Energy, exergy and exergoeconomic analysis of a cogeneration system for power and hydrogen production purpose based on TRR method and using low grade geothermal source

Geothermics 71 (2018) 132–145

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Energy, exergy and exergoeconomic analysis of a cogeneration system for power and hydrogen production purpose based on TRR method and using low grade geothermal source

MARK

⁎

Hadi Ghaebi , Behzad Farhang, Towhid Parikhani, Hadi Rostamzadeh Department of Mechanical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran

A R T I C L E I N F O

A B S T R A C T

Keywords: Geothermal energy Organic Rankine cycle Proton exchange membrane electrolyzer Working fluid Exergoeconomic analysis Cogeneration

In this research, a modified organic Rankine cycle (ORC) with a regeneration is used to generate power along with hydrogen. For hydrogen production purpose, a proton exchange membrane (PEM) electrolyzer is used, taking its required heating and power from the ORC. The proposed system is driven by geothermal energy. A comprehensive thermodynamic modelling (energy and exergy analysis) and exergoeconomic analysis are carried out for the proposed cycle, using various working fluids (i.e., R245fa, R114, R600 and R236fa) in order to compare their influences on performance of the integrated system. For this purpose, Engineering Equation Solver (EES) software is used in all conducted simulations which is proven to be the most professional and commercial software in thermodynamics. In addition, a comprehensive parametric study is carried out for investigating the effects of main thermodynamic flow parameters on the energetic, exergetic and economic factors of the integrated system. The results showed that R245fa had the highest energy and exergy efficiencies of 3.511% and 67.58%, respectively. Furthermore, it is the most cost-efficient working fluid with 11.54 $/GJ and 4.921 $/GJ average costs per exergy unit for output power and hydrogen production, respectively. Regarding their operational features and cost effectiveness, the working fluids R114, R600 and R236fa ranked successively after R245fa. Also R245fa had the lowest cost associated with the exergy destruction. Moreover, the results of parametric study showed that increasing of the evaporator pressure results in increasing of the output power, hydrogen production, and energy and exergy efficiencies, whereas the costs of output power and hydrogen production decreased. In addition, increasing the geothermal fluid temperature increases the output power, hydrogen production, and also their costs, while decreases the energy and exergy efficiencies. It is also found that an increase in the turbine extracted steam pressure (mean pressure) will increase the exergy efficiency, costs of produced power and hydrogen, whereas decrease the output power, hydrogen production, and energy efficiency.

1. Introduction Nowadays, due tothe decreasing fossil fuel sources and environmental pollutions caused by such fuels, most countries are trying to decrease their dependence on fossil fuels. Therefore, they carry out various research and experimentations on renewable and clean energies. Geothermal energy is considered to be a clean and renewable energy. Also, it is very cost-effective to generate high capacities of electrical power using geothermal energy (Alhamid et al., 2016; Michaelides, 2016). Geothermal energy temperature is varying in a range of 50 °C to 350 °C. Obviously high-temperature sources (larger than 220 °C) are the most appropriate kind of sources from the

⁎

Corresponding author. E-mail address: [email protected] (H. Ghaebi).

http://dx.doi.org/10.1016/j.geothermics.2017.08.011 Received 31 May 2017; Received in revised form 17 July 2017; Accepted 24 August 2017 0375-6505/ © 2017 Elsevier Ltd. All rights reserved.

commercial standpoint. However, most geothermal sources are in a range of 90–220 °C and it is predicted that the next generation of geothermal power plants are going to use low-temperature sources (Shokati et al., 2015a,2015b). The organic Rankine cycle (ORC) is a power generating cycle that uses organic fluids with low boiling point which is established by low-temperature energy sources (Kalina, 1983). Meanwhile, hydrogen is considered as a clean energy carrier for generating environment adapting energies, which is used mostly in power plants and chemical industries (Balat, 2008; Winter, 2009). Furthermore, it can be used in fuel cell systems to produce electricity more effectively and with inconsiderable greenhouse consequences (Dincer, 2014; Kang et al., 2007). Nowadays, hydrogen can be produced through fossil fuels, reforming processes of hydrocarbons and

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W˙ X Z Z˙

Nomenclature A c C˙ CC CELF CI CRF D Eact , i ex E˙X E˙ product E˙Electrolyzer F FC FFH fk G h ieff J J0 Jiref L LHV m˙ N˙ OMC ORC P PEC PEM Q˙

q˙ R rFC rk rOMC RPEM s T TRR V0 Vact Vact , a Vact , c

Heat transfer area (m2) Cost per exergy unit ($/GJ) Cost rate ($/s) Carrying charges Constant escalation levelized factor Capital investment Capital recovery factor membrane thickness (μm) Activation energy in cathode or anode (KJ) Specific exergy (kJ/kg) Exergy rate (kW) Direct use power (kW) Electrolyzer energy input (kW) Faraday constant (C/mol) Fuel cost Feed fluid heater Exergoeconomic factor (%) Gibbs free energy (J/mol) Specific enthalpy (kJ/kg) Effective mean annual average discount Current density (A/m2) Exchange current density (A/m2) Pre-exponential factor (A/m2) Length (m) Lower heating value (MJ/kg) Mass flow rate (kg/s) Mole flow rate (mol/s) Operating & maintenance cost Organic rankine cycle Pressure (kPa) Purchase cost of component Proton exchange membrane Heat transfer rate (kW) Specific heat rate (kJ/kg) Universal gas constant (kJ/kg K) Nominal escalation rate for fuel cost Relative cost difference (%) Nominal escalation rate for OMC Ohmic resistance (Ω) Specific entropy (kJ/kg K) Temperature (°C) Total revenue requirement Reversible potential (V) Activation overpotential (V) Anode activation overpotential (V) Cathode activation overpotential (V)

Power (kW) Turbine mass fraction Capital cost of a component ($) Capital cost rate ($/s)

Greek letters

η λa λc λ(x) σPEM σ (x )

Efficiency (%) Water content at the anode-membrane interface (Ω−1) Water content at the cathode-membrane interface (Ω−1) Water content at location x in the membrane (Ω−1) Proton conductivity in PEM (s/m) Local ionic PEM conductivity (s/m)

Subscript and superscript a act Brine C c ch D e Eva FFH F Gth Hea i isen k l L Mean net ohm ORC P PEM PH ph Pu Q T W

