Analysis and performance assessment of a new solar-based multigeneration system integrated with ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle

Journal of Power Sources 370 (2017) 138e154

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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

Analysis and performance assessment of a new solar-based multigeneration system integrated with ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle Osamah Siddiqui*, Ibrahim Dincer Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario L1H 7K4, Canada

h i g h l i g h t s
New solar-based system integrated with ammonia fuel cell and SOFC-GT cycle.
Ammonia fuel cell integrated with molten salt thermal energy storage.
Thermodynamic analyses and modeling through both energy and exergy approaches.
Increase of 19.3% in energy efficiency as compared to single generation system.
Increase of 17.8% in exergy efficiency as compared to single generation system.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 August 2017 Received in revised form 29 September 2017 Accepted 2 October 2017

In the present study, a new solar-based multigeneration system integrated with an ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle to produce electricity, hydrogen, cooling and hot water is developed for analysis and performance assessment. In this regard, thermodynamic analyses and modeling through both energy and exergy approaches are employed to assess and evaluate the overall system performance. Various parametric studies are conducted to study the effects of varying system parameters and operating conditions on the energy and exergy efficiencies. The results of this study show that the overall multigeneration system energy efficiency is obtained as 39.1% while the overall system exergy efficiency is calculated as 38.7%, respectively. The performance of this multigeneration system results in an increase of 19.3% in energy efficiency as compared to single generation system. Furthermore, the exergy efficiency of the multigeneration system is 17.8% higher than the single generation system. Moreover, both energy and exergy efficiencies of the solid oxide fuel cell-gas turbine combined cycle are determined as 68.5% and 55.9% respectively. © 2017 Elsevier B.V. All rights reserved.

Keywords: Solar energy Ammonia fuel cell Solid oxide fuel cell Energy Exergy Multigeneration

1. Introduction Energy demands have increased significantly and incessantly across the globe over the past several decades. The global primary energy demands have been estimated to increase by about 50% between the years 2016 and 2030 [1]. The primary method of energy production globally relies on fossil fuels. They form nearly 80% of the world's total energy consumption [2]. Energy production by fossil fuels is considered the primary cause of environmental

* Corresponding author. E-mail addresses: [email protected] (O. Siddiqui), ibrahim.dincer@uoit. ca (I. Dincer). https://doi.org/10.1016/j.jpowsour.2017.10.008 0378-7753/© 2017 Elsevier B.V. All rights reserved.

pollution. In addition, the associated emissions are also detrimental to human health. It is essential to overcome the massive dependence on fossil fuels. Renewable sources of energy, such as solar energy provide a solution to the problems encountered due to the usage of fossil fuels. However, solar-based power generation facilities have low efficiencies and need to be supplemented with other energy resources in order to meet energy demands. Power generation facilities utilizing combined solar and other resources of energy can reduce the dependence on fossil fuels. For instance, Hosseini et al. [3] proposed and analysed a hybrid solar energy and fuel cell based system for combined heating and power generation. The proposed system was designed for residential applications and was found to have an exergy efficiency of 49% and an energy efficiency of 55.7%.

O. Siddiqui, I. Dincer / Journal of Power Sources 370 (2017) 138e154

It is known that conventional gas turbine power plants utilizing natural gas (i.e., methane) as fuel have high amount of irreversibilities, specifically in the combustion chamber. This particularly leads to the low overall efficiencies and high amounts of greenhouse emissions of the power generation cycle. In order to increase the efficiencies and reduce the greenhouse emissions of gas turbine power plants, a combined solid oxide fuel cell (SOFC)-gas turbine cycle can be utilized. Milewski et al. [4] presented the numerical modeling and simulation of a hybrid SOFC system operating at part load. The results of their study concluded that the hybrid SOFC system attains a stable thermal efficiency and the system operating parameters can be varied along a wide range providing high control flexibility. Moreover, the combined cycle proposed by Haseli et al. [5] was found to have 27.8% and 26.6% higher energy and exergy efficiency than a conventional cycle respectively. Furthermore, it will help in reducing the environmental emissions. In addition, Chan et al. [6] modeled a hybrid SOFC and gas turbine system. The SOFC comprised internal reforming. The proposed system was found to have an efficiency of greater than 60% for single generation and higher than 80% in case of co-generation with waste heat recovery. Furthermore, Calise et al. [7] simulated and performed an exergy analysis on a 1.5 MW hybrid SOFC-gas turbine system. The system electrical efficiency was found to be nearly 60% without waste heat recovery. Moreover, multi-generation energy systems providing multiple useful commodities are also being investigated. These systems help to enhance the overall efficiencies of integrated energy systems. In addition to this, they provide a solution to improve the low efficiencies of conventional renewable energy based power generation facilities. Al-Sulaiman et al. [8] proposed and investigated an organic Rankine cycle and SOFC based integrated system providing electricity, heating and cooling. The trigeneration system was found to have considerably higher efficiencies than the single generation system. Yan et al. [9] investigated a combined SOFC, gas turbine and organic Rankine cycle system with liquefied methane serving as the heat sink. The waste heat of the SOFC was utilized to improve the system efficiencies. The overall system efficiency was obtained as 67%. Malico et al. [10] designed a trigeneration system for power, cooling and heating by utilizing a SOFC. A thermal efficiency of 68% was obtained by them. Tse et al. [11] investigated a SOFC-GT trigeneration system. A maximum overall efficiency of 43.2% was obtained. The utilization of waste heat recovery was found to increase the system efficiencies. Utilizing hydrogen as a carbon-free fuel that avoids formation of carbon emissions during combustion is considered a promising alternative to fossil fuels. It is an exceptional energy carrier and is thus considered a viable energy storage option. Various studies have investigated the potential to utilize hydrogen as a replacement of fossil fuels [12,13]. However, conventional fossil fuel based hydrogen production methods form nearly 96% of the production carried out to meet market demands, approximately half of the hydrogen production is carried out using natural gas steam reforming, nearly 30% is carried out by utilizing oil refineries and approximately 18% is carried out through coal gasification [14]. These methods produce large quantities of greenhouse gas emissions. Every ton of hydrogen produced may result in the release of approximately 2.5e5 ton of carbon dioxide. Thus, hydrogen production through renewable energy resources needs to be investigated. An environmentally benign way of hydrogen production is to integrate the electrolyzer with renewable energy based power generation facilities. This provides a viable solution to improve the efficiency of multi-generation systems by producing hydrogen in an environmentally benign way. However, there are several challenges associated with the utilization of hydrogen. It does not have a high volumetric energy density. The storage as well as the transportation

