Working-fluid selection and thermoeconomic optimisation of a combined cycle cogeneration dual-loop organic Rankine cycle (ORC) system for solid oxide fuel cell (SOFC) waste-heat recovery

Applied Energy 261 (2020) 114384

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Working-fluid selection and thermoeconomic optimisation of a combined cycle cogeneration dual-loop organic Rankine cycle (ORC) system for solid oxide fuel cell (SOFC) waste-heat recovery

T

Mohammad Ali Emadia, Nazanin Chitgara, Oyeniyi A. Oyewunmib,⁎, Christos N. Markidesb a b

School of Mechanical Engineering, Iran University of Science and Technology, Tehran 16844, Iran Clean Energy Processes (CEP) Laboratory, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK

HIGHLIGHTS

cogeneration system with an ORC waste heat recovery system is proposed. • ATheSOFC performance of the dual-loop ORC system with 20 working fluids is explored. • Thermodynamic economic multi-objective optimisations are performed. • Exergy efficiencyand 969 kW electricity and 564 kW cooling is achieved. • The system LCoE isof up52%to with 74% lower than those of traditional SOFC configurations. • ARTICLE INFO

ABSTRACT

Keywords: Solid oxide fuel cell (SOFC) Organic Rankine cycle (ORC) Liquefied natural gas (LNG) Thermoeconomic analysis Working-fluid selection Multi-objective optimisation

A novel combined-cycle system is proposed for the cogeneration of electricity and cooling, in which a dual-loop organic Rankine cycle (ORC) engine is used for waste-heat recovery from a solid oxide fuel cell system equipped with a gas turbine (SOFC-GT). Electricity is generated by the SOFC, its associated gas turbine, the two ORC turbines and a liquefied natural gas (LNG) turbine; the LNG supply to the fuel cell is also used as the heat sink to the ORC engines and as a cooling medium for domestic applications. The performance of the system with 20 different combinations of ORC working fluids is investigated by multi-objective optimisation of its capital cost rate and exergy efficiency, using an integration of a genetic algorithm and a neural network. The combination of R601 (top cycle) and Ethane (bottom cycle) is proposed for the dual-loop ORC system, due to the satisfaction of the optimisation goals, i.e., an optimal trade-off between efficiency and cost. With these working fluids, the overall system achieves an exergy efficiency of 51.6%, a total electrical power generation of 1040 kW, with the ORC waste-heat recovery system supplying 20.7% of this power, and a cooling capacity of 567 kW. In addition, an economic analysis of the proposed SOFC-GT-ORC system shows that the cost of production of an electrical unit amounts to $33.2 per MWh, which is 12.9% and 73.9% lower than the levelized cost of electricity of separate SOFC-GT and SOFC systems, respectively. Exergy flow diagrams are used to determine the flow rate of the exergy and the value of exergy destruction in each component. In the waste-heat recovery system, exergy destruction mainly occurs within the heat exchangers, the highest of which is in the LNG cooling unit followed by the LNG vaporiser and the evaporator of the bottom-cycle ORC system, highlighting the importance of these components’ design in maximising the performance of the overall system.

1. Introduction Population growth as well as economic development has been acting to drive an ever-increasing rise in the demand for energy (including for power, heating, cooling, transportation, etc.) and a series of associated environmental implications, which have become important

⁎

global challenges in need of serious attention. The use of advanced technologies has featured prominently in various solutions proposed for improving the efficient use of resources so as to lead to clean and sustainable energy systems. Multi-generation, such as by combined cooling heating and power (CCHP) systems, is among the methods that have attracted interest of late. In this method, the useful outputs

Corresponding author. E-mail address: [email protected] (O.A. Oyewunmi).

https://doi.org/10.1016/j.apenergy.2019.114384 Received 13 August 2019; Received in revised form 20 November 2019; Accepted 14 December 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

Applied Energy 261 (2020) 114384

M.A. Emadi, et al.

Nomenclature

Aact cp Daffe Dcffe ex ¯ ich,0 E Ech ED Eph F ¯g° h ΔH I j jas jcs joa joc K Kp,ref Kp,shift l m ne n Ncell P PF Q rsc R R¯ T T0 Ua Uf Vcell VN Vloss W Wstack x y Z Z z

CU e env ex Eva f FPH GT in int inv is M net N NBT ohm out pen ph P PP Q ref shift SH th tot T

active surface area, m2 specific heat at constant pressure, J/kg K effective gaseous diffusivity through anode, m2/s effective gaseous diffusivity through cathode, m2/s standard chemical exergy of species i, J/mol exergy rate, W chemical exergy rate, W exergy destruction rate, W physical exergy rate, W Faraday constant, C/kmol change in molar Gibbs free energy, J/mol specific enthalpy, J/kg enthalpy change of reaction, J/mol current, A current density, A/m2 anode-limiting current density, A/m2 cathode-limiting current density, A/m2 exchange current density of anode, A/m2 exchange current density of cathode, A/m2 chemical (or electrochemical) reaction equilibrium constant, Pa2 equilibrium constant, – thickness of SOFC layers, m mass flow rate, kg/s number of electrons molar flow rate, mol/s total number of fuel cells pressure, bar pressure factor heat rate, W steam to carbon ratio reaction rate, mol/s universal gas constant, J/mol.K temperature, K reference Temperature, K air utilisation factor fuel utilisation factor cell voltage, V reversible cell voltage, V loss voltage, V power, W power output of fuel cell, W extent of steam reforming reaction, mol/s extent of water gas shift reaction, mol/s capital cost of component, $ capital cost rate of component, $ per hr extent of electrochemical reaction, mol/s

Greek symbols

η ρ φ

stoichiometric coefficient voltage losses efficiency electrical resistivity of cell, Ωm maintenance factor

Abbreviations ANN ARC CCHP CRF GA GT GWP ICE LCoE LHV LINMAP

Subscripts 0 A Ac act AB AC APH C Ch Con conc cr CW

cooling unit electrolyte environment exergy evaporator fuel fuel preheater gas turbine inlet interconnect DC to AC inverter isentropic mixer net output Nernst normal boiling temperature ohmic outlet penalty physical pump pinch point heat transfer reforming shifting Superheating thermal total turbine

atmospheric condition anode alternating current activation afterburner air compressor air preheater cathode chemical condenser concentration critical chilled water

LNG MGT NG ODP ORC PEME RC SOFC TC TCOE WHR

2

artificial neural network absorption refrigeration cycle combined cooling, heating and power capital recovery factor genetic algorithm gas turbine global warming potential internal combustion engine levelized cost of electricity lower heating value linear programming technique for multidimensional analysis of preference liquefied natural gas micro gas turbine natural gas ozone depletion potential organic Rankine cycle proton exchange membrane electrolyser Rankine cycle solid oxide fuel cell total cost thermoeconomic cost of electricity waste-heat recovery

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include, beyond electrical power, cooling and heating, clean water provision and hydrogen generation, which can be produced simultaneously from a single heat source [1,2]. Most multi-generation systems, including gas and diesel-based engines and gas turbines, utilise fossil fuels as the primary energy source. Among these, attention has been paid in particular to fuel-cell-based systems. Although fuel cell technology is relatively expensive, it has high electrical efficiency under various loads, flexibility in consuming fuel [3], and better environmental performance than other related technologies [4]. Aside from the anode and cathode, fuel cells have an electrolyte segment which can be made from several chemical substances among which the solid oxide (used in solid oxide fuel cells – SOFC) is a good choice for cogeneration systems due to its high operating temperature. In SOFC-based hybrid systems, the required hydrogen is supplied from the methane reforming process in a reformer that is fed with steam. This steam can be supplied either separately or from the steam produced inside the fuel cell itself. As a result, by using an internal reformer, in addition to the recovery of the anode outlet steam for the reforming process, the need for a cooling system for the fuel cell can be eliminated by exploiting the endothermic nature of the reforming process [5]. While fuel cells operate under normal pressure conditions, a highpressure fuel cell can be used to generate high-temperature exhaust gases required in a gas turbine (GT) to generate additional (electrical) power. In such hybrid SOFC-GT systems under pressure, SOFC exhaust gases are fed directly into the gas turbine at high temperatures and pressures. Gandiglio et al. [6] reported that SOFC-GT systems have 7.3% higher exergy efficiencies than atmospheric SOFC, as well as 20% less exergy destruction. Eisavi et al. [7] performed a comparative analysis for three different SOFC-GT configurations – conventional, series and parallel fuel cell arrangements – and indicated that the series arrangement had the highest energy and exergy efficiencies of 63% and 61% respectively. Burer et al. [8] optimised a SOFC-driven multi-generation CHP energy system by considering CO2 emissions and economic objective functions; it was concluded that the proposed system could be a good environmental and economical choice in future applications. Due to the high operating temperature of the SOFC, which results in production of high-temperature exhaust gases, the SOFC can be combined thermally with conventional power production cycles such as Brayton [9,10], Rankine [6], Kalina [11], organic Rankine [12], Stirling engine [13], or cooling systems [14] directly or indirectly to form a co-/ multi-generation system, thereby improving the overall system efficiency. In recovering the hitherto wasted energy from the exhaust gas of the SOFC, the conventional power system can be used to generate additional power or used to meet the energy demands (heating and/or cooling) of residential/industrial buildings. Other (waste-) heat conversion technologies at various levels of technological development can also be deployed for this purpose. These include the Non-InertiveFeedback Thermofluidic Engine (NIFTE) [15–17] and the Up-THERM heat converter [18–20] which, due to their low capital and maintenance costs, and despite their early stages of development, have been demonstrated to be competitive with more established technologies, such as the organic Rankine cycle (ORC) [21,22]. Amongst the aforementioned technologies, the ORC, while being commercially available, is uniquely suited for waste-heat recovery and power generation from low- and high-temperature heat sources [23–25]; it has thus been selected for this study. The ORC operates in a similar manner to the conventional steam Rankine cycle, with the exception that by using an organic working fluid, its evaporation temperature is reduced and therefore low-temperature input energy can be exploited. As a result, combining the SOFC with the ORC is a suitable solution that could improve system performance. Akkaya and Sahin [26] studied a combined system composed of a SOFC and an ORC; it was demonstrated that the energy efficiency of the SOFC system is improved by 14–25% when the exhaust gas is recovered by an ORC engine. Al-sulaiman et al. [27] proposed and analysed an integrated

