Multi-objective optimization of molten carbonate fuel cell system for reducing CO₂ emission from exhaust gases

Abstract

The aim of this paper is to investigate the implementation of a molten carbonate fuel cell (MCFC) as a CO₂ separator. By applying multi-objective optimization (MOO) using the genetic algorithm, the optimal values of operating load and the corresponding values of objective functions are obtained. Objective functions are minimization of the cost of electricity (COE) and minimization of CO₂ emission rate. CO₂ tax that is accounted as the pollution-related cost, transforming the environmental objective to the cost function. The results show that the MCFC stack which is fed by the syngas and gas turbine exhaust, not only reduces CO₂ emission rate, but also produces electricity and reduces environmental cost of the system.

Graphical abstract

Keywords

molten carbonate fuel cell (MCFC) / multi-objective optimization (MOO) / Pareto curve / genetic algorithm / CO₂ separation

1 Introduction

Carbon dioxide, water vapor, methane, nitrogen oxide (NO_x) and chlorofluorocarbons (CFCs) are the most important factors responsible for climate changes [1]. Thereupon, reduction of the released carbon dioxide, especially in energy production and conversion activities is a worldwide concern. CO₂ emissions should be also reduced to avoid the economic limitations planned by the Kyoto Protocol for the nations that do not respect the limits [2]. The main part of these emissions could be avoided by the carbon capture and storage technologies [3]. High temperature fuel cells, because of their higher efficiency and the ability to integrate with the other energy conversion technologies, have more applications in stationary power production [4–6]. Molten carbonate fuel cells (MCFCs) can be used as carbon dioxide separators besides electric power generators [7].

As an applied case, Campanari [8] suggested that MCFCs could be successfully applied as carbon dioxide separators from the conventional power plant exhausts. In this way, CO₂ emissions could be reduced by 77% and the output power increased by 20% in a steam turbine power plant. Lusardi et al. [9] investigated the possibility of producing electrical energy, meanwhile, being able to respect Kyoto Protocol and IPCC environmental limitations using MCFC based system.

Discepoli et al. [10] studied the experimental behavior of MCFC, in order to analyze the fuel cell critical operating conditions, such as the operating load and partial pressure ratio between oxygen and carbon dioxide in the cathode side.

Optimization of the critical operating parameters such as operating load is one of the best ways to improve MCFC performance. Desideri et al. [7] identified the optimal operating conditions of the cell and maximize the CO₂ removal efficiency. The results showed that the optimal combination of fuel cell critical operating conditions such as operating load could result in a CO₂ removal efficiency of 98.7% and an electrical efficiency of 35.6%. Milewski and Lewandowski [11] developed different objective functions such as maximization of efficiency as well as maximization of CO₂ emission reduction to optimize the MCFC performance. It was shown that the CO₂ emission reduction factor could reach 70%. The obtained MCFC efficiency had a moderate value of around 40%.

Usually several objective functions are important while they are in contrast with each other. The multi-objective optimization (MOO) will protect objective functions to simultaneously optimize [12]. There are important objectives in a MCFC system which conflict with each other such as CO₂ removal efficiency, electrical power generation and electrical efficiency. However these objective functions are not simultaneously considered in a MOO problem in the above review of literatures.

In this paper, the cost of electricity (COE) and emission rate are chosen as objective functions where COE is simultaneously affected by both electrical power generation and electrical efficiency.

Carbon dioxide taxes offer a potentially cost-effective means of reducing greenhouse gas emissions. So, if COE includes carbon dioxide tax, it can lead to economic and environmental benefits. To achieve this aim, the objective functions are considered as the emission rate and COE including CO₂ tax. Operating load is one of the most important parameters that affect MCFC behavior. High operating load values result in high fuel consumption and consequently high operating cost of the system, while causing high CO₂ separation. So there should be values of operating load that lead to the optimal value of objective functions. In this paper, the operating load is chosen as the only decision variable. At the end, a complete Pareto curve which includes the optimal results of objective functions is represented.

In short, the main innovations of this paper can be presented as follows:

1)‚Considering the cost of electricity and CO₂ emission rate as the objective functions for the proposed MOO problem.