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of hydrogen are hindered with various constraints owing to the low volumetric energy density. Moreover, hydrogen is flammable, which makes it dangerous while transportation or storage. To overcome these drawbacks, studies on alternative hydrogen carriers are being conducted. Several hydrogen carriers including ammonia, alcohols and hydrocarbons have been studied. Ammonia is a promising candidate due to various advantages. It has a high energy density of 4 kWh/kg and is easy to liquefy as it has a boiling point of 33.4  C at standard atmospheric pressure. Furthermore, it has a comparatively high hydrogen content of 17.7 wt% and has a constricted flammable range of approximately 16e25 vol % in air [15,16]. Ammonia is free of carbon and is cost effective, hence, it provides an alternative fuel source to achieve lower environmentally harmful emissions in the process of energy generation. Generation of electricity through fuel cells is being considered as a clean source of energy production. Currently, hydrogen is the prominent fuel for fuel cell technology. However, in order to overcome the drawbacks of hydrogen, ammonia can be used as an alternative fuel. Incorporating ammonia as a fuel for fuel cells is being considered in various studies. In the utilization of ammonia as a fuel for fuel cells, either it can be decomposed into nitrogen and hydrogen externally or it can be directly fed into the cell. Direct ammonia fuel cells allow feeding of ammonia as a fuel directly without requiring an external decomposition unit. Hence, provide more applicability for various uses. Ammonia was initially investigated as a source of electricity generation from fuel cells as well as a source to produce nitrogen oxide as a useful chemical [17,18]. Several studies have followed which investigated ammonia as a fuel source for different types of fuel cells. Ganley [19] developed and tested a molten KOH-NaOH based ammonia fed fuel cell working at temperatures between 200 and 450  C. The fuel cell was found to provide a peak power density of 40 mW/cm2 at a temperature of 450  C. In addition, Yang et al. [20] investigated a molten NaOH-KOH electrolyte based direct ammonia fuel cell. A peak power density of 16 mW/cm2 was obtained at a temperature of 220  C. Although, separate studies have been conducted on solarbased multi-generation systems, integrated solid oxide fuel cellgas turbine cycles and ammonia fuel cells. Efforts have not been made to develop a solar-based multi-generation system integrated with molten alkaline electrolyte ammonia fuel cell and solid oxide fuel cell-gas turbine cycle. The molten salt utilized in thermal energy storage systems in solar thermal power plants can be used as an electrolyte for molten alkaline ammonia fuel cells. Furthermore, solar tower based power plants can be integrated with a solid oxide fuel cell-gas turbine cycle to achieve higher energy outputs. Furthermore, these integrated systems can be utilized for multigeneration to produce multiple useful outputs. Hence, in the current study, we develop and thermodynamically analyze a new solar-based multigeneration system integrated with an ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle to produce electricity, hydrogen, cooling and hot water. The specific objectives of this study include (a) developing a new solar-tower based multigeneration system integrated with ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle for electricity generation, hydrogen production, cooling and hot water (b) analysing the system through thermodynamic approaches of energy and exergy analyses, (c) determining the energy efficiency and exergy efficiency of the proposed system as well as system components, and (d) conducting a parametric study to analyze how varying parameters will affect both energy and exergy efficiencies of the proposed system and system constituents.

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2. System description A solar-based multigeneration system integrated with ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle is developed. The schematic diagram of the system is illustrated with state points in Fig. 1. The system comprises of central solar tower receiver, steam Rankine cycles, solid oxide fuel cell-gas turbine cycle fueled with methane, molten alkaline ammonia fuel cell, proton exchange membrane electrolyzer, absorption cooling system and hot water storage. The useful system outputs include electricity, hot water, cooling and hydrogen. Electricity is generated by the primary steam Rankine cycle powered by the solar tower, the solid oxide fuel cell, the combined gas turbine cycle, the secondary Rankine cycle powered by waste heat and the ammonia fuel cell. Hydrogen is produced by a proton exchange membrane electrolyzer. The cooling is provided by an absorption cooling system. 2.1. Primary steam Rankine cycle The solar energy concentrated on the central solar tower receiver by the heliostat field is absorbed by the molten salt, which is utilized for thermal energy storage. The molten salt thermal energy storage comprises of a hot and cold tank. The temperature of the hot tank is maintained at 650  C, and the cold tank

temperature is maintained at 400  C. The thermal energy absorbed by the molten salt is transferred to the primary steam Rankine cycle for electricity generation. The liquid water leaves pump 1 and enters heat exchanger 1, where thermal energy is transferred from the hot molten salt to water. The generated superheated steam is passed through turbine 1 to generate power. The exhaust stream of turbine 1 is passed through heat exchanger 4 where it transfers thermal energy to the secondary Rankine cycle. 2.2. Solid oxide fuel cell-gas turbine combined cycle The solid oxide fuel cell-gas turbine cycle comprises of (a) compressor, (b) solid oxide fuel cell, (c) combustion chamber, (d) gas turbine 3 and (e) heat exchanger 2. Air enters the compressor, where the pressure level is increased to the required cycle pressure. After leaving the compressor, air enters the heat exchanger 2 where it gains thermal energy from the exhaust flue gases. After leaving Heat exchanger 2, it enters the cathode side of the solid oxide fuel cell. Methane gas is utilized as the fuel and enters the fuel cell at the anode side. The electrochemical reactions occurring within the fuel cell produce DC power. The Ohmic resistance in the fuel cell results in an increase in the temperature of formed products. A small fraction of the methane is utilized in the fuel cell, the remaining is passed through the combustion chamber, where the combustion of

Fig. 1. Schematic of solar-based multigeneration system integrated with ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle.

O. Siddiqui, I. Dincer / Journal of Power Sources 370 (2017) 138e154

methane raises the temperature considerably. The high temperature flue gas is passed through gas turbine 3 for power generation. After leaving turbine 3, the flue gas passes through heat exchanger 2 to provide thermal energy to the compressed air. After leaving heat exchanger 2, the flue gas transfers heat to the generator of the absorption cooling system. After transferring heat to generator, flue gas is passed through heat exchanger 3, where it provides heat to the secondary Rankine cycle. 2.3. Secondary Rankine cycle The waste heat of the primary Rankine cycle and solid oxide fuel cell-gas turbine cycle is utilized to power the secondary Rankine cycle comprising of steam turbine 2. Firstly, water enters heat exchanger 3 where it gains thermal energy from the hot flue gas. After leaving heat exchanger 3, it passes through heat exchanger 4 where it is converted to superheated vapor. The generated steam passes through steam turbine 2 to produce power. Waste heat of the secondary Rankine cycle is used to obtain hot water for domestic usage. 2.4. Molten alkaline electrolyte ammonia fuel cell The molten alkaline electrolyte ammonia fuel cell uses the molten salt stored in the cold tank as an electrolyte to generate electricity. The cold tank is maintained at a temperature of 400  C. The molten salt (KOH þ NaOH) is passed through the fuel cell at this temperature, where it acts as an electrolyte for the transfer of OH anions. Ammonia gas is fed at the anode and oxygen gas is fed at the cathode. The fuel cell converts the stored chemical energy of the reactants into electrical energy. The molten electrolyte comprises of a mixture of sodium and potassium hydroxide. 2.5. Proton exchange membrane (PEM) electrolyzer The PEM electrolyzer generates hydrogen by utilizing a fraction of the electricity generated by steam turbine 1. Water is fed into the electrolyzer at the PEM temperature. By utilizing electricity, water is converted into hydrogen gas by electrochemical reactions. Hydrogen is considered a promising carbon-free fuel that avoids formation of carbon emissions during combustion. In addition, it is an exceptional energy carrier and is thus considered a viable energy storage option.

141

reference pressure P0 ¼ 100 kPa. The assumptions utilized to facilitate the analysis are
The pumps and turbines are adiabatic.
The changes in both kinetic and potential energies and exergies are negligible.
The pumps and turbines have an isentropic efficiency of 80%.
The throttling process is adiabatic.
The pressure losses are negligible.
Steady state conditions exist. The principle of conservation of mass for a given control volume can be applied to denote the general mass balance equation:

X X dmcv m_ i  m_ e ¼ dt e i

(1)

The first law of thermodynamics can be applied to obtain the energy balance equation for a control volume on a rate basis:

_ þ Q_  W ¼

X V2 m_ i hi þ i þ gZi 2 i

!

X V2 m_ e he þ e þ gZe  2 e

dEcv dt

!

(2)

The entropy is generated during a process due to irreversibilities. The rate of entropy generation for a control volume is expressed by Bejan [21] as follows:

dScv þ S_gen ¼ dt

X X X Q_ k m_ e se  m_ i si  T k e i

(3)

k

The exergy balance equation for a given control volume is expressed as:

_ Qþ Ex

X X _ w þ Ex _ m_ i exi ¼ m_ e exe þ Ex d i

(4)

e

3.1. Primary Rankine cycle balance equations Pump 1: The mass balance per unit time for pump 1 can be denoted as follows:

2.6. Absorption cooling system

m_ 1 ¼ m_ 2

An ammonia-water mixture based absorption cooling system is incorporated to provide cooling. The heat required by the generator of the absorption cooling system is obtained from the exit stream of the gas turbine 3. A concentrated ammonia vapor is formed in the generator, which passes through the condenser to reject heat. After leaving the condenser, it passes through throttle valve 1, where its temperature and pressure drop before entering the evaporator. The cold concentrated ammonia vapor passes through the evaporator to absorb heat and provide the required cooling effect. The weak solution (state 26) leaves the generator and passes through heat exchanger 5 to provide heat to incoming stream from the absorber. This reduces the amount of heat required by the generator.

