Numerical simulation of the L-glutamic acid polymorphic system

The research detailed in this dissertation expands the field of knowledge in the area of numerical modelling of polymorphic systems and the suspension of polymorphs in stirred tanks. The L-glutamic acid polymorphic system has been the focus of numerous detailed studies in the literature and was chosen to provide a solid foundation on which to develop the numerical model in this treatise. This system consists of two polymorphs, a prismatic shaped [alpha] polymorph and a needle-like [beta] polymorph. The analysis of the L-glutamic acid system required a comprehensive study of nucleation, growth and dissolution processes. The rate of nucleation was calculated based on classical nucleation theory, with the birth and spread growth model chosen as the most appropriate method of describing the growth of the [alpha] and [beta] polymorphs. The kinetic equations developed by Scholl et al. (2006a) were used in the numerical model to calculate the change in size and number of crystals present in the system. A mass transfer dissolution model incorporating the Sherwood correlation was used to describe the dissolution process. An equation was developed to quantify the reduction of solute in the system throughout the transformation process. This work also included the development of a particle death term to account for the loss of [alpha] particles due to the dissolution process. This was required to account for the reduction in the zeroth moment in the system. The Method of Moments (MOM) was used to solve the governing dynamic equation. The MOM also formed the basis for the reconstruction of the particle size distribution which had been developed by Hutton (2009) but refined in this dissertation. The refinement consisted of the development of a more stable and robust method of calculating the intersection of moment iso-lines. This new approach to the reconstruction of particle size distributions (PSDs) was tested and verified for a typical distribution encountered in the L-glutamic acid system. A series of experiments were performed to verify that the experimental methods used in the literature were accurate and repeatable. The crystal yield was calculated for a range of initial conditions and the results compared to the published data. A very close agreement was achieved with a maximum error of less than 8% present. This verified the applicability of the experimental methods to the system under investigation. Numerically derived solid and solution concentration profiles achieved excellent agreement with published experimental results. A deviation between the experimental and simulated PSDs arose and was attributed to the presence of agglomeration and particle fragmentation within the experimental system. Agglomeration and fragmentation processes had not been considered in the kinetic equations extracted from the literature resulting in discrepancies in the numerical model. The performance of stirred tank reactors was analysed with particular emphasis on the cloud height and drag in suspensions. The fundamental theory behind suspension modelling and the influence of tank geometry were investigated. The drag induced by non-spherical particles was also examined. An expression for the drag coefficient developed by Loth (2008) was chosen to describe the drag induced by [beta] particles in the suspension. Numerical modelling of the suspension of L-glutamic acid was performed using Fluent 6.3.26. The RNG k-[epsilon] turbulence model was employed to solve the Reynolds-averaged Navier-Stokes equations in conjunction with a multiple reference frame model. An examination of the fluid phase in a stirred tank was carried out and the results successfully compared to the results of Wu and Patterson (1989). The stirred tank model contained a 10% solids volume loading which permitted the use of the Eulerian multiphase model. In order to predict the drag induced by the needle-like [beta] particles it was necessary to supplement the CFD code with the drag coefficient expression. This novel method of predicting the drag of the non-spherical [beta] particles was successfully verified by comparison with the widely validated Wen and Yu drag law within Fluent. The simulation of [alpha] and [beta] polymorphic suspensions in a stirred tank were also performed. The solid-liquid interfaces were calculated by monitoring the volume fraction levels at various heights throughout the tank. The simulated results were successfully validated against experiments. An average error of 4% and 8% existed for the [alpha] and [beta] suspensions, respectively. Further simulations were successfully carried out with combined [alpha] and [beta] suspensions. The homogeneity within the [alpha] and [beta] suspensions was examined with the bulk of the solid phase providing constant levels of volume fraction indicating good mixing within the tanks. A reduction in the solid volume fractions was apparent near the impeller shaft as the solid-liquid interface was approached. This was attributed to the decrease in velocity around the impeller shaft which reduced the energy available for particle suspension.