Numerical modeling of the Mg(OH)2 precipitation process in double feed semibatch reactors

Magnesium hydroxide, Mg(OH)₂, is increasingly adopted as a green halogen-free flame retardant (HFFR) for polymer formulations, where it acts by absorbing heat during decomposition and limiting smoke production. However, this application requires a strict control of particle size distribution (PSD), aggregation level and specific surface area (SSA), as they determine dispersion, melt rheology, and mechanical performance of the composite material. Reactive crystallization from Mg-rich saline solutions (e.g., reverse osmosis brine and saltworks bitterns) and a strong base stream (e.g., NaOH) offers a circular route to synthesize Mg(OH)₂. In practice, the very low solubility of Mg(OH)₂ (≈9 mg/L at 20 °C) makes precipitation process mixing-controlled. Supersaturation gradients generated by the flow govern molecular processes, nucleation and growth, and thus the resulting PSD strongly depends on hydrodynamics and geometry design. Literature on Mg(OH)₂ precipitation reports several tested reactor configurations aimed at controlling supersaturation to suppress nucleation and favor crystal growth. Double-feed semi-batch operation emerges as the most promising [FM5.1]option because it spatially distributes reactant addition, mitigating localized nucleation bursts and enabling growth-dominated regimes [1]. Accordingly, this work develops a CFD–PBE model of a double-feed semi-batch stirred reactor to predict key PSD information, like characteristic diameters, and to guide hydrodynamic optimization of the process. The investigated system is a standard stirred tank (T = 0.10 m, liquid height H = 0.10 m) equipped with a six-blade Rushton turbine (D = 0.05 m). A constant volume approximation is adopted (set to the final liquid level), since the volume increase during the run is modest (≈10%[FM6.1]). Numerical simulations were carried out using the open-source platform OpenFOAM adopting the k-ω SST turbulence model (Re<20000) and the MRF approach [2]. Reactants are fed in stoichiometric ratio as NaOH (0.25–2.0 M) and MgCl₂ (0.125–1.0 M) aqueous streams. Micromixing is accounted through a β-PDF model, which yields effective molecular-scale reactant concentrations and enables a consistent evaluation of local supersaturation, which is then used as the driving force for nucleation and growth. Finally, population balance equations are solved by adopting QMOM closure method (3 nodes, 6 moments of distribution), accounting for nucleation, growth and aggregation phenomena. Parameters of crystallization kinetics are selected from relevant literature works [3] and, where needed, refined through optimization against available experimental data. The coupled CFD–PBE model reliably predicts Mg(OH)₂ characteristic particle sizes (d10, d32, d43) in double-feed semi-batch reactor and is validated against experimental datasets. Following validation, the model was used to optimize the main operating variables (reagent flow rates and concentrations, and agitation speed) to obtain target Mg(OH)₂ particle size. The model will next be deployed for the design of semi-industrial crystallizers (~100 t/y) in the framework of the European project MareMagLIFE.[