The energy balance on a rate basis for pump 1 can be expressed as follows:

3. Thermodynamic analysis Energy and exergy analyses are performed on each system component of the proposed integrated system to determine their performance and to obtain the overall system efficiencies. The reference environment temperature is taken as T0 ¼ 298 K and the

_ _ 2 h2 m_ 1 h1 þ W P1 ¼ m

(5)

(6)

The entropy balance on a rate basis for pump 1 is expressed as follows:

m_ 1 s1 þ S_gen;P1 ¼ m_ 2 s2

(7)

The exergy balance on a rate basis for pump 1 can be expressed as follows:

_ _ _ 2 ex2 þ Ex m_ 1 ex1 þ W P1 ¼ m d;P1

(8)

Heat exchanger 1: The mass balance per unit time for heat exchanger 1 is expressed as follows:

m_ st;h ¼ m_ st;c and m_ 2 ¼ m_ 3

(9)

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The energy balance per unit time for Heat exchanger 1 is expressed as follows:

_ ¼ m_ h m_ 10 h10 þ W C 11 11

m_ 2 h2 þ m_ st;h hst;h ¼ m_ 3 h3 þ m_ st;c hst;c

The entropy balance on a rate basis for the compressor is expressed as follows:

(10)

(22)

The entropy balance per unit time for Heat exchanger 1 is expressed as follows:

m_ 10 s10 þ S_gen;C1 ¼ m_ 11 s11

m_ 2 s2 þ m_ st;h sst;h þ S_gen;HX1 ¼ m_ 3 s3 þ m_ st;c sst;c

The exergy balance on a rate basis for the compressor can be expressed as follows:

(11)

The exergy balance per unit time for Heat exchanger 1 is expressed as follows:

_ m_ 2 ex2 þ m_ st;h exst;h ¼ m_ 3 ex3 þ m_ st;c exst;c þ Ex d;HX1

(12)

Turbine 1: The mass balance on a rate basis for turbine 1 is denoted as follows:

m_ 3 ¼ m_ 4

(13)

The energy balance on a rate basis for the primary turbine is denoted as follows:

_ _ 4 h4 m_ 3 h3 ¼ W T1 þ m

(14)

The entropy balance on a rate basis for Turbine 1 is denoted as follows:

m_ 3 s3 þ S_gen;T1 ¼ m_ 4 s4

(15)

The exergy balance on a rate basis for Turbine 1 is denoted as follows

_ _ _ 4 ex4 þ Ex m_ 3 ex3 ¼ W T1 þ m d;T1

(16)

Heat exchanger 4: The mass balance per unit time for heat exchanger 4 is expressed as follows:

m_ 5 ¼ m_ 6 and m_ 4 ¼ m_ 1

(17)

The energy balance per unit time for heat exchanger 4 is expressed as follows:

m_ 5 h5 þ m_ 4 h4 ¼ m_ 6 h6 þ m_ 1 h1

(18)

_ ¼ m_ ex þ Ex _ m_ 10 ex10 þ W C 11 11 d;C

(23)

(24)

The isentropic efficiency of the compressor can be denoted as

hC;is ¼

h11;is  h10 wC;is ¼ h11  h10 wC

(25)

where wC;is and wC denote the isentropic and actual work of the compressor respectively. For isentropic compressor operation, the outlet temperature can be determined as

T11;is ¼ T10



P11 P10

ðg1Þ=g (26)

Heat exchanger 2: The mass balance per unit time for heat exchanger 2 is expressed as follows:

m_ 11 ¼ m_ 12 and m_ 15 ¼ m_ 16

(27)

The energy balance per unit time for heat exchanger 2 is expressed as follows:

m_ 11 h11 þ m_ 15 h15 ¼ m_ 12 h12 þ m_ 16 h16

(28)

The entropy balance per unit time for heat exchanger 2 can be written as follows:

m_ 11 s11 þ m_ 15 s15 þ S_gen;HX2 ¼ m_ 12 s12 þ m_ 16 s16

(29)

The exergy balance per unit time for heat exchanger 2 can be written as follows:

_ m_ 11 ex11 þ m_ 15 ex15 ¼ m_ 12 ex12 þ m_ 16 ex16 þ Ex d;HX2

(30)

The entropy balance per unit time for heat exchanger 4 can be written as follows:

m_ 5 s5 þ m_ 4 s4 þ S_gen;HX4 ¼ m_ 6 s6 þ m_ 1 s1

(19)

The exergy balance per unit time for heat exchanger 4 can be written as follows:

_ m_ 5 ex5 þ m_ 4 ex4 ¼ m_ 6 ex6 þ m_ 1 ex1 þ Ex d;HX4

(20)

3.2. Solid oxide fuel cell-gas turbine combined cycle Compressor: The mass balance per unit time for the compressor can be denoted as follows:

m_ 10 ¼ m_ 11

(21)

The energy balance on a rate basis for the compressor can be expressed as follows:

3.3. Solid oxide fuel cell The solid oxide fuel cell is fed with methane fuel. There are several anodic reactions possible due to the water gas shift and steam-reforming reactions depending on the how methane reacts within the fuel cell. Methane can undergo a complete oxidation; in this case, CO2 and H2O are the formed products. In addition, a partial oxidation of methane is also possible. In this case, CO and H2 are the products formed due to the oxidation. Furthermore, steam reforming, dry reforming, and water gas shift reactions can also occur [22]. The anodic and cathodic reactions occurring in the fuel cell can be expressed as: Anode:

H2 þ O2 /H2 O þ 2e

(31a)

CO þ O2 /CO2 þ 2e

(31b)

O. Siddiqui, I. Dincer / Journal of Power Sources 370 (2017) 138e154

CH4 þ 4O2 /2H2 O þ CO2 þ 8e

(31c)

Cathode:

0:5O2 þ 2e /O2

(32)

The amount of direct oxidation of CH4 and CO can be insignificant. Generally, in an analysis, it is assumed that H2 is produced by the water gas shift reaction of CO with H2O and the steam reforming reaction of CH4 with H2O. However, different anode materials and catalysts may support direct oxidation reactions. This affects the amount pre-reforming required for the fuel. In case of complete electro-oxidation of methane, the overall cell reaction can be expressed as:

CH4 þ 2O2 /CO2 þ 2H2 O

(33)

In case of complete electro-oxidation of methane, the reversible cell voltage for the fuel cell can be determined as [5]:

DGðT0 ;P0 Þ

E¼

nF

PCH4 PO2 2 RT ln þ 2 nF PCO2 PH 2O

H2 þ 0:5O2 /H2 O

(35)

The corresponding reversible cell voltage can be evaluated as:

DGðT0 ;P0 Þ nF

þ

PH2 O RT ln   0:5 nF PH2 PO2

! (36)

In addition, reactants at the anode can affect the partial pressures of other formed products. Milewski et al. [24] proposed a mathematical model to determine the reversible cell potential of solid oxide fuel cells for such cases:

rev ESOFC

pciO2 BT BT ln K þ ln ¼ 2F 4F pai H2 ! 1  h BT f ln s þ 2F þ hf h

!

     azFVact ð1  aÞzFVact  exp  J ¼ J0 exp RT RT

(38)

where J0 denotes the exchange current density, which quantifies the electron activity at the equilibrium potential. It is dependent on the material and structure of the electrodes used. In addition, it is also affected by the reaction temperature and the triple-phase boundary length. The ratio of forward to backward activation barrier is affected by the electrical potential. This effect is described by the charge transfer coefficient (aÞ, which lies numerically between zero and one. However, experimentally it is generally found to be around the value of 0.5. The activation over-potential can thus be expressed as:

! RT J ln ; i ¼ cathode or anode J0;i anF

(39)

(34)

where DGðT0 ;P0 Þ denotes the change in Gibbs function at standard temperature and pressure conditions, P denotes the partial pressure, F is the Faradays constant, T represents the fuel cell stack temperature, R denotes the universal gas constant. The Nernst equation (Eq. (34)) allows the calculation of the reversible fuel cell voltage at varying partial pressures of the reactants and products and the fuel cell stack temperature. For the sold oxide fuel cell operating at 800  C, the ideal cell voltage is typically 0.99 V [23]. However, studies also consider Eq. (31a) as the anodic reaction as H2 is produced due to the water gas shift and steam reforming reactions, in this case, the overall cell reaction can be expressed as:

E¼

known as activation over-potential. The relationship between the activation over-potential and the current density of the fuel cell is expressed by the Butler-Volmer expression as:

Vact;i ¼

!

