High‐order simulation of polymorphic crystallization using weighted essentially nonoscillatory methods

Abstract

in Wiley InterScience (www.interscience.wiley.com).Most pharmaceutical manufacturing processes include a series of crystallization processes to increase purity with the last crystallization used to produce crystals of desired size, shape, and crystal form. The fact that different crystal forms (known as polymorphs) can have vastly different characteristics has motivated efforts to understand, simulate, and control polymorphic crystallization processes. This article proposes the use of weighted essentially nonoscillatory (WENO) methods for the numerical simulation of population balance models (PBMs) for crystallization processes, which provide much higher order accuracy than previously considered methods for simulating PBMs, and also excellent accuracy for sharp or discontinuous distributions. Three different WENO methods are shown to provide substantial reductions in numerical diffusion or dispersion compared with the other finite difference and finite volume methods described in the literature for solving PBMs, in an application to the polymorphic crystallization of L-glutamic acid.

The space time CE/SE method for solving one-dimensional batch crystallization model with fines dissolution

“…4 and 5 compare the proposed scheme and the finite volume Koren scheme for fines dissolution with and without time delay for both size-independent and size dependent growth rates. The results with the same model are established by [20]. The numerical results for both the schemes are almost overlapping, but the current scheme gives better results for the proposed model.…”

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

“…Numerous discretisation methods for the PB equations with different orders of accuracy have been investigated and applied to various particulate systems (see for example [82,90,108,[129][130][131]). An alternative approach, high resolution finite volume method, was proposed [90,129,132] to provide high accuracy while avoiding the numerical diffusion (that is, smearing) and numerical dispersion (that is, nonphysical oscillations) associated with other finite difference and finite volume methods. This method has been shown to be a promising method and applied to various crystallisation systems [90,105,111,129,130] and further developed for effectively reducing the computation time using either an adaptive mesh technique [130] through redistributing the mesh by moving the spatial grid points iteratively and obtaining the corresponding numerical solution at the new grid points by solving a linear advection equation or a coordinate transformation technique [131] which utilizes a coordinate transformation technique to convert a size-dependent growth rate process into a size-independent growth rate problem with a larger time step to be allowed.…”

Simulation of metastable zone width and induction time for a seeded aqueous solution of potassium sulfate

“…According to this definition, Eqs. (15), (16) and (19) have been derived [21] as briefly as explained above. However, either MSZW or induction time was determined from the point the number density of the total (not seed-originated) crystals has reached a fixed value (N/M) det both in experiments [19] and in simulation.…”

“…In their simulation, no secondary nucleation was assumed to occur. This is an only one simulation study of MSZW found in the literature, although there have been many simulation studies on optimization of batch crystallization processes [14][15][16][17][18][19][20]. One reason for this may be that the point of appearance of ''first crystals'', which is usually treated as the point either the MSZW or the induction time is reached [1][2][3][4][5][6][7][8][9][10][11][12][13], is difficult to relate with nucleation kinetics.…”