Anode Activation Geothermal fluid Condenser Cathode Chemical Destruction Exit Evaporator Feed fluid heater Fuel Geothermal Heater Inlet Isentropic Kth component Loss Levelized Mean value Net power Ohmic Organic rankine cycle Product Proton exchange membrane Preheater Physical Pump Heat Turbine Work

hydrogen than others. All or part of the energy generated by a geothermal power station could be used for producing hydrogen through water electrolysis. It seems that hydrogen production through water electrolysis (based on the geothermal energy) will have an undeniable effect on hydrogen production economy (Momirlan and Veziroglu, 2005). There are numerous researches on using geothermal energy for hydrogen production. For example, Ratlamwala and Dincer (2012) incorporated an integrated geothermal output power system and an electrolyzer with several flashes (1–5 flashes). They used three different definitions for energy efficiency and exergy of system in order to do a comparative evaluation. Their findings demonstrated that an increase in the environment and geothermal temperatures will result in a higher energy and exergy efficiencies. Their findings also demonstrated that the incorporated system with 5 flashes is the most practical system. Yilmaz et al. (2012) used 7 models for a geothermal system, integrated

water electrolyzing. However, due to the limited fossil fuel resources and climate changes (due to carbon dioxide release and other contaminants), the use of clean and renewable energy has gained more interest instead (Braga et al., 2013). Water electrolysis is an accepted technology to produce great amounts of hydrogen. Hydrogen production, through the proton exchange membrane (PEM) electrolyzer, has many advantageous, because its effect on the environment is inconsiderable and its maintenance is easy (Ahmadi et al., 2013). On the other hand, cogeneration is introduced as a great approach that saves energy while allows an effective application of energy resources and helps to protect the environment. Also, cogeneration allows electricity generation alongside other useful forms of energy (e.g., heat, cool, hot water, potable water, hydrogen etc.) from a unique source of energy (Jiang et al., 2016). Considering all the other kinds of energy sources, geothermal energy has a lot more potential in producing 133

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respectively. As it is seen in the above literature reviews, there are numerous researches on analyzing the energy and exergy of the geothermal power cycle for producing hydrogen. However, it is notable that there are very few researches analyzing the exergoeconomic utilization of geothermal energy for hydrogen production through water electrolysis. The researches carried out so far are limited to price data collection for equipment. In this research, a modified ORC with a feed-fluid heater (FFH) is integrated with a PEM electrolyzer for power and hydrogen production purpose. The objectives of this research are multifold and are as follows:

with an electrolyzer for hydrogen production, and concluded that at high temperature of the geothermal source, lower costs for producing and liquidating of hydrogen is predicTable Similarly, Balta et al. (2010a,2010b) made an energy and exergy analysis of a geothermal cycle aimed at producing hydrogen. In order to attain thermochemical catalysis of water, they simulated a four-step copper–chlorine cycle and calculated energy and exergy efficiencies of 21.67% and 19.35%, respectively. In another study, Yilmaz et al. (2015a,2015b) worked on a geothermal and binary flash system combined with a water catalysis system. Their thermodynamic and exergoeconomic analysis showed that the exergetic costs of electricity and hydrogen production are 11.1 $/GJ (or 0.0400 $/kWh) and 26.1 $/GJ (or 3.14 $/kg hydrogen), respectively. Balta et al. (2011) carried out energy, exergy, and economic analysis of a thermochemical copper-chlorine water catalysis system combined with geothermal in order to produce hydrogen. They found that the cost of hydrogen production is highly and closely dependent upon the plant capacity and exergy efficiency. Gouareh et al. (2015) produced hydrogen by using geothermal as heat source energy and CO2 as working fluid, considering GIS analysis in Algeria. Their results showed that the Northeast and Southwest of Algeria are the best places to carry this work. Cai et al. (2014) investigated on various optimized methods for controlling hydrogen production when the electrolyzer is connected to an alternative renewable energy. Their control strategy ensured a temperature controlling of the SOEC stack and local temperature gradient with the SOEC stack. They also compared the efficiency of the methods with each other, showing a satisfactory result with literatures. Balta et al. (2010a,2010b) investigated on four potential methods for hydrogen production by using geothermal energy. Their research was focused on uplifting efficiency of different methods and the possibility that their findings would bring a potential method for hydrogen production based on low thermochemical temperatures and combined cycles. They also presented copper-chlorine cycle as the most promising cycle for geothermal hydrogen production. Ouali et al. (2011) worked on producing hydrogen through hydrogen sulfide in geothermal regions. Their work aimed at marking different aspects of hydrogen production from hydrogen sulfide and the possibility of utilizing such a method in Algeria’s geothermal sources. They introduced hydrogen production by hydrogen sulfide process as economic and environmental process. Kanoglu et al. (2010) used four different models and two reversible and irreversible states in a geothermal hydrogen production system. Their findings demonstrated that the exergy efficiency of models (1–4) can be obtained 28.5%, 29.9%, 37.2% and 16.1%, respectively. Yilmaz et al. (2015a,2015b) studied the costs of exergetic electricity and hydrogen production in an integrated geothermal output power system with an electrolyzer system for hydrogen production. Their results showed that the exergetic costs of electricity and hydrogen production in the system can be calculated 6.495 $/GJ (or 0.0234 $/kWh) and 19.07 $/GJ (or 2.366 $/kWh hydrogen),

• Using geothermal energy as a low-temperature energy source for cogeneration of power and hydrogen production. • Using a modified ORC with four different working fluids for hy• • •

drogen production through a PEM electrolyzer and comparing them with each other. Performing a comprehensive thermodynamic modelling of the proposed integrated system for each working fluids. Presenting a comprehensive exergoeconomic analysis of the proposed integrated system for each working fluids, using TRR method. Conducting a comprehensive sensitivity analysis to see the effect of operating parameters on performance of the system.

2. System description In this study, a regenerative ORC and a PEM electrolyzer are integrated to produce power and hydrogen, simultaneously. Fig. 1 depicts a schematic thermodynamic diagram of the proposed combined system which benefits from geothermal energy as heat source. The organic fluid is evaporated in the evaporator (4–5) by a geothermal heat source with a cold and hot fluids interaction mechanism. Then, a part of the steam enters turbine where portion of fluid is expanded to a lower pressure of condenser (6). The expanded fluid at turbine outlet (7) is cooled by an external heat exchanger (preheater) and then enters the condenser with relatively high temperature (8), after transferring specific amount of heating capacity to input water of the PEM electrolyzer system (13–14). The fluid is liquefied in condenser (1) and then pumped to a higher pressure of FFH by pump 1 (2) and then mixes with extracted steam at FFH. In the FFH, due to the extracted steam from the turbine (6), the steam experiences a raise in temperature once again (3) and pumped back to a higher pressure of evaporator by pump 2 (4), completing power sub-system process. Meanwhile, a portion of the generated power of turbine is used directly (E˙ product ) and another part is used to run the PEM electrolyzer (E˙Electrolyzer ). The input water (at the environment temperature and pressure values) enters the preheater and receives an amount of heat (13–14) from ORC. It then enters the heater of the electrolyzer system Fig. 1. Schematic diagram of the regenerative ORC coupled with geothermal energy and PEM electrolyzer.