143

0 h 1 1  2 fo BT @ ðhÞA ln þ 4F 1 þ hs (37)

where K denotes the chemical equilibrium constant, hf denotes the fuel utilization factor, pai H2 denotes the partial pressure of hydrogen at the anode inlet, pciO2 represents the partial pressure of oxygen at the cathode inlet, hs denotes the steam to hydrogen ratio and ho denotes the oxygen to hydrogen ratio. In the current study, complete oxidation of methane is considered, which is possible in the presence of different anode and catalyst materials. Hence, equation (34) is utilized. Eq (34) allows the calculation of the open circuit voltage of the cell. However, when current is drawn from the cell for an external load, polarization and Ohmic losses occur within the cell. The loss occurring in a fuel cell due to electrode kinetics irreversibilities is

The Ohmic over-potential (VU ) accounts for the ionic and electronic resistance of the cell. Ohmic losses occur due the ionic and electronic resistance of the electrolyte and other components. The Ohmic over-potential can be evaluated based on the Ohm's law. An expression in terms of the current density, electrolyte resistance and electrolyte thickness is:

VU ¼ J dRU

(40)

The magnitude of the electrolyte resistance depends on the material utilized. In addition, it is also affected by the operating temperatures. When the fuel cell current density is increased, an increase in the electrochemical reaction rate occurs in order to supply the required amount of electron transfer required. As the reaction rates increase, the reactants are consumed more swiftly at the electrodes. However, the mass transfer rate of the reactants is limited. Due to this, the reactant availability near the available reaction sites is limited. Furthermore, as the fed reactants are converted into reaction products, the reaction products can over accumulate at the reaction sites. This also hinders the transport of new reactant molecules from reaching the reaction sites. This phenomenon creates an upper limit on the amount of current that can be drawn from the cell. The maximum current density that can be drawn from the fuel cell is referred to as the limiting current density. As the current density approaches the limiting current density, the limiting mass transfer rate inhibits any further increase. The polarization loss occurring due to this phenomenon is known as concentration overpotential ðVconc ). For a given half-cell reaction at an electrode, the rate at which the ionic species diffuse towards the electrode can be expressed according to the Fick's law:

dC M_ i ¼ Di i dx 00

(41)

00

where M_ i denotes the molar diffusion rate flux, Di represents the diffusion coefficient of the ionic specie. The diffusion coefficient depends on various factors including solute molecular size and temperature. Furthermore, the rate of ion transport given in equation (12) can be related to the current density as: 00

Ji ¼ nF M_ i

(42)

Substituting equation (12) in equation (13), the above equation

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can be expressed as:

Ji ¼ nFDi

 m_ 12 þ ðUÞm_ fu;SOFC h13 þ Q_ CC ¼ m_ 14 h14 þ Q_ l;CC

Ci;B  Ci;S

d

where

where Ci;B denotes the bulk concentration of the specie, Ci;S represents the specie concentration at the electrode surface and d represents the diffusion layer thickness. At the limiting current density, the specie concentration at the electrode surface (Ci;S ) approaches zero. Hence, the limiting current density at the cathode or anode can be expressed as:

JL;i ¼ nFD

CB

(44)

d

The concentration overpotential can be expressed as a function of the limiting current density:

!

Vconc;i ¼

(52)

(43)

JL;i RT ln ; i ¼ cathode or anode nF JL;i  J

Considering the voltage losses, the fuel cell voltage can thus be expressed as:

V ¼ E  Vact;an  Vact;ca  VU  Vconc;an  Vconc;ca

(45)

The irreversibilities due to activation, concentration and Ohmic losses cause an internal heat generation within the cell. The heat generation rate can be expressed as:

Q_ gen;SOFC ¼ jAcell ðE  VÞ

(46)

where Acell denotes the cell area. The mass balance on a rate basis for the SOFC is expressed as:

m_ 12 þ m_ fu;SOFC ¼ m_ 13

(47)

(48)

where U represents the utilization factor of the fuel. Considering adiabatic operation, the energy balance on a rate basis for the SOFC is expressed as:

m_ 12 h12 þ ðUÞm_ fu;SOFC LHVCH4 þ ð1  UÞm_ fu;SOFC hCH4 ;in _ _ 13 h13 ¼W SOFC;DC þ m

(49)

where LHVCH4 represents the lower heating value of methane. The entropy balance on a rate basis for the solid oxide fuel cell can be expressed as:

m_ 12 s12 þ m_ fu;SOFC sfu;SOFC þ S_gen;SOFC ¼ m_ 13 s13

(53)

i h Q_ l;CC ¼ ð1  UÞm_ fu;SOFC þ m_ fu;CC ð1  hCC ÞLHVCH4

(54)

The efficiency of the combustion chamber (hCC Þ is considered to be 98%. The exergy balance on a rate basis for the combustion chamber is expressed as:

 CH PH _ m_ 13 ex13 þ ð1  UÞm_ fu;SOFC exCH CH4 þ mfu;CC exCH4 þ exCH4   To _ þ Ex ¼ m_ 14 ex14 þ Q_ l;CC 1  d;CC Tsink

(55)

When the ambient (To Þ and sink ðTsink Þ temperatures are equal, the second term on right side of the equation will be zero. The design and operating parameters of the solid oxide fuel cell-gas turbine cycle are listed in Table 1.

3.5. Secondary Rankine cycle balance equations Pump 2: The mass balance per unit time for pump 2 can be denoted as follows:

m_ 8 ¼ m_ 9

(56)

The energy balance on a rate basis for pump 2 can be expressed as follows:

where m_ 13 can be expressed as [5]:

m_ 13 ¼ m_ 12 þ ðUÞm_ fu;SOFC þ ð1  UÞm_ fu;SOFC

i h Q_ CC ¼ ð1  UÞm_ fu;SOFC þ m_ fu;CC LHVCH4

(50)

_ _ 9 h9 m_ 8 h8 þ W P2 ¼ m

(57)

The entropy balance on a rate basis for pump 2 is expressed as follows:

m_ 8 s8 þ S_gen;P2 ¼ m_ 9 s9

(58)

The exergy balance on a rate basis for pump 2 can be expressed as follows:

_ _ _ 9 ex9 þ Ex m_ 8 ex8 þ W P2 ¼ m d;P2

(59)

Heat exchanger 3: The mass balance per unit time for heat exchanger 3 is expressed as follows:

m_ 9 ¼ m_ 5 and m_ 17 ¼ m_ 18

(60)

The energy balance per unit time for heat exchanger 3 is expressed as follows:

3.4. Combustion chamber

m_ 9 h9 þ m_ 17 h17 ¼ m_ 5 h5 þ m_ 18 h18

As depicted in Fig. 1, a fraction of the fuel input to the cycle is passed through the solid oxide fuel cell. The remaining fuel (m_ fu;CC Þ is fed into the combustion chamber. The mass balance per unit time for the combustion chamber is expressed as:

The entropy balance per unit time for heat exchanger 3 is expressed as follows:

m_ 13 þ m_ fu;CC ¼ m_ 14

m_ 9 s9 þ m_ 17 s17 þ S_gen;HX3 ¼ m_ 5 s5 þ m_ 18 s18

(51)

The energy balance on a rate basis for the combustion chamber is expressed as [5]:

(61)

(62)

The exergy balance per unit time for heat exchanger 3 is expressed as follows:

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145

Table 1 Design and operating parameters of the solid oxide fuel cell-gas turbine system. Parameter

Value

Compressor isentropic efficiency ðhC;is Þ Compressor compression ratio Utilization factor (U) Fuel cell stack temperature Current density ðjÞ

80% 4 0:85 800 o C 300 mA cm2 0:85

DC to AC inverter efficiency ðhconv Þ _ fu;SOFC Þ Fuel mass flow rate to the fuel cell ðm