system consisting of a SOFC-GT, an ORC engine and an absorption chiller to provide cooling; it was shown that the overall efficiency of the tri-generation system could approach 74% indicating a 22% improvement on conventional SOFC power generation systems. The performance of an ORC system is largely influenced by its design parameters and its working fluid(s); thus, many studies have been conducted on working fluid selection for ORC systems. For example, Freeman et al. [28,29] and Ramos et al. [30] examined the potential of heat and power co-generation based on solar collectors and an ORC system, including an in-depth consideration of thermal-energy storage [31]. In these studies, the performance of the system with various refrigerants was investigated and it was concluded that R245ca is a particularly suitable working fluid for this application. Chatzopoulou and Markides [32] evaluated a different type of cogeneration system based on a combined-cycle ICE and ORC engine arrangement, and optimised this for either maximum total power or minimum fuel consumption, also accounting explicitly performance variations in off-design operation [33], while in both cases considered a selection of working fluids for the ORC engine, concluding that R1233zd(E) is a promising fluid for these high-temperature applications. Oyewunmi et al. [34,35] demonstrated that by deploying equations of state based on the statistical associating fluid theory (SAFT), computer-aided molecular design (CAMD) techniques can be used to simultaneously design ORC systems and their working fluids [36,37], including the consideration of working-fluid mixtures and multiple system design objectives [34,38]. These have led to the design of novel working fluids for ORC systems in waste-heat recovery and other industrial applications as exemplified by van Kleef et al. [39]. Further ORC engine performance can be sought by lowering its heat sink temperature, using heat sinks such as liquefied natural gas (LNG) to achieve a significant reduction in the condenser temperature and thus increase the power output and efficiency of the cycle; the LNG gasification process is also carried out simultaneously [40–42] with the possibility of using the natural gas as the primary fuel in fuel cells [43,44]. In conventional plants where LNG at −161 °C is fed to a vaporiser to be converted to natural gas at the ambient temperature and pressure using seawater as a heat transfer medium, a large amount of exergy (which can otherwise be used more efficiently) is destroyed. Yan et al. [43] proposed an integrated SOFC driven system in which an ORC system with an LNG heat sink was used to recover the SOFC waste heat; an electrical efficiency of 67% was achieved in comparison to 48% for the stand-alone SOFC. A similar system driven by a molten carbonate fuel cell was proposed by Mahmoudi and Ghavimi [45]. The LNG utilised as the ORC heat sink was afterwards fed to the fuel cell resulting in an optimal exergy efficiency of 65% compared to 56% for the standalone fuel cell equipped with a gas turbine. As expatiated above, SOFC-based systems are increasingly being proposed and researched due to their high conversion efficiencies, thus, a summary of such SOFC-based hybrid systems and their performance indices is presented in Table 1. Referring to this table, it is clear that in most of the published literature, the proposed systems were examined from energetic and exergetic points of view, with only a few studies focusing on analysing these systems comprehensively from both thermodynamic and economic perspectives. Based on the above information about solid oxide fuel cell systems with gas turbines, a new cogeneration scheme for providing electricity and cooling is proposed. The key novelty of the proposed scheme lies in the deployment of a dual-loop ORC system for waste-heat recovery and an LNG supply that doubles as a heat sink for the ORC and a means of providing domestic/industrial cooling. The dual-loop ORC system (split into top and bottom cycles), in maximising the potential of the temperature difference between the SOFC exhaust gases and the LNG heat sink, is expected to offer improved performance over basic ORC systems for waste-heat recovery. Such a scheme is an advancement on traditional SOFC-gas turbine arrangements. Other key aspects of this novel scheme are broken down as follows: 3

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Table 1 Summary of results of some published works relating to cogeneration system based on solid oxide fuel cell (SOFC). Research

Plant type

Wang et al. [4] Gandiglio et al. [6] Pierobon et al. [12] Rokni [13]

SOFC-GT-Kalina SOFC-GT-RC Gasifier-SOFC-ORC Gasifier-SOFC-Stirling

Al-Sulaiman et al. [27]

SOFC-ORC

Eveloy et al. [46] Yan et al. [43] Habibollahzade et al. [47] Ozcan et al. [48] Bang-Møller and Rokni [49]

SOFC-GT-ORC SOFC-GT-ORC-LNG SOFC-Stirling-PEME Gasifier-SOFC-ORC-ARC Gasifier-SOFC-MGT

Gholamian et al. [50] Zhao et al. [51]

Gasifier-SOFC-ARC SOFC-GT-ARC

Baghernejad et al. [52] Tian et al. [53]

SOGC-RC-ARC SOFC-ORC-ARC

Hosseinpour et al. [54] Singh and Singh [55] Bang-Møller et al. [56]

SOFC-Stirling SOFC-GT-ORC Gasifier-SOFC-MGT

Ebrahimi and Moradpoor [57]

SOFC-MGT-ORC

Ogorure et al. [58]

Gasifier-SOFC-GT-ARC-RC-ORC

Thermodynamic efficiencies

Economic analysis

First law (%)

Second law (%)

Electrical: 70% Electrical: 71.9% Electrical: 56.4% Total: 95% Electrical: 48% Total: 74% Electrical: 46% Total: 64% Electrical: 67% Total: 66.4% Total: 78% Total: 79.7% Electrical: 50.3% Total: 81.7% Total: 90% Electrical: 70% – Total: 72.2% Electrical: 52.8% Total: 76.3% Electrical: 75.8% Total: 87.5% Electrical: 58.2% Total: 65.8% Electrical: 61.0% Total: 63.6%

Total: 67% – – –

– Thermoeconomic cost of electricity: $47.7 per MWh – –

–

–

Total: 62% – Total: 38.0% Total: 50% Total: 68.7% Electrical: 43.4% Total: 37.9% –

Total capital investment: $28.5 million – Total product cost: $24.9 per GJ – –

Total: 64.5% Total: 60.0%

Unit product cost: $0.727 per kWh –

Total: 56.4% – Total: 53.4% Electrical: 50.4% –

– Unit cost of electricity: $1955 per kW –

Total: 58.5%

Cost per unit power: $0.011 per kWh

• the solid oxide fuel cell (SOFC) is the primary source of electricity and waste heat; • the dual-loop ORC engine is used for waste-heat recovery and secondary electricity generation; • the LNG is used as heat sink for the ORC, as fuel supply to the fuel cell and to provide cooling; • the SOFC gas turbine and LNG turbine provide additional sources of electricity; and • a methodology to determine the best combination of optimal

