Integrating solid oxide fuel cell and vapour absorption cooling with MSW gasification: process modelling and exergo-enviro-economic analysis

Abstract

The paper deals with a conceptual design and exergo-enviro-economic analysis of a municipal solid waste-based plant that employs steam–air gasification, solid oxide fuel cell, heat recovery steam turbine cycle and a vapour absorption refrigeration unit to coproduce electricity and cooling. Process simulation platform of Cycle Tempo was used to carry out major part of the work. Parametric variations of major plant components were also assessed. The plant is found to yield maximum energy efficiency of 50.29%, producing electricity at 0.11 USD/kWh and giving a payback period of 6.5 years. The plant has a specific CO₂ emission of less than 0.9 kg/kWh with a high sustainability index of 1.8. The plant is found to have a annual carbon emission saving potential of about 65,000 with consequent emission cost saving of about 9.7 million USD. The plant shows an impressive exergo-economic factor of 0.55, thus reinforcing the economic feasibility of such type of plants.

Introduction

Municipal solid waste (MSW) disposal and management are two burning topics gaining utmost importance day by day. MSW disposal has been a serious issue due to the problem of land-filling as the latter is responsible for the contamination of land, air, water and soil for a prolonged period of time. With ever-increasing urban population, the issues of MSW disposal and conversion became more acute. Waste pyrolysis and gasification offer viable and economically competitive waste-to-energy conversion technologies [1, 2]. Kheiri et al. [3] modelled and analysed (5E assessment) a tri-generation plant based on MSW and with an externally fired gas turbine (EFGT) cycle, establishing that such plant were both thermo-economically as well as environmentally feasible. Lee et al. [4] performed life cycle analysis (LCA) of gasification of MSW followed by Fischer–Tropsch (FT) conversion of MSW for transportation and fuel production. Mondal et al. [5] modelled a novel MSW fired combined power plant integrated with an organic Rankine cycle (ORC), to supply electricity to an urban municipality. The optimised values of the parameters obtained through simulation such as exergetic efficiency and unit cost of electricity obtained were 39% and 0.085 USD/kWh, respectively.

Many past studies suggest that integrating a fuel cell with a gasifier in any power plant results in power and efficiency improvement. Shayan et al. [6] assessed thermo-economic performance of a biomass gasifier using wood as fuel linked to SOFC. From the simulated results, it was noted that maximum calorific value of the producer gas obtained was almost 11 MJ/Nm³ achieved through steam gasification route. Mojaver et al. [7] investigated the performance of biomass gasifier coupled with an internal reforming solid oxide fuel cell (IR-SOFC) and high-temperature sodium heat pipes with rice husk used as feedstock. At the optimised scenario, electrical efficiency of 43.71% and the thermal efficiency of 30.6% were achieved. A comprehensive review paper was presented by Din and Zainal [8] which emphasised on biomass gasification process and its integration with other suitable components like SOFC and gas turbine (GT) systems. The review comprehensively talked about different types of biomass used as fuel for gasification and different types of gasifiers that can be used in gasification. Rokni [9] proposed an MSW gasification-based tri-generation system comprising power, cooling and district heating employing SOFC collaborated with a vapour absorption chiller. Apart from techno-economic and techno-environmental analysis, many researchers have performed exergo-economic analysis also for their proposed plants. Ran et al. [10] performed techno-economic and environmental analysis of a biomass gasification-based SOFC hybrid power generation system along with a waste heat utilisation unit. From the proposed plant, good simulation results were obtained with exergetic efficiency being 37.4%, net power generation of 351 kW along with effective cost of electricity being 0.08 USD/kWh. Hosseinpour et al. [11] analysed the performance of a biomass gasification-based IR-SOFC where the gasification process was done using four different gasifying agents: air, oxygen, oxygen enriched air and steam. Exergo-enviro-economic assessment of the plant was done to determine the best case scenario. Abuadallah and Liu [12] comprehensively studied the micro-structural features of an SOFC like particle size, pore diameter, particle coordination number and TPB area which could even act at low operating temperatures. The study revealed that the optimisation of the graded micro-structure of SOFC electrodes increased TPB area and reduced the total voltage loss. Huang et al. [13] performed analysed the performance of a novel SOFC-based polygeneration and condensation dehumidification system and performed multi-objective optimisation on the same. The impact of system parameters like inlet temperature of fuel cell, steam-to-carbon ratio, air flow rate and high-temperature generator temperature on system performance were analysed. Liu et al. [14] developed a novel transfer-free in situ method for preparation poly (2, 5-benzimidazole) (ABPBI)-grafted electrolytic graphene oxide (EGO) composites (ABPBI-EGO) for high-temperature proton exchange membrane (PEM) fuel cells applications. Zhu et al. [15] developed a tri-generation model that involved combined cooling, heating and power (CCHP) by integrating a gas turbine (GT) cycle along with transcritical and supercritical CO₂ cycles, a high-pressure steam cycle, a Goswami cycle and a heating terminal. The study focused on improving the thermodynamic performance of the plant at the optimal level and reducing CO₂ emissions. A unique technique which is known by specific exergy costing (SPECO) method had been elaborately discussed by Lazaretto and Tsatsaronis [16] in order to perform exergo-economic analysis.

From a comprehensive survey of the literature, it is seen that there are quite a good number of works related to gasification of MSW and generation of power from SOFC. There has also been some works related to MSW gasification plant coupled with an SOFC for efficient power generation. Many researchers have also presented techno-economic and techno-environmental approaches for assessing the overall performance of their proposed plants. However, the exergo-economic approach has seldom been taken to analyse such combined electricity and cooling plant. Also, integrating a fuel cell with an MSW gasification-based cogeneration plant along with bottoming vapour absorption refrigeration (VAR) cycle has not been reported. Given this gap in research, this paper deals with modelling of MSW gasification-based cogeneration plant (electricity and cooling) employing an SOFC, a steam turbine (ST) for electricity generation and a bottoming VAR cycle for cooling demand. The assessment of the system is done in terms of exergo-enviro-economic analyses. Net electrical power output, overall generation efficiency, exergetic efficiency, COP, refrigeration effect, effective cost of electricity (ECOE), discounted period of payback, specific CO₂ emission, cost cutting due to reduction of CO₂ emission and exergo-economic factor are realised to be the essential output parameters for the proposed cogeneration plant.

System modelling of the plant and assumptions

The paper reports 5E analyses of an MSW gasification-based cogeneration plant employing high-temperature SOFC and an ST for power generation along with a bottoming VAR for cooling demand where a solution of aqua ammonia is taken as the refrigerant. MSW gasification is performed considering both air and steam as gasifying agents. Mondal et al. [5] have mentioned a composition of segregated MSW by collecting the gravimetric properties of segregated MSW. The composition of MSW (on wet basis) is presented in Table 1.

Table 1. Ultimate analysis of MSW [5]

Constituents	C	H	N	O	Cl	Ash	Moisture	LCV (kJ/kg)
Mass percentage	40	5.5	0.60	30	0.90	10.10	12.9	17,120

A downdraft gasifier having a fixed bed is chosen for the present study as such type of gasifiers generate very minimal amount of tar. The syngas is used as a fuel being fed to the anode side of the SOFC. The unutilised fuel in the SOFC is allowed to burn in the afterburner (AB). The burnt gas expelling out of the afterburner has a substantial amount of heat energy. This heat energy is effectively utilised to heat the compressed air which is then surpassed to the cathode of the SOFC and to in the heat recovery steam generator (HRSG) to produce superheated steam. A feed pump (FP) has been included in the HRSG to raise the pressure of feedwater for allowing this superheated steam to enter into the steam turbine (ST) for power generation. The low-pressure steam developed at the exit of the ST is partially allowed to enter into the gasifier by working as a gasifying agent and the rest for heating the generator of the VAR block for cooling. The VAR cycle runs a solution of aqua ammonia. The schematic representation of the proposed plant is illustrated in Fig. 1.

[See PDF for image]

Fig. 1

Schematic representation of the combined power and cooling plant

There are some assumptions that have been taken into account for numerical investigation of the proposed cogeneration plant while developing custom-built codes in the Cycle Tempo software for the sake of feasibility and compatibility of the analyses. They are:

1. The plant is running in steady state.

2. Every gas is treated as an ideal gas.

3. The generator attached with the ST and the motors attached with the AC and pumps are devoid of any electrical losses.

4. The isentropic efficiency of the steam turbine is assumed to be 90% and that for the compressor and pump to be 85%.

5. The convective and radiative losses from the SOFC stack are negligible

6. Heat losses occurring in the connecting pipes are negligible

Energetic assessment

To analyse the plant performance energetically, the performance of each of the components needs to be performed separately. The entire schematic of the cogeneration plant presented in Fig. 1 can be considered as five sub-units: gasifier, SOFC, HRSG, steam turbine (ST) and VAR unit. Energy or heat balance equations involved with the chief components are provided in the subsequent sections.

