conditions and design of the cogeneration system are carried out in the second stage using genetic algorithms. A modular sequential simulation approach is proposed including several correlations to determine the properties for the streams in the ORC. The proposed approach is applied to a case study which addresses the tradeoffs among the different forms of energy and associated costs. The results show that the optimal selection of the operating conditions and working fluid is very important to reduce the costs associated to the process.
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Abbreviations
 AR:

Absorption refrigeration
 CW:

Cooling water
 CPS:

Cold process streams
 GCC:

Grand composite curve
 HPS:

Hot process streams
 H :

Enthalpy
 Max:

Maximization
 NU:

Number of units
 ORC:

Organic Rankine cycle
 P :

Pressure
 Ref:

Refrigerant
 R245fa:

Coolant R245fa
 R123:

Coolant R123
 S :

Entropy
 T _{in} :

Inlet temperature
 T _{out} :

Outlet temperature
 T _{Sat} :

Saturation temperature
 T :

Temperature
 C _{ E } :

Unit electric power cost
 FC _{ p } :

Heat capacity flow rate
 \(C_{\text{cw}}^{\text{ORC}}\) :

Unit cost for the cooling water used in the ORC
 H _{Y} :

Operating hours for the plant per year
 K _{F} :

Factor used to annualize the capital costs
 η _{turbine} :

Turbine efficiency
 η _{pump} :

Pump efficiency
 N _{pop} :

Number of individuals
 PW_{Cost} :

Price of electric power
 RC_{refrigerant} :

Unit refrigerant cost
 t _{filling} :

Time required to fill the ORC
 CAP:

Installed capital cost
 CAP_{cond} :

Capital cost for the condenser
 CAP_{boiler} :

Capital cost for the boiler
 CAP_{turb} :

Capital cost for the turbine
 CAP_{pump} :

Capital cost for the centrifugal pump
 CAP_{ u } :

Capital cost for each unit of the cycle
 COPA:

Total annual operating cost
 \({\text{Cost}}_{\text{coolingwater}}^{\text{ORC}}\) :

Cost for the cooling water used in the condenser of the ORC
 Cost_{refrigerant} :

Cost for the selected refrigerant in the system
 Density:

Density for the working fluid
 F _{refrigerant} :

Flow rate for the refrigerant in the ORC
 GROSS PROFIT:

Annual gross profit
 PROFIT:

Profit for the electric power produced in the ORC
 Q ^{C} :

Minimum cooling through cooling water for hot process streams
 Q ^{H} :

Minimum heating for cold process streams
 Q _{L} :

Heat removed from the condenser in the ORC
 \(Q_{\text{Cost}}^{\text{CW}} \,\) :

Cost for cooling using cooling water for process streams
 \(Q_{\text{Cost}}^{\text{Ref}} \,\) :

Cost for refrigeration for process streams
 Q ^{ORC} :

Heat inlet to the boiler of the ORC
 Q ^{Ref} :

Heat sent to the refrigeration
 Q ^{CW} :

Cooling of the process streams using water as the cooling medium
 \({\text{Total}}_{\text{Cost}}^{\text{ORC}}\) :

Total cost for the ORC
 v :

Volume for the stream inlet to the pump
 W _{P} :

Pump power
 W _{T} :

Power produced in the turbine of the ORC
 W _{ u } :

