# Operational Parameter Analysis and Performance Optimization of Zinc–Bromine Redox Flow Battery

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## Abstract

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## 1. Introduction

## 2. Numerical Modeling

#### 2.1. Electrochemical Reactions

#### 2.2. Governing Equations

#### 2.2.1. Transport in Electrodes

#### 2.2.2. Electrochemical Kinetics

#### 2.2.3. Tanks

#### 2.2.4. Side Reactions

#### 2.3. Calculation Area and Boundary Conditions

#### 2.4. Assumptions and Solutions

#### 2.5. Performance Indicators

#### 2.6. Model Validations

## 3. Results and Discussion

#### 3.1. Effect of Electrolyte Flow Rate

#### 3.2. Effect of Electrode Thickness

#### 3.3. Effect of Electrode Porosity

#### 3.4. Parameter Optimization to Further Improve Battery Performance

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the structure and principle of ZBFB (BCA = bromine complex agent; OPC = oily polybromide complex).

**Figure 3.**Simulated voltage of ZBFB at a current density of $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ compared with the experimental voltage.

**Figure 4.**Battery voltages with different positive electrolyte flow rates at current densities of (

**a**) $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and (

**b**) $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 6.**Bromine concentration distribution in the positive electrode at the end of discharge for battery with different positive electrolyte flow rates at a current density of $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 7.**Voltage, coulomb, and energy efficiency of battery with different positive electrolyte flow rates at current densities of (

**a**) $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and (

**b**) $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 8.**Battery voltages with different electrode thicknesses at current densities of (

**a**) $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and (

**b**) $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 9.**Bromine concentration distribution in the positive electrode at t = 0.85 h for battery with different electrode thicknesses at current densities of (

**a**) $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and (

**b**) $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 10.**Voltage, coulomb, and energy efficiency of battery with different electrode thicknesses at current densities of (

**a**) $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and (

**b**) $40{\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 11.**Battery voltages with different electrode porosities at current densities of (

**a**) $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and (

**b**) $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 12.**Bromine concentration distribution in the positive electrode at (

**a**) t = 0.2 h and (

**b**) t = 0.9 h for battery with different electrode porosities at a current density of $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and at (

**c**) t = 0.2 h and (

**d**) t = 0.9 h for battery with different electrode porosities at a current density of $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 13.**Voltage, coulomb, and energy efficiency of battery with different electrode porosities at current densities of (

**a**) $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and (

**b**) $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 14.**Coulomb efficiency of battery with (

**a**) different electrolyte flow rates and electrode thicknesses and (

**b**) different electrolyte flow rates and electrode porosities at a current density of $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 15.**Energy efficiency of battery with (

**a**) different electrolyte flow rates and different electrode thicknesses and (

**b**) different electrolyte flow rates and different electrode porosities at current densities of $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ and $40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$.

**Figure 16.**Comparison of the bromine concentration distribution in the positive electrode at 0.9 h at a current density of $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$: (

**a**) Pristine and (

**b**) Optimization.

**Figure 17.**Comparison of electrode current density distribution at different moments at a current density of $20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$: (

**a**) Pristine and (

**b**) Optimization.

**Figure 18.**Comparison of energy efficiency of battery before and after optimization at different current densities.

RFB | Advantage | Disadvantage | Energy Density $(\mathbf{Wh}{\mathbf{kg}}^{-1})$ | Energy Efficiency (%) | Electrolyte Cost $\left(\mathbf{USD}\text{}{\mathbf{KWh}}^{-1}\right)$ | Ref. |
---|---|---|---|---|---|---|

VRFB | Single active species; Long cycle life; No pollution to environment. | High electrolyte costs; Low energy density; Low operating voltage. | 15–43 | 82.7 ($120{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$) | 87 | [9,10] |

ZIRFB | Low system costs; Large PH range; No pollution to environment. | Zinc dendrites; Low solubility of ferrocyanide; High separator resistance. | 56 | 82.8 ($160{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$) | 5 | [11,12] |

ZBFB | High energy density; Long cycle life; Low system costs; Wide operating temperature. | Bromine is corrosive and toxic; Zinc dendrites; Slower reaction rate. | 70 | 85.3 ($40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$) | 5 | [13,14] |

Parameter | Value | Unit |
---|---|---|

Flow rate | 10–50 | ${\mathrm{mL}\text{}\mathrm{min}}^{-1}$ |

Applied current density | 20,40 | ${\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ |

Operating temperature | 293 | $\mathrm{K}$ |

Charging time | 0.5 | $\mathrm{h}$ |

Discharging time | 0.5 | $\mathrm{h}$ |

Symbol | Value | Description | Ref. |
---|---|---|---|

${H}_{cell}$ | $3.2\left(\mathrm{cm}\right)$ | Battery height | [33] |

${W}_{cell}$ | $3.2\left(\mathrm{cm}\right)$ | Battery width | [33] |

${L}_{e}$ | $3\left(\mathrm{mm}\right)$ | Thickness of the electrode | [33] |

${L}_{m}$ | $1\left(\mathrm{mm}\right)$ | Thickness of the membrane | [33] |

${U}_{in}$ | $0.3\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | Electrolyte inlet velocity | [33] |

$V$ | $80\left({\mathrm{cm}}^{3}\right)$ | Tank volume | [33] |

${c}_{B{r}^{-}}^{0}$ | $6000\left({\mathrm{mol}\text{}\mathrm{m}}^{-3}\right)$ | Initial bromine ion concentration | [33] |

${c}_{Z{n}^{2+}}^{0}$ | $4000\left({\mathrm{mol}\text{}\mathrm{m}}^{-3}\right)$ | Initial zinc ion concentration | [33] |

