Numerical Solution of Batch Crystallization Models

An efficient and accurate numerical technique is introduced for the simulation of a batch crystallizer equipped with a fines dissolution unit incorporating a time-delay. The dissolution of small crystals (fines dissolution) improves the product quality and facilitates the downstream processes. The proposed method follows two steps. In the first step, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest, giving the discrete values of growth and nucleation rates. In the second step, theses discrete values are used along with the initial crystal size distribution (CSD) to construct the final CSD. The method of characteristics and Duhamel's principle are employed for deriving an expression for CSD from the given population balance model (PBM). An alternative quadrature method of moments (QMOM) is introduced for approximating integrals in the ODE system of moments and mass balance. In this technique, orthogonal polynomials, obtained from the lower order moments, are used to find the quadrature abscissas and weights. The numerical results of our scheme are validated against the results of high resolution finite volume scheme results. Our scheme was found to be efficient, accurate, and free from numerical dissipation and dispersion.