– –

–

the fuel cell cathode to participate in the electrochemical reactions. The desired fuel (methane), which is gasified through the LNG (State 4′′), is also fed into a fuel cell after passing through a preheater (FPH, State 6). The high-pressure fuel is combined with recycled water vapour (and other outputs) leaving the anode in a mixer; the mixture is then fed to the SOFC stack (State 7). The fuel mixture and the preheated air undergo electrochemical redox reactions in the fuel-cell stack (SOFC) to generate electricity (the direct current is converted to alternating current via the DC/AC inverter). Thereafter, the excess air from the cathode (State 11) and unconsumed fuel from the anode (State 12′) are completely combusted in the afterburner (AB) to produce high-temperature combustion gases which are fed into the gas turbine (GT, State 14) to produce additional electrical power. It is worth mentioning that there are other auxiliary equipment required for the complete implementation of the system; these include a recirculation blower for the recycle SOFC product, valves and bypass arrangements. However, due to the low cost and power required, these items are not individually included in the modelling and subsequent analyses. The thermoeconomic effect of these items on the overall system cost is addressed with the operation and maintenance factor (introduced in Eq. (19)). The exhaust gases from the gas turbine, after passing through the preheaters to preheat the SOFC fuel and combustion air, enters the waste-heat recovery system (WHR, State 17) as the heat source to the organic Rankine cycle system (ORC1) before being exhausted into the atmosphere (State 18). The large temperature difference between this exhaust gas from the gas turbine and the cryogenic (LNG) thermal sink necessitates the use of another ORC system (ORC2) as a bottoming cycle for ORC1 to maximise the heat recovery and power generation from such a large temperature difference. Consequently, two separate refrigerants are required as working fluids for the ORC systems. The selection of the refrigerant working fluids is discussed in Section 2.2. The LNG is compressed by a pump and sent to the condenser (which acts as the LNG vaporiser) to act as the heat sink for ORC2 (State 2). After the heat transfer in the condenser, the LNG stream is still at a low temperature, it is thus directed to a cooling unit (State 3) to produce chilled water for air conditioning units in domestic applications (Cin and Cout, the chilled water serves as the heat source in vaporising the

working fluids for the ORC engine.

Although several articles have addressed the thermodynamic analysis of SOFC-based power generation systems, there is still a lack of information about the economic analysis of these systems. Therefore, in this paper, in addition to analysing the proposed system from the energy and exergy point of view, economic relations are applied to each component of the system to enable an overall economic appraisal of the proposed system. Exergy flow diagrams are also generated to determine the exergy flow rate in each component, as well as the value and location of exergy destruction in the cycles. In order to determine the optimal design parameters and to establish a trade-off between the system’s thermodynamic performance and economic attractiveness, multi-objective optimisation was incorporated using an integration of a genetic algorithm and a neural network. In Section 2 of this article, the proposed system is described, and its thermodynamic and economic models are presented while the optimisation algorithms are presented in Section 3. The results from the multi-objective optimisation, working-fluid selection and economic appraisals are discussed in Section 4, followed by a summary of the article with conclusions. 2. System description and modelling A schematic of the proposed SOFC-GT system combined with the dual-loop ORC and LNG cycles is shown in Fig. 1. The operating principles of the combined system can be summarised as follows. The air required for the fuel cell is pressurised through the air compressor (AC, State 9) and heated in the preheater (APH, State 10) prior to entering 4

Applied Energy 261 (2020) 114384

M.A. Emadi, et al.

Fig. 1. Schematic of the proposed cogeneration system featuring a combined dual-loop ORC arrangement for waste-heat recovery from a SOFC equipped with a gas turbine.

LNG in the cooling unit), as well as to complete the gasification process and conversion to natural gas (NG). Due to the high pressure of the natural gas, it can be used for electricity generation by passing it through a gas turbine. Thus, a large portion of the gas (about 97%) is passed through a gas turbine and injected into the natural gas distribution network after expansion in the turbine (State 5); only a small portion of the main flow is directed to the stack to supply the required fuel for the SOFC (State 4′′). In summary, the thermodynamic processes described herewith are generally arranged to recover the thermal waste of SOFC output gases and utilise the cold energy in LNG flow. In the first instance, the SOFC is modelled and the exhaust gas mass flow rate and temperature are determined. This flow is then supplied to the dual-loop ORC; the ORC parameters such as its power generation, heat transfer, etc., as well as the required cooling load for the condenser of ORC2 are then obtained. With this, the LNG required as heat sink for (and to ensure feasible pinch conditions in) ORC2 is calculated. After that, the LNG is split, with the required fuel being sent to the SOFC unit while the remainder is sent to the natural gas piping network. The energy and exergy analyses applied in this work are presented in the following sections. Every component is considered as a control volume, and material, energy and exergy balance equations are applied to each one:

m in =

Q EQ

W + W +

m out

(mh) in = m in ex in =

2.1. Solid oxide fuel cell In the SOFC stack, the structure and performance of its individual cells can directly affect the overall structure and performance of the stack and power system. Each cell consists of two electrodes (the anode and the cathode) and an electrolyte between them. The SOFC performance mainly depends on the anode structure, which is the main reason why anode-supported SOFCs are used more frequently than other configurations such as cathode-supported and electrolyte-supported SOFCs. The shape of the anode support determines the shape of a single SOFC cell, which can be either flat plate, tubular, or other more complex geometries. Currently, the commonest way of making large, flat anode supports is by casting; this process is simple and affordable and requires only basic equipment [59]. In the SOFC, the anode not only acts as a site for electrochemical oxidation of the fuel, but it also transfers the charge to a conductive contact. Therefore, the commonest materials used in SOFC anodes are Ni-YSZ cermet (a heat-resistant alloy of ceramic and sintered metal) in which nickel (Ni) plays the role of electronic conduction while YSZ (yttria-stabilized zirconia) acts as the ion-conducting part. In addition, the cathode, in which oxygen gains electrons to form oxygen ion, must be able to dissociate O2 and be electronically conductive. The common cathode material is LSM – a strontium-doped lanthanum manganite (LaMnO3) crystal [60]. The schematic of the fuel cell group that includes a mixer, two preheaters and SOFC stack is shown in Fig. 1. The modelled SOFC in this study is of the tubular type. Although oxygen and hydrogen are the main elements for the electrochemical reaction, the fuel cell can use methane (CH4) and other hydrocarbons from natural gas as fuel. In such a case, the fuel must be converted into hydrogen via chemical reactions known as reforming. The following assumptions are considered in modelling the fuel cell:

(1)

(mh)out mout ex out + ED

(2) (3)

where h denotes enthalpy and subscripts indicate inlet and outlet boundaries of the control volume. 5

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• the system is at steady state and the chemical reactions in the fuel cell are at equilibrium; • oxygen is supplied from air consisting of 21% O and 79% N ; air is treated as an ideal gas; • unreacted gases are fully oxidised in the afterburner; • there is no heat loss from the system to the environment (perfect insulation) [61,62]; • radiation heat transfer is negligible. 2

constants for the reforming (Kp,ref) and shifting (Kp,shift) reactions, and the electrochemical reaction rate (z ) calculated from Eq. (9). Also, α represents the stoichiometric coefficients of the reactants and products. The energy balance of the fuel cell includes enthalpy changes of the chemical and electrochemical reactions as well as the generated electrical power; from these, the outlet temperature of the SOFC can be calculated. Since this temperature is needed in the early stages of modelling the fuel cell, it is necessary to calculate it from an iterative procedure, which begins with an initial guess for the outlet temperature. The stages of this iterative procedure involved in modelling the fuel cell are shown in Fig. 2.

2

The chemical reactions occurring in the SOFC reformer are as follows:

x

[CH 4 + H2 O

y

[CO + H2 O

3H2 + CO] H2 + CO2 ]

Reforming Shifting

(4)

2.2. Working fluid selection for the organic Rankine cycles

(5)

The hydrogen produced in Eqs. (4) and (5) is utilised to generate electricity by the electrochemical reaction:

z

[H2 + 1/2O2

H2 O]

Overall electrochemical reaction

Each organic Rankine cycle (ORC) system is composed of a turbine, a pump, a condenser and an evaporator. In modelling the ORC, it was assumed that the working fluid exits the condenser in the saturated liquid state. The temperature–entropy (T–s) diagram of a typical dual-

(6)

In Eqs. (4)–(6), x , y and z are respectively the reforming, shifting and electrochemical reactions molar conversion rates. Since the electrochemical reaction is not a complete reaction, the unreacted H2 from the electrochemical reaction is burned in the Afterburner. Thus, to find the molar composition of each of the species in the Mixer, Cathode and Anode, as presented in Table A1 in Appendix A, defining such molar conversion rates are necessary. The air and fuel utilisation factors are defined as follows:

Uf =

Ua =

(H2 )consumed (H2 )supplied

Table 2 Fundamental equations for the simulation of the fuel cell group. Component

Term

Equation

Mixer

Material and energy balance

niout =

Equilibrium constants

Kp,ref =

Reformer

(7) (8)

Fuel cell stack

With a given value of fuel and air utilisation factors, the molar flow rates of each stream can be calculated by applying material balances to Eqs. (4)–(6) and solving a system of equations; these are listed in Table A1 in Appendix A. The current density and current generated from the fuel cell can be determined as:

2Fz j= Ncell Aact

Nernst voltage Ohmic overvoltage

(9) (10)

I = jAact

Activation overvoltage

where F is Faraday constant (96,500 C/mol), Ncell is number of cells and Aact is active surface area. The power generated from the fuel cell is calculated as:

Wstack,ac = I ·Ncell·Vcell·

inv

(11)

