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Experimental tests for lead–acid batteries
APPENDIX A
Experimental tests for lead–acid batteries Contents A.1. A.2. A.3. A.4. A.5.
Cell-I Cell-II Cell-III Cell-IV Cell-V
353 353 355 356 356
To verify the numerical simulations, many different batteries are tested by different researchers. In the literature, there are some good papers that provide necessary data for simulation of batteries by means of governing equations. In this appendix, we present some of the available data, and each test is given a name for better reference. The obtained data from different references are tabulated for each experiment.
A.1 Cell-I The cell was tested by Tiedemann and Newman [92], and the results were reported. This cell was also reused by many other researchers such as Gu et al. [37] and Esfahanian and Torabi [49]. The cell is a flooded lead–acid battery with characteristics tabulated in Table A.1. The operating conditions of the test are also available in Table A.2. Note that the negative sign for current density in Table A.2 indicates the discharging process.
A.2 Cell-II Gu et al. [48] used Cell-II for studying the discharging process in constant temperature. They used the results of the cell tested in the General Motors company. Cell-II is a flooded SLI lead–acid battery with characteristics tabulated in Table A.3. The operating conditions of the test are also available in Table A.4. Simulation of Battery Systems https://doi.org/10.1016/B978-0-12-816212-5.00014-3
Copyright © 2020 Elsevier Inc. All rights reserved.
353
354
Simulation of Battery Systems
Table A.1 Cell-I parameters. Parameter
Full thickness, cm Porosity, – Exchange current density, mA cm−2 Maximum active area, cm2 cm−3 Maximum electrode capacity, C cm−3 Exponent in the Butler–Volmer equation, γ Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
Positive electrode 0.173 0.55 6 × 10−4
Electrolyte
Separator
0.16 1.0
0.056 0.6
−
−
Negative electrode 0.163 0.61 8 × 10−3
2.05 × 105
−
−
2.5 × 104
2800
−
−
2471
0.5
−
−
0.5
1.0
−
−
1.0
1.0
−
−
1.0
Table A.2 Cell-I operating conditions. Parameter
Value
Initial electrolyte concentration, mol cm−3 Temperature, ◦ C Ionic transfer number of H+ , – Current density, mA cm−3 Table A.3 Cell-II parameters. Parameter
Full thickness, cm Porosity, – Exchange current density, mA cm−2 Maximum active area, cm2 cm−3 Maximum electrode charge, C cm−3 Exponent in the Butler–Volmer equation, γ Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
4.9 × 10−3 21.7 0.9 −10, −40
Positive electrode 0.12 0.53
Electrolyte
Separator
0.055 1.0
0.014 0.73
Negative electrode 0.12 0.53
10
−
−
10
100
−
−
100
5660
−
−
5660
1.5
−
−
1.5
1.0
−
−
1.0
1.0
−
−
1.0
Experimental tests for lead–acid batteries
Table A.4 Cell-II operating conditions. Parameter
Value
Initial electrolyte concentration, mol cm−3 Temperature, ◦ C Ionic transfer number, – Current density, mA cm−3 Table A.5 Cell-III parameters. Parameter
Full thickness, cm Porosity, – Exchange current density at 25◦ C, A cm−2 Exchange current density at −18◦ C, A cm−2 Maximum Active Material, cm2 cm−3 Maximum electrode capacity, C cm−3 Exponent in Butler–Volmer equation,
355
4.9 × 10−3 25 and −18 0.72 −340
Positive electrode 0.16 0.62 3.19 × 10−7
Electrolyte
Separator
− 0.0 −
0.1 0.912 −
Negative electrode 0.18 0.6 4.96 × 10−6
3.19 × 10−8
−
−
4.96 × 10−7
2.3 × 105
−
−
2.3 × 104
2620
−
−
3120
1.5
−
−
1.5
1.15
−
−
1.55
0.85
−
−
0.45
γ
Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
Table A.6 Cell-III operating conditions. Parameter
Initial electrolyte concentration, mol cm−3 Temperature, ◦ C Ionic transfer number, – Current density, mA cm−3
Value
4.9 × 10−3 25 and −18 0.72 −408
A.3 Cell-III This cell was used by Nguyen et al. [93] to investigate the effect of separator design on starved lead–acid batteries. The characteristics of the cell are tabulated in Table A.5, and the operating conditions in Table A.6.