0:063 kg s1

_ fu;CC Þ Fuel mass flow rate to the combustion chamber ðm

0:017 kg s1 20 mm 98%

Electrolyte thickness Combustion chamber efficiency (hCC Þ

_ m_ 9 ex9 þ m_ 17 ex17 ¼ m_ 5 ex5 þ m_ 18 ex18 þ Ex d;HX3

(63)

The entropy balance per unit time for heat exchanger 6 can be written as follows:

Heat exchanger 4: The mass balance per unit time for heat exchanger 4 is expressed as follows:

m_ 7 s7 þ m_ 29 s29 þ S_gen;HX6 ¼ m_ 8 s8 þ m_ 30 s30 þ

m_ 5 ¼ m_ 6 and m_ 4 ¼ m_ 1

The exergy balance per unit time for heat exchanger 6 can be written as follows:

(64)

The energy balance per unit time for heat exchanger 4 is expressed as follows:

m_ 5 h5 þ m_ 4 h4 ¼ m_ 6 h6 þ m_ 1 h1

(65)

Q_ l;HX6 T0

(74)

  T0 _ _ 1  þ Q m_ 7 ex7 þ m_ 29 ex29 ¼ m_ 8 ex8 þ m_ 30 ex30 þ Ex d;HX6 l;HX6 Tabs (75)

The entropy balance per unit time for heat exchanger 4 can be written as follows:

m_ 5 s5 þ m_ 4 s4 þ S_gen;HX4 ¼ m_ 6 s6 þ m_ 1 s1

(66)

The exergy balance per unit time for heat exchanger 4 can be written as follows:

_ m_ 5 ex5 þ m_ 4 ex4 ¼ m_ 6 ex6 þ m_ 1 ex1 þ Ex d;HX4

(67)

Turbine 2: The mass balance on a rate basis for turbine 2 is denoted as follows:

m_ 6 ¼ m_ 7

(68)

The energy balance on a rate basis for the turbine 2 is denoted as follows:

_ _ 7 h7 m_ 6 h6 ¼ W T2 þ m

(69)

The entropy balance on a rate basis for turbine 2 is denoted as follows:

m_ 6 s6 þ S_gen;T2 ¼ m_ 7 s7

(70)

The exergy balance on a rate basis for turbine 2 is denoted as follows

_ _ _ 7 ex7 þ Ex m_ 6 ex6 ¼ W T2 þ m d;T2

(71)

Heat exchanger 6: The mass balance per unit time for heat exchanger 6 is expressed as follows:

m_ 7 ¼ m_ 8 and m_ 29 ¼ m_ 30

(72)

The energy balance per unit time for heat exchanger 6 is expressed as follows:

m_ 7 h7 þ m_ 29 h29 ¼ m_ 8 h8 þ m_ 30 h30 þ Q_ l;HX6

(73)

3.6. Proton exchange membrane (PEM) electrolyzer The PEM electrolyzer is utilized for hydrogen production. The overall water electrolysis reaction can be expressed as:

1 H2 O þ DH/H2 þ O2 2

(76)

where the change in enthalpy for the reaction is denoted by DHR. The reaction is endothermic and electricity is utilized by the electrolyser to decompose the water molecules to hydrogen and oxygen. The half-cell electrochemical reactions can be expressed as:

1 Anodic: H2 O/ O2 þ 2H þ þ 2e 2

(77)

Cathodic: 2H þ þ 2e/H2

(78)

The total amount of energy required by the electrolyzer can be expressed as

DH ¼ DG þ T DS

(79)

where DG denotes the Gibbs function and T DS is the thermal energy required. The rate of hydrogen produced by the electrolyzer can be determined as [25].

J N_ H2 ¼ 2F

(80)

where J denotes the current density and F represents the faradays constant. The electrical energy input rate taken by the electrolyzer is expressed as:

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_ PEM ¼ JV W

(81)

where the voltage V can be determined as

V ¼ Vo þ Vact;a þ Vact;c þ VOhmic þ Vconc;a þ Vconc;c

(82)

where Vo denotes the reversible ideal cell potential and can be evaluated by utilizing the Nernst equation as:

Vo ¼

DG nF

þ

RT ln nF



pH2



pO2 pH2 O

0:5 ! (83)

  Eact;i ref Jo;i ¼ Ji exp  RT

(84)

VOhmic ¼ RPEM J

(85)

where RPEM denotes the Ohmic resistance, which is determined as:

0

1

80

Activation energy at cathode (Eact;c Þ

18000 J mol1 14 10

oC

76000 J mol1

4a 4c

1:7x105 A m2

ref

Anode pre-exponential factor (Ja Þ

4:6 x103 A m2 100 mm 96486 C mol1

Cathode pre-exponential factor ( Jc ) Membrane thickness (DÞ Faraday's constant

reactants into electrical energy. The electrochemical reactions occurring in the fuel cell are: Anodic reaction:

2NH3 þ 6OH /N2 þ 6H2 O þ 6e

(89)

1:5O2 þ 3H2 O þ 6e/6OH

(90)

The overall cell reaction can be written as:

where i represents anode or cathode, Eact denotes the activation ref energy for either electrode and Ji represents the pre-exponential factor. The Ohmic over-potential in the PEM electrolyzer is due to the membrane resistance to the transport of hydrogen ions. The membrane ionic resistance is dependent on the humidification and the membrane thickness. The total Ohmic over-potential is evaluated as:

s½4ðxÞ

Value

Temperature (Tpem Þ Activation energy at anode (Eact;a )

Cathodic reaction:

c. The exchange current density can be determined as:

RPEM ¼

Parameter

ref

where DG denotes the change in Gibbs's function, n denotes the number of moles of transferred electrons, F represents the Faraday's constant, T denotes the electrolyser temperature and p represents the partial pressures. The activation over-potential can be evaluated !   1 J as.Vact;i ¼ RT F sinh 2Jo;i , where i represents anode a or cathode

ZD

Table 2 Design and operating parameters of the PEM electrolyzer.

dx

(86)

where s denotes the ionic conductivity of the PEM, 4ðxÞ represents the water content at a given membrane location x, and can be evaluated from the content of water at the interfaces of membraneanode ð4a Þ and membrane-cathode ð4c Þ and the thickness of the membrane (DÞ:

ð4  4c Þ x þ 4c 4ðxÞ ¼ a D 



1 1  303 T

(91)

The standard reversible cell potential for the above reaction can be calculated as:

DG

E0 ¼ 

(92)

6F

where F denotes the Faraday's constant and the Gibbs function of reaction DG can be determined as:

DG ¼ DH  T DS

(93) E0

The standard reversible cell potential for reaction (77) can be evaluated as 1.17 V. However, at varying cell temperature and partial pressures, the reversible open circuit voltage can be calculated as:

" 2  1:5 # PNH3 PO2 RT ln  E¼E þ 3   6F P P 0

H2 O

(94)

N2

(87)

As discussed earlier, when current is drawn from the cell for an external load, activation and concentration polarization and Ohmic losses occur within the cell. Considering the voltage losses, the cell voltage can be expressed as:

(88)

VAFC ¼ E0  Vact  VOhmic  Vconc

The local ionic conductivity can be evaluated as:

s½4ðxÞ ¼ ð0:51394ðxÞ  0:326Þexp 1268

2NH3 þ 1:5O2 /N2 þ 3H2 O



The design parameters used for the PEM electrolyzer are summarized in Table 2.