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is acquired by:

and is heated until it hits the temperature point of the PEM electrolyzer and finally enters the electrolyzer (15). In the electrolyzer, the outgoing hydrogen from the cathode releases its heating to the environment, and then the hydrogen is stored in a storage tank (16). Emerged in the PEM electrolyzer anode (17), the water-oxygen combination enters the oxygen separator, in which oxygen is separated from water. Then, hot water returns to the PEM electrolyzer once again to produce more hydrogen, completing hydrogen sub-system operation.

in which, ΔG is the Gibbs free energy and TΔS is the required thermal energy. The values for the Gibbs free energy, enthalpy and entropy for hydrogen and oxygen are obtained from thermodynamic tables (Cengel and Boles, 2006). Moreover, the molar rate for hydrogen is obtained as follows:

3. Energy analysis

J N˙ H 2, out = = N˙ H 2O, out 2F

E˙Electrolyzer = JV

(11)

where, E˙Electrolyzer is the energy given to the system electrolyzer and V is the required electric potential that is obtained as follows:

3.1. The organic rankine cycle

V = V0 + Vohm + Vact , a + Vact , c

The heat given to the evaporator could be calculated by energy balance equations between the working fluid and the geothermal fluid at the input and output of the evaporator:

(12)

in which, Vact,c, Vact,a, and Vohm are the cathode activation overpotential, the anode activation overpotential and the ohmic overpotential, respectively. In the above equation, V0 is the reversible potential which is expressed, using the Nernst equation (Ni et al., 2008):

(1)

in which, m˙ Brine is the mass flow rate of the geothermal water and m˙ ORC is the mass flow rate of ORC working fluid. Applying energy balance equation, the generated power in turbine can be acquired as follows:

W˙ T = W˙ T , isen ηT , isen = ηT , isen m˙ ORC ((h5 − h6s ) + X (h6s − h 7s ))

(10)

where, J is the current density, F is the Faraday constant and N˙ H 2O, out is the molar mass flow rate of hydrogen and N˙ H 2O, out is the molar mass flow rate for the water entering the electrolyzer. The energy given to the electrolyzer is defined as follows:

In this part, energy analysis of the proposed system is presented, using EES (Engineering Equation Solver) software as the most robust instrument for thermodynamic analysis. It has to be mentioned here that in energy analysis, mass and energy conservation laws are taken into consideration for each component, separately.

Q˙ Eva = m˙ Brine (h11 − h12) = m˙ ORC (h5 − h4 )

(9)

ΔH = ΔG + TΔS

V0 = 1.229 − 8.5 × 10−4 (TPEM − 298)

(13)

The ionic resistance of the membrane is dependent on the moisture, the thickness and the temperature of the membrane (Ni et al., 2008). The local ionic conductivity of the PEM electrolyzer (σ (x ) ) is obtained through (Ni et al., 2008):

(2)

where, ηT,isen is the isentropic efficiency of the turbine and X is the mass fraction of the turbine extracted steam:

1 1 ⎞⎤ σPEM [λ (x )] = [0.5139λ (x ) − 0.326] exp ⎡1268 ⎛ − ⎢ TPEM ⎠ ⎥ ⎝ 303 ⎦ ⎣ ⎜

m˙ X= 6 m˙ 5

(3)

⎟

(14)

The heat, transferred to the cooling process in the condenser then can be calculated as follows:

Here, x indicates the measured depth of the membrane from the surface of the cathode membrane and λ(x) can be acquired from the water in the electrode membrane surface as follows:

Q˙ C = m˙ ORC (1 − X )(h1 − h8)

λ (x ) =

(4)

The pump power is calculated by:

m˙ m˙ W˙ Pu = W˙ Pu1 + W˙ Pu2 = ORC (1 − X )(h1 − h2s ) + ORC (h3 − h4s ) ηPu, isen ηPu, isen

λa − λ c x + λc D

(5)

where, ηPu,isen is the pump isentropic efficiency. If the heater is energy balanced, then the mass fraction of the extracted steam from the turbine would be calculated as follows:

D

RPEM =

∫ 0

h − h2 X= 3 h6 − h2

dx σPEM [λ (x )]

Vohm = JRPEM

W˙ net = W˙ T − W˙ Pu = E˙Electrolyzer + E˙ product

Vact,i =

(17)

Accordingly, the anode and cathode activation over potential is acquired through (Ni et al., 2008):

(7)

The energy efficiency of ORC is calculated through:

ηenergy, ORC

(16)

According to the ohm law, the ohmic overpotential is acquired through:

(6)

The absolute generated power of ORC is sum of the generated power by the turbine and consumed power of the pump, which is divided into two parts after its conversion in the generator. A part is consumed directly (E˙ product ) and the rest is taken by the electrolyzer to produce hydrogen (E˙Electrolyzer ):

W˙ = net Q˙ Eva

(15)

In this equation, D stands for the membrane thickness and λa and λc are the membrane anode and cathode surface water, respectively. In addition, the overall resistance of the system (RPEM) could be acquired from (Ni et al., 2008):

RT J sinh−1 ⎛⎜ ⎞⎟, i= a, c F J ⎝ 0,i ⎠

(18)

J0,i is the exchange current density which is obtained by (Ni et al., 2008):

Eact , i ⎞ i = a, c J0, i = Jiref exp ⎛− ⎝ RT ⎠

(8)

Jiref is

(19)

the pre-expotential factor and Eact,i is the anode and where, cathode activation energy. The value of the heat given to water in the heat exchanger PEM electrolyzer is expressed by:

3.2. PEM electrolyzer The thermodynamic evaluation of the PEM electrolyzer system is carried out by electrochemical modelling. The system’s required energy 135

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to the reference conditions. A specific chemical exergy for a gas compound is obtained as follows (Bejan et al., 1996):

Table 1 Fuel and product exergy equations for each component of the proposed system. Component

.

.

ExF

ExP

Pump 1

W˙ Pu1 .

.

n

.

Ex2 − Ex1

.

.

.

Preheater

Ex7 − Ex 8

Ex14 − Ex13

FFH

Ex2 + Ex 6 W˙ Pu2

Ex3

.

Pump 2

.

.

.

Ex 4 − Ex3

.

.

.

Evaporator

Ex11 − Ex12

Turbine

Ex5 − Ex 6 − Ex7

Condenser

Ex 8 − Ex1 ˙ Hea Ex

Ex10 − Ex 9

Heater PEM Electrolyzer

E˙Electrolyzer

Ex16 + Ex17 − Ex15

.