356
Simulation of Battery Systems
Table A.7 Cell-IV parameters. Parameter
Height, cm Width, cm Porosity, – Exchange current density, mA cm−2 Maximum Active Material, cm2 cm−3 Maximum electrode capacity, C cm−3 Exponent in Butler–Volmer equation, γ Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
Positive electrode 3.2 0.2 0.5 0.1
Electrolyte
Separator
3.2 0.2 1.0
0.0 0.0
−
−
Negative electrode 3.2 0.2 0.5 0.1
100
−
−
100
3130
−
−
3700
1.5
−
−
1.5
1.0
−
−
1.0
1.0
−
−
1.0
Table A.8 Cell-IV operating conditions. Parameter
Initial electrolyte concentration, Temperature, ◦ C Ionic transfer number, – Current, mA cm−3
mol cm−3
−
Value 2.0 × 10−4
25 0.8 9.434
A.4 Cell-IV Alaviyoon et al. [50] used this cell to experimentally measure the free convection and stratification of electrolyte in a lead–acid cell during recharge. They also gave a mathematical model to simulate and study the cell. The cell was also resimulated by other researchers such as Gu et al. [37] and Esfahanian and Torabi [79]. The characteristics of the cell are tabulated in Table A.7, and the operating conditions in Table A.8.
A.5 Cell-V The cell was used by Srinivasan et al. [39] for investigation of current– interrupt and pulse charge on valve-regulated lead–acid batteries. The cell properties are tabulated in Tables A.9–A.13.
Experimental tests for lead–acid batteries
Table A.9 Parameters used for battery simulation. Parameter Definition/Dimension
Battery Weight Width of Electrodes Thickness of Battery Case Height of Head Space Electrolyte concentration at fully charged state. Reference electrolyte concentration Reference oxygen concentration Transference number of hydrogen ion
kg cm cm cm mol cm−3 +
357
Value 19.3 10.16 0.5 2.0 5.65 × 10−3
H (mol cm−3 ) cref
5.65 × 10−3
2 ceO,ref (mol cm−3 ) t◦+
1.0 × 10−3 0.72
Table A.10 The properties of different region of the battery cell. Parameter Negative Separator electrode Height, cm 12.7 12.7 0.0785 0.1146 Width, cm Porosity, – 0.57 0.92 0.85 0.93 Saturation, % − 2 0.1 − Exchange current density, mA cm − Maximum electroactive area, cm2 cm−3 2.3 × 104 Porosity correction factor, ξ 0.6 −
Positive electrode 12.7 0.1145 0.53 0.85 0.1 2.3 × 105 0.6
Table A.11 Electrochemical parameters of reactions at positive electrode. Parameter Value
Main reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, γ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc
4 × 10−7 59.08 0.3 1.21 0.79
Oxygen reaction, Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, δ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc Open circuit voltage, U (V)
2.5 × 10−27 326.359 0 2 2 1.649
358
Simulation of Battery Systems
Table A.12 Electrochemical parameters of reactions at negative electrode. Parameter Value
Main reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, γ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc
4.96 × 10−6 −84.34 0 1.55 0.45
Oxygen reduction reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, δ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc Open circuit voltage, U (V)
2.5 × 10−36 −326.359 0 2 2 1.649
Hydrogen evolution reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency facto, γ Anodic transfer coefficient, αc Open circuit voltage, U (V)
1.56 × 10−15 0 1 0.5 0.356
Table A.13 Thermal conductivity, W m−1 K−1 . Parameter Value Thermal conductivity case 0.14 Thermal conductivity of battery air 0.0255
Experimental tests for lead–acid batteries Contents A.1. A.2. A.3. A.4. A.5.