Concentration overvoltage

Here, VN is the Nernst voltage calculated as described in Table 2 and Vloss is voltage loss which is composed of ohmic, activation and concentration voltage losses:

Vloss =

ohm

+

act

+

conc

ohm

¯g° ne F

)

exp

A2c Tcell

c

=

A1c Tcell

e

= A1e exp

act

=

A1int Tcell act,a

(13)

The calculation procedure and the information required to obtain the Nernst voltage and other voltage losses, as well as the equations used in simulating the various elements of the SOFC are reported in Table 2 and Table A2. To obtain the output flow temperature from the mixer, the material and energy balance equations are used for this component. In the fuel cell material balance, the index k represents the type of reaction occurring inside the fuel cell, i.e., reforming, shifting or electrochemical reaction. The corresponding reaction rates that are indicated with Rk in the table are obtained from the equilibrium

+

act,a

=

act,c

=

¯ cell RT F

6

e le 1

+

int lint ) j

1

1

A2e Tcell

1

A2int Tcell

exp

¯ cell RT F

act,c

Sinh

1

j 2joa

Sinh

1

j 2joc

( ) ( ) exp = 7 × 10 ( ) exp

conc

conc,a

P H2 O

P0

P0

P O2 0.25

9

=

P H2

+

conc,c

conc,a

=

ln 1

j jas

conc,c

=

¯ cell RT 4F

ln 1

j jcs

jas =

2FP H2 Daeff ¯ cell la RT 4FP O2 Dceff P O2,11

¯ cell lc (1 RT

Cell voltage and power

Vcell = VN

Material balance

niout = niin + T out =

(

P11 ohm

k

110000 ¯ cell RT

155000 ¯ cell RT

P0

¯ cell RT 2F

jcs =

Energy balance

+

exp

=

=

c lc A2a Tcell

a

int

(shifting)

¯ cell PH2 O RT ln ne F P H2 P O2

= ( a la + A1a Tcell

joc

(12)

Vloss

(

VN =

(reforming)

PCO2 P H2 PCO P H2 O

joa = 7 × 109

where ηinv is the DC/AC inverter efficiency and Vcell is the voltage from the fuel cell which is expressed as:

Vcell = VN

3 P PH 2 CO PCH4 P H2 O

Kp,shift =

(O2 )consumed (O2 )supplied

in j ni, j T j out i ni c p, i

i c p, i

out = niin , j and T

j

+

ln 1 +

P H2 j P H2 O jas

)

act

+

conc ) ;

Wstack = I ·Vcell·Ncell

i, k R k

in in i ni c p, i T +

k Rk ( Hk ) out i ni c p, i

WFC,stack

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Fig. 2. Flowchart used in modelling the SOFC.

loop ORC system is shown in Fig. 3. In this figure, the pinch point temperature difference and the degree of superheat are also shown. The turbine inlet temperature is calculated when the saturation temperature and the degree of superheat are given. The LNG stream is introduced as the heat sink to the condenser of ORC2 with an initial state of −161 °C and 101 kPa. The outlet pressure of the LNG turbine is kept at 30 bar to meet natural gas pipeline requirements. The optimal utilisation of heat sources and the achievement of high thermal efficiencies are two important factors in the selection of ORC

working fluids [37]. However, in addition to these factors, other environmental parameters such as toxicity, flammability, global warming potential (GWP) and ozone depletion potential (ODP) need to be considered in selecting working fluids for ORC systems. To satisfy the selection of environmentally benign working fluids, only refrigerants with zero ODP and GWP below 200 are considered in this research as presented in Table 3. However, some of these refrigerants are flammable and are only allowed for use in applications which fulfil the requirements mentioned in safety standards. Both ORC systems are assumed to operate under subcritical conditions. While transcritical ORC operation may show a better performance to subcritical cycles, there is limited use of systems with such cycles in the ORC industry [63]. As shown in Fig. 1, the heat source for ORC1 is the high-temperature exhaust gas from the fuel cell. As a result, the appropriate working fluid for this cycle should have a high critical temperature as this determines the maximum evaporation temperature possible in a subcritical cycle. For the top cycle, fluids with critical temperatures greater than 160 °C are selected. Thus, from Table 3, R123, R601, R601a and R1233zd(E) are selected as the candidate working fluids for the top cycle. Despite their high critical temperatures, toluene, hexane and octane have not been selected due to their high normal boiling temperatures that will require sub-atmospheric conditions in the condenser (needed to maximise the power generated by condensing the fluids at lower temperatures) which may cause air leakage into the condenser thereby significantly increasing system complexity and cost. On the other hand, the condenser of the bottom cycle (ORC2) is associated with a very low-temperature LNG heat sink. Therefore, unlike the top cycle, its working fluid should be able to operate at low temperatures, with those with normal boiling temperature below −30 °C considered for effective heat transfer. In addition, fluids with high triple-point temperatures can become frozen in the condenser; hence, only fluids with triple-point temperatures below −50 °C are considered. These leave R290, Ethane, CO2, Propene and R1234yf as

Fig. 3. Qualitative temperature–entropy (T–s) diagram of the proposed combined system. 7

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Table 3 Properties of some working fluids investigated in literature.

Table 4 Expressions for exergy destruction rate.

Refrigerant

Critical pressure (bar)

Critical temperature (°C)

Normal boiling temperature (°C)

Triple point temperature (°C)

ODP

GWP

R152a R290** R123* R600 R600a R601* R601a R1234yf** R1234ze(E) R1233zd(E)* Ammonia Propene** Ethane** CO2** Toluene Hexane Octane

45.2 42.5 36.7 38.0 36.3 33.7 33.8 33.8 36.4 35.7 113 45.6 48.7 73.8 41.3 30.3 25.0

113 96.7 183.7 152 134 197 187 94.7 109 166 132 91.1 32.2 31.0 319 235 296

−24.3 −42.4 27.5 −0.840 −12.1 35.7 27.5 −29.8 −19.3 18.0 −33.6 −47.9 −88.8 −78.5 110 68.7 125

−119 −188 −107 −138 −159 −130 −161 −53.2 −105 −78.0 −77.7 −185 −183 −56.6 −95.2 −95.2 −56.8

0 0 0.02 0 0 0 0 0 0 0 0 0 0 0 0 0 0

124 3.3 77 4 3 4 4 4 6 1 0 1.8 5.5 1 0 0 0

* **

Selected for top cycle. selected for bottom cycle.

candidate working fluids for the bottom cycle (ORC2). parameter(s). For example, the cost of a heat exchanger is related to its heat duty and/or its heat transfer area; similarly, the pressure difference plays an important role in the cost of a pump. As a result, by obtaining the relevant performance parameters of each system component through the thermodynamic analysis, the cost of the component can be obtained from a cost function. The cost functions of all the components encountered in this SOFC-GT-ORC system are presented in Table 5. The procedure for obtaining heat transfer areas of the heat exchangers (air/fuel preheaters and ORC heat exchangers) is described in Appendix B. The total system cost, expressed in cost per hour is obtained by the following [64]:

2.3. Exergy and economic analyses Exergy analysis is a powerful tool for evaluating the performance of thermodynamic systems, which, by determining the irreversibility and exergy destruction from each component, enables a more comprehensive analysis of the system. By applying an exergy balance to each component, the exergy destruction relations are listed in Table 4. The exergy efficiency of the overall system and the waste-heat recovery system are respectively defined as: ex,overall

ex,WHR

=

=

WSOFC

GT

+ WORC1 + WORC2 + WLNG + Ecooling E1

E5

WORC1 + WORC2 + WLNG + Ecooling E1 + E17

E5

E 4''

.

,

(14) (15)

In the above equations, Ẇ represents the electrical power generated from the SOFC, ORC and LNG turbines respectively, while Ecooling represents the cooling exergy provided by the cold LNG for domestic application (Cooling unit, State 3). E1, E 4'' , E5 and E7 represent both the physical and chemical parts of exergy. In engineering systems, thermodynamic analyses do not usually give a full picture of the strength and weaknesses of a project; economic analyses are usually required to establish the cost-benefit (or otherwise) of improving the performance of such systems. In fact, in many engineering problems, achieving better performance from a well-designed thermodynamic system will be accompanied by the penalty of a dramatic rise in the price of system components. As a result, in this paper, in addition to the energy and exergy analyses, an economic analysis is also carried out in order to obtain a better understanding of both the thermodynamic and the economic points of view. An appropriate method for the economic evaluation of engineering systems is to relate the cost of each equipment to its functional

Ctot = Cf + Cenv + Ztot

(16)

Cf = (Cf m f LHV ) × 3600

(17)

Cenv = mCO2 × Cpen × 3600

(18)

Ztot = CRF ×

×

Zk / thour k

(19)

where Zk is the cost of each component (see Table 5). Cf, Cpen and LHV denote the fuel cost, CO2 emission penalty cost and lower heating value of the fuel. These values are $0.003 per MJ [65], $0.024 per kg [1] and 50.0 MJ/kg respectively. Considering a yearly operating duration (thour) of 7500 operating hours in a year, the total cost rate (Ztot ) can be calculated from Eq. (19). In Eq. (19), φ is the operation and maintenance factor which is assumed to be 1.06 [66] and CRF is the capital recovery factor which is evaluated as:

CRF =

8

i (1 + i) N (1 + i) N 1

(20)

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Table 5 Cost relation of components .