.

.

.

.

Q˙ H 2O = m˙ H 2O (h15 − h14 ) = m˙ H 2O q˙Hea, PEM

Ex5 − Ex 4 W˙ T . .

. .

Ex15 − Ex14 .

.

.

˙ F = Ex ˙ P + Ex ˙ D + Ex ˙ l Ex

(20)

LHVH 2 N˙ H 2 Q˙ Hea, PEM + E˙Electrolyzer

(21)

ηexergy =

3.3. The overall system

LHVH 2 N˙ H 2 + E˙ product Q˙ Eva + Q˙ Hea, PEM

˙ P Ex ˙ F Ex

(30)

The exergy rate for heat transfer in the evaporator and heater of system are respectively calculated through:

To calculate the overall energy efficiency of the system, we have:

ηenergy, tot =

(22)

4. Exergy analysis

T0 ⎞ ˙ ˙ Eva = ⎜⎛1 − Ex ⎟ QEva TGth, Mean ⎠ ⎝

(31)

˙ Hea, PEM = ⎛1 − T0 ⎞ Q˙ Hea, PEM Ex TPEM ⎠ ⎝

(32)

⎜

A flow’s exergy is known as the maximum theoretical work possible from that flow, under the conditions of exchanging heat only with its surrounding, following which the flow is brought back to the pressure and temperature of the environment. Since the concept of exergy is used in exergoeconomic analysis, the amount of exergy for all flows as well as exergy destruction for all equipment must be calculated. To this end, 4factors are to be involved: physical, chemical, kinetic and potential. However, since we can neglect the height and velocity of the flows, then the kinetic and potential exergies are pardonable. The physical exergy is the maximum possible work from the system, when the system is interacting with its environment and reaches a state of temperature and pressure equilibrium (Bejan et al., 1996). Accordingly, chemical exergy is considered only when a combustion process is dealt with (Ahmadi et al., 2013). Combining the first and second laws of thermodynamics, the exergy balance equation for each component of the system is thus obtained by:

˙ Q+ Ex

∑ m˙ i

˙ W + Ex ˙ D ex i=∑ m˙ e ex e + Ex

i

e

⎜

ηexergy, ORC =

ηexergy, PEM =

ηexergy, tot =

ex ph = (h − h 0) − T0 (s − s0)

(27)

Ex H2 . ExHea, PEM + E˙Electrolyzer

˙ H2 E˙ product + Ex ˙ ˙ ExEva + ExHea, PEM

(34)

(35)

An economic model for the different components of the system include the amortization, repair and maintenance as well as the fuel consumption costs. In order to define a cost function dependent upon design parameters, the cost of different components must be expressed based on the thermodynamic variables (Bejan et al., 1996). The functions for the purchasing costs of each component of the system and their dependent constants are given in Table 2. In this paper, the TRR method (Total Revenue Requirement) has been used for an economic analysis of the total cost. The TRR method is calculated annually, based on investment cost estimations and some assumptions regarding economic, financial, operational and

.

(26)

(33)

5. Economic model

(24)

ex = ex ph + ex ch

.

ExEva

˙ Eva and Ex ˙ Hea, PEM are exergy rate of the evaporator and PEM where, Ex heater electrolyzer, respectively. Furthermore, E˙ product represents a part of the generated power by turbine and consumed directly.

⎟

(25)

W˙ net .

(23)

ExW = W˙ r

⎟

In the above relations, TGth,Mean refers to the mean thermodynamic temperature for the geothermal fluid and TPEM is the electrolyzer temperature. Therefore, exergy efficiency of the ORC, PEM electrolyzer and overall integrated system are respectively obtained by:

˙ D is related to exergy destruction rate. All other expressions of where, Ex the above equation are obtained as follows (Bejan et al., 1996): . T Ex Q = ⎛1 − 0 ⎞ Q˙ r Tr ⎠ ⎝

(29)

˙ P are the fuel and product exergy rates, respectively. In ˙ F and Ex Here, Ex ˙ D and Ex ˙ l are related to the exergy destruction and the same vein, Ex exergy loss rates for each component of the system, respectively. Table 1 listed some fuel and product exergy equations for each component of the system. Exergy efficiency could be defined as a ratio of product exergy rate to fuel exergy rate:

where, m˙ H 2O is the input water mass flow rate and q˙Hea, PEM signifies the specific heat given to the heater. Similarly, the PEM electrolyzer energy efficiency is calculated by:

ηenergy, PEM =

(28)

where, xi stands for the molar concentration and exch,i is the specific chemical exergy of the substance. In the present study, the specific exergy costing method (SPECO) is used for an exergoeconomic analysis (Shokati et al., 2015a,2015b). In this method, both the fuel and the product must be defined for each component of the system. An exergy product is what we would expect from a specific component. In addition, exergy fuel is required for production. Hence, the exergy balance equation can be stated as follows:

.

.

n

˙ ch = m˙ ⎡∑ x i ex ch, i + RT0 ∑ x i lnx i⎤ Ex ⎢ ⎥ i=1 ⎣ i=1 ⎦

˙ Q and Ex ˙ W indicate exergy related to the in the above equations, Ex heat transfer and work through the system boundaries, respectively, while T represents the absolute temperature and the subscript 0 relates 136

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Table 2 Economic data and cost functions for economic modelling.

Table 5 Required input data for electrolyzer (Ahmadi et al., 2013).

Cost function System component Turbine

ZT = 6000(W˙ T )0.7 *

Capital investment cost function

Condenser

ZC = 588(AC )0.8 *

Evaporator

ZEva = 588(AEva )0.8 *

Pump

ZPu = 1120(W˙ Pu)0.8 * ˙ ZGth = 2500exp[−0.0025(mcΔT − 5)]**

Geothermal FFH Heater

ZHea

Preheater

ZPH

Electrolyzer

AFFH 0.78 * 0.093 AHea 0.78 * 0.093 APH 0.78 * 0.093

( ) = 130 ( ) = 130 ( )

ZFFH = 130

12 5 5 6 5 85 20

Component

Cost flow rate balance equation

Auxiliary equation

Pump 1

C˙1 + C˙ Pu1 + Z˙ Pu1 = C˙ 2

C˙ Electric W˙ T

Preheater

C˙ 7 + C˙13 + Z˙ PH = C˙ 8 + C˙14 C˙ 2 + C˙ 6 + Z˙ FFH = C˙ 3 C˙ 3 + C˙ Pu2 + Z˙ Pu2 = C˙ 4

c 7 = c8

C˙ 4 + C˙11 + Z˙ Eva = C˙ 5 + C˙12 C˙ 5 + Z˙ T = C˙ 6 + C˙ 7 + C˙ Electric C˙ 9 + C˙ 8 + Z˙ C = C˙10 + C˙1

c11 = c12

C˙14 + C˙ Q + Z˙ Hea = C˙15 C˙ Electric + C˙15 + Z˙ Electrolyzer = C˙16 + C˙17

c13 = 0

Condenser Heater PEM Electrolyzer

4.6 × 103 96486 80

Table 6 Operational parameters of the regenerative ORC: A. current model B. Safarian and Aramoun, (2015).

