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. 2023 Jun 23;23(7):4748-4759.
doi: 10.1021/acs.cgd.2c01179. eCollection 2023 Jul 5.

Computational Modeling of Magnesium Hydroxide Precipitation and Kinetics Parameters Identification

Antonello Raponi  1 , Salvatore Romano  2 , Giuseppe Battaglia  2 , Antonio Buffo  1 , Marco Vanni  1 , Andrea Cipollina  2 , Daniele Marchisio  1
Affiliations

Computational Modeling of Magnesium Hydroxide Precipitation and Kinetics Parameters Identification

Antonello Raponi et al. Cryst Growth Des. .

Abstract

Magnesium is a critical raw material and its recovery as Mg(OH)2 from saltwork brines can be realized via precipitation. The effective design, optimization, and scale-up of such a process require the development of a computational model accounting for the effect of fluid dynamics, homogeneous and heterogeneous nucleation, molecular growth, and aggregation. The unknown kinetics parameters are inferred and validated in this work by using experimental data produced with a T2mm-mixer and a T3mm-mixer, guaranteeing fast and efficient mixing. The flow field in the T-mixers is fully characterized by using the k-ε turbulence model implemented in the computational fluid dynamics (CFD) code OpenFOAM. The model is based on a simplified plug flow reactor model, instructed by detailed CFD simulations. It incorporates Bromley's activity coefficient correction and a micro-mixing model for the calculation of the supersaturation ratio. The population balance equation is solved by exploiting the quadrature method of moments, and mass balances are used for updating the reactive ions concentrations, accounting for the precipitated solid. To avoid unphysical results, global constrained optimization is used for kinetics parameters identification, exploiting experimentally measured particle size distribution (PSD). The inferred kinetics set is validated by comparing PSDs at different operative conditions both in the T2mm-mixer and the T3mm-mixer. The developed computational model, including the kinetics parameters estimated for the first time in this work, will be used for the design of a prototype for the industrial precipitation of Mg(OH)2 from saltwork brines in an industrial environment.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
Mg(OH)2 PSDs for Cases #1–5. PSDs were obtained after 5 min of ultrasound treatment and using PAA as a dispersant. Measurements were carried out using the Malvern Zetasizer Nano ZSP.
Figure 2
Figure 2
Characteristic sizes from left to right and top to bottom, d10, d21, d32, d43, derived from PSDs, versus initial MgCl2 concentrations (d10, top-left/d top-right/d32 bottom-left/d43 bottom-right).
Figure 3
Figure 3
1D model flow chart.
Figure 4
Figure 4
Spatial evolution of TDR, ε, (red line) and kinetic energy, k, (blue line) over the mixing channel length. Case study operative conditions: T2mm-mixer, 12.3 m/s velocity in the mixing channel namely flow rate of cases #1–5 (top). T2mm-mixer, 4.1 m/s velocity in the mixing channel, namely the flow rate of case #7 (bottom).
Figure 5
Figure 5
Variance evolution obtained using the TDR and kinetic energy from CFD simulations as a function of the residence time (s) for three flow rates (cases #5–7). The solid line refers to case #5, the dashed line refers to case #6, and the dotted line refers to case #7.
Figure 6
Figure 6
Supersaturation profile reconstructed from the ions concentrations calculated through the model for different flow rates as a function of the residence time (s) for cases #5–7. The solid line refers to case #5, the dashed line refers to case #6, and the dotted line refers to case #7.
Figure 7
Figure 7
Characteristic sizes, from left to right and top to bottom, d10, d21, d32, d43, derived from the measured PSD (red symbols) and predicted by the model (black lines—all phenomena, green line—molecular processes only), versus the initial MgCl2 concentrations.
Figure 8
Figure 8
SEM analysis for case #5.
Figure 9
Figure 9
Reconstructed PSDs from their moments, compared with the experimental ones. Each comparison refers to the concentration set investigated #1, #2, #3, #4, #5, and #6. Black lines are the PSDs from simulations, whereas the red dotted lines are the PSDs from experimental tests (#1, top-left/#2, top-middle/#3, top-right/#4, bottom-left/#5, bottom-middle/#6, bottom-right).
Figure 10
Figure 10
Characteristic sizes, from left to right and top to bottom, d10, d21, d32, d43, derived from the measured PSDs and predicted by the model at different flow rates or different mean velocities in the mixing channel. Effect of the velocity on the PSDs in two different systems. Experimental results in the T2mm-mixer (red squares) (i), experimental results in the T3mm-mixer (blue dot) (ii), simulations for the T2mm-mixer (solid line) (iii), and computational predictions for the T3mm-mixer (dashed line) (iv).
Figure 11
Figure 11
Homogeneous nucleation rate (solid line) compared with the heterogeneous one (dashed line) using the inferred primary nucleation parameters.
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