2)‚Considering carbon dioxide tax in the cost of electricity.

3)‚Considering the CO₂ tax that is quantified conveniently as the pollution-related costs in the economic objective function, transforming the environmental objective to a cost function.

2 Problem under study

The quality of crude oils produced around the world is degrading. It means that the crude oil specific gravity and sulfur content increases [13]. These trends mean the production of the more residual heavy bottom products at a typical refinery [14]. The integrated gasification combined cycle power plant is a technically proven technology for producing electrical energy from low cost refinery residues in an environmentally-friendly manner [15]. Integrating the MCFC system to the conventional power section removes CO₂ from gas turbine exhaust gases. Therefore, a lower emission rate and higher system efficiency can be achieved.

As shown in Fig. 1 carbon dioxide is moved from the cathode side to the anode side via CO₃²⁻ ions and concentrates at the anode exhaust gases. Hence, because anode exhaust is rich in carbon dioxide and water vapor, CO₂ separation is easier than CO₂ separation from flue gases produced from combined cycle activities that are rich from unused oxygen and nitrogen.

In this paper, the MCFC anode is fed by the syngas produced from heavy refinery residue gasification via an oxygen blown gasifier energy plant. The shifted syngas composition is listed in Table 1 with a fuel utilization percentage of 75% [15]. The cathode side is fed by the exhaust gases of a gas turbine cycle and its composition is listed in Table 1 [16]. The flow rate of the exhaust gases of the gas turbine is assumed to be around 4 kg/s. It is noticed that the gas turbine power is 3.4 times of the MCFC output power. The temperature and pressure of the anode and cathode side are assumed to be 650°C and 1atm, respectively.

3 MCFC mathematical modeling

A mathematical model of MCFC is represented in order to calculate MCFC output variables such as electrical power, electrical efficiency and CO₂ emission rate.

3.1 Model assumptions

Model assumptions are expressed below:

1)Reactants and products are considered ideal gas mixture.

2)Plates are considered to be ideal conductors and voltage gradients going through them are negligible.

3)Water-gas shift reaction is fast enough and at equilibrium.

4)Fuel cell operates isothermally.

5)Pressure loss in fuel cell is not considered.

6)Fuel cell operates in steady-state condition.

3.2 Electrochemical reactions

An MCFC is mainly composed of porous anode Ni electrocatalyst, porous cathode NiO electrocatalyst and molten carbonate salt electrolyte. In the MCFC, the shifted syngas is fed to the anode side and the gas turbine exhaust gases are fed into the cathode side. At a temperature of around 650°C, the MCFC electrolyte which is constituted of carbonate salts, melts into a molten state and becomes capable of transporting carbonate ions from cathode to the anode side. There, it combines with the syngas hydrogen content and the hydrogen produced from water-gas shift reaction to produce water, carbon dioxide and electrons [7]. Figure 2 illustrates the operating configuration of a MCFC. The half-cell electrochemical reactions are listed in Table 2.

3.3 Governing equations

3.3.1 Electrochemical modeling

A basic mathematical model was developed in order to analyze MCFC behavior by Baranak and Atakul [17]. According to the results, LiNaCO₃ was chosen as the MCFC proper electrolyte. LiNaCO₃ constants in fuel cell related equations were extracted from Morita et al. [18] experimental test. The MCFC modeling and assumptions here are referred to the basic model of Baranak and Atakul [17].

MCFC cell voltage is obtained by considering the cell losses, depending on the cell current density. Fuel cell electrical potential can be calculated from

(1)V=E-{\eta }_{\mathrm{ne}}-j{R}_{\mathrm{tot}},

where E is the maximum attainable reversible voltage, {\eta }_{\mathrm{ne}} is the Nernst loss, j is the electrical current density, and R_{\mathrm{tot}} is the sum of the irreversibilities due to anode, cathode and internal cell resistance. The total cell current is equal to the sum of the electrical currents of discrete units.