3. Optimisation routines and algorithms

(See above-mentioned references for further information.)

3.1. Optimisation methodology

In this equation, N and i indicate the system lifetime and interest rate which are assumed to be 20 years and 12% respectively [1]. Since the cost relations listed in Table 5 were generated using equipment cost data from past years, the component costs are updated to the present year by using CEPCI [67] cost indexes as:

Using the data obtained from the thermodynamic analysis of the SOFC-GT-ORC system, a total number of 400 samples of input-output points were used to train the network. This network is introduced as a fitness function to the genetic algorithm and multi-objective optimisation is performed on it. To measure the performance and accuracy of the network in predicting the output responses, a coefficient of determination (varying between 0 and 1) is introduced; a value of 1 indicates perfect prediction. The main advantage of this method is that the time-consuming thermodynamic calculations inherent in the SOFCGT-ORC model are performed only once at this first stage and are not repeated during optimisation stages. This generally results in a significant reduction in the computation time of the multi-objective optimisation steps. In Fig. 4, the optimisation procedure showing the

Z2018 = Z

CI2018 CIreference

A multi-objective optimisation problem requires the simultaneous fulfilment of several different and often conflicting objectives. Hence, all the individual objective functions in such a multi-objective problem cannot be at their optimal state at the same time. Thus, instead of one optimal point, a set of non-superior optimal points called the Pareto front is obtained. Due to the nonlinear nature and the large number of decision variables involved in the SOFC-GT-ORC model, an evolutionary (genetic) algorithm appears to be the most suitable optimisation method. This genetic algorithm coupled with an artificial neural network (ANN) to combat the time-consuming calculations of the genetic algorithm, is applied to the optimisation of the SOFC-GT-ORC system. Once trained and verified, the model obtained from an artificial neural network does not require detailed information about the system or equipment for further simulations; it acts as a black box model in which the relationship between input and output data has been determined via the initial training step. The ANN is executed with a set of randomly generated input and output data obtained from experimental methods or theoretical calculations (from the SOFC-GT-ORC model in this case), as well as by selecting the appropriate training function and setting the weighting coefficient between neuronal processes (train) [74]. Once executed, the ANN becomes the model of the SOFC-GT-ORC system that serves as the objective function for the optimisation algorithm.

(21)

where CIreference is the reference-year cost index and CI2018 is the present year cost index which is 603.

Fig. 4. Schematic diagram of the optimisation methodology. 9

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coupling between the SOFC-GT-ORC thermodynamic model and the neural network, and between the neural network and the genetic algorithm is presented. The multi-objective optimisation problem is formulated as follows:

minimise or maximise subject to:

f (x ), gj (x )

x = (x1 , …, xD) 0, j = 1, ..., q

the pinch point is defined as follows:

T25 = T19

RD

3.2. Model validation and ANN accuracy Experimental data reported in literature is used to validate the developed model for the solid oxide fuel cell fed with methane. In Fig. 5, a comparison between the model prediction and experimental data is presented. It can be seen that there is a good agreement between the data reported by Tao et al. [75] and the results obtained from the developed SOFC-GT-ORC model, spanning a range of current densities, with the deviations lower than an acceptable maximum value of 10% in all cases. In Fig. 6, the exact results obtained from the model of the SOFC-GTORC are compared with those predicted by the neural network. To evaluate the performance of the neural network, the coefficient of determination (R2) is used. The R2 value quantifies the variability of the response data; values closer to 1 indicate a more accurate prediction. As shown in Fig. 6, the R2 values for the exergy efficiency and cost rate were 0.99996 and 0.99990 respectively, indicating that the trained ANN model has good accuracy.

h j (x ) = 0, j = q + 1, ..., n x iL

xi

x iU , i = 1, ..., D

(27)

TPP,ORC2

(22)

Here, f(x) is the objective function; x is a vector containing the (D in total) design variables; hj(x) and gj(x) are equality and inequality constraints respectively; q is the number of inequality constraints and n is the total number of constraints (n − q is the number of equality constraints); xiU and xiL are the upper and lower bounds of the variable xi, respectively. To limit the results to a range of technically and economically feasible points, a set of constraints has been applied to the range of decision-making variability. The range of variation and design parameter constraints are reported in Table 6. Different parameters can be considered as the objective function in an optimisation process. In this work, the exergy efficiency of the wasteheat recovery system (ηex,WHR), which is an important parameter for evaluating the thermodynamic performance of the system and the capital cost rate are considered as the objective functions. The design parameters considered in optimising the SOFC-GT-ORC system are: ORC1 degree of superheat ( TSH ), ORC1 and ORC2 pinch point temperature differences ( TPP,ORC1, TPP,ORC2 ), ORC1 and ORC2 condenser temperatures ( TCon,ORC1, TCon,ORC2 ), and ORC1 pressure factor (PF). The lower and upper bounds of these parameters and related constraints are listed in Table 6. For ORC1 turbine inlet temperature, the degree of superheat is defined as follows: (23)

T21 = TSat + TSH

For ORC1, a pressure factor (PF) is used to evaluate the pressure in the evaporator: (24)

P21 = PF × Pcr

For condenser temperature, the design parameters are expressed as:

T19 = TNBT + TCon,ORC1

(25)

T23 = TNBT + TCon,ORC2

(26)

Here, TNBT is normal boiling temperature of the working fluid and the relations ensure that the temperatures in the condenser are above TNBT, thus preventing the formation of a vacuum in the condenser. For ORC2 evaporator temperature (or turbine inlet temperature),

Fig. 5. Comparison of present SOFC modelling results with experimental data reported in Ref. [75].

Table 6 List of constraints used in the optimisation of the SOFC-GT-ORC system and the range of variation of design parameters. Constraint

T21 > TSat TGas > TSat T25 < T19 T19 > TNBT T23 > TNBT P21 < Pcr

Description

Design parameter

Prevent the formation of liquid droplets at the turbine The temperature of the cold stream cannot exceed the hot stream temperature in ORC1 The temperature of the cold stream cannot exceed the hot stream temperature in ORC1 The condenser temperature should be above normal boiling temperature value to avoid The condenser temperature should be above normal boiling temperature value to avoid Turbine inlet pressure limit

10

evaporator condenser vacuum vacuum

TSH TPP,ORC1 TPP,ORC2 TCon,ORC1 TCon,ORC2 PF

Range of variation Lower

Upper

10 °C 10 °C 2 °C 2 °C 2 °C 0.2

100 °C 50 °C 20 °C 20 °C 20 °C 0.9

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Fig. 6. Comparison of actual data generated from the SOFC-GT-ORC model and the predictions from the artificial neural network, ANN for (a) the exergy efficiency and (b) the cost rate.

4. Results and discussion

On each Pareto front curve, there are two terminal points located on the top-right and bottom-left corners of the graph; these show the maximum exergy efficiency and the minimum cost rate respectively. These points are the corresponding optimum points when each optimisation objective is applied separately. For the bi-objective optimisation results presented in Fig. 7, each point on a Pareto front curve could be individually considered as an optimum point. Therefore, a decisionmaking method that balances the relative importance or attainability of both objectives needs to be applied. In this research, the LINMAP (linear programming technique for multidimensional analysis of preference) selection method was used in determining one final optimum point from each Pareto front curve. For each Pareto curve, the LINMAP method is executed with the following four steps:

Following the flowchart illustrated in Fig. 2, the SOFC and the ORC waste-heat recovery system models were implemented with the MATLAB software, with working-fluid properties provided from REFPROP V9 [76]. Using input parameters from previous sections and from Table 7, the results of the optimisation, working-fluid selection and thermoeconomic analyses are presented in the following sub-sections. 4.1. Optimal working fluid and system performance A genetic algorithm multi-objective optimisation solver was used to optimise the proposed waste-heat recovery system; this solver was coupled with an artificial neural network (ANN). Using the proposed optimization method, a set of optimal working fluids and suitable operating conditions can be generated. However, the final choice of the operating conditions requires consideration of other factors such as the availability of working fluids or the discretion of the design/plant engineer. Consequently, during the detailed design stage of the cogeneration system, the working fluids and operating conditions derived by using the methods of this research can be considered as possible options by the engineers. Four refrigerants (R123, R601, R601a and R1233zd (E)) are considered for the top cycle (ORC1) while five (R290, Ethane, CO2, Propene and R1234yf) are considered for the bottom cycle (ORC2). The multi-objective optimisation results in Pareto front curves with two objectives of maximising the exergy efficiency and minimising the cost rate. These curves for the twenty various refrigerant combinations in the top and bottom cycles are illustrated in Fig. 7. In each refrigerant combination, (e.g., R123-R290), the first fluid (i.e., R123) is for the top cycle (ORC1) and the second (i.e., R290) is for the bottom cycle (ORC2).

