Simulation of Mixing Effects in Antisolvent Crystallization Using a Coupled CFD-PDF-PBE Approach

Abstract

Antisolvent crystallization is widely used in the production of pharmaceuticals. Although it has been observed experimentally that the crystal size distribution is strongly influenced by the imperfect mixing of the antisolvent with the solution, these effects have not been adequately quantified. In this work, a turbulent computational fluid dynamics (CFD) code was coupled with a multienvironment probability density function (PDF) model, which captures the micromixing in the subgrid scale, and the population balance equation, which models the evolution of the crystal size distribution. The population balance equation (PBE) was discretized along the internal coordinate using a high-resolution central scheme. The presence of solids was addressed by treating the suspension as a pseudo-homogeneous phase with a spatial variation in the effective viscosity. This coupled CFD-PDF-PBE algorithm was applied to an antisolvent crystallization process in an agitated semibatch vessel, where the rising liquid level was modeled by a dynamic mesh. The effects of agitation speed, addition mode, and scale-up on the local primary nucleation and size-dependent growth and dissolution rates, as well as the crystal size distribution, were numerically investigated.

An explicit adaptive grid approach for the numerical solution of the population balance equation

“…(38) and (43) are both sufficient (a) and necessary (b) conditions for ρ ∞ = ρ(·, s ∞ ) to be a steady-state solution of Eq. (46) for some s ∞ ≥ 0.…”

“…Alternative approaches such as the method of moments and stochastic solution schemes have been reviewed by Ramkrishna [33] and Rigopoulos [35], for instance. In the context of discretization-based methods, the PBE is commonly discretized on a fixed grid in particle property space and the resulting semi-discrete equations are solved by applying a standard Eulerian solution scheme [43]. Here, the semi-discrete system consists of scalar transport equations for so-called discrete number densities.…”

From form to function: Crystallization of active pharmaceutical ingredients

“…While at first glance these two seem like conflicting objectives, our ability to realize both of these may be facilitated by the thoughtful application of scientific and engineering fundamentals, new enabling technologies, such as process analytical technology (PAT), process modeling tools including population balance and computational fluid dynamics (CFD) models, 27,28 and innovative solutions in the area of continuous processing. The last of these concepts deserves a brief discussion as continuous processing has found limited application in the pharmaceutical industry relative to the rest of the chemical industry, and there are many who feel that this has been a missed opportunity.…”

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

“…Campos and Lage [9] pointed out that, strictly, DPBs are not function approximation methods and that the particle size distribution hence converges slower than its moments as the number of bins is increased. This is at variance with direct discretization approaches such as finite volume [72] or finite element methods [12,13]. Here, however, both the particle property distribution and all of its moments are affected by a discretization error [63].…”

“…In the context of BaSO 4 precipitation in a tubular reactor, Marchisio et al [38,40] formulated a three-environment model in terms of mixture fraction, a reaction progress variable as well as the first few moments of the particle size distribution. Woo et al [72] also considered a three-environment model, but combined it with a discrete finite volume-based representation of the particle size distribution in order to analyze an antisolvent crystallization process in a semibatch stirred reactor. The DQMOM-IEM method, on the other hand, was applied by Gavi et al [21] in conjunction with the QMOM and by Akroyd et al [1] in combination with the MOMIC.…”