Modeling, Validation, and Operational Variables Optimization of a Solid Oxide Fuel Cell

ANDRADE, SAMUEL TADEU DE P.; HUEBNER, RUDOLF; MATENCIO, TULIO; STADLER, INGO; DOMINGUES, ROSANA Z.; COSTA JÚNIOR, ESLY FERREIRA DA

doi:10.1590/0001-3765202520241413

person SAMUEL TADEU DE P. ANDRADE

Samuel Andrade established the numerical model and conducted simulations for the manuscript under the supervision of Esly Júnior, Tulio Matencio, and Rudolf Huebner

schoolFederal University of Minas Gerais, Department of Mechanical Engineering, Antônio Carlos Avenue, 6627, 31270-901 Belo Horizonte, MG, Brazil

0000-0003-4016-1135

person RUDOLF HUEBNER

Samuel Andrade established the numerical model and conducted simulations for the manuscript under the supervision of Esly Júnior, Tulio Matencio, and Rudolf Huebner · Also, Ingo Stadler, Rudolf Huebner and Rosana Zacarias gave their effort to analyze and discuss the detailed results, and they made useful comments on which the quality of study could be improved · Above all, Esly Júnior, Tulio Matencio, Ingo Stadler and Rudolf Huebner (equally contributed), have provided useful suggestions and have discussed research progress.

schoolFederal University of Minas Gerais, Department of Mechanical Engineering, Antônio Carlos Avenue, 6627, 31270-901 Belo Horizonte, MG, Brazil

0000-0003-2613-304X

person TULIO MATENCIO

Samuel Andrade established the numerical model and conducted simulations for the manuscript under the supervision of Esly Júnior, Tulio Matencio, and Rudolf Huebner · Above all, Esly Júnior, Tulio Matencio, Ingo Stadler and Rudolf Huebner (equally contributed), have provided useful suggestions and have discussed research progress.

schoolFederal University of Minas Gerais, Department of Chemistry, Antônio Carlos Avenue, 6627, 31270-901 Belo Horizonte, MG, Brazil

0000-0002-5660-8125

person INGO STADLER

Also, Ingo Stadler, Rudolf Huebner and Rosana Zacarias gave their effort to analyze and discuss the detailed results, and they made useful comments on which the quality of study could be improved · Above all, Esly Júnior, Tulio Matencio, Ingo Stadler and Rudolf Huebner (equally contributed), have provided useful suggestions and have discussed research progress.

schoolTechnische Hochschule Köln, Cologne Institute for Renewable Energy, Betzdorfer Straße 2, 50679 Köln, NRW, Germany

0000-0002-9689-8518

person ROSANA Z. DOMINGUES

Also, Ingo Stadler, Rudolf Huebner and Rosana Zacarias gave their effort to analyze and discuss the detailed results, and they made useful comments on which the quality of study could be improved

schoolFederal University of Minas Gerais, Department of Chemistry, Antônio Carlos Avenue, 6627, 31270-901 Belo Horizonte, MG, Brazil

0000-0001-5667-2031

person ESLY FERREIRA DA COSTA JÚNIOR

Samuel Andrade established the numerical model and conducted simulations for the manuscript under the supervision of Esly Júnior, Tulio Matencio, and Rudolf Huebner · Above all, Esly Júnior, Tulio Matencio, Ingo Stadler and Rudolf Huebner (equally contributed), have provided useful suggestions and have discussed research progress.

schoolFederal University of Minas Gerais, Department of Chemical Engineering, Antônio Carlos Avenue, 6627, 31270-901 Belo Horizonte, MG, Brazil

0000-0002-9245-4223

Correspondence to: Samuel Tadeu de Paula Andrade
emailsamuelt@ufmg.br

Parameter	Type	Original Value	Modified	Unit	Ref.
$∆ So$	Theoretical	-22.38		J/mol∙K	(Boles & Yunus A. Cengel 2014)
$∆ Ho$	Theoretical	-241,820		J/mol	(Boles & Yunus A. Cengel 2014)
$R$	Theoretical	8.314		J/K∙mol	(Boles & Yunus A. Cengel 2014)
$F$	Theoretical	96,485		C/mol	(Boles & Yunus A. Cengel 2014)
$A$	Arbitrary	0.01 • 0.01	0.04 • 0.04	m²	(Leonide et al. 2009)
n anodic	Theoretical	2		-	(O’Hayre et al. 2016)
n cathodic	Theoretical	4		-	(O’Hayre et al. 2016)
$α_{anode}$	Experimental	0.59		-	(Leonide et al. 2009)
$α_{cathode}$	Experimental	0.65		-	(Leonide et al. 2009)
$γ_{anode}$	Experimental	1.82527 • 108 T_sofc		A/m²	(Leonide et al. 2009)
$γ_{cathode}$	Experimental	1.51556 • 108 T_sofc		A/m²	(Leonide et al. 2009)
$E_{activation, anode}$	Experimental	105.04 • 103	115.04 • 103	J/mol	(Leonide et al. 2009)
$E_{activation, cathode}$	Experimental	139.86 • 103		J/mol	(Leonide et al. 2009)
a	Experimental	-0.1		-	(Leonide et al. 2009)
b	Experimental	0.33		-	(Leonide et al. 2009)
c	Experimental	0.22		-	(Leonide et al. 2009)
$E_{Ohm, cell}$	Experimental	90.31 • 103		J/mol	(Leonide et al. 2009)
$B_{cell}$	Experimental	4.1879 • 1012		S∙K/m²	(Leonide et al. 2009)
$t_{anode}$	Experimental	1 • 10-3		m	(Leonide et al. 2009)
$t_{cathode}$	Experimental	30 • 10-6		m	(Leonide et al. 2009)
$d_{pore, anode}$	Experimental	1,200 • 10-9	800 • 10-9	m	(Leonide et al. 2009)
$d_{pore, cathode}$	Experimental	1,200 • 10-9	800 • 10-9	m	(Leonide et al. 2009)
$σ_{H_{2}}$	Tabular	2.915			(Cussler 2009)
$σ_{H_{2} O}$	Tabular	2.641			(Cussler 2009)
$σ_{O_{2}}$	Tabular	3.467			(Cussler 2009)
$σ_{N_{2}}$	Tabular	3.789			(Cussler 2009)
$ε_{H_{2}}$	Tabular			K	(Cussler 2009)
$ε_{H_{2} O}$	Tabular			K	(Cussler 2009)
$ε_{O_{2}}$	Tabular			K	(Cussler 2009)
$ε_{N_{2}}$	Tabular			K	(Cussler 2009)
$ψ_{anode}$	Experimental	0.13	0.10	-	(Leonide et al. 2009)
$ψ_{cathode}$	Experimental	0.06		-	(Leonide et al. 2009)