• the points and the two axes of a Pareto front curve are made nondimensional by Eq. (28); • an unattainable ideal point that has the best value for both objective • •

functions is selected (this point does not fall on the Pareto front as shown in Fig. 7(a) for the R123-Ethane curve); the distances (norms) of the points on the Pareto front from this ideal point are obtained with Eq. (29); the point having the lowest distance (from all others) is selected as the preferred optimal solution.

f i,1 = di =

2

fi,1 2

i

(fi,1

w1 (f i,1

)2

, f i,2 =

fi,2 2

i

(fi,2 )2

f ideal,1 )2 + w2 (f i,2

(28)

f ideal,2 ) 2

(29)

In the above equations, d and f are the special distance and the objective function respectively. f i,1 and f i,2 represent the non-dimensional objective function values for each point on the Pareto front while f ideal,1

Table 7 Input parameters used in the system modelling. Input parameter

Value

Input parameter

Value

SOFC: Ambient temperature (°C) Ambient pressure (bar) SOFC inlet temperature (oC) [13] Active surface area (m2) [58] Number of cells Current density (A/m2) [47] Steam to carbon ratio (rsc) [6] Fuel utilisation factor [48] Air utilisation factor [52] Air compressor isentropic efficiency [7] DC-AC inverter efficiency [7] Afterburner combustion efficiency [7]

25.0 1.01 600 0.0834 2500 5500 2 0.75 0.15 85% 97% 99%

Afterburner pressure drop [7] Fuel cell pressure drop [7] Heat exchangers pressure drop [7] Organic Rankine cycles: Turbine isentropic efficiency (%) [25] Pump isentropic efficiency (%) [25] LNG stream: Turbine inlet pressure (bar) [77] NG network pressure (bar) [77] Turbine isentropic efficiency (%) [25] Pump isentropic efficiency (%) [25] Chilled water inlet temperature (oC) Chilled water outlet temperature (oC)

3% 2% 2%

11

85 80 65 30 85 80 15 8

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Fig. 7. The Pareto fronts for the proposed system showing designs with maximum exergy efficiency and minimum cost rate with: (a) R123, (b) R601, (c) R601a and (d) R1233zd(E) as the working fluid of top cycle; the final and preferred optimal points selected by the LINMAP method are indicated with arrows.

and f ideal,2 represent the non-dimensional objective function values for the ideal point. In formulating this LINMAP method, both objectives have been taken to be equally important (i.e., w1 = w2 = 1); in cases where one of the objectives is relatively more important, the system designer can decide to apply weights such that w1 > w2 or w1 < w2. In Fig. 7, there are four plots (7a – 7d) corresponding to the four working fluids investigated for the top cycle; each plot contains five Pareto fronts, with each front corresponding to one of the fluids investigated in the bottom cycle. It is found that all the Pareto fronts are within an exergy efficiency range of 20% to 45% and a price range of $2.5 to $5.5 per hr. Irrespective of the refrigerant in the top cycle (ORC1), the WHR system is least efficient when R1234yf is used as the refrigerant in the bottom cycle (ORC2). Conversely, at the same cost rates, the WHR system with Ethane used as the refrigerant in ORC2 always results in the highest exergy efficiency. In addition, the Pareto fronts of the system with CO2, Propene or R290 as the refrigerant in ORC2, are very close to each other with their objective functions attaining approximately the same values. After applying the LINMAP method to the results on each of the Pareto curves, the final preferred optimal point on each of the Pareto front curve is marked with a circle and an arrow as indicated in Fig. 7. The design parameters and objective functions related to the final selection of optimal point for all the combinations of refrigerants are listed in Table 8 and these points are collated and plotted in Fig. 8. From Fig. 8, the system with R1233zd(E)-Ethane as refrigerants has the highest exergy efficiency (34.3%) while that with R601a-R1234yf has the lowest price ($2.82 per hr); they represent the limits of both objective functions. Every other point in this figure can be compared with another point in terms of the two objectives if it represents a superior selection, leading to a system with higher exergy efficiency and lower cost. If not, i.e., if it is only superior in one of the objective functions, then no definitive comparison can be made between the two

points. For example, due to its higher efficiency and lower cost, the system with R601-R290 as refrigerants is better than that with the R123-R1234yf refrigerants; however, the same cannot be said for the case of R601-R290 vs. R123-R290, because in each case one of the objective functions is superior to the other. Thus, a new Pareto front in which, none of the points are superior to the other can be obtained from the points in Fig. 8; this new front consists of the R601a-R1234yf, R601R1234yf, R601-R290, R601-Propene, R123-Propene, R601-Ethane, R123-Ethane and R1233zd(E)-Ethane refrigerants. To select a system with the preferred optimum point, the LINMAP method is re-applied to the points in Fig. 8 and the R601-Ethane refrigerant is selected as the final optimal combination and is used for the further analyses in the later sections. It is worth noting that the LINMAP method is re-applied to select the preferred solution in comparison to all the selected points in Fig. 7 (which were also obtained by the LINMAP method). In Fig. 9, the sensitivity of the Pareto front of the SOFC-GT-ORC system (with the final optimum point obtained in Fig. 8, i.e., the R601Ethane working fluids used as the base case) to equipment prices (up to ±50%) is presented. The results indicate that with a rise of 20% and 50% in equipment prices, the slope of the Pareto front increases and the Pareto front especially in the regions with high exergy efficiencies, shifts upward by a large margin. As a result, the system cost rate is significantly increased in exchange for a slight increase in exergy efficiency. On the contrary, for low prices (−20% and −50%), the slope of the chart is very low; therefore, with marginal increases in equipment prices, higher system efficiencies can be achieved. 4.2. System rating and cost distribution The electrical power and cooling power generated from the SOFCGT-ORC system for the optimal points obtained from Fig. 8 are presented in Fig. 10. The system with the R1233zd(E)-Ethane fluid 12

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Table 8 The optimum values of the design parameters and the corresponding values of the objective functions of the proposed system, at the optimal points selected by the LINMAP method from Fig. 7. Refrigerants R123-R290 R123-Ethane R123-CO2 R123-Propene R123-R1234yf R601-R290 R601-Ethane* R601-CO2 R601-Propene R601-R1234yf R601a-R290 R601a-Ethane R601a-CO2 R601a-Propene R601a-R1234yf*** R1233zd(E)-R290 R1233zd(E)-Ethane** R1233zd(E)-CO2 R1233zd(E)-Propene R1233zd(E)-R1234yf

Design parameters

TSH 83.4 84.8 87.4 88.5 87.1 88.6 81.6 74.4 76.2 73.6 71.9 63.2 87.1 91.8 89.8 91.5 86.4 91.8 87.9 93.8

PF 0.870 0.853 0.885 0.891 0.877 0.890 0.896 0.890 0.897 0.894 0.880 0.878 0.890 0.895 0.898 0.885 0.877 0.867 0.868 0.876

TPP,ORC1 47.1 48.1 46.0 48.0 46.0 44.4 45.8 49.0 47.9 48.2 47.7 49.2 47.5 47.8 49.4 48.7 42.7 48.8 45.8 47.3

TCon,ORC1 12.0 3.44 3.45 11.4 14.4 12.1 4.67 2.86 14.5 14.3 11.7 5.30 3.15 11.2 14.8 14.2 4.52 4.62 10.4 14.2

Objective functions

TPP,ORC2 2.62 11.9 12.1 3.33 3.92 3.59 14.9 13.4 2.89 4.00 3.06 11.1 7.67 3.02 2.38 3.85 10.1 4.63 6.02 4.04

TCon,ORC2 2.64 2.54 2.19 2.25 2.81 2.79 2.36 2.22 2.52 2.93 2.91 3.17 2.33 2.72 2.73 2.25 2.55 2.70 3.58 4.12

ηex,WHR (%)

Cost ($ per hr)

29.6 34.0 29.9 30.3 27.7 28.5 32.5 28.6 29.4 30.0 28.5 33.0 28.6 28.8 26.5 28.9 34.3 29.8 29.4 26.9

3.11 3.36 3.23 3.10 3.01 2.87 3.15 3.03 2.94 2.85 3.11 3.46 3.10 2.96 2.82 3.23 3.71 3.38 3.34 3.13

*

Optimal refrigerants selected by LINMAP. Refrigerants with maximum value of exergy efficiency. *** Refrigerants with minimum value of cost rate. See Fig. 8. **

Fig. 9. The sensitivity of Pareto front to changes in equipment capital cost with R601-Ethane as working fluids.