Cell-I Cell-II Cell-III Cell-IV Cell-V
353 353 355 356 356
To verify the numerical simulations, many different batteries are tested by different researchers. In the literature, there are some good papers that provide necessary data for simulation of batteries by means of governing equations. In this appendix, we present some of the available data, and each test is given a name for better reference. The obtained data from different references are tabulated for each experiment.
A.1 Cell-I The cell was tested by Tiedemann and Newman [92], and the results were reported. This cell was also reused by many other researchers such as Gu et al. [37] and Esfahanian and Torabi [49]. The cell is a flooded lead–acid battery with characteristics tabulated in Table A.1. The operating conditions of the test are also available in Table A.2. Note that the negative sign for current density in Table A.2 indicates the discharging process.
A.2 Cell-II Gu et al. [48] used Cell-II for studying the discharging process in constant temperature. They used the results of the cell tested in the General Motors company. Cell-II is a flooded SLI lead–acid battery with characteristics tabulated in Table A.3. The operating conditions of the test are also available in Table A.4. Simulation of Battery Systems https://doi.org/10.1016/B978-0-12-816212-5.00014-3
Copyright © 2020 Elsevier Inc. All rights reserved.
353
354
Simulation of Battery Systems
Table A.1 Cell-I parameters. Parameter
Full thickness, cm Porosity, – Exchange current density, mA cm−2 Maximum active area, cm2 cm−3 Maximum electrode capacity, C cm−3 Exponent in the Butler–Volmer equation, γ Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
Positive electrode 0.173 0.55 6 × 10−4
Electrolyte
Separator
0.16 1.0
0.056 0.6
−
−
Negative electrode 0.163 0.61 8 × 10−3
2.05 × 105
−
−
2.5 × 104
2800
−
−
2471
0.5
−
−
0.5
1.0
−
−
1.0
1.0
−
−
1.0
Table A.2 Cell-I operating conditions. Parameter
Value
Initial electrolyte concentration, mol cm−3 Temperature, ◦ C Ionic transfer number of H+ , – Current density, mA cm−3 Table A.3 Cell-II parameters. Parameter
Full thickness, cm Porosity, – Exchange current density, mA cm−2 Maximum active area, cm2 cm−3 Maximum electrode charge, C cm−3 Exponent in the Butler–Volmer equation, γ Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
4.9 × 10−3 21.7 0.9 −10, −40
Positive electrode 0.12 0.53
Electrolyte
Separator
0.055 1.0
0.014 0.73
Negative electrode 0.12 0.53
10
−
−
10
100
−
−
100
5660
−
−
5660
1.5
−
−
1.5
1.0
−
−
1.0
1.0
−
−
1.0
Experimental tests for lead–acid batteries
Table A.4 Cell-II operating conditions. Parameter
Value
Initial electrolyte concentration, mol cm−3 Temperature, ◦ C Ionic transfer number, – Current density, mA cm−3 Table A.5 Cell-III parameters. Parameter
Full thickness, cm Porosity, – Exchange current density at 25◦ C, A cm−2 Exchange current density at −18◦ C, A cm−2 Maximum Active Material, cm2 cm−3 Maximum electrode capacity, C cm−3 Exponent in Butler–Volmer equation,
355
4.9 × 10−3 25 and −18 0.72 −340
Positive electrode 0.16 0.62 3.19 × 10−7
Electrolyte
Separator
− 0.0 −
0.1 0.912 −
Negative electrode 0.18 0.6 4.96 × 10−6
3.19 × 10−8
−
−
4.96 × 10−7
2.3 × 105
−
−
2.3 × 104
2620
−
−
3120
1.5
−
−
1.5
1.15
−
−
1.55
0.85
−
−
0.45
γ
Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
Table A.6 Cell-III operating conditions. Parameter
Initial electrolyte concentration, mol cm−3 Temperature, ◦ C Ionic transfer number, – Current density, mA cm−3
Value
4.9 × 10−3 25 and −18 0.72 −408
A.3 Cell-III This cell was used by Nguyen et al. [93] to investigate the effect of separator design on starved lead–acid batteries. The characteristics of the cell are tabulated in Table A.5, and the operating conditions in Table A.6.