Gasifier

MSW has been selected as a fuel for the gasification process owing to its high calorific value. In steam–air gasification of MSW, a complex set of thermo-chemical reactions occur inside the gasifier to generate producer gas which is rich in hydrogen (H₂) along with carbon monoxide (CO), carbon dioxide (CO₂), water vapour (H₂O) and some minimal amount of methane (CH₄). The molecular formula of MSW (dry) is written as CH_sO_tN_u where s, t and u are constants obtained from the global gasification equation by balancing the masses carbon, nitrogen, hydrogen and oxygen, respectively. Inside the gasifier, many thermo-chemical reactions occur and those reactions are mentioned in Table 2 in a detailed manner.

Table 2. Different thermo-chemical reactions occurring during the gasification process [17]

Reaction name	Reaction process	Reaction no
Boudouard reaction	${\text{CO}}_2\text{+ C}\to \text{2CO}$	(a)
Methanation reaction	${\text{2H}}_2\text{+ C}\to {\text{CH}}_4$	(b)
Water gasification	${\text{H}}_2\text{O + C}\to {\text{CO + H}}_2$	(c)
Water gas shift reaction	${\text{H}}_2\text{O + CO}\to {\text{CO}}_2{\text{+ H}}_2$	(d)

The global gasification reaction for air–steam gasification of MSW is written as follows:

e

$$\begin{array}{c}C{H}_s{O}_t{N}_u+w{H}_{2}O+\gamma H_{2}O+\lambda \left(O_2+3.76N_2\right)\\ \to {\alpha }_1{H}_2+{\alpha }_{2}CO+{\alpha }_{3}C{O}_2+{\alpha }_{4}C{H}_4+{\alpha }_5{H}_{2}O+{\alpha }_6{N}_2\\ \end{array}$$

By doing carbon balance,

1

$$1={\alpha }_2+{\alpha }_3+{\alpha }_4$$

By doing hydrogen balance,

2

$$s+2w+2\gamma =2{\alpha }_1+4{\alpha }_4+2{\alpha }_5$$

By doing oxygen balance,

3

$$t+w+\gamma ={\alpha }_2+2{\alpha }_3+{\alpha }_5$$

By doing nitrogen balance,

4

$$u=2{\alpha }_6$$

The quantity of moisture content in MSW is evaluated as follows:

5

$$w=\frac{M_{\text{MSW}}·\text{Moisture}}{M_{{\text{H}}_2\text{O}}·\left(\text{1 - Moisture}\right)·\left(1-\text{Ash}\right)}$$

Here, M_MSW is the molecular mass of segregated MSW, Moisture is the percentage of moisture content in MSW and Ash is the of ash content present in MSW in percentage. The steam-to-fuel ratio $\left(S/F\right)$ can be expressed as follows:

6

$$S\left./\phantom{SF}\right)F=\frac{M_{{\text{H}}_2\text{O}}·\gamma }{M_{\text{MSW}}+M_{{\text{H}}_2\text{O}}·w}$$

The lower calorific value (LCV_MSW) and higher calorific value (HCV_MSW) of the MSW are computed by the following correlations got from the work of Mendiburu et al. [18]:

7

$${\text{LCV}}_{\text{MSW}}={\text{HCV}}_{\text{MSW}}-h_{\text{fg}}\left(9\times H+\text{Moisture}\right)$$

8

$${\text{HCV}}_{\text{MSW}}=1178.3\times H+349.1\times C-15.1\times N-103.4\times O-21.1\times \text{Ash}$$

Cold gas efficiency (CGE) of the gasifier can be expressed in the following way:

9

$${\eta }_{\text{CGE}}=\frac{{\dot{m}}_{\text{pg}}·{\text{LCV}}_{\text{pg}}}{{\dot{m}}_{\text{MSW}}·{\text{LCV}}_{\text{MSW}}+{\dot{m}}_{\text{steam}}·H_{\text{steam}}+{\dot{Q}}_{\text{in}}}$$

SOFC

An internal reforming SOFC is considered for the present investigation. Three chemical reactions, viz, steam reforming, shifting and electrochemical reaction are presented below:

f

$${\text{CH}}_4{\text{+ 3H}}_2\text{O}\leftrightarrow {\text{CO + 3H}}_2\left(\text{Internal}\text{reforming}\right)$$

g

$${\text{CO + H}}_2\text{O}\leftrightarrow {\text{H}}_2+{\text{CO}}_2\left(\text{Water}-\text{gas}\text{shift}\text{reaction}\right)$$

h

$${\text{H}}_2+\frac{1}{2}{\text{O}}_2\leftrightarrow {\text{H}}_2\text{O}\left(\text{Electro}-\text{chemical}\text{reaction}\right)$$

The fuel utilisation factor in the SOFC stack is written as follows [19, 20]:

10

$$U_{\text{f}}=\frac{n_{{\text{H}}_2\text{,utilised}}}{n_{\text{H}_2^{}\text{,in}}^{}+n_{{\text{CH}}_4\text{,in}}+n_{\text{CO,in}}}$$

Equilibrium constants, K_r and K_s, for the corresponding reforming reaction along with water–gas shift reaction are as follows:

11

$$K_r=exp\left(-\frac{\mathrm{\Delta }{g}_r}{{\text{RT}}_{\text{cell}}}\right)$$

12

$$K_s=exp\left(-\frac{\mathrm{\Delta }{g}_s}{{\text{RT}}_{\text{cell}}}\right)$$

The Nernst equation for the reversible cell potential for the electrochemical reaction is written as:

13

$$E_{\text{nernst}}=-\frac{\mathrm{\Delta }{G}_0}{2F}-\frac{{\text{RT}}_{\text{cell}}}{2F}\left(\frac{p_{{\text{H}}_2\text{O}}}{p_{{\text{H}}_2}^{}.p_{{\text{O}}_2}^{0.5}}\right)$$where F is the Faraday’s number.

However, this equation does not take care of the losses occurring in the SOFC. The effective cell after considering all the losses in the main governing equation is given by:

14

$$E_{\text{net}}=E_{\text{nernst}}-E_{\text{loss}}$$

The voltage loss (total) is equal to the summation of three voltage losses, i.e. activation loss (E_act), ohmic loss (E_ohmic) and concentration loss (E_conc)

15

$$E_{\text{loss}}=E_{\text{act}}+E_{\text{conc}}+E_{\text{ohmic}}$$

Current flowing across each cell of the SOFC in terms of current density is given by:

16

$$i=j·A_{\text{cell}}$$

Power developed in every individual stack is given by:

17

$$W_{\text{SOFC,stack}}=N_{\text{cell}}·E_{\text{net}}·i$$where N_cell represent the number of cells

18

$$W_{\text{SOFC}}=W_{\text{SOFC,stack}}·N_{\text{SOFC}}$$where N_SOFC represent the number of SOFC stacks.

HRSG

The HRSG block consists of economiser, evaporator and superheater as its sub-components. The pressurised feedwater is allowed to the economiser flow at 20 bar pressure in order to raise the temperature of feedwater at a saturation temperature corresponding to the desired pressure. A feed pump (FP) has been incorporated pressurise the flow of inlet water stream to the pressure of steam turbine.

The electrical power input to the FP is evaluated by the following equation:

19

$$W_{\text{FP}}={\dot{m}}_{\text{fw}}·\left(h_{24}-h_{15}\right)$$

The feedwater at the exit of the economiser is surpassed to the evaporator to generate dry saturated steam and then to the superheater for the generation of superheated steam. The steam obtained from the exit of the turbine is then used for two purposes, i.e. for supplying steam to the gasifier and to heat the generator of the VAR. The energy balance equations are provided so as to determine the mass flow rate of feedwater and refrigerant of the bottoming VAR.

