Next, we estimate the capital cost penalty factor caused by acid-base crossover. The penalty factor a0 is from the energy cost of acid-base crossover recovery, because the energy consumed during recovery cannot be considered as stored capacity. Basically, faster crossover costs more energy, which penalizes energy storage efficiency. Therefore, by multiplying a0 with capital cost of the whole system that has a certain crossover flux J, we achieve the capital cost of the system with considering acid-base crossover energy consumption. The capital cost penalty factor of the combined battery and BPM recovery sub-cell is shown in Fig. . The system energy storage cost is less penalized with higher OCV of the three-chamber cell and with lower acid-base crossover flux. The capital cost of the whole system can be calculated by adding BPM recovery sub-cell capital cost, then multiplying by the penalty factor a0. The capital cost penalty factor a0 and BPM recovery sub-cell capital cost is plotted against pH crossover rate in Fig. , assuming a 4 h project and 1.7 V OCV of the three-chamber cell for battery cycling.