Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.