The maximum attainable voltage of the fuel cell may be calculated from Gibbs free energy change of hydrogen oxidation reaction

(2)E={\displaystyle \frac{-\mathrm{\Delta }G}{\mathrm{2}F}},

where \mathrm{\Delta }G is the Gibbs free energy change and F is Faraday constant. The Gibbs free energy change as the function of temperature is calculated from

(3)\mathrm{\Delta }G=-\mathrm{242000}+\mathrm{45.8}T.

The second term on the right hand side of Eq. (1) is Nernst loss that is calculated from

(4){\eta }_{\mathrm{Nernst}}={\displaystyle \frac{RT}{\mathrm{2}F}}\ln \left[{\displaystyle \frac{P_{{\mathrm{H}}_2\mathrm{,an}}{\left(P_{{\mathrm{O}}_2\mathrm{,ca}}\right)}^{\mathrm{1}/\mathrm{2}}{P}_{{\mathrm{CO}}_2\mathrm{,ca}}}{P_{{\mathrm{H}}_2\mathrm{O,an}}{P}_{{\mathrm{CO}}_2\mathrm{,an}}}}\right].

The sum of the irreversibilities is expressed as

(5)R_{\mathrm{tot}}=R_{\mathrm{an}}+R_{\mathrm{ca}}+R_{\mathrm{ir}},

where R_{\mathrm{an}} and R_{\mathrm{ca}} are anode and cathode irreversibilities, respectively, and R_{\mathrm{ir}} is the cell internal resistance.

MCFC irreversibilities can be calculated as

(6)R_{\mathrm{an}}=C_{\mathrm{a}}{\mathrm{e}}^{\mathrm{\Delta }{H}_{\mathrm{a}}/RT}{P}_{{\mathrm{H}}_{\mathrm{2,an}}}^{-0.5},

(7)R_{\mathrm{ca}}=C_{\mathrm{1}}{\mathrm{e}}^{\mathrm{\Delta }{H}_{\mathrm{C}\mathrm{1}}/RT}{P}_{{\mathrm{O}}_2\mathrm{,ca}}^{-0.75}{P}_{{\mathrm{CO}}_2\mathrm{,ca}}^{0.5}+C_{\mathrm{2}}{\mathrm{e}}^{\mathrm{\Delta }{H}_{\mathrm{C2}}/RT}{P}_{{\mathrm{CO}}_2\mathrm{,ca}}^{-\mathrm{1}},

(8)R_{\mathrm{ir}}=C_{\mathrm{ir}}{\mathrm{e}}^{\mathrm{\Delta }{H}_{\mathrm{ir}}/RT},

where C_i(i= 1,2) is related to electrodes and electrolyte and its values for LiNaCO₃ electrolyte were extracted from the experimental test of Morita et al. [18].

These equations show that electrodes irreversibilities are related to temperature, pressure, anode and cathode inlet gases partial pressures while other parameters are related to electrodes and electrolyte.

The electrical current density of each discrete unit can be calculated from

(9)j={\displaystyle \frac{E-V-{\eta }_{\mathrm{ne}}}{R_{\mathrm{tot}}}}.

The electrical current of each discrete unit is the product of current density and area of each unit.

(10)i=j{A}_{\mathrm{unit}},

where A_{\mathrm{unit}} is the surface area of each discrete unit which is 1/25 of the total cell area equal to 2000 cm². The produced electrical current is proportional to reactants consumption in reactions. The relationships between molar flow rates of the current and gases are shown as

(11)\mathrm{\Delta }{F}_{{\mathrm{H}}_2\mathrm{,an}}=-\mathrm{0.018655}i,

(12)\mathrm{\Delta }{F}_{{\mathrm{CO}}_2\mathrm{,ca}}=-\mathrm{0.018655}i,

(13)\mathrm{\Delta }{F}_{{\mathrm{O}}_2\mathrm{,ca}}=-\mathrm{0.0093275}i,

(14)\mathrm{\Delta }{F}_{{\mathrm{H}}_2\mathrm{O,an}}=\mathrm{0.018655}i,

(15)\mathrm{\Delta }{F}_{{\mathrm{CO}}_2\mathrm{,an}}=\mathrm{0.018655}i,

where \mathrm{\Delta }{F}_{i,\mathrm{an}} and \mathrm{\Delta }{F}_{i,\mathrm{ca}} are the changes of molar flow rates of components i at anode and cathode respectively.