356
Simulation of Battery Systems
Table A.7 Cell-IV parameters. Parameter
Height, cm Width, cm Porosity, – Exchange current density, mA cm−2 Maximum Active Material, cm2 cm−3 Maximum electrode capacity, C cm−3 Exponent in Butler–Volmer equation, γ Anodic charge transfer coefficient, αa Cathodic charge transfer coefficient, αc
Positive electrode 3.2 0.2 0.5 0.1
Electrolyte
Separator
3.2 0.2 1.0
0.0 0.0
−
−
Negative electrode 3.2 0.2 0.5 0.1
100
−
−
100
3130
−
−
3700
1.5
−
−
1.5
1.0
−
−
1.0
1.0
−
−
1.0
Table A.8 Cell-IV operating conditions. Parameter
Initial electrolyte concentration, Temperature, ◦ C Ionic transfer number, – Current, mA cm−3
mol cm−3
−
Value 2.0 × 10−4
25 0.8 9.434
A.4 Cell-IV Alaviyoon et al. [50] used this cell to experimentally measure the free convection and stratification of electrolyte in a lead–acid cell during recharge. They also gave a mathematical model to simulate and study the cell. The cell was also resimulated by other researchers such as Gu et al. [37] and Esfahanian and Torabi [79]. The characteristics of the cell are tabulated in Table A.7, and the operating conditions in Table A.8.
A.5 Cell-V The cell was used by Srinivasan et al. [39] for investigation of current– interrupt and pulse charge on valve-regulated lead–acid batteries. The cell properties are tabulated in Tables A.9–A.13.
Experimental tests for lead–acid batteries
Table A.9 Parameters used for battery simulation. Parameter Definition/Dimension
Battery Weight Width of Electrodes Thickness of Battery Case Height of Head Space Electrolyte concentration at fully charged state. Reference electrolyte concentration Reference oxygen concentration Transference number of hydrogen ion
kg cm cm cm mol cm−3 +
357
Value 19.3 10.16 0.5 2.0 5.65 × 10−3
H (mol cm−3 ) cref
5.65 × 10−3
2 ceO,ref (mol cm−3 ) t◦+
1.0 × 10−3 0.72
Table A.10 The properties of different region of the battery cell. Parameter Negative Separator electrode Height, cm 12.7 12.7 0.0785 0.1146 Width, cm Porosity, – 0.57 0.92 0.85 0.93 Saturation, % − 2 0.1 − Exchange current density, mA cm − Maximum electroactive area, cm2 cm−3 2.3 × 104 Porosity correction factor, ξ 0.6 −
Positive electrode 12.7 0.1145 0.53 0.85 0.1 2.3 × 105 0.6
Table A.11 Electrochemical parameters of reactions at positive electrode. Parameter Value
Main reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, γ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc
4 × 10−7 59.08 0.3 1.21 0.79
Oxygen reaction, Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, δ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc Open circuit voltage, U (V)
2.5 × 10−27 326.359 0 2 2 1.649
358
Simulation of Battery Systems
Table A.12 Electrochemical parameters of reactions at negative electrode. Parameter Value
Main reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, γ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc
4.96 × 10−6 −84.34 0 1.55 0.45
Oxygen reduction reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency factor, δ Anodic transfer coefficient, αa Cathodic transfer coefficient, αc Open circuit voltage, U (V)
2.5 × 10−36 −326.359 0 2 2 1.649
Hydrogen evolution reaction Exchange current density, i◦,ref (A cm−2 ) Entropy change, Sj (J mol−1 K−1 cm−3 ) Acid concentration dependency facto, γ Anodic transfer coefficient, αc Open circuit voltage, U (V)
1.56 × 10−15 0 1 0.5 0.356
Table A.13 Thermal conductivity, W m−1 K−1 . Parameter Value Thermal conductivity case 0.14 Thermal conductivity of battery air 0.0255