The heat balance equation between the flue gas and the feedwater in the economiser is expressed with the help of the following equation:

20

$${\dot{m}}_{\text{fg}}·\left(h_{12}-h_{13}\right)={\dot{m}}_{\text{fw}}·\left(h_{17}-h_{16}\right)$$

The heat balance equation in the evaporator is mentioned below:

21

$${\dot{m}}_{\text{fg}}·\left(h_{11}-h_{12}\right)={\dot{m}}_{\text{fw}}·H_{\text{vap}}$$

The heat balance equation in the superheater is written below:

22

$${\dot{m}}_{\text{fg}}·\left(h_{10}-h_{11}\right)={\dot{m}}_{\text{fw}}·\left(h_{21}-h_{20}\right)$$

Steam turbine

A steam turbine (ST) is taken into the present study where the turbine blades are allowed to rotate from the steam generated in the HRSG. The turbine inlet temperature is considered to be 550 °C and pressure of 20 bar at the base case conditions.

The electrical power output obtained from the ST is mentioned in Eq. (23):

23

$$W_{\text{ST}}={\dot{m}}_{\text{fw}}·\left(h_{21}-h_{22}-h_{23}\right)$$

VAR unit

A bottoming VAR unit has been incorporated for the above cogeneration plant for cooling purpose with aqua ammonia solution as the working fluid. In this VAR unit, the generator is heated with the help of the low-pressure steam from the turbine outlet. The amount of heat input, provided to the generator is given by the following expression:

24

$$Q_{\text{gen}}={\dot{m}}_{\text{steam}}·\left(h_{23}-h_{24}\right)$$

The refrigerant then transforms into gaseous phase, separating the refrigerant from the liquid solution, and surpasses the weak solution to a condenser while the strong solution retrieves back to the absorber post-surpassing thorough a solution valve.

The absorber load can be expressed in the following manner:

25

$$Q_{\text{abs}}={\dot{m}}_{\text{strong}}·\left(h_{30}-h_{29}\right)$$

The heat rejection in the condenser is provided in the following equation:

26

$$Q_{\text{Cond}}={\dot{m}}_{\text{weak}}·\left(h_{31}-h_{32}\right)$$

The amount of cooling load produced in the evaporator is given in the equation given below:

27

$$Q_{\text{eva}}={\dot{m}}_{\text{weak}}·\left(h_{35}-h_{36}\right)$$

The COP of a cooling plant is the ratio of refrigeration effect to the amount of energy given as input. For a VAR cycle, major energy input is the form of heat supplied to the generator (Q_gen). Some nominal power consumption occurs due to the solution pump (SP). Therefore, the COP of the bottoming VAR block can be expressed as follows:

28

$$\text{COP}=\frac{Q_{\text{eva}}}{Q_{\text{gen}}+W_{\text{SP}}}$$

By integrating the VAR cooling plant with the gasifier SOFC and by using the exhaust heat to run the cooling system, the plant saves substantial amount of input work if the cooling plant were to be operated separately using a conventional vapour compression refrigeration (VCR) cycle. It is thus pertinent to take that avoided compression work in estimating the overall generation efficiency of the plant and the same may be expressed as:

29

$${\eta }_{\text{gen}}=\frac{W_{\text{SOFC}}+W_{\text{ST}}+W_{\text{EVA}}-W_{\text{AC}}-W_{\text{FP}}-W_{\text{SP}}}{{\dot{m}}_{\text{MSW}}·{\text{LCV}}_{\text{MSW}}}$$where $W_{\text{EVA}}$ is the amount of compressor work saved by a VAR system.

The operating ranges of the major input parameters of the plant are illustrated in Table 3.

Table 3. Operating ranges for various input parameters

Block	Parameter (s)	Operating range
Gasifier	Air–fuel equivalence ratio	0.20–0.35
	Steam-to-fuel (S/F) ratio	1.0–2.5
	Reactor temperature	700–1000 °C
	Fuel utilisation factor	0.65–0.90
SOFC	Current density	2000–8000 A/m2
	Fuel cell temperature	800–1000 °C
	Steam turbine inlet temperature	450–600 °C
HRSG	Condensate extraction pump pressure	20–50 bar
	Generator temperature	120–130 °C
VAR	Evaporator temperature	− 10–10 °C
	Condenser temperature	25–40 °C

For an initial thermodynamic assessment of the proposed plant, a base case condition is identified and the input parameters at the base case operating conditions are mentioned in Table 4.

Table 4. Base case operating parameters

Input parameters	Value(s)	Units
Steam turbine inlet temperature	550	°C
Air inlet conditions	1, 25	Bar, °C
Gasifier temperature	800	°C
Air–fuel equivalence ratio $\left(\lambda \right)$	0.20	–
Steam-to-fuel (S/F) ratio	1.5	–
Fuel utilisation factor	0.8	–
Current density	2000	A/m2
SOFC inlet temperature	700	°C
Feed pump pressure	20	Bar
Generator temperature	120	°C
Condenser pressure	0.08	Bar
Evaporator temperature of VAR	− 10	°C

Exergetic assessment

By finding exergy value at any state point, the finest possible thermodynamic performance of any plant can be determined. Exergy at any state point takes into account physical as well as chemical exergy. The physical exergy at a particular state point is provided with the given equation [19]:

30

$${\text{Ex}}_{\text{phy}}=\dot{m}·\left(h-h_0-T_0·\left(s-s_0\right)\right)$$

The chemical exergy at any state point determined with the help of the given equation:

31

$${\text{Ex}}_{\text{che}}=R{T}_0·\left(\sum y_{i}ln\left(y_i\right)\right)+\sum y_i·{\text{ex}}_i^{\text{ch}}$$

Fuel exergy (input to the plant) of MSW can be determined as:

32

$${\text{Ex}}_{\text{MSW}}={\dot{m}}_{\text{MSW}}·{\text{Ex}}_{\text{che,MSW}}$$where ${\text{Ex}}_{\text{che,MSW}}$ is the chemical exergy of the MSW expressed in the following way:

33

$${\text{Ex}}_{\text{che,MSW}}=\xi ·{\text{LCV}}_{\text{MSW}}$$

The chemical exergy coefficient $\xi$ is evaluated by the following correlation [21]:

34

$$\xi =\frac{0.016\frac{H}{C}+1.044-0.3449\frac{O}{C}\left(5.31\times {10}^{-2}\frac{H}{C}+1\right)}{1-4.12\times {10}^{-2}\frac{O}{C}}$$

Now, the refrigeration effect (exergetic), ${\text{Ex}}_R$ produced is written as follows:

35

$${\text{Ex}}_R=Q_{\text{EVA}}·\left(\frac{T_0}{T_{\text{EVA}}}-1\right)$$

Within a given control volume, the amount exergy destruction occurring in a particular component is expressed as follows:

36

$${\text{ED}}_{\text{comp}}=\sum _j{Q}_j\left(1-\frac{T_0}{T_j}\right)-W_{\text{CV}}+\sum E_{\text{in}}\sum E_{\text{out}}$$

Table 5 presents the exergy destruction rate and exergetic efficiency value of every individual plant component.

Table 5. Exergy destruction and exergetic efficiency of different components of cogeneration plant