Table 3 The flow balance rate and auxiliary equations for each component of the proposed system.

Turbine

1.0 1.0 80 76 18 14 10 100 1.7 × 105

ZElectrolyzer = (24.4 × m˙ H 2O )0.7 ***

*Shokati et al. (2015a,b). *Bejan et al. (1996). ***HPCEUWE (2009).

Evaporator

PO2 (atm) PH2 (atm) TElectrolyzer (°C) Eact,a (kJ/mol) Eact,c (kJ/mol) λa λc D (μm)

Jcref F (C/mol) Isentropic efficiency (%) (%)

Average annual rate of the cost of money (%) Average general inflation rate (%) Average nominal escalation rate for all (except fuel) costs (%) Average nominal escalation rate for fuel cost (%) Financing fraction for debt (%) Average capacity factor (%) Plant economic life (book life) (year)

Pump 2

Value

Jaref

Economic data

FFH

Parameter

=

=

A

B

Working fluid Evaporator capacity (kW) Condenser duty (kW) Turbine output power (kW) Pump power consumption (kW) Net power (kW) ORC energy efficiency (%) Working fluid mass flow rate (kg/s)

R113 252 191.8 60.86 2.955 57.9 22.98 4.58

R113 252 194.6 61 3.46 57.54 22.83 4.51

Table 7 Operational parameters of PEM electrolyzer system: A. current model B. Ahmadi et al. (2013).

C˙ Pu1 W˙ Pu1

c6 = c 7 C˙ Electric W˙ T

Parameter

C˙ Pu2 W˙ Pu2

c5 = c6 c8 = c1

B

A

Parameter

80 25 1 101.96 3.6 22.7 56.34 1.2

80 25 1 101.43 3.75 23.1 57.15 1.197

Electrolyzer temperature ( °C) Water primary temperature ( °C) Water pressure (atm) Net output power (kW) Energy efficiency (%) Exergy efficiency (%) Electrolyzer exergy efficiency (%) Hydrogen production rate (kg/s)

c17 = 0 Table 8 Energy, exergy, and exergoeconomic operational parameters of the proposed system.

Table 4 Required input data for ORC (Basaran and Ozgener, 2013). Value

Parameter

500 75 96 61 200 1000 500 75

Geothermal fluid pressure (kPa) Geothermal fluid mass flow rate (kg/s) Output fluid temperature to the injection wells ( °C) Input fluid temperature to the injection wells ( °C) Direct used power (kW) Evaporator pressure (kPa) Mean pressure (kPa) Isentropic efficiency (%)

commercial parameters (Bejan et al., 1996).

Parameters

R245fa

R114

R600

R236fa

Direct used power (kW) Evaporator capacity (kW) Condenser duty (kW) Turbine power production (kW) Pump power consumption (kW) Preheater duty (kW) Heater duty (kW) Net output power (kW) ORC thermal efficiency (%) PEM thermal efficiency (%) System thermal efficiency (%) ORC exergy efficiency (%) PEM exergy efficiency (%) Total exergy efficiency (%) Cost of produced hydrogen ($/GJ) Cost of produced power ($/GJ)

200 7705 6313 941.5 24.88 475.4 547.3 916.7 11.9 9.241 3.511 75.45 36 67.58 11.54 4.291

200 7705 6201 859.6 29.83 674.7 373.8 829.8 10.77 9.926 3.45 74.39 38.79 67.56 15.37 6.02

200 7705 6484 8.32.2 26.22 415.2 501.5 806 10.46 9.78 3.42 73.51 38.07 67.54 16.85 6.81

200 7705 6568 707.7 26.35 456.3 380.3 681.4 8.843 10.72 3.315 68.88 41.73 64.86 17.46 7.636

5.1. Calculation of revenue requirements the system. These costs are divided into two parts, namely: carrying charges (CC) and expenses. Carrying charges is a comprehensive title for all the costs related to

The annual total revenue requirement for a system is defined as the amount of income acquired through selling the system’s produced merchandise, in a way that it accounts for all the expenses of the system in a year, which in turn, guarantees a good economical operation for 137

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Table 9 Exergoeconomic parameters for different components of the proposed system, using R245fa. Component

Pump 1 Preheater FFH Pump 2 Evaporator Turbine Condenser Heater Electrolyzer

cF , k

( ) $ GJ

cP, k

4.291 2.991 5.99 4.291 1.3 2.991 2.991 1.3 4.291

( ) $ GJ

C˙ D, k

0.17 8.864 7.297 0.18 1.658 4.291 13.6 2.256 15.25

.

() $ s

0 0.1824 1.91 0 1.605 3.132 1.176 0.244 7.664

() $ s

ExD, k (kW )

Z˙ k

0.002 16.94 88.57 0.01 343 290.9 109.2 52.17 496.2

1.493 7.013 0.23 2.606 29.99 353.8 50.48 6.5 4.248

Z˙ k + C˙ D, k + C˙ L, k

() $ s

1.49 7.2 1.91 2.6 31.6 356.93 51.66 6.75 11.91

r k (%)

fk (%)

96.02 196.4 21.83 95.93 27.54 43.46 354.9 73.53 255.4

100 97.46 10.7 100 94.92 99.12 97.72 96.38 35.66

r k (%)

fk (%)

98.02 117.4 8.075 96.84 38.88 39.45 490.7 136.9 203.6

89.13 97.79 11.1 88.5 94.63 98.79 96.69 95.15 31.41

Table 10 Exergoeconomic parameters for different components of the proposed system, using R114. Component

