CRYSTAL GROWTH Simulation of Mixing Effects in Antisolvent Crystallization Using a & DESIGN Coupled CFD-PDF-PBE Approach 2006 Xing Yi Woo,†,‡ Reginald B. H. Tan,‡,§ Pui Shan Chow,§ and Richard D. Braatz*,† VOL. 6, NO. 6 - Department of Chemical and Biomolecular Engineering, UniVersity of Illinois at Urbana-Champaign, 1291 1303 600 South Mathews AVenue, Urbana, Illinois 61801, Department of Chemical and Biomolecular Engineering, National UniVersity of Singapore, 4 Engineering DriVe 4, Singapore 117576, and Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833 ReceiVed July 1, 2005; ReVised Manuscript ReceiVed February 27, 2006 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. Introduction vent crystallization process to quantify the effects of mixing on the product crystal characteristics such as the CSD, which Antisolvent crystallization is used widely in the pharmaceuti- determines the bioavailability of the drug and efficiency of cal industry. This enables the crystallization of thermally downstream processes (e.g., filtration and drying).31 sensitive pharmaceuticals without introducing large temperature changes in the process.1,2 Current state-of-the-art crystallization The modeling of well-mixed crystallizers involves the technology such as impinging jet crystallizers utilizes high- computation of the population balance equation (PBE) together intensity mixing of the antisolvent and the solution to produce with the material balance equations for each species in solution. crystals smaller than 25 µm with improved bioavailability and Numerous numerical techniques that compute the full CSD have increased dissolution rates,3-5 which, at the same time, reduces been used to model well-mixed batch, semibatch, or continuous 32-45 the undesirable effects of milling.6,7 Various experimental studies crystallizers. To account for nonideal mixing, the PBE has of antisolvent crystallization in an agitated semibatch vessel to be coupled with the transport equations of mass, momentum, 46 indicate that the crystal size distribution (CSD) depends strongly and energy. One approach is to couple turbulent computational on the operating conditions, such as agitation rate, mode of fluid dynamics (CFD) codes with the solution of the PBE, and addition (direct or reverse), addition rate, solvent composition, most of the literature studies focus on reactive crystallization 47-50 51 and size of the crystallizer.5,8-20 The polymorphic or pseudopoly- systems. A recent paper by Choi et al. models the morphic form can also depend on the operating conditions.21-26 antisolvent crystallization process in a jet Y-mixer using a hybrid Most variations in the operating conditions have a direct CFD-PBE approach but neglects the micromixing effects. influence on the mixing of the antisolvent and the solution, Compartmental modeling, where the crystallizer is divided into which affects the localized supersaturation and, thus, the crystal a number of well-mixed compartments connected by inter- 52 product. Because the dependence of nucleation and growth rates changing flows, is a less computationally intensive approach. on supersaturation is highly system specific, determining the One strategy is to compartmentalize the crystallizer into regions optimal process conditions that produce the desirable crystal that are, to some degree, homogeneous in properties of interest product can require numerous bench-scale laboratory experi- (e.g., suspension density, energy dissipation, supersaturation), ments, which might not be optimal after the scale-up of the as determined by CFD simulations.53 However, compartmental crystallizer, as the mixing effects and spatial distribution of modeling oversimplifies the flow field and, most importantly, supersaturation can be vastly different.27,28 In addition, control it loses the spatial resolution of the supersaturation and turbulent strategies developed on the basis of the assumption of perfect energy dissipation distribution in the crystallizer. mixing may not result in the intended crystal product when Subsequently, the effects of micromixing have been included implemented at the industrial scale.29 A pressing issue for the in coupled CFD-PBE computations to model turbulent prec- pharmaceutical industry is the regulatory requirement of con- ipitators54-62 (here, the term “precipitation” is reserved to refer sistency in the various chemical and physical properties of the to reactive crystallization), in which a variety of methods were crystals, including the CSD.30 Such concerns motivate the used to approximate the probability density function (PDF),63,64 development of a computational model to simulate the antisol- which is a statistical description of the fluctuating scalars (e.g., species concentrations) at a subgrid scale. The solution of the * To whom correspondence should be addressed. Tel: 217-333-5073. PBE was obtained by the method of moments, which only Fax: 217-333-5052. E-mail: [email protected]. computes the average and aggregate properties of the crystalline † University of Illinois at Urbana-Champaign. ‡ National University of Singapore. phase. Recently, a supercritical antisolvent crystallization process § Institute of Chemical and Engineering Sciences. was modeled using this strategy.65 10.1021/cg0503090 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/20/2006 1292 Crystal Growth & Design, Vol. 6, No. 6, 2006 Woo et al. An alternative method used to include micromixing effects Integration of CFD, PBE, and PDF Models in precipitation models utilizes a multizonal approach in a This section describes the numerical methods used to compute Lagrangian framework,66 in which the precipitator is divided (1) the PBE for the evolution of CSD and (2) the PDF of the into a few segregated zones (e.g., feed/reactant zone, mixed/ local turbulent fluctuations, which are directly integrated into a reaction zone, contact zone, bulk zone). The volume change of CFD code. In addition, the expressions for the crystallization the zones and the material exchange between the zones are kinetics and the effective viscosity are presented. determined by the meso- and micromixing rates.67 The reduction High-Resolution, Finite-Volume, Semidiscrete Central in the computational expense by eliminating the direct linkage Schemes. High-resolution finite-volume methods have been to CFD computations enabled the simulation of the PBE investigated primarily in the applied mathematics and compu- equation for the full CSD.68-72 In some instances, additional tational physics literature.90 These methods provide high ac- approximations included the confinement of nucleation and curacy for simulating hyperbolic conservation laws while crystal growth to certain zones. A variation of this approach by reducing numerical diffusion and eliminating nonphysical Kresta et al.73 used a multiscale Eulerian-Lagrangian frame- oscillations that can occur with classical methods. Being in the work to couple the zones in the bulk fluid, governed by long class of finite volume methods, such methods are conservative, time and length scales, with the discretized volumes of the feed which ensures the accurate tracking of discontinuities and plume, governed by short time and length scales. preserves the total mass within the computational domain subject Compartmental modeling, coupled to the solution of the PBE to the applied boundary conditions. Another advantage is that for the full particle size and shape distribution, also has been these numerical schemes can be easily extended to solve applied to cooling crystallization and polymerization processes.74 multidimensional and variable-coefficient conservation laws. The simulations of CSD by Ma et al.29,75 and Sha and Palosaari76 High-resolution central schemes for nonlinear conservation took into account the spatial distribution of the solid particles laws, starting from the NT scheme of Nessyahu and Tadmor,91 of different sizes, which is important when the crystalline phase have the advantages of retaining the simplicity of the Riemann- is much denser than the solution. This was an advance over the solver-free approach, while achieving at least second-order earlier works in modeling crystallizers that assumed that the accuracy. Kurganov and Tadmor86 and Kurganov et al.92