Consumed electric power of unit u
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Acknowledgments
The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT) and the Scientific Research Council of the Universidad Michoacana de San Nicolás de Hidalgo in Mexico. Also, this work was founded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grand No. 334/RG. The authors, therefore, acknowledge with thanks DSR technical and financial support.
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Appendix 1: Correlations for the thermodynamic properties
Appendix 1: Correlations for the thermodynamic properties
In this section, representative correlations for the properties of the refrigerant R245fa are described. Additional relationships for other refrigerants are presented in the Electronic Supplementary Material. The correlation coefficients for these relationships are greater than 0.99 with respect to REFPROP (Lemmon et al. 2014), which is software dedicated to determine refrigerant properties. The streams involved are identified in Fig. 2.
The saturation temperature, T _{Sat1} (°C), for stream 1 at the output of the boiler is a function of the pressure P _{1} (bar) as follows.
For pressures from 0.6 to 5 bars:
For pressures from 5 to 10 bars:
For pressures from 10 to 36 bars:
The enthalpy for stream 1, H _{1} (kJ/kg), is a function of the inlet pressure to the turbine, and for pressures between 1 and 10 bars, this is given as follows:
For pressures between 10 and 30 bars:
For pressures between 30 and 36 bars:
The entropy for stream 1 (S _{1} (kJ/kg °C)) is a function of the inlet pressure to the turbine. For pressures between 1 and 25 bars, this is given as follows:
For pressures between 25 and 36 bars:
The isentropic temperature at the exit of the turbine for stream 2 (T _{2S} (°C)) is calculated in terms of the inlet entropy S _{1} (kJ/kg °C) as follows:
The isentropic enthalpy at the exit of the turbine (H _{2S} (kJ/kg)) is given in terms of the outlet temperature (T _{2S} (°C)) as follows:
The enthalpy at the exit of the turbine (H _{2} (kJ/kg)) is given in terms of the efficiency of the turbine (η _{turbine}), the isentropic enthalpy H _{2S} (kJ/kg), and the inlet enthalpy H _{1} (kJ/kg) as follows:
The temperature at the exit of the turbine (T _{2} (°C)) is obtained in terms of the enthalpy H _{2} (kJ/kg) at a pressure P _{2} (bar) as follows:
The entropy at the exit of the turbine (S _{2} (kJ/kg °C)) is given in terms of the enthalpy H _{2} (kJ/kg) as follows:
The saturation temperature T _{Sat3} (°C) at the outlet of the condenser (stream 3) is the function of the pressure P _{2} (bar) as follows. For pressures from 0.6 to 5 bars, the correlation is
For pressures from 5 to 10 bars:
For pressures from 10 to 36 bars:
In addition, the enthalpy H _{3} (kJ/kg) for the stream 3 at the inlet to the pump is function of the saturation temperature T _{Sat3} (°C):
while the entropy S _{3} (kJ/kg) is given in terms of the saturation temperature T _{Sat3} (°C), which is as follows,
The power consumed by the pump is obtained through the following equation:
where \(\eta_{\text{pump}}\) is the efficiency for the pump, and \(v\) (m^{3}/kg) is the volume of the stream inlet to the pump, which is determined by the inverse of the density of this fluid that is calculated as follows:
The enthalpy H _{4} (kJ/kg) for the stream at the outlet of the pump is calculated with the following relationship:
The entropy for the stream 4 at the exit of the pump (S _{4} (kJ/kg °C)) is given in terms of the enthalpy H _{4} (kJ/kg) at a pressure P _{1} (bar) as follows:
The temperature for stream 4 at the exit of the pump (T _{4} (°C)) is obtained in terms of the enthalpy H _{4} (kJ/kg) at a pressure P _{1} (bar) as follows:
The isentropic enthalpy for stream 4 at the exit of the pump (H _{4S} (kJ/kg)) is given in terms of the following expression:
The isentropic entropy for stream 4 at the exit of the pump (S _{4S} (kJ/kg °C)) is given in terms of the enthalpy H _{4S} (kJ/kg) at a pressure P _{1} (bar) as follows:
The isentropic temperature for stream 4 at the exit of the pump (T _{4S} (°C)) is obtained in terms of the isentropic enthalpy H _{4S} (kJ/kg) at a pressure P _{1} (bar) as follows:
The produced power in the turbine is calculated using the following expression:
The needed cooling in the ORC is calculated from the following relationship:
where Q ^{ORC} is the heat required in the boiler (kJ/s) and F _{refrigerant} is the flow rate for the refrigerant (kg/s) in the ORC.
The proposed correlations to determine the thermodynamic properties for refrigerants R123 and nbutane are shown in Tables 5 and 6, respectively. These tables are in the Electronic Supplementary Material available in the WEB.
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GutiérrezArriaga, C.G., Abdelhady, F., Bamufleh, H.S. et al. Industrial waste heat recovery and cogeneration involving organic Rankine cycles. Clean Techn Environ Policy 17, 767–779 (2015). https://doi.org/10.1007/s1009801408335
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DOI: https://doi.org/10.1007/s1009801408335