Monte Carlo simulation of the induction time and particle size distribution in the nucleation of calcium carbonate

• A cluster always breaks up into two random sized fragments.
• MMC–ABM was used to predict the induction time and the particle size distribution.
• The MMC–ABM had better accuracy than other models.
• Control of supersaturation is crucial to improving the performance of the reactor.

In water treatment, the crystallization of insoluble salts may produce a large number of fines, thereby increasing the turbidity and reducing the treatment efficiency. The induction time (tind) is a crucial indicator of nucleation during crystallization. Previous studies have predicted tind using an aggregation model (AM) proposed by Qian (QIAN-AM), which ignores cluster breakup during nucleus formation. The present study incorporated a hypothesized “binary breakup” mechanism into the AM, thus creating an aggregation–breakup model (ABM). This ABM was combined with a multi-Monte Carlo method (MMC–ABM) and applied to simulate the nucleation of calcium carbonate. Compared with the QIAN-AM and MMC–AM, the MMC–ABM showed improved accuracy, especially at high supersaturation conditions. Moreover, the MMC–ABM was used to predict the particle size distribution during nucleation and to simulate tind for a water-softening reactor. The simulation suggested that the nucleation in the reactor was faster than the macromixing; in this case, a large number of fines would form before homogeneous mixing, which would make the subsequent sedimentation process difficult. Therefore, effective control of the dosing point supersaturation is crucial to improving the performance of the reactor.

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