The water-gas shift reaction that takes place on nickel catalyst at high temperatures is fast enough and reaches equilibrium. The water-gas shift reaction equilibrium constant can be calculated from

(16)K_{\mathrm{p}}={\displaystyle \frac{P_{{\mathrm{CO}}_2}{P}_{{\mathrm{H}}_{\mathrm{2}}}}{P_{\mathrm{CO}}{P}_{{\mathrm{H}}_2\mathrm{O}}}}.

And its dependency on temperature is expressed as

(17)\ln \left(K_{\mathrm{p}}\right)={\displaystyle \frac{\mathrm{4276}}{T}}-\mathrm{3.961.}

For X mol/h consumption of reactants in shift reaction to reach equilibrium condition, the equilibrium constant can be obtained as

(18)K_{\mathrm{p}}={\displaystyle \frac{\left(F_{{\mathrm{CO}}_{\mathrm{2}}}+X\right)\left(F_{{\mathrm{H}}_{\mathrm{2}}}+X\right)}{\left(F_{\mathrm{CO}}-X\right)\left(F_{{\mathrm{H}}_{2}O}-X\right)}},

Rearrangement of the above equation results in

(19)\left(\mathrm{1}-K_{\mathrm{p}}\right)X^{\mathrm{2}}+\left[F_{{\mathrm{H}}_{\mathrm{2}}}+F_{\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}+K_{\mathrm{p}}\left(F_{\mathrm{C}\mathrm{O}}+F_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\right)\right]X+\left[\left(F_{\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{F}_{{\mathrm{H}}_{\mathrm{2}}}\right)-\left(F_{\mathrm{C}\mathrm{O}}{F}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\right)K_{\mathrm{p}}\right]=\mathrm{0},

Solving the above equation gives the flow rates of molar as function of conversion degree.

The overall cell current is equal to the sum of the electric current produced in discrete units.

(20)i_{\mathrm{tot}}={\displaystyle \sum i}.

3.3.2 Cost modeling

The output variables of the MCFC mathematical model are utilized to obtain COE. CO₂ tax is also considered in the operating cost to calculate the COE.

The MCFC investment cost relation is shown in Eq. (21).

(21)I_{\mathrm{1}}=\left(I_{\mathrm{si}}+I_{\mathrm{in}}\right)\times P_{\mathrm{p}},

where I_{\mathrm{si}} and I_{\mathrm{in}} are investment cost of a stack and investment cost of the installation respectively and can be extracted from Table 3. P_{\mathrm{p}} in Eq. (21) is the MCFC power (kW).

Operating cost is one of the most important parts of MCFC cost model, because it considers fuel price. Its relation is shown in Eq. (22).

(22)C_{\mathrm{OP},\mathrm{1}}={\displaystyle \frac{E_{\mathrm{pry}}}{{\eta }_{\mathrm{elec}}}}\times G_{\mathrm{pr},\mathrm{1}},

where C_{\mathrm{OP},\mathrm{1}} is the annual fuel cost ($/a), E_{\mathrm{pry}} is the annual electric energy produced (kWh/a), {\eta }_{\mathrm{elec}} is electrical efficiency, and G_{\mathrm{pr},\mathrm{1}} is the annual fuel price ($/kWh).

Here, the syngas that is fed to MCFC anode is produced by asphalt gasification plant as are represented by Greppi et al. [15]. Asphalt price is around 450 $/t [20]. Other operation cost parameters can be found in Table 3.

The amount of reduced tax per year due to CO₂ separation characteristic of MCFC is calculated by

(23){\mathrm{RT}}_{\mathrm{tot,1}}=\mathrm{CT}\times {\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}},\mathrm{sep}}\times \mathrm{PF,}

where {\mathrm{RT}}_{\mathrm{tot,1}} is the total annual reduced carbon dioxide tax ($/a), \mathrm{CT} is carbon dioxide tax ($/t), {\dot{m}}_{{\mathrm{CO}}_2\mathrm{,sep}} is the separated carbon dioxide flow rate (ton/h), and \mathrm{PF} is the plant factor (h/a).