Component	Exergy destruction	Exergetic efficiency
Gasifier	${\text{ED}}_{\text{gasf}}={\text{Ex}}_1+{\text{Ex}}_2+{\text{Ex}}_{22}-{\text{Ex}}_3$	${\eta }_{\text{gasf}}=\frac{{\text{Ex}}_3}{{\text{Ex}}_1+{\text{Ex}}_2+{\text{Ex}}_{22}}$
Solid oxide fuel cell (SOFC)	$\begin{array}{cc}\hfill {\text{ED}}_{\text{SOFC}}& ={\text{Ex}}_3+{\text{Ex}}_7-{\text{Ex}}_4\hfill \\ \hfill & {-}_8-W_{\text{SOFC}}\hfill \\ \hfill \end{array}$	${\eta }_{\text{SOFC}}=\frac{W_{\text{SOFC}}}{\left({\text{Ex}}_3-{\text{Ex}}_4\right)+\left({\text{Ex}}_7-{\text{Ex}}_8\right)}$
Afterburner (AB)	${\text{ED}}_{\text{AB}}={\text{Ex}}_4+{\text{Ex}}_8-{\text{Ex}}_9$	${\eta }_{\text{AB}}=\frac{{\text{Ex}}_9}{{\text{Ex}}_4+{\text{Ex}}_8}$
Air heat exchanger (AHX)	${\text{ED}}_{\text{AHX}}={\text{Ex}}_6+{\text{Ex}}_9-{\text{Ex}}_7-{\text{Ex}}_{10}$	${\eta }_{\text{AHX}}=\frac{{\text{Ex}}_6-{\text{Ex}}_7}{{\text{Ex}}_9-{\text{Ex}}_{10}}$
Air compressor (AC)	${\text{ED}}_{\text{AC}}=W_{\text{AC}}+{\text{Ex}}_5-{\text{Ex}}_6$	${\eta }_{\text{AC}}=\frac{{\text{Ex}}_5-{\text{Ex}}_6}{W_{\text{AC}}}$
Steam turbine (ST)	${\text{ED}}_{\text{ST}}={\text{Ex}}_{21}-{\text{Ex}}_{22}-{\text{Ex}}_{23}-W_{\text{ST}}$	${\eta }_{\text{ST}}=\frac{W_{\text{ST}}}{{\text{Ex}}_{21}-{\text{Ex}}_{22}-{\text{Ex}}_{23}}$
Superheater (Sup)	${\text{ED}}_{\text{Sup}}={\text{Ex}}_{10}+{\text{Ex}}_{20}-{\text{Ex}}_{11}-{\text{Ex}}_{21}$	${\eta }_{\text{Sup}}=\frac{{\text{Ex}}_{20}-{\text{Ex}}_{21}}{{\text{Ex}}_{10}-{\text{Ex}}_{11}}$
Evaporator (Evap)	${\text{ED}}_{\text{evap}}={\text{Ex}}_{11}+{\text{Ex}}_{19}-{\text{Ex}}_{12}-{\text{Ex}}_{18}$	${\eta }_{\text{Evap}}=\frac{{\text{Ex}}_{18}-{\text{Ex}}_{19}}{{\text{Ex}}_{11}-{\text{Ex}}_{12}}$
Economiser (Econ)	${\text{ED}}_{\text{econ}}={\text{Ex}}_{16}+{\text{Ex}}_{12}-{\text{Ex}}_{13}-{\text{Ex}}_{17}$	${\eta }_{\text{Econ}}=\frac{{\text{Ex}}_{16}-{\text{Ex}}_{17}}{{\text{Ex}}_{12}-{\text{Ex}}_{13}}$
Feed pump (FP)	${\text{ED}}_{\text{FP}}=W_{\text{FP}}+{\text{Ex}}_{24}-{\text{Ex}}_{15}$	${\eta }_{\text{FP}}=\frac{{\text{Ex}}_{24}-{\text{Ex}}_{15}}{W_{\text{FP}}}$
Generator (Gen)	${\text{ED}}_{\text{Gen}}={\text{Ex}}_{23}+{\text{Ex}}_{25}-{\text{Ex}}_{24}-{\text{Ex}}_{26}$	${\eta }_{\text{Gen}}=\frac{{\text{Ex}}_{25}-{\text{Ex}}_{26}}{{\text{Ex}}_{23}-{\text{Ex}}_{24}}$
Condenser (Cond)	${\text{ED}}_{\text{Cond}}={\text{Ex}}_{31}+{\text{Ex}}_{35}-{\text{Ex}}_{32}-{\text{Ex}}_{36}$	${\eta }_{\text{Cond}}=\frac{{\text{Ex}}_{31}-{\text{Ex}}_{32}}{{\text{Ex}}_{35}-{\text{Ex}}_{36}}$
Absorber (Abs)	$\begin{array}{cc}\hfill E{D}_{\text{Abs}}& ={\text{Ex}}_{33}+{\text{Ex}}_{29}+{\text{Ex}}_{28}\hfill \\ \hfill & -{\text{Ex}}_{30}-{\text{Ex}}_{34}\hfill \\ \hfill \end{array}$	${\eta }_{\text{Abs}}=\frac{{\text{Ex}}_{29}-{\text{Ex}}_{30}}{{\text{Ex}}_{33}-{\text{Ex}}_{34}}$
Evaporator (EVA)	${\text{ED}}_{\text{Eva}}={\text{Ex}}_{35}+{\text{Ex}}_{28}-{\text{Ex}}_{36}-{\text{Ex}}_{29}$	${\eta }_{\text{Eva}}=\frac{{\text{Ex}}_{35}-{\text{Ex}}_{36}}{{\text{Ex}}_{28}-{\text{Ex}}_{29}}$
Solution valve (SV)	${\text{ED}}_{\text{SV}}={\text{Ex}}_{37}-{\text{Ex}}_{38}$	${\eta }_{\text{SV}}=\frac{{\text{Ex}}_{38}}{{\text{Ex}}_{37}}$
Expansion valve (EV)	${\text{ED}}_{\text{EV}}={\text{Ex}}_{27}-{\text{Ex}}_{28}$	${\eta }_{\text{EV}}=\frac{{\text{Ex}}_{27}}{{\text{Ex}}_{28}}$
Solution pump (SP)	${\text{ED}}_{\text{SP}}=W_{\text{SP}}+{\text{Ex}}_{30}-{\text{Ex}}_{25}$	${\eta }_{\text{SP}}=\frac{{\text{Ex}}_{30}-{\text{Ex}}_{25}}{W_{\text{SP}}}$

Finally, the overall exergetic efficiency can be written in the following manner:

37

$${\eta }_{\text{ex}}=\frac{W_{\text{SOFC}}+W_{\text{ST}}-W_{\text{AC}}-W_{\text{FP}}-W_{\text{SP}}+Q_{\text{EVA}}.\left(\frac{T_0}{T_{\text{EVA}}}-1\right)}{E{x}_{\text{MSW}}}$$where ${\text{Ex}}_{\text{MSW}}$ is the input fuel exergy, i.e. MSW.

Economic assessment

Economic assessment of any plant is performed in order to decipher whether the proposed system is financially acceptable. The economic aspects of the plant are deduced preliminarily by a parameter known as cost of electricity (COE) of the plant. The COE is evaluated as follows [22].

38

$$\text{COE}=\frac{Z_{\text{CAP}}+Z_{\text{O/M}}+Z_{\text{fuel}}}{P_{\text{AE}}}$$

The annual electricity delivery of the proposed cogeneration plant, P_AE, is expressed as follows:

39

$$P_{\text{AE}}=W_{\text{net}}·H·\text{PCF}·\left(1-A_{\text{P}}\right)·\left(1-L_P\right)$$

The standard value for PCF, i.e. plant capacity factor, is 0.85, that for L_p, i.e. power loss from transmission lines, is 0.10, and that for A_p, i.e. auxiliary components’ power consumption, is 0.04.

The fuel cost, i.e. Z_fuel, can be computed as follows [22]:

40

$$Z_{\text{fuel}}={\text{CF}}_{\text{fuel}}·{\dot{m}}_{\text{MSW}}·{\text{LCV}}_{\text{MSW}}·\text{YOH}·3600$$where CF_fuel is the price of fuel taken as 0.0073 USD/MJ.

Yearly capital cost of the plant is evaluated as follows:

41

$$Z_{\text{CAP}}=Z_{\text{TOC}}·\text{CRF}$$

The expression for capital recovery factor is mentioned below:

42

$$\text{CRF}=\frac{{\left(r+1\right)}^{\theta }·r}{{\left(r+1\right)}^{\theta }-1}$$where $\theta$ and r represent the plant life (assumed as 20 years) and the discount rate, respectively.

The value discount rate is determined with the help of the equation given below:

43

$$r=\frac{N_0-f_{\text{annual}}}{f_{\text{annual}}+1}$$where $N_0$ and $f_{\text{annual}}$ are nominal interest rate and annual inflation rate, respectively.

Z_TOC of the plant is determined by the given equation:

44

$$Z_{\text{TOC}}=Z_{\text{TPC}}·\left(1+f_{\text{TOC}}\right)$$

The correction factor, f_TOC, considering preproduction cost, financing, inventory and capital cost and owner’s fees is taken to be 20.2% [22].

The overall price of the plant can be calculated by the following equation:

45

$$Z_{\text{TPC}}=Z_{\text{EPCC}}·\left(1+f_{\text{TPC}}\right)$$

The engineering, procurement and construction cost, ZEPCC, is expressed as follows:

46

$$Z_{\text{EPCC}}=Z_{\text{equipment}}·\left(1+f_{\text{EPCC}}\right)$$

The EPCC correction factor, i.e. f_EPCC value, is taken as 10%.

The total equipment cost of the components of the plant accessories is evaluated as follows:

47

$$Z_{\text{equipment}}=\sum Z_{\text{components}}$$

The cost functions of plant components are written in the form of some correlations mentioned by earlier researchers in Table 6. All the cost functions are in terms of USD.

