Positive electrode Negative electrode
Membrane
Negative cell
reservoir cell
reservoir Positive
he
we
wm
we
Figure 4.1: Schematic of the all-vanadium redox flow battery showing the compo- nents, current collectors, porous electrodes, membrane and reservoirs.
ii) Accounting the effects of mass transfer and crossover in the model : Effects of temperature on diffusion coefficients and reaction rate constants, effects of temper- ature and porosity on the cell potential response is studied for different membrane materials.
4.3 Results and Discussion
The governing equations for lumped model as shown in Section 3.2 are solved in this study. The structural dimensions of the VRFB are based on the experimental setup taken from Ref. [27]. The full detail of the derivation calculation of cell and reservoir concentration are shown in Appendix A. The default parameters related to structural dimensions and initial conditions are given in Table B.1-B.4 in Appendix B. Figure 4.2 shows the comparison between simulated and experimental cell po- tential difference. The cell temperature was297 K, the vanadium concentration was 1200 mol/m3 , the flow rate was 1×10−6m3/s and the current density was 1000 A/m2. The model results are validated with the available experimental result of Shah et al. [27] and it shows good agreement. Figure 4.3 shows cell concentration variation inside the negative half of the cell. The cell temperature was 300 K, the
Figure 4.2: Comparison between simulated and experimental cell potential differ- ence. The cell temperature was297 K, the vanadium concentration was1200 mol/m3 , the flow rate was 1×10−6m3/s and the current density was1000 A/m2.
Figure 4.3: Cell concentration V(II) and V(III) variation with time during the full charge-discharge cycle. The cell temperature was300 K, the vanadium concentration was 1200 mol/m3 , the flow rate was1×10−6m3/s and the current density was1000 A/m2.
4.3 Results and Discussion 57
Figure 4.4: Reservoir concentration V(II) and V(III) variation with time during the full charge-discharge cycle. The cell temperature was 300 K, the vanadium concentration was 1200 mol/m3 , the flow rate was 1×10−6m3/s and the current density was 1000 A/m2
vanadium concentration was 1200 mol/m3, the flow rate of 1 × 10−6 m3/s and the current density of 750 A/m2. The concentration of vanadium V(III) decreases dur- ing charging from maximum i.e. 1200 mol/m3to minimum value. While discharging process the vanadium V(III) concentration increases from minimum to maximum value. This is due to the fact that during charging of the cell vanadium V(III) ions reduces to vanadium V(II) ions. Similarly, while discharging the cell vanadium V(II) ions reduces to V(III), this phenomena can be seen in Fig. 4.3. For V(II) con- centration increases linearly from zero to maximum value during charging process.
While discharging the cell vanadium V(II) concentration decreases linearly from maximum to zero. This phenomena is due to the oxidation and reduction reaction of vanadium ions in the process of charging and discharging. Figure 4.4 shows the variation of the vanadium concentration of the negative electrode side reservoir, the vanadium V(III) concentration decreases linearly, before charging process comple- tion (short duration) concentration drops suddenly to minimum, then concentration increases linearly during discharging the cell. Similarly, the reservoir concentration of vanadium V(II) increases linearly from zero to below maximum value before com- pletion of charging process (small duration) the concentration suddenly increases to maximum value, then decreases linearly during discharging process.
Figure 4.5: Model simulated results obtained cell potential difference, Ecell at flow rates, ω = 1mLs−1, ω = 2mLs−1 and ω = 3mLs−1. In all cases the vanadium concentration was 1200 mol m−3 , the temperature was 297 K and the current density was 1000 A m−2
4.3.1 Effects of flow rate
Electrolyte flow rate is very important parameter in the operation of vanadium redox flow battery. If the electrolyte flow rate is very high, it leads to risk of leakage or may not give good performance for the extra power required. On the other hand low electrolyte flow rate leads to insufficient circulation of electrolyte and stagnant regions are formed in the electrode. The effects of flow rate variations are shown in Fig. 4.5. In all the simulations the total vanadium concentrations for each electrode/reservoir 1200 mol m−3 has been taken. Results suggest that electrolyte flow rate increases the potential difference of the cell increases which leads to better performance of the cell. The reason behind the improvement in the performance is that concentration in the electrode is more evenly distributed for higher flow rate.
4.3.2 Effects of applied current densities
Simulated cell potential difference, Ecell curves while charge/discharge at three different applied current densities are shown in Fig. 4.6. In these calculations, CV0(III) = CV0(IV) = 1200 mol m−3 and flow rate ω=1 mL s−1. As the current density increases, the cell voltage decreases and it gives lesser performance of the cell. The reason behind that as the current density increases there is possibility of gas evolution inside the cell which leads to decrease in performance of the cell.
4.3 Results and Discussion 59
Figure 4.6: Comparison of the model simulated charge/discharge curves at three different applied current densities. In all the cases the temperature was 300 K, the vanadium concentration was 1200 mol m−3 and the flow rate was1×10−6m3/s
4.3.3 Effects of vanadium concentrations
Figure 4.7 shows simulation results of three different concentrations of vanadium.
In all cases the temperature was 300 K, the current density was 1000 A m−2 and flow rate was 1×10−6 m3 s−1. As the concentration increases cell terminal voltage and charge time increases which gives better performance.
4.3.4 Effects of electrode porosity
Simulated potential difference, Ecell curves during charge/discharge at three differ- ent electrode porosity values are shown in Fig. 4.8. The total volume of electrolyte was kept same in all cases. In all the simulations vanadium concentration was 1200 mol m−3 , the current density was 1000 A m−2 and the electrolyte flow rate was 1×10−6m3/s and the temperature was300 K. There are several effects associated with increase in porosity such as, increased permeability, decreased bulk conduc- tivity, increased bulk diffusion coefficients and higher the electrolyte volume in the electrode. As the porosity of the electrode decreases, cell voltage and charging time increase and this results in better performance of the cell. The polarization is greater at higher porosity, therefore side reactions rate is increased during charging.
Figure 4.7: Model simulated results obtained cell potential difference, Ecell at three different vanadium concentrations. In all cases the flow rate was 1×10−6 m3 s−1, the temperature was 300 K and the current density was 1000 A m−2
Figure 4.8: Comparison of the model simulated cell voltage curves for three elec- trode porosity values. In all the cases the temperature was 300 K, the vanadium concentration was 1200 mol m−3, the flow rate was 1×10−6m3/s and the current density was 1000 A m−2