An Implicit FEM Solution of a PBE Model of Gibbsite Crystallization with Constant and Nonlinear Kinetics

Bekker, Andrey V.; Livk, Iztok

doi:10.1021/ie1019326

Cited by 6 publications

(18 citation statements)

References 23 publications

(42 reference statements)

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“…Since PBE cannot be solved explicitly, various numerical approaches have been introduced, i.e. the method of moments (MoM), the finite element method (FEM), , the finite difference method (FDM), , the method of characteristics (MoC), , the Monte Carlo method, , etc. For the purposes of this section, some studies based on modeling have been collected and reviewed.…”

Section: Mechanistic Multiscale Modeling Simulation and Optimizationmentioning

confidence: 99%

Continuous Crystallization Processes in Pharmaceutical Manufacturing: A Review

Orehek

Teslić

Likozar

2020

Org. Process Res. Dev.

107

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This scientific paper presents an overview of continuous solution crystallization in the pharmaceutical industry. Since the specific knowledge spectrum of precipitation is very broad, topics covering the following were analyzed and assessed in detail: a comparison between batch and continuous crystallizers, their engineering advantages/disadvantages, the introduction of the solid form structuring to continuously oriented chemical production, and the usage of the online process analytical technology (PAT) methodologies in interacting functional systems. Furthermore, mechanistic multiscale modeling, whose understanding is of decisive importance for further control application development, was thoroughly discussed as well. The multiscale modeling section also includes the simulation of processes and the optimization of crystallizers. In the last section, model-based predictive control (MPC) is considered, which also covers the intensification approach methods in the field of crystal formation and the introduction of new, highly potential continuous systems, e.g. the coiled flow inverter (CFI) crystallizer, in industry and academia. In the mentioned main sections, individual theme-related articles are collected, discussed, and compared; therefore, a reader can get acquainted with pieces of research, their found results, which have been developed until now, and various emerging perspectives. With regard to the importance of crystallization in the pharmaceutical industry, a reader can already find literature on continuous crystallization. However, due to the growing tendency toward the synthesis of products with specific properties which cannot be achieved with conventional approaches, more attention has been paid in the present work to the establishment of continuous systems for the production of specific fine chemicals. In addition, continuous crystallization could also enable more efficient and "on-demand" production, modeling for optimization, MPC, and intensification approaches. A review of the literature classifying studies according to the choice of a continuous system and their description was omitted in this study, as such reviews are already available in the literature.

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Section: Mechanistic Multiscale Modeling Simulation and Optimizationmentioning

confidence: 99%

Continuous Crystallization Processes in Pharmaceutical Manufacturing: A Review

Orehek

Teslić

Likozar

2020

Org. Process Res. Dev.

107

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“…Also, elliptic regularization is carried out to smooth the discontinuity between the values of the initial and boundary conditions in the convection equations by adding an artificial diffusion term. 23…”

Section: Formulation Of a Pde Agglomeration Model From The Safronov E...mentioning

confidence: 99%

“…A flowchart of the numerical algorithm can be found in Bekker and Livk. 23 The numerical algorithm refines a finite-element mesh with a second-order polynomial basis until the relative error in any dependent variable is less than a specified tolerance, which was set to 10 -7 for every cell of the mesh. The Gear method with a second-order fully implicit two-step backward-difference formula is used for variable time steps.…”

Section: Numerical Solution Of the Agglomeration Model And Its Valida...mentioning

confidence: 99%

Agglomeration Process Modeling Based on a PDE Approximation of the Safronov Agglomeration Equation

Bekker

Livk

2011

Ind. Eng. Chem. Res.

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A one-dimensional dynamic partial differential equation (PDE) agglomeration model is derived based on the continuous Safronov agglomeration equation. A regularized PDE agglomeration model, represented by a set of convectionreaction-diffusion PDEs, can be solved within a standard adaptive-mesh implicit numerical framework that does not require additional quadrature assumptions to evaluate the aggregation integral. The PDE agglomeration model is solved numerically using a general Newton's-method-based implicit Galerkin finite-element algorithm. The applied algorithm uses an automatic Gear-type time step and nonuniform adaptive-mesh strategies, which aids solution convergence. A numerical solution of the model for an agglomeration degree of 99.9% closely matches an asymptotic analytic solution of the original Safronov equation, which confirms the accuracy of the numerical procedure used. It is also shown that the number density function predicted by the new PDE agglomeration model satisfactorily agrees with the analytic solution of the Smoluchowski agglomeration equation. For small particle sizes and first and zeroth full moments, the two models give similar solutions. However, for larger particle sizes and the second full moment, the difference between the two models increases with increasing degree of agglomeration. Industrially important gibbsite agglomeration is used as a case study to demonstrate the application of the new numerical approach for agglomeration modeling.

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“…MAH is usually produced by the cooling crystallization of concentrated sodium aluminate solutions such as a postleaching solutions of bauxite . This process is quite different from the extensively investigated gibbsite precipitation, − which is usually performed from dilute sodium aluminate solutions through carbonation decomposition in the sintering process for alumina production or seeded hydrolysis in the Bayer process. Little systematic investigation of the crystallization of MAH has been carried out.…”

Section: Introductionmentioning

confidence: 99%

Crystallization Kinetics of Monosodium Aluminate Hydrate in Concentrated Sodium Aluminate Solutions

You

Zhang

Cao

et al. 2012

Ind. Eng. Chem. Res.

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The nucleation, growth, and agglomeration of monosodium aluminate hydrate (MAH) crystallization in concentrated sodium aluminate solutions were investigated in a steady-state mixed-suspension−mixed-product-removal (MSMPR) crystallizer, and the mechanism was analyzed in detail. The crystal growth was diffusion-and surface-integration-controlled, and the secondary nucleation, as a result of crystal−agitator and crystal−crystallizer collisions, was determined further. The agglomeration kernel, expressed in terms of mean residence time, growth rate, and suspension density, was found to have a positive order of about 0.52 in the suspension density, indicating that the agglomeration kernel increased at higher frequencies of collisions between particles. The growth rate of MAH was found to be higher than that of gibbsite in active NaAl(OH) 4 − NaHCO 3 systems, but the nucleation rate of MAH was lower than that of gibbsite in seeded-hydrolysis processes.

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An Implicit FEM Solution of a PBE Model of Gibbsite Crystallization with Constant and Nonlinear Kinetics

Cited by 6 publications

References 23 publications

Continuous Crystallization Processes in Pharmaceutical Manufacturing: A Review

Continuous Crystallization Processes in Pharmaceutical Manufacturing: A Review

Agglomeration Process Modeling Based on a PDE Approximation of the Safronov Agglomeration Equation

Crystallization Kinetics of Monosodium Aluminate Hydrate in Concentrated Sodium Aluminate Solutions

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