Table 6. Different plant components and their cost functions

Component	Cost functions	Reference(s)
Gasifier	$Z_{\text{Gasifier}}=1600·{\left(3600·{\dot{m}}_{\text{fuel}}\right)}^{0.67}$	[23]
Afterburner (AB)	$Z_{\text{AB}}=\frac{46.08\times {\dot{m}}_{\text{air}}}{0.995-\frac{p_{\text{out}}}{p_{\text{in}}}}\times \left[1+exp\left(0.018\times T_c-26.4\right)\right]$	[5, 24]
Air compressor	$Z_{\text{AC}}=\frac{72\times {\dot{m}}_{\text{air}}}{0.9-{\eta }_{i,\text{AC}}}·p_r·ln\left(p_r\right)$	[25]
Air heat exchanger	$Z_{\text{AHX}}=4122·{\left(A_{\text{AHX}}\right)}^{0.6}$	[26]
Steam turbine (ST)	$Z_{\text{ST}}=6000·{\left(W_{\text{ST}}\right)}^{0.7}$	[26]
HRSG	$Z_{\text{HRSG}}=6570\left[\begin{array}{c}{\left(\frac{Q_{\text{SUP}}}{{\text{LMTD}}_{\text{SUP}}}\right)}^{0.78}+{\left(\frac{Q_{\text{ECON}}}{{\text{LMTD}}_{\text{ECON}}}\right)}^{0.78}\\ +{\left(\frac{Q_{\text{EVAP}}}{{\text{LMTD}}_{\text{EVAP}}}\right)}^{0.78}+21276{\dot{m}}_{\text{fw}}+1184.4{\left({\dot{m}}_{\text{fg}}\right)}^{1.2}\\ \end{array}\right]$	[26]
SOFC	$Z_{\text{SOFC}}=A_{\text{SOFC}}\left(2.96\times T_{\text{Cell}}-1907\right)$	[19]
VAR	$Z_{\text{VAR}}=1143.3{\left(Q_{\text{eva}}\right)}^{0.67}$	[9]

The operational and maintenance cost (on annual basis) can be calculated as follows:

48

$$Z_{\text{O/M}}=0.04\times Z_{\text{CAP}}$$

But for the proposed cogeneration plant, there is no requirement of electricity for producing any refrigeration effect separately. So, the COE term is tailored with another parameter; effective cost of electricity (ECOE). The ECOE takes into account (on yearly basis), the electricity extractable from the plant as well as the electricity avoided for cooling purpose, which is equivalent to the electricity input supplied to a compressor when a vapour compression refrigeration (VCR) system is incorporated for refrigeration. The ECOE is given by the following expression [22]:

49

$$\text{ECOE}=\frac{Z_{\text{O/M}}+Z_{\text{CAP}}+Z_{\text{fuel}}}{P_{\text{AE}}+P_{\text{AEC}}}$$

Electricity avoided per annum for cooling plant, i.e. P_AEC, is expressed as follows:

50

$$P_{\text{AEC}}=\frac{\text{DCL}·365}{{\text{COP}}_{\text{std}}}$$where DCL represent the cooling effect achievable on daily basis from the bottoming VAR block and COP_std is the COP of a conventional VCR system, generally taken as 4.

However, only the parameter ECOE does not present the holistic economic performance of the modelled plant. Additionally, it is perceived that ECOE value elevates with elevated discount rates. Thus, a payback analysis is also necessary along with the calculation of cost of electricity. Further, net present value (NPV) is representative of the present investment value which can be perceived as the sum total of all credited discounted cash inflows.

The NPV is expressed with the help of the following equation [22]:

51

$$\text{NPV}=-C_0+\sum _{k=1}^{\theta }\frac{C_k}{{\left(1+r\right)}^k}$$

The total annualised cash inflow for the kth year is represented by C_i. The overall initial investment the plant is represented by C₀ which is same as the total overnight capital, $Z_{\text{TOC}}$.

For computing the discounted period of payback, the NPV value has to be zero. After modifying and doing some rearrangements in Eq. (51), it is rewritten as follows:

52

$$C_0=\sum _{k=1}^{{\theta }^{\prime }}\frac{C_k}{{\left(1+r\right)}^k}$$

The discounted period of payback is represented by the symbol, ${\theta }^{\prime }$.

Environmental assessment

Environmental concerns have been a burning and debatable issue for setting up any power or cogeneration plants. Governments from various countries have been rolling out certain schemes for curbing the effect of greenhouse gases and global warming. One such scheme is going carbon–neutral or carbon-negative. Prior to setting up any plant, its carbon emission is kept into check by a parameter known by specific CO₂ emission (${\psi }_{{\text{CO}}_2}$).

Specific CO₂ emission (${\psi }_{{\text{CO}}_2}$) is computed as follows [26]:

53

$${\psi }_{{\text{CO}}_2}=\frac{n_{{\text{CO}}_2}·M_{{\text{CO}}_2}·3600}{W_{\text{net}}}$$where $n_{{\text{CO}}_2}$ represents the number of moles of CO₂ present in the burnt gas.

Besides other parameters such as sustainability index (SI) and total annualised carbon capture (TACC) are taken into consideration. The measurement of overall contribution done towards the sustainability of the environment is defined via sustainability index.

SI of the modelled plant is determined as:

54

$$\text{SI}=\frac{1}{1-{\eta }_{\text{ex}}}$$

As a considerable quantity of carbon dioxide is utilised as fuel to the SOFC, so some CO₂ is absorbed annually. The total annualised carbon capture (TACC) is given by the following equation:

55

$$\text{TACC}=\text{MFR}\_ABG·n_{{\text{CO}}_2}·M_{{\text{CO}}_2}·\left(\frac{\text{YOH}·3600}{1000}\right)$$

The annual environmental benefit obtained from CO₂ capture by considering environmental damage cost (${\text{EDC}}_{{\text{CO}}_2}$) is written as follows:

56

$$\text{AEBCC}=\text{TACC}·{\text{EDC}}_{{\text{CO}}_2}$$

${\text{EDC}}_{{\text{CO}}_2}$ value is taken to be USD 150/ton.

Exergo-economic assessment

Exergo-economic analysis of any plant is done for checking out the thermodynamic as well as the economic feasibility of the plant. Specific exergy costing (SPECO) technique has been adopted for carrying the exergo-economic analysis of the proposed cogeneration plant. This method comprehensively involves three crucial steps: firstly, exergy flows at all the thermodynamic state point evaluation, secondly, development of stream-wise exergo-economic equations of each of the involved plant components and thirdly, modifications of the stream-wise equations in line with the product and fuel exergy values.

The principal equation for stream-based exergy flows associated with the total cost rate is mentioned in the subsequent equation:

57

$$\sum _{j=1}^n{\left(c_j·E{x}_j\right)}_{\text{in}}+\dot{C}=\sum _{j=1}^n{\left(c_j·E{x}_j\right)}_{\text{out}}$$where $\dot{C}$ is the indicative cost rate of the plant components considering both capital as well as operational and maintenance cost. Thus, Eq. (55) can be modified in terms of fuel exergy (responsible for generating cause) and product exergy (responsible for producing effect) as:

58

$$c_f·{\text{Ex}}_{\text{f}}+\dot{C}=c_p·{\text{Ex}}_{\text{p}}$$

Stream exergy associated with both fuel as well as the product exergy rates is computed by incorporating F-rule and P-rule suggested by Lazzaretto and Tsatsaronis [16]. Cost rate of each plant component is evaluated as a function of the total cost (C) of a plant component, the yearly operational hours (YOH) and the capital recovery factor (CRF) and is expressed as follows:

59

$$\dot{C}=\left(\frac{\text{CRF}}{\text{YOH}}\right)·c$$

Table 7 presents the cost balance equations along with certain auxiliary equations of respective components.