(95)

The voltage losses due to activation polarization can be evaluated as [26]:

  RT j ln j0 anF

3.7. Molten alkaline electrolyte ammonia fuel cell

Vact ¼

The molten salt stored in the cold tank at a temperature of 400  C is used as an electrolyte for the alkaline ammonia fuel cell. The molten salt is a mixture of 51 mol% NaOH and 49 mol% KOH. Ammonia gas is fed at the anode and oxygen gas is fed at the cathode. The fuel cell converts the stored chemical energy of the

where j0 denotes the exchange current density, j denotes the current density, T represents the fuel cell temperature, a is the transfer coefficient and F is the Faraday's constant. The voltage losses due to concentration polarization can be calculated as:

(96)

O. Siddiqui, I. Dincer / Journal of Power Sources 370 (2017) 138e154

Vconc ¼

  RT j ln L anF jL j

The exergy rate balance equation for the condenser is written

(97)

where jL denotes the limiting current density, which depends on the fuel cell stack construction). And the Ohmic losses can be evaluated using equation (38). The design and operating parameters for the ammonia fuel cell are listed in Table 3. The DC power generated by the ammonia fuel cell is converted to AC power by a DC-AC converter. Where, hconv denotes the efficiency of the converter, j represents the current density and Acell denotes the cell area, the AC power generated can be evaluated as:

_ W AFC;AC ¼ hconv VAFC jAcell

(98)

as:

  T _ m_ 19 ex19 ¼ m_ 20 ex20 þ Q_ l;con 1  0 þ Ex d;con Tcon

m_ 20 ¼ m_ 21

Q_ gen ¼ m_ 16 ðh16  h17 Þ

The energy rate balance equation for the throttling valve 1 is written as follows:

(99)

m_ 20 s20 þ S_gen;TV1 ¼ m_ 21 s21

m_ 25 ¼ m_ 26 þ m_ 19

(100)

The ammonia mass rate balance equation for the generator can be written as follows:

(109)

_ m_ 20 ex20 ¼ m_ 21 ex21 þ Ex d;TV1

(110)

Evaporator: The mass rate balance equation for the evaporator is written as:

m_ 21 ¼ m_ 22

(111)

The energy rate balance equation for the evaporator is written as:

x25 m_ 25 ¼ x26 m_ 26 þ x19 m_ 19

(101)

m_ 21 h21 þ Q_ EV ¼ m_ 22 h22

where x represents the ammonia mass fraction. The energy rate balance equation for the generator can be written as follows:

as:

m_ 25 h25 þ Q_ gen ¼ m_ 26 h26 þ m_ 19 h19

m_ 21 s21 þ

(102)

Condenser: The mass rate balance equation for the condenser is written as:

m_ 19 ¼ m_ 20

(103)

The energy rate balance equation for the condenser is written as:

m_ 19 h19 ¼ Q_ l;con þ m_ 20 h20

(104)

The entropy rate balance equation for the condenser is written as:

(112)

The entropy rate balance equation for the evaporator is written

Q_ EV þ S_gen;EV ¼ m_ 22 s22 T0

(113)

The exergy rate balance equation for the evaporator is written as:

  T _ m_ 21 ex21 þ Q_ EV 1  0 ¼ m_ 22 ex22 þ Ex d;EV TEV

(114)

Absorber: The total mass rate balance equation for the absorber is written as follows:

m_ 22 þ m_ 28 ¼ m_ 23

(115)

The ammonia mass rate balance equation for the absorber is written as:

Q_ l;con ¼ m_ 20 s20 þ T0

(105)

Table 3 Design and operating parameters of molten alkaline electrolyte ammonia fuel cell. Value

Exchange current density ðj0 Þ

0:037 mA cm2

Limiting current density ðjL Þ

2000 mA cm2 400o C 51 mol% NaOHþ40 mol% KOH

Cell area DC to AC inverter efficiency ðhconv Þ Faraday's constant (F)

(108)

The exergy rate balance equation for the throttling valve 1 is written as follows:

The total mass rate balance equation for the generator of the absorption cooling system can be written as follows:

Cell temperature Electrolyte Current density (jÞ

(107)

The entropy rate balance equation for the throttling valve 1 is written as follows:

Generator: The heat rate supplied to the generator of the absorption cooling system can be written as follows:

Parameter

(106)

Throttling valve 1: The mass rate balance equation for throttling valve 1 is written as follows:

m_ 20 h20 ¼ m_ 21 h21

3.8. Absorption cooling system

m_ 19 s19 þ S_gen;con

147

1100 mA cm2 20 m2 0.85 96486 C mol1

x22 m_ 22 þ x28 m_ 28 ¼ x23 m_ 23

(116)

where x represents the ammonia mass fraction. The energy rate balance equation for the absorber is written as follows:

m_ 22 h22 þ m_ 28 h28 ¼ m_ 23 h23 þ Q_ abs

(117)

The exergy rate balance equation for the absorber is written as:

  T m_ 22 ex22 þ m_ 28 ex28 ¼ m_ 23 ex23 þ Q_ abs 1  0 Tabs Throttling valve 2:

(118)

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The mass rate balance equation for throttling valve 2 is written as follows:

The entropy rate balance equation for heat exchanger 5 is written as:

m_ 27 ¼ m_ 28

m_ 24 s24 þ m_ 26 s26 þ S_gen;HX5 ¼ m_ 27 s27 þ m_ 25 s25

(119)

The energy rate balance equation for the throttling valve 2 is written as follows:

as:

m_ 27 h27 ¼ m_ 28 h28

_ m_ 24 ex24 þ m_ 26 ex26 ¼ m_ 25 ex25 þ m_ 27 ex27 þ Ex d;HX5

(120)

(129)

The exergy rate balance equation for heat exchanger 5 is written

(130)

The entropy rate balance equation for the throttling valve 2 is written as follows:

m_ 27 s27 þ S_gen;TV2 ¼ m_ 28 s28

(121)

The exergy rate balance equation for the throttling valve 2 is written as follows:

_ m_ 27 ex27 ¼ m_ 28 ex28 þ Ex d;TV2

(122)

Pump 2: The mass rate balance equation for pump 2 is written as follows:

m_ 23 ¼ m_ 24

(123)

The energy rate balance equation for pump 2 is written as follows:

hov ¼

3.9. Overall system and subsystems efficiencies The useful outputs of the multi-generation system include electric power, cooling, hydrogen and hot water. The solar energy input to the system can be evaluated as:

Q_ solar ¼ hhe I_b Ahe Nhe

(131)

where hhe denotes the heliostat efficiency, I_b represents the direct normal irradiance, Ahe denotes the area of the heliostat mirror and Nhe represent the number of heliostat mirrors. Table 4 lists the input and output parameters of the multi-generation system. The overall system energy efficiency can be evaluated as:

_ _ _ _ _ _ _ _ H2 LHVH2 þ m_ 29 ðh30  h29 Þ  W W T1 þ W T2 þ W T3 þ W SOFC;AC þ W AFC;AC þ Q EV þ m C _ _ Q solar þ Q CC þ ðUÞm_ fu;SOFC LHVCH4 þ m_ NH3 LHVNH3

(132)

The overall system exergy efficiency is evaluated as:

jov

 T0 _ _ _ _ _ _ _ _ H2 exH2 þ m_ 29 ðex30  ex29 Þ  W W T1 þ W T2 þ W T3 þ W SOFC;AC þ W AFC;AC þ Q EV TEV  1 þ m C   ¼ T T 0 þ Q_ CC 1  TCC0 þ ðUÞm_ fu;SOFC exCH4 þ m_ NH3 exNH3 Q_ solar 1  Tsun

_ _ 24 h24 m_ 23 h23 þ W P2 ¼ m

(124)

(133)

The COP of the absorption cooling system is calculated as:

The entropy rate balance equation for pump 2 is written as follows:

m_ 23 s23 þ S_gen;P2 ¼ m_ 24 s24

(125)

COPABCS ¼

Q_ EV Q_

(134)

GEN

The exergy rate balance equation for pump 2 is written as follows:

_ _ _ 24 ex24 þ Ex m_ 23 ex23 þ W P2 ¼ m d;P2

(126)

Heat exchanger 5: The mass rate balance equations for heat exchanger 5 are written as follows:

m_ 24 ¼ m_ 25 and m_ 26 ¼ m_ 27

(127)

The energy rate balance equation for heat exchanger 5 is written as follows:

m_ 24 h24 þ m_ 26 h26 ¼ m_ 27 h27 þ m_ 25 h25

The exergetic COP of the absorption cooling system can be determined as:

(128)