Carbon dioxide tax is reported to be around 30 $/t of released CO₂ in the years 2013–2014 [21], hence, this value was used as the basis of carbon dioxide tax estimation in this paper.

To calculate the cost of electricity including CO₂ tax, the reduced annually tax should be subtracted from the operating cost as shown in Eqs. (24) and (25).

(24)C_{\mathrm{tot,RT}}=I_{\mathrm{1}}+\left(C_{\mathrm{OP},\mathrm{1}}-{\mathrm{RT}}_{\mathrm{tot,1}}\right)\times {\displaystyle \frac{{\left(\mathrm{1}+I_{\inf }/\mathrm{100}\right)}^n-\mathrm{1}}{\left(I_{\inf }/\mathrm{100}\right)\times {\left(\mathrm{1}+I_{\inf }/\mathrm{100}\right)}^n}},

(25){\mathrm{C}\mathrm{O}\mathrm{E}}_{\mathrm{RT}}=\frac{C_{\mathrm{tot,RT}}}{E_{\mathrm{pry}}}\times {\displaystyle \frac{\left(I_{\inf }/\mathrm{100}\right)\times {\left(\mathrm{1}+I_{\inf }/\mathrm{100}\right)}^n}{{\left(\mathrm{1}+I_{\inf }/\mathrm{100}\right)}^n-\mathrm{1}}}.

In Eqs. (24) and (25), C_{\mathrm{tot,RT}} is the overall cost including reduced carbon dioxide tax ($) and {\mathrm{COE}}_{\mathrm{RT}} is the cost of electricity including reduced carbon dioxide tax ($/kWh).

4 Multi-objective optimization

In multi-objective problems, different objective functions are usually in contrast with each other, which will protect objective functions to optimize simultaneously [12]. The weighted-sum method is one of the common ways to solve multi-objective optimization problems. This method combines all objective functions together and optimizes the produced unique objective function as represented in Eq. (26).

(26)Z={\displaystyle \sum _{i=\mathrm{1}}^k{w}_i}{\left[F_i\left(x\right)\right]}^p,

(27){\displaystyle \sum _{i=1}^k{w}_i}=1,w>0,

where k is the number of objective functions and p is usually considered equal to 1 [12]. In order to plot the Pareto curve, different values should be assigned to w and for each value, calculate the optimal values of objective functions.

In this paper, objective functions are emission rate and COE as represented in Eq. (28).

(28)\min \hspace{0.17em}{Z}_{\mathrm{1}}=w\times \mathrm{COE}+\left(\mathrm{1}-w\right)\times \mathrm{ER,}

where ER is the CO₂ flow rate at cathode outlet in t/a.

5 Results and discussion

5.1 Model validation

To check the correctness of this MCFC model, the polarization curve developed by this model is compared with the experimental and modeling results developed by Milewski et al. [22] at the same operating conditions. The model predictions agree well with those of the experimental results with an average relative error of 2.3% (maximum error of 7%). The average relative error in comparison with the reference model is 0.63% (maximum error of 1.1%) as demonstrated in Fig. 3.

5.2 Multi-objective optimization

The purpose of this paper is to analyze the use of MCFC to separate CO₂ from gas turbine exhaust gases. Since the integration of MCFC imposes extra costs to the plant, operating conditions of MCFC should be chosen in such a way to persuade decision makers to use MCFC from an economic and environmentally-friendly point of view.

COE is chosen as one of the objective functions in this paper because it considers both output power and electrical efficiency simultaneously. Although COE can be the appropriate objective function from the economic aspect, CO₂ emission rate is also an important objective function which is not considered in COE. As displayed in Fig. 4, because of the conflicting behavior of COE and emission rate with respect to operating load, the MOO approach is the best method to achieve the optimal point.

5.3 Pareto frontier

In this paper, reduced CO₂ tax is considered in COE as the cost benefit. Thereupon, the amount of separated CO₂ by using MCFC is an economical motivation for decision makers.