Table 7. Cost balance equations for exergo-economic analysis of the cogeneration plant

Plant components	Equations for cost balance	Auxiliary equations
Gasifier	$c_1·{\text{Ex}}_1+c_2·{\text{Ex}}_2+c_{22}·{\text{Ex}}_{22}+{\dot{C}}_{\text{gasifier}}=c_3·{\text{Ex}}_3$	_
Afterburner	$c_4·{\text{Ex}}_4+c_8·{\text{Ex}}_8+{\dot{C}}_{\text{CC}}=c_9·{\text{Ex}}_9$	_
Air heat exchanger (AHX)	$c_3·{\text{Ex}}_3+c_6·{\text{Ex}}_6+{\dot{C}}_{\mathit{AHX}}=c_7·{\text{Ex}}_7+c_{10}·{\text{Ex}}_{10}$	$c_9=c_{10}$
Air compressor (AC)	$c_5·{\text{Ex}}_5+{\dot{C}}_{\text{AC}}+c_{\text{Motor}}·W_{\text{AC}}=c_6·{\text{Ex}}_6$	$c_5=0$
Steam turbine (ST)	$c_{21}·{\text{Ex}}_{21}+{\dot{C}}_{\text{ST}}=c_{22}·{\text{Ex}}_{22}+c_{23}·{\text{Ex}}_{23}+c_{\text{Shaft}}·W_{\text{ST}}$	$c_{22}=c_{23}$
Evaporator (HRSG)	$c_{18}·{\text{Ex}}_{18}+c_{11}·{\text{Ex}}_{11}+{\dot{C}}_{\text{Evap}}=c_{12}·{\text{Ex}}_{12}+c_{19}·{\text{Ex}}_{19}$	$c_{10}=c_{11}$
Economiser	$c_{16}·{\text{Ex}}_{16}+c_{12}·{\text{Ex}}_{12}+{\dot{C}}_{\text{Econ}}=c_{13}·{\text{Ex}}_{13}+c_{17}·{\text{Ex}}_{17}$	$c_{11}=c_{12}$
Feed Pump (FP)	$c_{24}·{\text{Ex}}_{24}+{\dot{C}}_{\mathit{FP}}+c_{\text{Motor}}·W_{\text{FP}}=c_{15}·{\text{Ex}}_{15}$	–
Generator	$c_{25}·{\text{Ex}}_{25}+c_{23}·{\text{Ex}}_{23}+{\dot{C}}_{\text{Gen}}=c_{26}·{\text{Ex}}_{26}+c_{24}·{\text{Ex}}_{24}$	$c_{12}=c_{13}$ $c_{19}=c_{20}$
Condenser	$c_{31}·{\text{Ex}}_{31}+c_{26}·{\text{Ex}}_{26}+{\dot{C}}_{\text{Cond}}=c_{32}·{\text{Ex}}_{32}+c_{27}·{\text{Ex}}_{27}$	$c_{27}=c_{26}$
Evaporator (VAR)	$c_{28}·{\text{Ex}}_{28}+c_{35}·{\text{Ex}}_{35}+{\dot{C}}_{\mathit{Eva}}=c_{36}·{\text{Ex}}_{36}+c_{29}·{\text{Ex}}_{29}$	$c_{29}=c_{28}$
Absorber	$c_{29}·{\text{Ex}}_{29}+c_{33}·{\text{Ex}}_{33}+{\dot{C}}_{\text{Abs}}=c_{30}·{\text{Ex}}_{30}+c_{34}·{\text{Ex}}_{34}$	$c_{29}=c_{30}$
Expansion valve (EV)	$c_{27}·{\text{Ex}}_{27}+{\dot{C}}_{\mathit{EV}}=c_{28}·{\text{Ex}}_{28}$	_
Solution valve (SV)	$c_{37}·{\text{Ex}}_{37}+{\dot{C}}_{\mathit{SV}}=c_{38}·{\text{Ex}}_{38}$	_
Solution pump (SP)	$c_{30}·{\text{Ex}}_{30}+{\dot{C}}_{\text{SP}}+c_{\text{Motor}}·W_{\text{SP}}=c_{25}·{\text{Ex}}_{25}$	_

By computing all such equations, the specific fuel exergy cost rate (c_f) and specific product exergy cost rate (c_p) associated can be deduced. The cost function responsible for exergy destruction of any component is computed by the following equation:

60

$${\dot{C}}_{D,j}=c_{\text{f},j}·E{D}_j$$

Finally, the exergo-economic key parameters like relative cost difference, rk, and the exergo-economic factor, f, are evaluated below [27]:

61

$$r_k=\left(c_{\text{p}}-c_{\text{f}}\right)/c_{\text{f}}$$

62

$$f=\frac{\dot{C}}{{\dot{C}}_{D,j}+{\dot{C}}_{L,j}+\dot{C}}$$where ${\dot{C}}_{L,j}$ is the cost function that accounts for exergy losses of the cogeneration plant.

Results and discussions

The proposed cogeneration plant has been numerically investigated in terms of its exergo-enviro-economic analyses. Before carrying out the numerical simulation, the computational model has been first validated from a reported literature source, and then, favourable operating conditions are been established from the reported plots. After exploring the favourable operating conditions, all the relevant output parameters are being written one by one for analysing the overall performance of the proposed plant.

Model validation

The integrated plant model is a combination of several component models built and integrated to simulate a combined power and cooling plant. A steady-state consideration allowed the authors to exclude transient conditions which could be a separate case study altogether for such a complex system. The two main component models, which are critical for the assessment of the integrated plant, are the SOFC and the gasifier models. The SOFC is the main power-producing unit of the plant, and its electrochemical activity is greatly influenced by the anode gas, which, in the present configuration, is the product gas derived from gasification. This necessitated the validation of the SOFC model and the gasifier model.

SOFC model validation

The SOFC model validation has been done with the reported experimental work of Tao et al. [28], presented in Table 8. The operating conditions have been taken similar to that of Tao et al. [28]. The simulated results obtained from establishing custom-built model ascertain that the data obtained synchronised well with that of the experimental one along with the maximum error obtained from every set of data point in the range of 2%–5%.

Table 8. Validation of the results of the SOFC model with Tao et al. [28]

Current density (A/m2)	Cell voltage (V) (simulated)	Cell voltage (V) (experimental)	Error (%)
2000	0.73	0.7124	2.47
3000	0.66	0.64	3.125
4000	0.62	0.59	5.08
5000	0.55	0.523	5.163
6000	0.49	0.468	4.7

Gasifier model validation

The producer gas data obtained from the gasifier model has been validated with the reported experimental work of Loha et al. [29] illustrated in Table 9. It is observed that the simulated results obtained from the Cycle Tempo model synchronised well with the experimental data of Loha et al. [29]. The root mean square (RMS) error obtained from every set of data point is in the range 4%–8%. However, the RMS error obtained for the gas data of methane is not taken into consideration as the methane content for the producer gas is very insignificant, leading to relatively large RMS values.

Table 9. Validation of the producer gas data (modelled) with that of experimental one [29]

Gas	H2		CO		CO2		CH4
STBM	Simulated work	Exp. work	Simulated work	Exp. work	Simulated work	Exp. work	Simulated work	Exp. work
0.75	51.32	48.5	19.88	21.5	21.61	20.81	0.11	0.09
1	53.57	49.6	18.25	20.33	22.08	21.7	0.06	0.07
1.25	55.12	50.25	15.76	17.5	23.71	22.62	0.04	0.05
1.5	53.26	50.75	13.87	14.95	24.96	23.89	0.02	0.03
1.75	54.12	51.1	12.37	11.87	25.94	24.41	0.02	0.03
2	55.81	52	11.16	10.5	26.73	25.66	0.01	0.02

As the two major component models stand validated, the process model of the cogeneration plant, which, besides the SOFC and the gasifier, integrates other usual heat and mass transfer processes (based on standard applicable thermodynamic relations and for which standard component modules are readily available in Cycle Tempo), becomes a credible tool for analysing the energetic and exergetic performance of the integrated plant. Results obtained from energetic and exergetic simulations were used in the subsequent economic, exergo-economic and environmental assessments of the proposed plant.

Energetic–exergetic performance at the base case

The key performance parameters of the plant for the base case are shown in Table 10

Table 10. Output parameters of the plant obtained at the base case scenario

Output parameter	Results obtained	Units (if any)
Overall generation efficiency	46.73	%
Exergetic efficiency	41.86	%
SOFC Power	339	kW
ST Power	120	kW
Net Power	429	kW
Net cooling effect	129	kW
Cooling-to-power ratio (CTPR)	0.3	–
Specific CO2 emission	1.03	kg/kWh
Environmental sustainability index (SI)	1.7	–

Impact of current density

The influence of current density on performance of the SOFC for three different fuel utilisation factor values is illustrated in Fig. 2. It is observed from the figure that the net power output surges with current density. With rise of current density value, fuel consumption by SOFC increases leading to high power generation at the SOFC. Along with the increase in fuel consumption, oxidant requirement for the SOFC also escalates. However, the fuel consumption increases in the gasifier to satisfy the increased fuel flow rate into the SOFC with current density. The increase in fuel consumption is more than the rise in total plant output. So after a certain point, one can observe a decrement in the SOFC power output.