Group	Setting (MATLAB Terminology)	Value or option
Population	PopulationSize	5 × optimization variables quantity
	InitialPopulationRange	practical ranges specified in this text
	PopulationType	doubleVector
	CreationFcn	gacreationlinearfeasible
	SelectionFcn	selectionstochunif
Reproduction	EliteCount	0.05 Population size*
	Mutation function	mutationadaptfeasible
	CrossoverFcn	crossoverintermediate
	CrossoverFraction	0.8
Stopping criteria	MaxStallGenerations	50
Stopping criteria	FunctionTolerance	1 • 10-10
Migration	MigrationDirection	forward
	MigrationFraction	0.2
	MigrationInterval	20

Run	Heuristic - Genetic Algorithm						Deterministic	Relative Difference [%]
	Obj. Func.	Optimized Variables					Obj. Func.
	Power [W]	Temperature [K]	H₂ Pressure [Pa]	H₂O Pressure [Pa]	Air Pressure [Pa]	Current [A]	Power [W]
1	38.64	1,171	100,407	918	101,325	63	57.84	-33.18
2	40.99	1,180	100,342	983	101,325	68		-29.13
3	35.97	1,170	100,740	585	101,325	56		-37.80
4	57.82	1,273	100,472	853	101,325	108		-0.12
5	57.84	1,273	100,647	678	101,325	108		-0.09
6	55.07	1,248	100,566	759	101,325	107		-4.87
7	35.17	1,168	100,428	897	101,325	54		-39.20
8	37.22	1,205	100,529	796	101,325	53		-35.65
9	57.83	1,273	100,524	801	101,325	108		-0.09
10	55.88	1,255	100,623	702	101,325	107		-3.46

mean	47.24	1,222	100,528	797	101,325	83
S.D.	10.3	46.8	121	121	0	26
max - min	22.7	104.9	398	398	0	55

Run	Heuristic - Genetic Algorithm						Deterministic	Relative Difference [%]
	Obj. Func.	Optimized Variables					Obj. Func.
	Power [W]	Temperature [K]	H₂ Pressure [Pa]	H₂O Pressure [Pa]	Air Pressure [Pa]	Current [A]	Power [W]
1	83.61	1,269	496,227	3,773	500,000	128	85.62	-2.35
2	83.42	1,268	495,921	4,079	500,000	128		-2.58
3	77.12	1,233	496,302	3,698	500,000	128		-9.93
4	84.43	1,273	495,137	4,863	500,000	128		-1.40
5	78.93	1,243	496,349	3,651	500,000	128		-7.82
6	83.81	1,272	497,191	2,809	500,000	128		-2.12
7	51.66	1,180	495,276	4,724	500,000	75		-39.47
8	78.90	1,242	495,961	4,039	500,000	128		-7.85
9	84.42	1,273	495,141	4,859	500,000	128		-1.41
10	77	1,234	496,303	3,697	500,000	128		-9.71

mean	78.36	1,249	495,981	4,019	500,000	123
S.D.	9.8	29.4	648	648	0	17
max - min	32.8	93.2	2,053	2,053	0	53

Run	Heuristic - Genetic Algorithm						Deterministic	Relative Difference [%]
	Obj. Func.	Optimized Variables					Obj. Func.
	Power [W]	Temperature [K]	H₂ Pressure [Pa]	H₂O Pressure [Pa]	Air Pressure [Pa]	Current [A]	Power [W]
1	51.78	1,288	100,413	912	101,325	77	66.11	-21.68
2	61.54	1,317	100,632	693	101,325	111		-6.93
3	39.75	1,286	100,629	696	101,325	52		-39.85
4	61.63	1,318	100,776	549	101,325	111		-6.79
5	61.14	1,312	100,117	1,208	101,325	110		-7.53
6	52.80	1,280	100,369	956	101,325	81		-20.14
7	39.10	1,354	99,981	1,344	101,325	49		-40.85
8	51.87	1,280	100,251	1,074	101,325	78		-21.54
9	64.70	1,379	100,691	634	101,325	112		-2.14
10	62	1,329	100,718	607	101,325	111		-5.69

mean	54.67	1,314	100,458	867	101,325	89
S.D.	9.3	33.1	275	275	0	25
max - min	25.6	99.5	794	794	0	63