The Pareto curve of the MOO problem is depicted in Fig. 5. In the Pareto curve, point A, (w = 1) corresponds the minimum COE of 0.12 $/kWh at 9502 t/a emission rate. By decreasing the weighting factor (w) or increasing the importance of the emission rate, lower CO₂ is released at a higher electricity cost. In the other side, point B (w = 0) is related to the minimum emission rate of 3985 t/a for the COE of 0.35 $/kWh. Table 4 tabulates all the optimum values of objective functions for points A, B.

The process of decision-making is performed with the aid of an imaginary point (the ideal point) in Fig. 5, at which both objective functions are in their optimal values independent of each other. It is impossible that both objectives are optimized simultaneously and, as shown in Fig. 5 the ideal point is not located at the Pareto frontier. The closest point of the Pareto frontier to the ideal point might be considered as a desirable final solution. Therefore, design point C can be a good candidate for the multi-objective optimization.

In point C, values of emission rate and COE are equal to around 5000 t/a and 0.2 $/kWh. The operating load that gives these values of objective functions, is 0.11 A/cm².

So, using gas turbine exhaust gases in the cathode of MCFC at an operating load of 0.11 A/cm², not only reduces CO₂ emission rate from 14200 t/a to 5000 t/a, but also produces electricity with 0.2 $/kWh and reduces environmental cost of approximately 276000 $/a of the system.

5.4 Economic analysis

MCFC researchers and manufacturers are making several efforts to decrease both the capital and the operational costs of the MCFC systems. The effect of CO₂ tax on MCFC operational costs was investigated in the previous section. In this section the investment cost of MCFC is considered and the cost of CO₂ avoided by MCFC is compared by the conventional post-combustion methods.

As reported by IEA, the published CO₂ capture cost data vary significantly over time and regions [23]. The most mature technology for post-combustion CO₂ capture is amine-based solvents. The average cost of CO₂ avoided by this technology in OECD countries is approximately 69 $/t [23]. The results show that the cost of CO₂ avoided by MCFC is approximately 100 $/t by considering the stack cost of 4126 $/kW [19]. MCFC stack cost will be reduced to 1082 $/kW in 2020 [24]. By considering this value for MCFC stack cost, the cost of CO₂ avoided by MCFC will be approximately 49 $/t. This value shows that the MCFC technology can compete with the conventional CO₂ capture technologies in the near future.

To express the effect of MCFC stack cost more clearly, the internal rate of return (IRR) and the pay-back period (PBP) of the integrated MCFC are represented here. As shown in Fig. 6, decreasing MCFC stack cost in the near future (in 2020) will lead to a decrease payback period of approximately 12 years and an increase internal rate of return of approximately 27%.

It seems that by decreasing the stack cost, MCFC can be a desirable technology for separating CO₂ from exhaust gases in the near future.

6 Conclusions

In this paper, a MCFC stack is modeled and analyzed from economic and environmental aspects. By applying the multi-objective optimization technique using the genetic algorithm, the optimal values of operating load as well as the corresponding values of objective functions are obtained and represented in Pareto curves.

This paper shows that MCFC can be a good candidate for separating CO₂ in a system with high CO₂ production. Therefore, the optimization of the MCFC system can improve the economic justification of the system. The proposed MCFC in this paper at the optimum condition, not only reduces CO₂ emission rate from 14200 t/a to 5000 t/a, but also produces electricity with 0.2 $/kWh and reduces an operating cost of approximately 276000 $/a of the system.

By decreasing MCFC stack cost to 1082 $/kW in 2020, the cost of CO₂ avoided is decreased from 100 $/t to 49 $/t and the MCFC technology can compete with conventional post-combustion methods as well.

Decreasing MCFC stack cost in the near future (in 2020) will lead to an improvement of the economics of this technology. It seems that increasing CO₂ tax and decreasing MCFC stack cost in the near future will lead to CO₂ separation using MCFC to be more economical.

Decreasing MCFC stack cost in the near future (in 2020) will lead to an improvement of the economics of this technology. It seems that increasing CO₂ tax and decreasing MCFC stack cost in the near future will lead to CO₂ separation using MCFC to be more economical.

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