[See PDF for image]

Fig. 2

Effect of current density on SOFC power output

Impact of fuel utilisation factor

Figure 3 shows the influence of fuel utilisation factor over the electrical and exergetic efficiencies. It is seen that both electrical and exergetic efficiencies increase with the fuel utilisation factor. The reason is that when more fuel is utilised, more SOFC power is obtained from a given current density which in turn adds more net power output to the plant. Thus, the efficiency values of the plant are enhanced.

[See PDF for image]

Fig. 3

Impact of U_f on thermodynamic performance parameters of the plant

Figure 4 shows the influence of fuel utilisation factor on the net power and net cooling effect of the plant. From the graph, it is noted that the net power output from the plant increases but simultaneously the net cooling of the plant decreases with the increase of fuel utilisation factor. This happens so because when more fuel is utilised, more power output is obtained from the SOFC and more output is obtained from the steam turbine also as more energy is available from the hot flue gas. Thus, with increase in fuel utilisation factor, the net power produced increases which in turn raise the efficiency of the plant. However, the net cooling deteriorates as the energy available from the waste heat becomes low enough to produce desirable cooling.

[See PDF for image]

Fig. 4

Impact of U_f on net power and net cooling effect

Impact of air–fuel equivalence ratio

Figure 5 shows the influence of equivalence ratio on the output performance parameters of the gasifier. Trends reveal that the gasifier parameters, i.e. the LHV of syngas and cold gas efficiency, deteriorate with the increment of equivalence ratio. This reason behind this observation is that when the equivalence ratio is enhanced the air–fuel mixture is made leaner which implies more amount of air provided as input for the same amount of fuel. Due to flame dilution, the air–fuel mixture results in quick termination of the gasification process. As the maximum thermodynamic performance is observed at equivalence ratio value of 0.2, so the favourable operating conditions are taken to be equivalence ratio value 0.2 for carrying the exergo-economic assessment of the proposed cogeneration plant.

[See PDF for image]

Fig. 5

Effect of air–fuel equivalence ratio on gasifier performance

Impact of S/F ratio

The impact of steam-to-fuel (S/F) ratio on the thermo-economic performance parameters have been plotted in Fig. 6. The figure shows that there is a very little decrement in the thermodynamic performance parameters. This is because with increase in the S/F ratio, the gasification efficiency is enhanced but the amount of steam generated increases for every unit mass of fuel which increases the input supplied to the plant. So, one can see a drop in the electrical and exergetic efficiency values.

[See PDF for image]

Fig. 6

Impact of steam-to-fuel ratio on thermal performance parameters

Exergy destruction in different plant components

Exergy analysis determines which component is responsible for maximum exergy destruction, the amount of useful exergy obtained from the plant and the exergy flow diagram of different streams of working fluids and exergy destructions in the individual plant components. Figure 7 shows the exergy destruction of different components of the proposed cogeneration plant. From the figure, a very high exergy destruction is observed in the gasifier. This is primarily because of the reactions and the associated irreversibilities that occur inside the gasifier that operates at a temperature much higher that the environment. So, the gasifier is realised to be the most vulnerable component from the exergy point of view. The SOFC has its own irreversibilities, manifested in the different types of losses accounted for in the SOFC model (as discussed in Sect. 2.1). Combustors and heat exchangers also contribute to the exergy destruction because of combustion reaction (afterburner, AB) or because of heat exchange across large temperature difference. If the bottoming VAR cycle is taken into account, the evaporator suffers the maximum exergy destruction because a considerable amount of heat is rejected from the evaporator for producing cooling effect.

[See PDF for image]

Fig. 7

Exergy destruction of different plant components

Exergy flow diagram of different units of the plant

Figure 8 illustrates the exergy flow diagram of the proposed cogeneration plant at the optimised scenario. In this configuration, the input exergy of 1097 kW is provided to the gasifier to generate syngas which can be further used as fuel to the SOFC unit. The DC power output obtained the SOFC is 339 kW. From the SOFC, the streams of air and syngas are sent to the afterburner for combustion. The flue gas generated from the afterburner is first sent to the air heat exchanger to preheat the inlet air before sending to the cathode of SOFC. After preheating, the flue gas stream is then sent to the HRSG unit for production of superheated steam. The high-pressure, high-temperature superheated steam is then fed to the steam turbine (ST) for rotating the turbine blades for the generation of electricity. The amount of electricity produced from the steam turbine unit is 138 kW. The remaining exergy hereby has the potential to generate a refrigeration effect of 278 kW. The figure also talks about the exergy loss of the proposed plant being only 94 kW. The VAR block has the potential to generate an exergetic cooling or refrigeration effect of almost 5 kW. Thus, it can be deduced that by integrating the bottoming refrigerating cycle with the power generating SOFC and ST units, the exergy is judiciously utilised. The components of the VAR have a cumulative exergy destruction of just 65 kW. Thus, the given cogeneration plant has the ability to generate 450–550 kW of electricity and cooling of around 100–150 kW.

[See PDF for image]

Fig. 8

Stream of exergy flow and exergy destruction of every plant component

Figure 9 shows a pie chart showing that the percentage of useful exergy obtained is 43.8% and the percentage of exergy destruction occurring due to different plant components is 47.61% of the total input fuel exergy of the plant. Given figure also reveals that the stack loss is just 8.59% of the total exergy input.

[See PDF for image]

Fig. 9

Pie chart depicting useful exergy, exergy destruction and stack loss

Environmental analysis

As mentioned earlier, environmental aspects are also taken into consideration prior to setting up of any plant. So, firstly the specific CO₂ emission is kept into check. At the favourable operating conditions, the specific CO₂ emission is found to be low as 0.8 kg/kWh along with the environmental sustainability index of the plant being 1.8 which is on the higher side. This is so because the amount of carbon dioxide present at the exit of the afterburner is present in traceable amount. Also, the computed value of the total annual CO₂ capture is expected to be 65,000 tons per annum. From this CO₂ capture, the penalty imposed by different countries due to CO₂ emission can be mitigated by almost USD 9.7 million per annum which can further boost the economic aspects of the plant.

Figure 10 shows the impact of S/F ratio on specific CO₂ emission at three different fuel utilisation factor values. It is observed from the figure that the specific CO₂ emission decreases initially with increase in S/F ratio. With increase in S/F ratio, yields of gasification reactions also increase up to a certain point with no further improvement thereafter. Higher S/F ratio also means an increased steam generation requiring more furl and consequent more combustion in the afterburner. As a result, net CO₂ emission starts increasing after a certain optimum value of S/F ratio (lowest emission occurring at S/F of 1.5).

[See PDF for image]

Fig. 10

Impact of S/F ratio on specific CO₂ emission

Exergo-economic performance

Exergo-economic performances of individual components of the proposed cogeneration plant are illustrated in Table 11 at the favourable operational conditions, which are: S/F = 1.5, $\lambda$ = 0.20, U_f = 0.8 and TIT = 550 °C.