Pump 1 Preheater FF Pump 2 Evaporator Turbine Condenser Heater Electrolyzer

cF , k

( ) $ GJ

cP, k

6.02 4.317 8.051 6.02 1.3 4.317 4.317 1.3 6.02

( ) $ GJ

C˙ D, k

0.119 9.383 8.701 0.19 1.805 6.02 25.5 3.08 18.27

() $ s

0.1942 0.3282 1.578 0.4067 2.095 4.075 1.703 0.233 8.775

˙ D, k (kW ) Ex

Z˙ k

8.96 21.12 54.44 18.77 447.7 262.2 109.6 49.79 404.9

1.592 14.53 0.198 3.131 36.94 331.9 49.76 4.571 4.019

() $ s

Z˙ k + C˙ D, k + C˙ L, k

() $ s

1.78 14.85 1.578 3.54 39.03 336 51.46 4.8 12.8

Table 11 Exergoeconomic parameters for different components of the proposed system, using R600. Component

cF , k

Pump 1 Preheater FFH Pump 2 Evaporator Turbine Condenser Heater Electrolyzer

( ) $ GJ

cP, k

6.808 4.892 8.713 6.808 1.3 4.892 4.892 1.3 6.808

( ) $ GJ

C˙ D, k

0.088 13.64 9.185 0.163 1.933 6.808 28.5 2.211 22.82

() $ s

0 0.236 1.317 0 2.502 4.572 2 0.22 10.01

˙ D, k (kW ) Ex

Z˙ k

0.01 13.42 42 0.02 534.6 259.6 114.1 47.12 408.3

1.4 7.11 0.17 2.85 25.19 324.5 51.57 4.262 3.95

() $ s

Z˙ k + C˙ D, k + C˙ L, k

()

1.4 7.34 1.32 2.85 27.7 329.1 53.57 4.29 13.96

$ s

r k (%)

fk (%)

98.72 178.8 5.42 97.61 48.69 39.16 482.6 178.8 70.07

98.61 96.78 11.5 100 90.97 98.61 96.25 95.08 28.32

Table 12 Exergoeconomic parameters for different components of the proposed system, using R236fa. Component

Pump 1 Preheater FFH Pump 2 Evaporator Turbine Condenser Heater Electrolyzer

cF , k

( ) $ GJ

7.636 5.509 9.057 7.636 1.3 5.509 5.509 1.3 7.636

cP, k

( ) $ GJ

0.09 13.13 9.36 0.186 2.221 7.636 26.1 2.453 22.24

C˙ D, k

() $ s

0.19 0.237 0.877 0.492 3.209 4.378 2.304 0.191 8.287

˙ D, k (kW ) Ex

Z˙ k

7.052 11.98 26.92 17.9 685.7 220.7 116.2 40.87 301.5

1.315 21.22 0.12 2.94 16.87 289.7 52.1 3.848 3.575

() $ s

Z˙ k + C˙ D, k + C˙ L, k 1.51 21.46 0.877 3.43 20.1 294.1 54.4 4.04 11.862

() $ s

r k (%)

fk (%)

98.87 138.4 3.344 97.56 90.83 38.62 373.7 88.72 191.3

87.15 98.89 12.03 85.66 84.02 98.51 95.77 95.26 30.14

5.2. Levelized costs

the initial investment, while, expenses are related to the costs of system operations. Carrying charges include: total capital recovery, return on investment for debt, preferred stock, common equity, income taxes as well as other taxes and insurances. In a similar way, expenses include fuel cost (FC), as well as operating and maintenance cost (OMC). It is noteworthy to mention that all the annual costs (carrying charges and expenses) must be estimated for each year during the economic life of the system.

The series related to carrying charges CCj and expenses (OMCj, FCj), for jth work year of the system’s life are not uniform. Generally speaking, the longer the system works, the higher the fuel consumption and costs will be, while the costs of carrying charges will decrease. The levelized costs of the annual total revenue requirement (TRRL) are calculated using the capital recovery factor (CRF) and the discount factor, as follows:

138

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Fig. 2. The effect of evaporator pressure on the output power and hydrogen production.

Fig. 3. The effect of evaporator pressure on the energy and exergy efficiencies.

n

TRRL = CRF ∑ 1

TRRj (1 + ieff ) j

FCL = FC0 × CELF = FC0 (36)

kFC =

1 + rFC , rFC = constant 1 + ieff

(39)

In the above relation, the terms,rFC andCRF are indicating the nominal escalation rate for fuel cost and the capital recovery factor of Eq. (38), respectively. Therefore, the annually levelized operation and maintenance cost (OMCL) is obtained through this relation:

ieff (1 + ieff )n (1 + ieff )n − 1

(38)

In the above relation, we have:

where, TRRj is the total revenue requirement in jth year of the system’s life, ieff is the mean annual average effective discount, while n represents the economic life of the system based on a year time span. Further detailed data on calculating TRRj are given in Refs. It is assumed in Eq. (37) that each money transaction is done at the end of each year. The capital recovery factor (CRF) is calculated as follows:

CRF =

n kFC (1 − kFC ) CRF (1 − kFC )

OMCL = OMC0 × CELF = OMC0

(37)

n kOMC (1 − kOMC ) CRF (1 − kOMC )

(40)

In the above relation, we have:

If the value series of annual expenses of FCj fuel experience only one rFC escalation and stay invariable with time (FCj = FC0 (1 + rFC ) ), then the levelized value of FCL in those series will be obtained by multiplying the fuel cost, in the beginning of the first year of system operation by the constant escalation levelization factor (CELF).

kFC =

1 + rFC , rOMC = constant 1 + ieff

(41)

Here, the term rOMC is the nominal escalation rate for operation and 139

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Fig. 4. The effect of evaporator pressure on the output power and hydrogen production costs.

Fig. 5. The effect of electrolyzer temperature on the hydrogen production and electrolyzer exergy destruction rate.

where, PECk is the purchase cost of the kth component and τrefers to the system work hours in full load for a year. The term Zk indicates the ratio of initial capital investment to operation and maintenance costs of the kth component. Combining Eqs. (43) and (44), we will have:

maintenance costs. Eventually, the levelized carrying charges (CCL) will be calculated as follows: (42)

CCL = TRRL − FCL − OMCL

OMCL + CCL OM CI Z˙ k = Z˙ k + Z˙ k = . τ

It has to be noted that the main difference between a typical economic analysis and a thermo-economical involved in the economic analysis is that the latter is done at component levels. Regarding the contribution of the kth component in the costs of equipment provision for the overall system PECtot=∑ PECk , the an-

FCL C˙ F = τ

k

k

OM Z˙ k

OMCL PECk = τ ∑ PECk k

PECk

(45)

The levelized cost rate of the fuel provided for the whole system is calculated as follows:

nual capital investment (superscripted as CI) and the annual operation and maintenance costs (superscripted as OM) for the overall system could be divided accordingly:

CCL PECk CI Z˙ k = τ ∑ PECk

PECk

∑k

(46) OM C˙ F , Z˙ k ,

Levelized costs, such as for thermoeconomic analysis.

(43)

CI Z˙ k ,

are usually used as input data

5.3. Exergoeconomic analysis The basic thermoeconomic equation for balancing the cost of a single component of an energy system is expressed through:

(44) 140

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Fig. 6. The effect of electrolyzer temperature on the energy and exergy efficiencies.

