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Section 2.4 Vanadium crossover Crossover of VO2+ or VO2+ ions from the positive into the negative half-cell: VO+2 +V3+ →2VO2+ VO+2 +2V2+ +4H+ →3V3+ +2H2 O VO2+ +V2+ +2H+ →2V3+ +H2 O Crossover of V2+ or V3+ ions from the negative into the positive half-cell: V2++VO2+ +2H+→2V3++H2O V2+ +2VO+2 +2H+ →3VO2+ +H2 O V3+ +VO+2 →2VO2+ (2-17) (2-18) (2-19) (2-20) (2-21) (2-22) 2.4.3 Ionic flux resulting from vanadium crossover and self-discharging reactions in the negative half-cell For each vanadium species, we have to consider the vanadium ions which leave or enter the respective half-cell due to the vanadium crossover. The resulting redox reactions oxidize and reduce vanadium ions, which we can express as an additional ionic flux into or out of the respective half-cell as well. In reality, all reactions occur simultaneously and not in a specific order. However, to compute the resulting reaction fluxes in one single step, we have to put the reactions into a certain order. In the negative half-cell, reaction (2-17) yields VO2+ ions as one of the reaction products. In normal operation, the battery SoC does not reach a value of 0 %, meaning that there are always sufficient V2+ ions present to let reaction (2-19) take place. Hence, the VO2+ ions resulting from reaction (2-17) further react to V3+ ions. Therefore, when put into an order, reaction (2-17) should not be considered at last, because then VO2+ ions are present in the negative half-cell at the end of the calculation time step. There are two reasonable orders for the sequence of the reactions, namely (2-17)→(2-18)→(2-19) and (2-18)→(2-17)→(2-19). In the first order, reaction (2-18) will not take place, since we can assume that there are always enough V3+ ions present in the negative half-cell to reduce all present VO2+ ions to VO2+ ions (reaction (2-17)). Thus, reaction (2-18) lacks the reaction partner VO2+ and the self-discharge process is reduced to the order (2-17)→(2-19). In normal operation, the second order can also be simplified. If the negative electrolyte is not completely discharged, there will be sufficient V2+ ions to reduce all entered VO2+ ions to V3+ ions. In this case, reaction (2-17) is skipped because no more VO2+ ions are present to react with V3+ ions. Hence, the reactions are considered in the order (2-18)→(2-19). The order in which the self-discharge reactions are considered is irrelevant for the resulting net ionic fluxes, as shown in Figure 2-2. In the first order, a VO2+ ions and 21PDF Image | Model-based Design Vanadium Redox Flow Batteries
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