Fig. 8. The objective functions of the proposed system selected by the LINMAP method from Fig. 7.

environmental costs were 31.1% and 19.7% of total cost respectively. In addition, the distribution of the investment costs amongst different subsystems is presented with the SOFC-GT accounting for the largest part (70.8%) of the capital cost. This is predominantly because SOFC systems are yet to be deployed on a large scale worldwide and thus, it is currently an expensive technology as evidenced by the fact that the SOFC stack accounts for 58% of the cost of the SOFC subsystem while the other more widely-available components (turbine, compressor, afterburner and heat exchangers) accounted for a combined 42%. As a result, the overall cost of the cogeneration system is most sensitive to the cost of the SOFC stack. The ORC2 subsystem accounts for 10.2% of the capital cost, while the LNG and ORC1 subsystems accounted for 9.9% and 9.1% respectively, with most of the costs of these subsystems being related to the turbines.

combination produces the highest power output of 273 kW while that with R1233zd(E)-R1234yf produces the highest cooling load of 728 kW. Although the preferred fluid combination from Fig. 8 (R601-Ethane, delivering electrical power of 216 kW and cooling capacity of 567 kW) does not maximise the power or cooling potential of the proposed SOFC-GT-ORC system, it is selected as the optimal option as it strikes the best balance between the thermodynamic (exergy) and economic objectives. As a result, despite resulting in a system with lower power and cooling capacity, it is the economically better choice. The total cost distribution of the cogeneration system is presented in Fig. 11. From this figure, 49.2% of the total cost is attributed to the operating and fuel costs while the investment costs for equipment and

13

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Fig. 10. Total electrical power output and cooling capacity of the SOFC-GT-ORC waste-heat recovery system at the optimum points selected by the LINMAP method from the Pareto front curves in Fig. 7.

Fig. 11. Cost distribution of the SOFC-GT-ORC cogeneration system with the R601-Ethane working fluids.

4.3. Exergy and thermoeconomic analyses

generating 1045 kW net electrical power; of these, 829 kW is produced by the fuel cell and its gas turbine (i.e., the SOFC-GT system) while the waste-heat recovery system supplies the remaining 216 kW from the ORC1, ORC2 and LNG turbines. It should be noted that the power required for compression and pumping (by the SOFC air compressor, the ORC pumps and the LNG pump) are taken directly from the turbines. The system also demonstrates a cooling capacity of 567 kW by

The economic and thermodynamic indicators of the SOFC-GT-ORC system with the R601-Ethane working fluids are presented in Table 9, while the thermodynamic characteristics of the flow and state points of the fuel cell system and the ORC waste-heat recovery system are listed in Tables 10 and 11 respectively. The proposed system is capable of 14

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environmental penalty of $6.84 per hr; this penalty is unavoidable as the fuel cell reactions produce CO2 as a by-product. The system cost is further composed of the operating costs and the capital cost of the fuel cell and waste-heat recovery systems. A large percentage of the system cost is spent on the fuel (LNG) for the fuel cell at $17.1 per hr, compared to the equipment costs of the SOFC-GT and waste-heat recovery system at $7.64 per hr and $3.15 per hr respectively. By considering the overall system cost per megawatt of power produced, the system can be benchmarked against similar technologies. The levelized cost of electricity (LCoE) for the proposed SOFC-GT-ORC system is $33.2 per MWh which, in comparison to standalone systems, represents a 12.9% cost reduction on a SOFC-GT system (LCoE of $38.1 per MWh) and a 73.9% cost reduction on a SOFC system (LCoE of $127 per MWh). The proposed system becomes even more attractive when its levelized cost of power (in generating electrical and cooling power) of $21.6 per MWh is considered. To understand how exergy has been transferred around the system and to identify the locations of exergy destruction in the system, the exergy flow in each of the fluid streams in the proposed system (see Fig. 1 for the fluid streams) is calculated; the exergy flows are then plotted in an exergy flow diagram. It is worthy to mention that in the fuel cell (SOFC) exergy flow diagram, the exergy includes both physical and chemical exergy while in the waste-heat recovery system, only physical exergy is considered since there is no chemical reaction taking place and hence, no change in chemical exergy. As shown in Fig. 12 (for the SOFC system), atmospheric air first enters the compressor (AC) and its exergy increases after compression. Then, both air and fuel are introduced to the preheaters (APH, FPH) where their exergy increases with temperature. The fuel, with its high chemical exergy, is then, after mixing with the high-temperature flow from the SOFC anode, fed into the fuel cell. In the fuel cell, this chemical exergy is converted to electricity, and then the exhaust gases exit the cell. It is worth mentioning that the exhaust gas has low chemical exergy but high physical exergy because this flow absorbs the dissipated heat from the exothermic SOFC reactions and exits the fuel cell at high temperatures. The exhaust gas enters the afterburner (AB) and, by combustion with the remaining fuel, more chemical exergy is converted into physical exergy; this physical exergy is then converted to mechanical power in the gas turbine (GT). The available physical exergy in the exhaust gases from the gas turbine is used in preheating the air and fuel in their respective preheaters and afterwards sent as input exergy to the wasteheat recovery system. Overall, of the total physical and chemical exergy input by the LNG fuel and air (1510 kW), approximately 55.0% is converted to electricity (831 kW), while about 30.4% of it is destroyed (459 kW) and the remaining 14.6% leaves the system in the form of hot gasses (221 kW) that powers the waste-heat recovery system. In the SOFC-GT system, the highest exergy destruction occurs in the fuel cell, accounting for 38% of its total exergy destruction. The second highest exergy destruction occurs in the gas turbine and the third highest occurs in after-burner due to the presence of irreversibility. The exergy flow diagram of the proposed dual-loop ORC waste-heat recovery system is presented in Fig. 13. The exhaust gas flow from the SOFC turbine with 221 kW exergy enters the evaporator of ORC1. From this amount of exergy, 169 kW is consumed in the evaporator and the rest (52.0 kW) is rejected to the atmosphere. Also, 1170 kW of physical exergy is introduced to the system by the LNG heat sink. According to Fig. 13, 163 kW of cold exergy is transferred from the LNG to the flow of the bottom ORC system (ORC2). The cold exergy of LNG enters the cooling unit and produces 30.0 kW of cooling exergy and then enters the LNG turbine generating an electrical power of 56.7 kW after which

Table 9 Thermoeconomic parameters of the proposed SOFC-GT-ORC system with R601Ethane working fluids after a multi-objective optimisation of its total cost rate and waste-heat recovery exergy efficiency. Performance parameter

Value

Performance parameter

Value

SOFC-GT net power ORC1 net power ORC2 net power

829 kW 74.7 kW 84.5 kW

285 kg/hr $17.1 per hr $6.84 per hr

LNG stream net power Cooling unit capacity

56.7 kW 567 kW

Overall cycle exergy efficiency WHR system exergy efficiency

51.6%

CO2 emission Operation cost rate Environmental penalty cost rate SOFC-GT capital cost rate WHR system capital cost rate Levelized cost of electricity Levelized cost of power

32.5%

$7.64 per hr $3.15 per hr $33.2 per MWh $21.6 per MWh

Table 10 Stream properties at state points of the SOFC-GT system. State

T (°C)

P (bar)

n (mol/s)

6′ 6 7 8 9 10 11 12′ 13 14 15 16 17 18

–26.3 600 749 25.0 270 600 808 808 808 966 678 651 346 105

6.58 6.45 6.45 1.01 6.58 6.45 6.32 6.32 6.32 6.13 1.11 1.09 1.07 1.05

1.80 1.80 9.21 56.6 56.6 56.6 53.6 5.39 7.41 58.4 58.4 58.4 58.4 58.4

Molar flow rate (mol/s) CH4

H2O

H2

CO

CO2

O2

N2

1.80 1.80 1.80 0 0 0 0 0 0 0 0 0 0 0

0 0 3.79 0 0 0 0 2.76 3.79 3.60 3.60 3.60 3.60 3.60

0 0 1.15 0 0 0 0 0.83 1.15 0 0 0 0 0

0 0 0.57 0 0 0 0 0.42 0.57 0 0 0 0 0

0 0 1.90 0 0 0 0 1.38 1.90 1.8 1.8 1.8 1.8 1.8

0 0 0 11.9 11.9 11.9 8.90 0 0 8.28 8.28 8.28 8.28 8.28

0 0 0 44.7 44.7 44.7 44.7 0 0 44.7 44.7 44.7 44.7 44.7

Table 11 Thermodynamic properties at state points of the ORC waste-heat recovery system with R601-Ethane working fluids. State

Fluid

m (kg s−1)

T (°C)

P (bar)

h (kJ kg−1)

s (kJ kg−1 K−1)

1 2 3 4 4′' 5 19 20 21 22 23 24 25 26

LNG LNG LNG LNG LNG LNG R601 R601 R601 R601 Ethane Ethane Ethane Ethane

1.09 1.09 1.09 1.09 0.03 1.06 0.53 0.53 0.53 0.53 0.71 0.71 0.71 0.71

−161 −159 −93.2 5.00 5.00 −41.8 40.4 41.9 271 196 −86.5 −84.4 25.4 −86.5

1.01 65.0 65.0 65.0 65.0 30.0 1.17 30.3 30.3 1.17 1.13 42.3 42.3 1.13

−911 −892 −641 −121 −121 −194 −353 −347 474 327 −665 −655 −150 −279

0.00 0.03 1.75 4.16 4.16 4.22 0.03 0.04 1.94 1.99 0.03 0.04 1.97 2.09

recovering the cold energy of the LNG flow while the exergy efficiencies of the entire SOFC-GT-ORC system and the waste-heat recovery system (dual-loop ORC system) are 51.6% and 32.5%, respectively. The system produces CO2 at a rate of 285 kg/hr, incurring an

15

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Fig. 12. Exergy flow diagram of the SOFC-GT system after a multi-objective optimisation of its total cost rate and waste-heat recovery exergy efficiency.