Fig. 7. The effect of electrolyzer temperature on the output power and hydrogen production costs.

∑ (ce Ex˙ e)k + c w,k W˙ k = cQ,k Ex˙ k,Q + ∑ (ci Ex˙ i)k + Z˙ k e

i

There are some important parameters which play a very fundamental role in exergoeconomic analysis of energy systems. These include the average costs per exergy unit of fuel (cF,k), the average costs per exergy unit of product (cP,k), the relative cost difference (rk), the exergoeconomic factor (fk), and the cost associated with the exergy destruction rate (C˙ D, k ). These parameters are listed respectively as below (Bejan et al., 1996):\

(47)

˙ k, Q , Ex ˙ e and Ex ˙ i are calculated on the basis of thermodynamic W˙ k , Ex and exergetic analysis. Accordingly, ci, ce, cW, and cQ,k are the average costs per exergy unit (hence, the dimension could be $/GJ). The above equation indicates that, for any component of the system, the cost for the output exergy flow rate is equal to the cost of the input exergy flow rate summed up by the overall consumption rate. The cost rate for the products in a plant is very important and numerous engineers from all over the world have always been trying to reduce this cost rate. Since there are often more than one output and input flows for any component in the system, the number of equilibrium equations will be less than the number of unknown cost variables. Therefore, increasing the cost equilibrium and auxiliary equation for any component of the cycle will result in a system of linear equations. Through continuous solving of the linear equations, the cost rate values and cost of the exergy unit in exergy flows will be calculated. The flow balance rate and the auxiliary equations for each component of the cycle are presented in Table 3.

cF , k =

C˙ F , k ˙ F ,k Ex

(48)

cP, k =

C˙ P, k ˙ P, k Ex

(49)

˙ D, k C˙ D, k = cF , k Ex

141

(50)

rk =

cP, k − cF , k cF , k

(51)

fk =

Z˙ k Z˙ k + C˙ D, k + C˙ l, k

(52)

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Fig. 8. The effect of mean pressure on the output power and hydrogen production.

Fig. 9. The effect of mean pressure on the energy and exergy efficiencies.

6. Results and discussion

Xiaojun et al., 2004).

6.1. Assumptions and input parameters

6.2. Model validation

In order to model the proposed integrated system, an appropriate code has been developed in ESS software. To this end, the following hypotheses were taken into consideration:

In order to show the accuracy of the obtained results for the present study, two case studies are ; Safarian and Aramoun, 2015). Under the same internal and external coconsidered from literatures and the results are compared with these references (nditions, an appropriate code is developed in EES (Engineering Equation Solver) for each cases. The first benchmark is regenerative ORC and the second one is the PEM electrolyzer system. Doing this so, the results are listed in Tables 6 and 7 for regenerative ORC and PEM electrolyzer, respectively. As tables indicate, the results are in a great agreement for each cases.

• All processes are in a steady state. • All parts (components) of the system are adiabatic. • There is no pressure drop in the components of the system. • The pumps inputs are saturated liquids. Tables 4 and 5 listed the required parameters for simulating the regenerative ORC and the PEM electrolyzer, respectively. It is notable that the isentropic efficiency of the turbine is dependent upon the type of the working fluid. The current research employs various working fluids (i.e., R114, R245fa, R600, R236fa) for the ORC. Considering these working fluid for the ORC, the isentropic efficiency of the turbine can be selected in different values from previous studies (Badr et al., 1990; Yanagisawa et al., 2001; Manzagol et al., 2002; Kane et al., 2003;

6.3. Modelling results The operational characteristics of the system are listed in Table 8. As will be discussed, all of these values are calculated for four different working fluids and the results are listed for each case. It should be noted that use of R245fa as working fluid was proved to show the highest energy and exergy efficiencies of 3.511% and 67.58%, respectively. 142

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Fig. 10. The effect of mean pressure on the output power and hydrogen production costs.

working fluids, which is followed by R236fa, R600 and R114, respectively. Moreover, the average costs per exergy unit of product in the components of system for R245fa was found to be less than those of other working fluids.

Furthermore, it is the most cost-efficient working fluid with 11.54 $/GJ and 4.921 $/GJ average costs per exergy unit for output power and hydrogen production, respectively. Regarding their operational features and cost-effectiveness, the working fluids R114, R600 and R236fa ranked successively after R245fa. Tables 9–12 summarized the important exergoeconomic parameters and the exergy destruction rate for the different components of the cycle and working fluids. In exergetic investigation of the system components based on these tables, it was noticed that the evaporator and PEM electrolyzer had the most exergy destruction rate in the system, due to their high fuel exergy flow rate for all fluids. In addition, R245fa and R236fa were found to show the lowest and highest exergy destruction rate in the evaporator, respectively, while the trend is reversed in the PEM electrolyzer. Therefore, it can be concluded that, any working fluid with a low exergy destruction rate in the evaporator has the highest exergy destruction rate in the electrolyzer, and this working fluid has the highest output power. With regard to the economic investigation of system’s components, it is noteworthy that the relative cost difference in the condenser is very high, since the average costs per exergy unit of product is more than the average costs per exergy unit of fuel. On the other hand, in the feedfluid heater, because the average costs per exergy unit of fuel and product are close, the relative cost difference is very low. In comparison with other components of the system, capital investment cost rates and operation and maintenance costs are the highest in the turbine and the lowest in the pump. This is due to the large output power of turbine and very low input power of pump. In the same vein, the cost of the exergy destruction rate in the PEM electrolyzer is the highest in comparison with other components. The reason is that the generated power enters the PEM electrolyzer as exergy of fuel. Moreover, all components, except electrolyzer and feed-fluid heater (because of their low costs of the exergy destruction), have a high percentage of exergoeconomic factor. Electrolyzer has a low exergoeconomic factor which is mainly due to the its high exergy destruction rate. Similarly, in the feed-fluid heater, due to the low capital investment and operation and maintenance costs, the exergoeconomic factor is low. Comparing all suggested working fluids, it was observed that R245fa has the highest capital investment, operation and maintenance costs, due to its strong output power feature. Furthermore, this working fluid has the lowest exergy destruction costs. Accordingly, the working fluid R245fa has a low relative cost difference in comparison to other

