Method for predicting the size of Ni 1/3 Mn 1/3 Co 1/3 (OH) 2 particles precipitated in a stirred-tank semi-batch crystallizer using CFD and particle agglomeration models

Ni Mn Co (OH) is widely used as a precursor for the cathode active material LiNi Mn Co O in lithium ion batteries, and the precursor size, which determines the size of the active cathode material, affects the characteristics of lithium-ion batteries. This paper proposes a method for predicting the particle size of Ni Mn Co (OH) precipitated by semi-batch reaction crystallization. The distribution of supersaturated components formed in the reactor varies with the reactor scale, feed conditions of the raw material solution, and agitation conditions. Therefore, the method presented in this paper considers the effects of these conditions on particle growth. First, to identify the turbulent dispersion and concentration distribution of the supersaturated components formed in the reaction crystallizer, a computational fluid dynamics (CFD) model was constructed consisting of the governing equations of hydrodynamics and the mass balance equations of the supersaturated components considering the production by neutralization and consumption by precipitation. Next, a model of agglomeration was constructed that focused on the balance of the binding and breaking up energies for the particle pairs. The binding energy was quantified based on the bridging between particle pairs by surface deposition. The breaking up-energy was quantified based on the hydrodynamic forces when the agglomerate passes through the impeller. These models were fitted using experimental results for the final average size of the Ni Mn Co (OH) secondary aggregate, which was precipitated in a small-scale stirred-tank type semi-batch reaction crystallizer. The models predicted the experimental results of the final average size in a large-scale crystallizer, with the feeding conditions of the raw material solution and stirring conditions as experimental parameters, within ±20%. The models may be used to analyze semi-batch reaction crystallization systems of Ni Mn Co (OH) of any composition by adjusting the model parameters according to the procedure developed in this study.