(225b) 2-D Population Balance Modelling of Gibbsite Crystallization

Crystallization from solution represents a separation and purification technique with a wide spectrum of applications ranging from the specialty chemicals production to the bulk chemicals manufacturing, such as manufacturing of gibbsite used in the production of aluminium.

In most cases crystal size distribution (CSD) significantly affects the product quality and process productivity. Population balance equation has been well accepted as an appropriate mathematical framework for modeling CSD in such systems. However, with ever increasing complexity of population balance models, resulting from either multiple coordinates, model nonlinearities, or complex process layouts, there is a strong incentive to develop more efficient numerical solution algorithms.

In this work, we solve a gibbsite crystallization model, which involves nonlinear nucleation and crystal growth kinetics, using a finite-element based methodology. Our purpose is to investigate the potential of a general Newton's method-based finite element algorithms to solve nonlinear crystallization population balance models. Applicability of Newton's method for solving discrete population balance equations for a steady-state crystallization problem was demonstrated, for example, in the work of Hounslow et al. (2005), whereas advantages of the finite-element discretization scheme with self-adaptive grid and a Rothe's type time discretization for time dependant statement of population balance was revealed by Wulkow et al. (2001). In our approach, a dynamic 1-D problem is first transformed into a 2-D steady-state problem. It is then demonstrated that while they both lead to the same result, the computational effort needed to solve the 2-D problem is smaller than the effort required for the 1-D problem. The numerical procedures are compared to the analytical solution, which has been developed for the constant crystallization kinetics as a benchmark for testing different numerical solution schemes.

References

Hounslow M.J., Lewis A.E., Sanders S.J. & Bondy R. (2005). Generic crystalliser model: I. A model framework for a well-mixed compartment. AIChE Journal, 51, 2942.

Wulkow M., Gerstlauer A., & Nieken U. (2001). Modeling and simulation of crystallization processes using parsival. Chemical Engineering Science, 56, 2575.