6.4. Parametric study 6.4.1. The effect of evaporator pressure on the system One of the influential factors in designing output power in the ORC is evaporator pressure which affects the output power, energy efficiency, as well as the exergy efficiency. Fig. 2. is plotted to show the variation of the total output power and hydrogen production of the system for different working fluids with different levels of the evaporator pressure. It is observed that in all working fluids, the output power is increased with an increase in the evaporator pressure. This can be attributed to the fact that an increase in the evaporator pressure increases the turbine input enthalpy, and hence the output power is increased. Given the fact that output power of the turbine is transferred directly as electric energy to the electrolyzer, an increase in the output power gives a raise to the current density of the electrolyzer. Hence, regarding Eq. (10), the mass flow rate of hydrogen is increased. Therefore, the working fluid R245fa has the most output power and hydrogen production in comparison with other working fluids. Fig. 3. displays variation of the total energy and exergy efficiencies with various evaporator pressures. As can be viewed, as evaporator pressure increases, the energy efficiency and exergy efficiencies are increased. This may be due to the fact that, increasing the evaporator pressure will result in a higher output power and mass flow rate of hydrogen, while other parameters are fixed. As a result, the overall energy efficiency of the system is increased with an increase in the evaporator pressure. In addition, the maximum theoretical work produced during system operation is increased as evaporator pressure increases., which gives a rise to the overall exergy efficiency. Fig. 4. depicts variation of the output power and hydrogen production costs for various evaporator pressure levels. As can be seen, the working fluid R245fa has the lowest output power and hydrogen production costs, due to a higher output power of R245fa. Furthermore, it is observed that, increasing the evaporator pressure results in a reduction in the costs of both power and hydrogen production. This is mainly because, the turbine output power is augmented when the evaporator pressure is increased, which in turn reduces the cost for 143

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inferred that at high mean pressures, output power cost is slightly large. The reason for this process is that, at high mean pressure the fuel exergy flow rate of the turbine will be increased, while the product exergy flow rate of the turbine will be decreased. Besides, it is observed that the hydrogen production cost undergoes a slight increase because of higher output power costs.

output power, and hence leads to lower cost of hydrogen production. 6.4.2. The effect of electrolyzer temperature on system In Fig. 5, the variation of hydrogen production and exergy destruction rate of the electrolyzer are shown for different electrolyzer temperatures. The figure indicates that increasing the temperature of the electrolyzer is followed by a fall in the electric potential, while the output power is constant, and thus, the current density is enhanced which results in an increase of hydrogen production. Furthermore, it is observed that exergy destruction rate is low at high electrolyzer temperature. This observation could be justified by the fact that, by increasing temperature of the PEM electrolyzer, the exergy flow in the electrolyzer output is improved, which in turn reduces the exergy destruction rate. Fig. 6 illustrates the effect of electrolyzer temperature on the total energy and exergy efficiencies of the proposed system. The figure shows that exergy efficiency is increased at higher temperatures of the electrolyzer. This process is the result of increasing temperature of the produced hydrogen in the electrolyzer output. Nevertheless, a rise in the temperature given to the water can increase the electrolyzer temperature, and hence the energy efficiency is decreased at higher electrolyzer temperatures. Fig. 7 presents variation of the output power and hydrogen production costs which is followed by any changes in the electrolyzer temperature. As shown, at higher electrolyzer temperatures, the hydrogen production cost is reduced, while the output power cost is remained constant. The main reason behind this process is that the flow exergy rate of hydrogen production is increased with an increase in the electrolyzer temperature, while the electrical power provided for the system and the input water costs are remained constant throughout this variation. The output power cost is constant, since the system output power and the turbine input and output are remained at the same level as the electrolyzer temperature is increasing. As a result, the output power cost is remained constant with any changes in electrolyzer temperature.

7. Conclusions This research presented an energy, exergy and thermoeconomic analysis of a synchronous output power and hydrogen production system through integrating a regenerative organic Rankine cycle with proton exchange membrane electrolyzer. A comprehensive thermodynamic modelling, exergoeconomic analysis, as well as a parametric study were conducted for all selected working fluids. The significant results obtained from this research are as described below:

• The working fluid R245fa had the highest total energy and exergy

• • • • • •

6.4.3. The effect of mean pressure on the system In Fig. 8, the variation of output power and hydrogen production caused by any changes in the mean pressure is shown. It is observable that, in the pressure range of 500–700 kPa, there is a slight reduction in net output power with mean pressure augmentation. Afterwards, this reduction is much greater. In other words, increasing the mean pressure enhances the enthalpy of extracted steam, while decreases the mass flow rate of the extracted steam. Eventually, according to Eq. (2), it can be implied from the findings that these two factors have negative effects on the power. Moreover, a decrease in output power will also reduce the input energy of the electrolyzer, and this gives a drop in the current density. Therefore, increasing the mean pressure will reduce the hydrogen production. Fig. 9 shows the variation of total exergy and energy efficiencies resulting from varying the mean pressure value. The implication is that, increasing the mean pressure reduces the energy efficiency. The main reason for this process is the reduction of the hydrogen production which directly influences the energy efficiency. Additionally, following an increase in the mean pressure, a higher exergy efficiency can be observed. As was stated before, a rise in the mean pressure will lead to a high enthalpy of extracted steam and a reduction in its mass fraction. These two factors will reduce the flow rate of fuel exergy in the turbine. In addition, increasing the mean pressure results in a reduction of output power, and hence the fuel exergy flow rate in the electrolyzer will be reduced. Each of the above mentioned factors has positive effects on the exergy efficiency and can increase it. Moreover, it is indicated that at higher mean pressures R114 has the highest exergy efficiency. Accordingly, the variation of output power and hydrogen production costs with different mean pressures is presented in Fig. 10. It can be

• •

efficiencies of 3.511% and 67.58%, respectively. Furthermore, it was the most cost-efficient working fluid with 11.54 $/GJ and 4.921 $/GJ average costs per exergy unit for output power and hydrogen production, respectively. Regarding its operational features and cost effectiveness, the working fluids R114, R600 and R236fa ranked successively after R245fa. Any working fluid with a low exergy destruction rate in the evaporator had the highest exergy destruction rate in the electrolyzer. Compared to the other components of the system, capital investment cost rates and operation and maintenance costs were the highest in the turbine and lowest in the pump. The costs of the exergy destruction rate in the electrolyzer were the highest in comparison with other components. All components (except the electrolyzer and the feed-fluid heater) had a high percentage of exergoeconomic factor. R245fa had the highest capital investment, operation and maintenance costs, whereas it had the lowest exergy destruction costs. Increasing of the evaporator pressure resulted an increase in the output power, hydrogen production, energy efficiency, and exergy efficiency, whereas the costs of output power and hydrogen production decreased by the evaporator pressure augmentation. An increase in the electrolyzer temperature increased hydrogen production, exergy efficiency, while decreased the energy efficiency, hydrogen production cost and exergy destruction rate. However, the output power and its costs stayed constant through this variation. An increase in the mean pressure of turbine increased the exergy efficiency and costs of the output power and hydrogen production, while decreased the output power, hydrogen production and energy efficiency.

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