COPABCS;ex



1  ¼ 0 Q_ GEN 1  TTGEN Q_ EV

T0 TEV

(135)

where Q_ EV denotes the cooling load that is obtained from the evaporator, and Q_ GEN denotes the heat input to the absorption cooling system in the generator. The energy efficiency of the solid oxide fuel cell-gas turbine cycle is evaluated as:

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149

Table 4 Solar field parameters and evaluated power outputs and inputs of major system components. Parameter

Value

Direct normal irradiance ðI_b Þ Heliostat efficiency ðhhe Þ Number of heliostats ðNhe Þ Heliostat mirror dimensions _ ) Turbine 1 power output ðW T1 _ ) Turbine 2 power output ðW

0.85 200 11 m  11 m 3490 kW

0.85 kW m2

2993 kW

T2

_ ) Turbine 3 power outputðW T3

1584 kW

_ Solid oxide fuel cell power output ðW SOFC;AC Þ _ Ammonia fuel cell power output ðW Þ

212 kW

_ Þ Power input to compressor ðW C

955 kW

1608 kW

AFC;AC

_ W

_ þW

_ W

T3 C hSOFC=GT ¼ _ SOFC;AC Q CC þ ðUÞm_ fu;SOFC LHVCH

(136) 4

The exergy efficiency of the solid oxide fuel cell-gas turbine cycle is evaluated as:

jSOFC=GT ¼

_ _ _ W SOFC;AC þ W T3  W C m_ fu;SOFC exCH4

jPRC ¼

hSRC ¼

_ W T2 m_ 9 ðh5  h9 Þ þ m_ 5 ðh6  h5 Þ

jSRC ¼



Furthermore, the energy and exergy efficiencies of the Primary Rankine cycle are expressed as:

_ W

(138)

(139)

Similarly, the energy efficiency and exergy efficiency of the Secondary Rankine cycle can be expressed as

(137)

hPRC ¼ _ T1 Q solar

_ W  T1 _ 0 Q solar 1  TTsun

m_ 9 ðh5  h9 Þ 1 

T0 THX3

(140)

_ W T2  0 þ m_ 5 ðh6  h5 Þ 1  TTHX4

(141)

Table 5 Input and evaluated thermodynamic data. State no. Fluid

Temperature ( C) Pressure (kPa) Mass flow rate (kg s1) Specific Enthalpy (kJ kg1) Specific Entropy (kJ kg1 K1) Specific Exergy (kJ kg1)

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

25 25 64.9 65.1 634.1 298.5 96.32 263.7 69.1 69.1 69.3 25 213.4 569.9 691.4 976.9 708.2 357.4 200.9 80.0 107.3 40.0 14.1 10.0 40.0 40.4 110 130.3 40.4 40.7 30 80

Water Air Water Water Water Water Water Water Water Water Water Air Air Air Air/Methane Combustion gases Exhaust gases Exhaust gases Exhaust gases Exhaust gases Ammonia/Water Ammonia/Water Ammonia/Water Ammonia/Water Ammonia/Water Ammonia/Water Ammonia/Water Ammonia/Water Ammonia/Water Ammonia/Water Water Water

101.3 101.3 25 1500 1500 25 1600 1600 30 30 1600 101.3 405 388.8 373.2 373.2 105.5 101.3 101.3 101.3 1555.757 1555.757 244.851 244.851 244.851 1555.757 1555.757 1555.757 1555.757 244.851 101.3 101.3

e e 5.0 5.0 5.0 5.0 5.5 5.5 5.5 5.5 5.5 5.0 5.0 5.0 5.063 5.08 5.08 5.08 5.08 5.08 0.412 0.412 0.412 0.412 3.000 3.000 3.000 2.588 2.588 2.588 2.2 2.2

104.8 298.6 272 273.9 3771 3073 404.7 2951 2407 289.3 291.3 298.6 489.6 869.8 1006 1337 1025 639.6 476.7 353.9 1544.008 190.759 190.759 1258.828 43.258 40.215 302.146 396.092 0.724 0.724 125.8 335

0.367 5.696 0.893 0.894 8.521 8.852 1.264 6.733 7.131 0.944 0.945 5.696 5.794 6.389 6.552 6.852 6.934 6.461 6.165 5.866 4.882 0.658 0.753 4.861 0.472 0.477 1.454 1.641 0.531 0.535 0.437 1.075

0 0 10.2 11.8 1235 438.1 32.4 948 285.3 12.37 14.02 0 161.9 364.4 452.2 693.7 357.3 112.8 38.4 4.5 409.6 315.7 287.4 130.6 2.89 4.45 55.51 68.91 3.13 1.94 0.1734 18.94

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Fig. 2. Exergy destruction rates in major system components.

4. Results and discussion In conducting the thermodynamic analysis, the temperature, pressure, enthalpy, entropy and exergy of each state are determined and tabulated in Table 5. The thermodynamic properties are evaluated using the Engineering Equation Solver (EES) software. The reference ambient conditions considered in this study are a temperature of 25  C and a pressure of 101 kPa. The utilized solar field parameters and the evaluated power outputs of major system components are listed in Table 4. The exergy destruction rates of major system components are shown in Fig. 2. As can be depicted, the highest exergy destruction rate occurs in Turbine 2. This can be attributed to the high entropy generation rate. The entropy generated in Turbine 2 is 2.19 kW/K, this value is higher than other system components. Hence, efforts to reduce irreversibilities in Turbine 2 can be implemented. Reducing the exergy destruction rates will decrease the irreversibilities in the system resulting in higher efficiencies. Exergy destruction rate in Turbine 1 is also found to be comparatively higher. An exergy destruction rate of 494 kW occurs in this turbine. This is also attributed to high irreversibilities in Turbine 1, which cause an entropy generation of 1.66 kW/K. Thus, reducing irreversibilities in this system component will help in increasing the overall system efficiencies. The overall system energy efficiency is obtained as 39.1% and the overall system exergy efficiency is calculated as 38.7%. The Primary Rankine cycle has an energy efficiency of 19.9% and an exergy efficiency of 21%. Hence, the multi-generation system results in an increase of 19.3% in energy efficiency as compared to single generation system. Furthermore, the exergy efficiency of the multigeneration system is 17.8% higher than single generation system. Thus, the results show that implementation of multi-generation

Fig. 3. Effect of compression ratio on the efficiencies of the multi-generation system and subsystems.

systems can improve the efficiencies of conventional single generation systems. Furthermore, the exergy efficiency and energy efficiency of the solid oxide fuel cell-gas turbine combined cycle are evaluated as 68.5% and 55.9% respectively. In addition, the Secondary Rankine cycle is evaluated to have an energy efficiency of 20.5% and an exergy efficiency of 59.4%. The energetic COP of the absorption cooling system in obtained as 0.54, and the exergetic COP is evaluated as 0.31. The lower exergetic COP of the absorption cooling system is due to the losses within the system. These losses are considered in the exergy analysis and are not accounted for in energy analysis.

Table 6 Estimated capital cost of the multigeneration system. Subsystem

Installed Cost (USD/kW)

Solar tower based power generating system with primary Rankine cycle and molten salt storage Secondary Rankine cycle turbine Solid oxide fuel cell SOFC Gas Turbine Proton Exchange membrane electrolyser Absorption cooling system Ammonia alkaline fuel cell Total estimated cost

6300e10500 [27] 682 [28] 1170 [29] 427 [29] 940 [30] 10 [31] 643 [32] 10172e14372

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Fig. 4. Effect of compression ratio on the efficiencies of the solid oxide fuel cell-gas turbine cycle.