Fig. 13. Exergy flow diagram of the ORC waste-heat recovery system with R601-Ethane working fluids.

16

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some portion of it enters the fuel cell while the rest is sent to the urban gas distribution network. The highest amount of exergy destruction occurs in the cooling unit (36.7%) and then in the LNG vaporiser (23.6%). This is due to the high temperature difference between the fluids passing through these heat exchangers as the LNG is supplied to the bottom ORC condenser at −159 °C while ORC working fluid (Ethane in this case) is condensed at −86.5 °C. After these components, the other heat exchangers in the ORC loops (i.e., the evaporator of ORC2 – which is the condenser of ORC1 – and that of ORC1) account for the largest amount of exergy destruction.

system, 49.2% of the total cost is attributed to operating and fuel costs, while the equipment and environmental costs respectively account for 31.1% and 19.7% of the total costs, with the SOFC accounting for the largest part (70.8%) of the total capital cost. It is also demonstrated that the cost of production of an electrical unit for the proposed SOFC-GTORC is $33.2 per MWh, which is 12.9% and 73.9% less than the electrical unit costs of separate SOFC-GT and SOFC cycles, respectively; the system also demonstrates an attractive levelized cost of power (electrical and cooling power) of $21.6 per MWh. In a bid to suggest areas for efficiency improvement in the system, exergy flow diagrams are used to identify the main sources of irreversibility and exergy destruction. In the prime mover, the fuel cell has the highest exergy destruction, while the cooling unit and LNG vaporiser are the components with the highest exergy destruction in the wasteheat recovery system. Thus, these components are highlighted for design modifications to enhance their performance; as long as such thermodynamic benefits can be achieved at low cost, the overall economic outlook of the investigated SOFC-GT-ORC system can be considerably improved.

5. Conclusions In this study, a novel combined-cycle cogeneration configuration in which a dual-loop loop organic Rankine cycle (ORC) system is integrated with a solid oxide fuel cell system connected to a gas turbine (SOFC-GT) is proposed to recover waste heat from the SOFC and to utilise cold energy in the liquefied natural gas (LNG) stream. In the dual-loop ORC system, the top ORC recovers waste heat from the SOFCGT while the bottom ORC utilises the LNG cold energy as a heat rejection medium; the LNG stream is further used to provide cooling in possible domestic applications after which it goes through a turbine to generate additional electricity. The importance of working-fluid choice on system performance is investigated using an artificial neural network and multi-objective optimisation approach. From 20 different combinations of fluids, the combination of R601 (top cycle) and Ethane (bottom cycle) is suggested as optimal by the LINMAP method due to the satisfaction of optimisation goals (a trade-off between high exergy efficiency of 33.0% and low cost rate of $3.15 per hr), leading to an overall system exergy efficiency of 51.6% and a total electrical power output of 1040 kW. The dual-loop ORC waste-recovery system, in combination with the LNG turbine, supplies 20.7% (216 kW) of the total electricity generation while also producing 564 kW of cooling. The efficiency-cost Pareto fronts are sensitive to equipment prices; increases in prices (+20%–+50%) lead to significant rise in the slope of the Pareto front, such that for a slight increase in the exergy efficiency of the system, the cost rate increases significantly making it uneconomical. On the contrary, for similar low prices, the front has a lower slope; therefore, higher exergy efficiencies can be achieved with only a small penalty in the equipment costs. Moreover, the total cost distribution of the SOFC-GT-ORC cogeneration system is also investigated. Over the (20-year) lifetime of the

CRediT authorship contribution statement Mohammad Ali Emadi: Conceptualization, Methodology, Validation, Formal analysis, Writing - original draft. Nazanin Chitgar: Conceptualization, Methodology, Validation, Formal analysis, Writing original draft. Oyeniyi A. Oyewunmi: Conceptualization, Formal analysis, Supervision, Writing - review & editing. Christos N. Markides: Conceptualization, Funding acquisition, Supervision, Project administration, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) [grant numbers EP/P004709/1, and EP/R045518/1]. Data supporting this publication can be obtained on request from [email protected].

Appendix A The calculation of molar flow rates in the fuel cell group and constant parameters for voltage losses are presented in Tables A1 and A2.

Table A1 Molar flow rates of the flowing gases in the fuel cell group. Mixer

Anode

CH 4 n7CH4 = n6CH4 + n13 H2 O CH4 H2 O n7 = rsc n7 = n13 H2 H2 n7 = n13

CH 4 n12 = n 7CH4 H2 O n12 = n7H2O H2 n12 = n 7H2 + 3x

CO n7CO = n13

CO n12 = n 7CO + x

CO2 n7CO2 = n13

CO2 n12 = n 7CO2 + y

Uf =

Cathode

z H n7 2 + 3x + y

17

N2 N2 O2 n11 = n10 = 3.76n10

x

x

y+z

+y

y

z

O2 O2 n11 = n10

Ua =

0.5z O n102

0.5z

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Table A2 Constant parameters for voltage losses [78]. Parameter (unit)

Symbol

Value

Anode thickness (m) Anode conductivity constants Cathode thickness (m) Cathode conductivity constants Electrolyte thickness (m) Electrolyte conductivity constants Interconnect thickness (m) Interconnect conductivity constants Effective gaseous diffusivity through anode (m2/s) Effective gaseous diffusivity through cathode (m2/s)

la A1a ; A2a lc A1c ; A2c le A1e ; A2e lint A1int ; A2int Daeff

0.05 × 10-2 95 × 106; −1150 0.005 × 10-2 42 × 106; −1200 0.001 × 10-2 3.34 × 104; −10300 0.3 × 10-2 9.3 × 106; −1100 0.2 × 10-4

Dceff

0.05 × 10-4

Appendix B The procedure for obtaining heat exchanger areas is presented in Table B1.

Table B1 Equations used for calculating heat exchangers surface area [79–81]. Term

Description

Correlation

Heat transfer rate (kW)

Qk is the heat rate between the hot and cold fluid, is the logarithmic mean temperature, Uk is the overall heat transfer coefficient, and Ak is the heat transfer surface area

Qk = Uk Ak TkLMTD

Overall heat transfer coefficient (kW m−2 K−1)

hG and hOF are the convection heat transfer coefficients of the hot exhaust gas and the organic fluid. Also, k and t denote the thermal conductivity and thickness of the heat exchanger material

1 U

Nusselt number

The convection heat transfer coefficients can be calculated using Nusselt number. Deq is the approximate diameter equals to twice of the heat exchanger’s plate clearance

The organic fluid heat transfer coefficient at the evaporator of the ORC

fp is the pressure factor which is a function of the critical pressure (Pcr) and the atmospheric pressure (Pa), H represents the ratio of sensible to latent heat, X is dimensionless number, ρl and ρv are the density of fluid liquid state and vapour state

ΔTkLMTD

=

Nu =

Nu =

δh, p and L are the depth of the flutes, the pitch of the flutes and the heat transfer length. Also, Gr and Bo are the Grashof and Bond number

The hot exhaust gas heat transfer coefficient

Reg is the hot exhaust gas Reynolds number and fg is the friction factor

+

t k

1 hG

+

hDeq k

1.18(fp X )0.919. H

( )

P 3 Pcr

Nu = 2.018 Bo

[6] [7] [8]

18

0.1

·

(

Nug = (fg /8)·(Reg

, fp X < 62

0.448

, fp X > 62

)

Gr l Pr l 1/4 H

When 104 < Reg < 5 × 106,

1000)·

4

fg = (1.82logReg

[5]

l v

0.448

P 0.7 Pa

p2 l· h

Nug = (fg /8)·Reg ·

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