Table 11. Exergo-economic assessment of the proposed cogeneration plant

Plant components	$c_{\text{f}}$($/MJ)	$c_{\text{p}}$($/MJ)	$\dot{C}$($/h)	${\dot{C}}_D$($/h)	${\dot{C}}_L$($/h)	$r_k$(%)	$f$
Gasifier (Gasf)	0.0073	0.0080	0.4759	1.676	_	9.59	0.22
Solid oxide fuel cell (SOFC)	0.0080	0.0289	7.361	0.2044	_	261.2	0.97
Air heat exchanger (AHX)	0.0050	0.0102	0.0342	0.4135	_	104	0.08
Air compressor (AC)	0.0078	0.0090	0.0018	0.0387	_	15	0.04
Afterburner (AB)	0.0050	0.0065	0.0054	0.1536	_	30	0.03
Superheater (Sup)	0.0065	0.0091	0.0362	0.181	_	40	0.017
Evaporator of HRSG (Evap)	0.0065	0.0101	0.0666	0.4085	_	55.38	0.2
Economiser (Econ)	0.0065	0.0105	0.0864	0.1219	_	61.53	0.42
Feed pump (FP)	0.0078	0.0666	0.026	0.0031	_	753	0.9
Steam turbine (ST)	0.0099	0.0286	1.589	0.1741	_	189	0.9
Generator (Gen)	0.0025	0.0026	0.0043	0.0039	_	4	0.53
Condenser (Cond)	0.0152	0.0203	0.0396	0.8472	_	33.55	0.05
Absorber (Abs)	0.0027	0.0152	0.0646	0.008	_	463	0.09
Evaporator of VAR (Eva)	0.0027	0.0083	0.0837	0.3385	_	207	0.14
Solution pump (SP)	0.0078	0.0265	0.0448	0.0964	_	240	0.31
Solution valve (SV)	0.0203	0.0265	0.0004	0.0082	_	30.54	0.05
Expansion valve (EV)	0.0026	0.0027	0.0001	0.0009	_	3.84	0.1
Plant	0.0073	0.0289	6.176	4.398	0.6877	296	0.55

When all the plant components are taken into account, the capital cost rate of the SOFC is maximum followed by the ST. It must be taken into account that the exergo-economic factor of the afterburner, the air heat exchanger and the air compressor are quite low owing to their tremendous exergy destruction rate and low cost factor. The cost rate incurred due to exergy loss is just 0.69 USD/h. The r_k value is obtained to be 296% along with the exergo-economic factor of 0.55. The unit product cost of electricity is obtained to be 0.03 USD/MJ or 0.1 USD per unit of electricity when the operational plant life is assumed to be 20 years.

Payback analysis

For capital-intensive plant of this configuration, where large initial investment is involved because of the advanced technology, payback period is greatly affected by the factors that influence the actual burden of the initial investment. Inflation is one such factor. Government subsidy, which is often available for clean energy investment, can substantially offset the increased burden due to inflation or the consequent increased lending interest. Figure 11 shows the influence of annual inflation rate on the payback period of the plant for a no-subsidy situation as well as for two other subsidy situations: 25% and 50% capital subsidy. It is evident that the payback period increases with the inflation rate of any country. It may be seen that with a moderate government subsidy of 25%, payback period could be kept within 5–5,5 years, even if the inflation runs high at 8–10%.

[See PDF for image]

Fig. 11

Effect of annual inflation rate on payback period of the plant

Performance parameters at the favourable operating conditions

Finally, it is worthwhile to note the plant’s major performance parameters at the most favourable set of operating conditions, as shown in Table 12.

Table 12. Performance parameters of the plant at the favourable operating conditions

Output parameter	Results obtained	Units (if any)
Overall generation efficiency	50.29	%
Exergetic efficiency	43.8	%
SOFC power	339	kW
ST power	107	kW
Net power	432	kW
Net cooling effect	130	kW
Cooling-to-power ratio (CTPR)	0.3	–
Effective cost of electricity (ECOE)	0.11	USD/kWh
Discounted payback period	6.5	years
Specific CO2 emission	0.9	kg/kWh
Environmental sustainability index (SI)	1.8	–
Total annual CO2 capture (TACC)	65,000	tons/year
Avoided CO2 penalty cost	9.7	million USD/year
Exergo-economic factor	0.55	–

It is worthwhile to note the predicted efficiency (both energetic and exergetic) of the combined cogeneration plant. The integration of the SOFC, which is an efficient direct energy conversion device, makes the plant electrically efficient too, while allowing recovery of considerable amount of heat from its exhaust streams (being combusted in an afterbuner) in multiple components, namely the air heat exchanger, the HRSG and the VAR cooling plant. Substantial efficiency gain is noted over the reported performances of similar power and cogeneration plants that employed biomass or MSW gasification but had no SOFC integrated to them. When compared with a similar gasification-based but power-only plant [24,30], which employed an externally fired gas turbine and also a bottoming steam turbine, it is observed that the integration of SOFC, instead of the externally fired gas turbine, results in a considerable efficiency gain. When compared with another recent analysis of a biomass gasification-based combined power and cooling plant (with no fuel cell, [31]), the superiority of present configuration is established, as the plant proposed herein yields an effective exergetic efficiency of over 43%, substantially higher than the reported exergetic efficiency of 27.6% for the earlier plant.

Conclusions

The paper encompasses the analytical performance of an MSW gasification-based combined power and cooling plant that is analysed in terms of exergo-enviro-economic approach. The maximum values of first and second efficiencies achieved are 50.29% and 43.8%, respectively. From the exergy analysis, it is witnessed that the gasifier is the most critical component owing to its highest exergy destruction. Economic aspects reveal that the effective cost of electricity (ECOE) obtained is 0.11 USD per unit of electricity with a period of payback of just 6.5 years. The results obtained from environmental analysis reveal that the specific CO₂ emission is 0.9 kg/kWh and sustainability index is 1.8. Also the environmental analysis suggests that the total annual CO₂ capture is 65,000 tons per annum, hereby reducing the penalty cost caused due to CO₂ emission by almost 9.7 million USD per annum. Finally, from the exergo-economic assessment, it is deduced that such plants can have a high exergo-economic factor value of 0.55 which reinforces the acceptability and feasibility in both thermo-economic and environmental aspects.

Abbreviations

CGE

Cold gas efficiency

LCV

Lower calorific value

HCV

Higher calorific value

SOFC

Solid oxide fuel cell

FP

Feed pump

ST

Steam turbine

AHX

Air heat exchanger

VAR

Vapour absorption refrigeration

COP

Coefficient of performance

MSW

Municipal solid waste

AC

Air compressor

EVA

Evaporator of VAR block

Evap

Evaporator of HRSG

Cond

Condenser

Sup

Superheater

Econ

Economiser

Abs

Absorber

EV

Expansion valve

SV

Solution valve

AB

Afterburner

COE

Cost of electricity

ECOE

Effective cost of electricity

PCF

Plant capacity factor

CRF

Capital recovery factor

DCL

Daily cooling load

NPV

Net present value

SPECO

Specific exergy costing

SI

Sustainability index

YOH

Yearly operational hours

ED

Exergy destruction

f

Exergo-economic factor

Letters with subscript

${\dot{m}}_{\text{fw}}$

Mass flow rate of feedwater

${\dot{m}}_{\text{fg}}$

Mass flow rate of burnt gases

${\dot{m}}_{\text{pg}}$

Mass flow rate of producer gas

${\dot{m}}_{\text{MSW}}$

Mass flow rate of segregated MSW

${\dot{m}}_{\text{steam}}$

Mass flow rate of steam

${\dot{m}}_{\text{strong}}$

Mass flow rate of strong solution

${\dot{m}}_{\text{weak}}$

Mass flow rate of weak solution

$M_{\text{MSW}}$

Molecular mass of segregated MSW

$W_{\text{SOFC}}$

SOFC output power

$W_{\text{ST}}$

Steam turbine output power

$W_{\text{SP}}$

Power input to solution pump

$W_{\text{FP}}$

Power input to feed pump

$W_{\text{AC}}$

Power input to air compressor

$Z_{\text{CAP}}$

Capital cost

$Z_{\text{O/M}}$

Operational maintenance cost

$Z_{\text{Fuel}}$

Fuel cost

$f_{\text{annual}}$

Annual inflation rate

$E{x}_{\text{f}}$

Fuel exergy

$r_k$

Relative cost difference

$M_{{\text{CO}}_2}$

Molecular mass of CO₂

$M_{{\text{H}}_2\text{O}}$

Molecular mass of H₂O

$E_{\text{nernst}}$

Nernst potential

$E_{\text{cell}}$

Cell voltage

$E_{\text{loss}}$

Voltage losses

$E_{\text{ohmic}}$

Ohmic loss

$E_{\text{act}}$

Activation loss

$E_{\text{conc}}$

Concentration loss

$h_{1,2,3...}$

Enthalpy at different state points

$h_0$

Enthalpy at dead state

${\text{ex}}_{\text{che}}$

Standard chemical exergy

$W_{\text{net}}$

Net power output

${\text{Ex}}_{\text{ch}}$

Chemical exergy

${\text{Ex}}_{\text{ph}}$

Physical exergy

$A_{\text{P}}$

Auxiliary power consumption

$L_P$

Transmission line loss

$C_0$

Total overnight capital

${\text{Ex}}_{\text{P}}$

Product exergy

Greek symbols

$\eta$

Efficiency

$\alpha$

Number of moles of different components of producer gas

$\xi$

Coefficient of exergy

$\gamma$

Amount of steam supplied

$\lambda$

Air–fuel equivalence ratio

$\theta$

Operational life of the plant

Monica Carvalho

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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