${\epsilon}_{e}$ | $0.5$ | Porosity of the electrode | [33] |

${\epsilon}_{m}$ | $0.5$ | Porosity of the membrane | [33] |

${\sigma}_{e}$ | $100\left({\mathrm{S}\text{}\mathrm{m}}^{-1}\right)$ | Conductivity of the electrode | [33] |

${\sigma}_{m}$ | $100\left({\mathrm{S}\text{}\mathrm{m}}^{-1}\right)$ | Conductivity of the membrane | [33] |

$a$ | $1\times {10}^{4}\left({\mathrm{m}}^{-1}\right)$ | Specific surface area of the electrode | [33] |

${E}_{neg}^{\mathsf{\Theta}}$ | $-0.76\left(\mathrm{V}\right)$ | Negative standard potential | [23] |

${E}_{pos}^{\mathsf{\Theta}}$ | $1.09\left(\mathrm{V}\right)$ | Positive standard potential | [23] |

${k}_{neg}^{0}$ | $7.5\times {10}^{-5}\left({\mathrm{m}\text{}\mathrm{s}}^{-1}\right)$ | Standard rate constant | [34] |

${k}_{pos}^{0}$ | $4\times {10}^{-7}\left({\mathrm{m}\text{}\mathrm{s}}^{-1}\right)$ | Standard rate constant | [34] |

${\alpha}_{neg}$ | $0.5$ | Transfer coefficient | [21] |

${\alpha}_{pos}$ | $1$ | Transfer coefficient | [21] |

${D}_{B{r}_{2}}$ | $1.31\times {10}^{-9}\left({\mathrm{m}}^{2}{\text{}\mathrm{s}}^{-1}\right)$ | Diffusion coefficient of bromine | [21] |

**Table 4.**Discharge capacities of battery with different positive electrolyte flow rates at different current densities (Ah).

$10\mathbf{mL}{\mathbf{min}}^{-1}$ | $20\mathbf{mL}{\mathbf{min}}^{-1}$ | $30\mathbf{mL}{\mathbf{min}}^{-1}$ | $40\mathbf{mL}{\mathbf{min}}^{-1}$ | $50\mathbf{mL}{\mathbf{min}}^{-1}$ | |
---|---|---|---|---|---|

$20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ | 2.31 | 2.68 | 2.80 | 2.86 | 2.89 |

$40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ | 4.63 | 5.35 | 5.60 | 5.72 | 5.79 |

**Table 5.**Discharge capacities of battery with different electrode thicknesses at different current densities (Ah).

3 mm | 5 mm | 7 mm | |
---|---|---|---|

$20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ | 2.68 | 4.49 | 6.30 |

$40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ | 5.35 | 8.97 | 12.60 |

**Table 6.**Discharge capacities of battery with different electrode porosities at different current densities (Ah).

0.5 | 0.7 | 0.9 | |
---|---|---|---|

$20{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ | 2.678 | 2.685 | 2.684 |

$40{\text{}\mathrm{mA}\text{}\mathrm{cm}}^{-2}$ | 5.353 | 5.605 | 5.338 |

Method | Principle | Advantages | Disadvantages | Ref. |
---|---|---|---|---|

PSO | Bird foraging behavior | Principle is simple, easy to implement, fewer parameters to adjust. | For discrete optimization problems, it is easy to fall into local optima. | [41] |

DE | Population differences | Fast convergence, few control parameters, and high accuracy | Premature convergence or search stops occur when optimizing complex problems. | [42] |

GA | Biological evolution | Strong global search capability, suitable for solving complex optimization problems | Slow convergence and many control variables. | [43] |

Parameter | Value Range |
---|---|

Flow rate | 10–50 ${\mathrm{mL}\text{}\mathrm{min}}^{-1}$ |

Thickness | 3–7 mm |

Porosity | 0.5–0.9 |

Br concentration | 5000–7000 ${\mathrm{mol}\text{}\mathrm{m}}^{-3}$ |

Zn concentration | 3000–6000 ${\mathrm{mol}\text{}\mathrm{m}}^{-3}$ |

Current Density | $20\mathbf{mA}{\mathbf{cm}}^{-2}$ | $40\mathbf{mA}{\mathbf{cm}}^{-2}$ |
---|---|---|

Flow rate | 50 ${\mathrm{mL}\text{}\mathrm{min}}^{-1}$ | 50 ${\mathrm{mL}\text{}\mathrm{min}}^{-1}$ |

Thickness | 5 mm | 3 mm |

Porosity | 0.5 | 0.5 |

Br concentration | 7000 ${\mathrm{mol}\text{}\mathrm{m}}^{-3}$ | 7000 ${\mathrm{mol}\text{}\mathrm{m}}^{-3}$ |

Zn concentration | 6000 ${\mathrm{mol}\text{}\mathrm{m}}^{-3}$ | 6000 ${\mathrm{mol}\text{}\mathrm{m}}^{-3}$ |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.-Q.; Wang, G.-X.; Liu, R.-Y.; Wang, T.-H. Operational Parameter Analysis and Performance Optimization of Zinc–Bromine Redox Flow Battery. *Energies* **2023**, *16*, 3043.
https://doi.org/10.3390/en16073043

**AMA Style**

Zhang Y-Q, Wang G-X, Liu R-Y, Wang T-H. Operational Parameter Analysis and Performance Optimization of Zinc–Bromine Redox Flow Battery. *Energies*. 2023; 16(7):3043.
https://doi.org/10.3390/en16073043

**Chicago/Turabian Style**

Zhang, Ye-Qi, Guang-Xu Wang, Ru-Yi Liu, and Tian-Hu Wang. 2023. "Operational Parameter Analysis and Performance Optimization of Zinc–Bromine Redox Flow Battery" *Energies* 16, no. 7: 3043.
https://doi.org/10.3390/en16073043