151

compression ratio of 3. However, as the compression ratio increases more than 3, the multi-generation system efficiencies are observed to decrease as can be depicted from Fig. 3. However, the efficiencies of the secondary Rankine cycle are observed to increase with decreasing compression ratio. At a compression ratio of 2, the energy efficiency of the secondary Rankine cycle is obtained as 21% and the exergy efficiency is evaluated as 61%. In addition, the effect of compression ratio on the energy efficiency and exergy efficiency of the solid oxide fuel cell-gas turbine cycle is depicted in Fig. 4. The maximum efficiencies are observed at a compression ratio of 6. The energy efficiency of the solid oxide fuel cell-gas turbine system increases to 56.6% and the exergy efficiency increases to 69.4% at a compression ratio of 6. However, at this compression ratio, the overall multi-generation system energy efficiency decreases to 38.8% and the exergy efficiency decreases to 38.5%. These changes in the efficiencies with varying compression ratio can be attributed to the changes in work inputs and outputs of various system components. 4.2. Effect of ambient temperature on the efficiencies of the multigeneration system and subsystems

The estimated capital cost breakdown of the multigeneration system is shown in Table 6. The estimated range of capital cost for the multigeneration system is obtained as 10172e14372 $/kW. In addition, a solar tower based power plant with molten salt storage used only for electricity generation, is estimated to have a cost between $6300e10500 per kW. The capital costs of the subsystems are obtained from the literature and published reports and are normalized to our system parameters. However, further studies pertaining to life cycle costing need to be conducted in order to assess the effect of multigeneration on capital costs. Although, multigeneration systems can increase the capital costs, they provide higher system efficiencies. This will result in lower payback periods. Thus, further research related to their pay back periods and life cycle costs need to be conducted. 4.1. Effect of compression ratio on the efficiencies of the multigeneration system and subsystems

The thermodynamic performance of the system is affected by the ambient temperature. Changes in the ambient temperature can increase or decrease the efficiencies of a given system. Fig. 5 depicts the variation of efficiencies with the ambient temperature. The exergy efficiency of the overall multi-generation system increases with increasing ambient temperature. At an ambient temperature of 36  C, the exergy efficiency increases to 38.9%. In addition, the exergy efficiencies of the primary Rankine cycle, secondary Rankine cycle and the solid oxide-fuel cell gas turbine cycle increase to 21%, 63.9% and 68.5% respectively. As the ambient temperature decreases to 10  C, the overall system exergy efficiency decreases to 38.5%. However, there is no change observed in the energy efficiencies. Hence, this asserts that exergy analysis forms an integral part of a thermodynamic analysis. 4.3. Effect of Turbine 1 inlet pressure on the efficiencies of the multigeneration system and subsystems

The compression ratio of the compressor in the solid oxide fuel cell-gas turbine cycle is an important system parameter. The effect of changing the compression ratio on the efficiencies is shown in Figs. 3e4. The maximum energy efficiency of 39.2% and exergy efficiency of 38.8% is obtained for the multi-generation system at a

The inlet pressure of Turbine 1 of the primary Rankine cycle is an important system parameter. As the inlet pressure varies, the system efficiencies also change. Fig. 6 shows the variation of the efficiencies of multi-generation system and other subsystems with

Fig. 5. Effect of ambient temperature on the efficiencies of the multi-generation system and subsystems.

Fig. 6. Effect of Turbine 1 inlet pressure on the efficiencies of the multi-generation system and subsystems.

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the mass flow rate is reduced from 5 kg/s to 4 kg/s. In addition to this, the primary Rankine cycle energy efficiency drops significantly to 5.4% from 19.9% and the exergy efficiency drops to 5.7% from 21% as the mass flow rate is varied from 5 kg/s to 4 kg/s. 4.5. Effect of secondary rankine cycle working fluid mass flow rate on the efficiencies of the multi-generation system and subsystems

Fig. 7. Effect of primary Rankine cycle working fluid mass flow rate on the efficiencies of the multi-generation system and subsystems.

The mass flow rate of water in the secondary Rankine cycle affects the system efficiencies. Fig. 8 depicts the effect of this mass flow rate on the energy efficiency and exergy efficiency of the overall multi-generation system and other sub-systems. As the mass flow rate is decreased to 2.5 kg/s, the overall multi-generation system energy efficiency increases to 46.5% and the exergy efficiency is observed to increases to 46.4%. Furthermore, the energy efficiency and exergy efficiency of the secondary Rankine cycle are also observed to increase considerably to 33.1% and 96.2% respectively as the mass flow rate of secondary Rankine cycle is decreased to 2.5 kg/s. The efficiencies of the primary Rankine cycle and the solid oxide fuel cell and gas turbine combined cycle remain unchanged. 5. Conclusions

Fig. 8. Effect of secondary Rankine cycle working fluid mass flow rate on the efficiencies of the multi-generation system and subsystems.

the Turbine 1 inlet pressure. The overall system energy efficiency increases to 41.3% as the inlet pressure is increased to 3000 kPa. In addition, the exergy efficiency is also observed to increase to 41% at this pressure. Furthermore, the energy efficiency of the primary Rankine cycle is also observed to increase considerably to 24.2% at 3000 kPa from 19.9% at 1500 kPa. The exergy efficiency of the primary Rankine cycle increases to 25.5% at 3000 kPa turbine inlet pressure from 21% at 1500 kPa. This can be attributed to the higher power output of Turbine 1 at higher inlet pressures. Hence, higher inlet pressures for Turbine 1 can be chosen if higher power outputs are required. However, increasing the inlet pressure of Turbine 1 is observed to decrease the energy efficiency of secondary Rankine cycle. The energy efficiency decreases from 20.5% at 1500 kPa to 20.2% at 3000 kPa. 4.4. Effect of Primary Rankine cycle working fluid mass flow rate on the efficiencies of the multi-generation system and subsystems The mass flow rate of water in the primary Rankine cycle is an important system parameter. The effect of this mass flow rate on the overall multi-generation system and sub-systems efficiencies is depicted in Fig. 7. Decreasing the mass flow rate to 4 kg/s reduces the overall system efficiencies considerably. The energy efficiency is decreased to 32.8% and the exergy efficiency is reduced as 32.2% as

In the current study, a new solar-based multigeneration system integrated with an ammonia fuel cell and solid oxide fuel cell-gas turbine combined cycle to produce electricity, hydrogen, cooling and hot water is developed and thermodynamically analysed. The overall system energy efficiency is obtained as 39.1% and the overall system exergy efficiency is calculated as 38.7%. The multigeneration system results in an increase of 19.3% in energy efficiency as compared to single generation system. Furthermore, the exergy efficiency of the multi-generation system is 17.8% higher than single generation system. Thus, the results show that implementation of the developed multi-generation system can improve the efficiencies of conventional single generation systems. Furthermore, the exergy efficiency and energy efficiency of the solid oxide fuel cell-gas turbine combined cycle are evaluated as 68.5% and 55.9% respectively. The highest exergy destruction rate is observed in the Turbine of the secondary Rankine cycle. Nomenclature abs A ABCS AC AFC C CC CH4 COP DC ex EV _ Ex F g G GT h HX J I_

absorber area (m2) absorption cooling system alternating current (mA or A) ammonia fuel cell compressor combustion chamber methane coefficient of performance direct current (mA or A) specific exergy (kJ kg1) evaporator exergy rate (kW) Faradays constant gravitational constant Gibbs free energy (J) gas turbine specific enthalpy (kJ kg1) heat exchanger current density (A m2 or mA cm2) solar light intensity (kW m2)

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LHV m_ N N_ NH3 P PEM PPRC Q Q_ s SOFC SRC T U V _ W Z

lower heating value (kJ) mass flow rate (kg s1) number of molar production rate (mol s1) ammonia Pressure (Pa or kPa) proton exchange membrane Primary Rankine cycle heat transfer (J or kJ) heat transfer rate (W or kW) specific entropy (kJ kg1 K1) solid oxide fuel cell secondary Rankine cycle temperature ( C) utilization factor voltage (mV or V), velocity (m s1) work rate (W or kW) height

Greek letters h energy efficiency j exergy efficiency Subscript a ABCS act AC AFC b c con cv C CC d DC e ex EV fu gen GEN GT h HX he hf i is l n o ov P PEM PRC SOFC SRC st T tv w x

anode, aerosols absorption cooling system activation alternating current ammonia fuel cell beam cold, condenser, cathode condenser control volume compressor combustion chamber destroyed direct current exit exergy evaporator fuel generated generator gas turbine hot heat exchanger heliostat heliostat field inlet isentropic lost normal ohmic overall pump proton exchange membrane primary Rankine cycle solid oxide fuel cell secondary Rankine cycle salt turbine throttle valve water, work molar ratio

y 0

153

mass ratio dead state

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