Simulation of counter-current equilibrium crystallizer

Abstract

A computer method has been developed for the simulation of crystallization units. It computes material and energy balances for multistage countercurrent crystallizers with vapor, liquid, and multiple solM phases In equilibrium. I t allows rigorous correlations for component and mixture properties but does not take into account rate effects in the design. The algorithm used in the block has been developed to solve difficult numerical problems inherent in the equilibrium calculations involving solids.Crystallization has always been an effective separation operation in chemical processes, especially for obtaining high-purity products. However, its application has been somewhat restricted because of the difficulty of handling solids as contrasted to handling gases or liquids. Rising energy costs now call for a renewed interest in crystallization, since it can be a very energy-efficient operation if refrigeration is not required to lower temperature to the freezinglmelting point.This operation has probably not been utilized to its potential in chemical processes due partially to a lack of design procedures. Specifically, a reliable method for the simulation and design of such processes has not been available. A computer method has been developed in this work to meet this need. Single-Stage Multiphase EquilibriumSteady-state simulation of multistage countercurrent crystallization processes has been a challenging problem for many years. The difficulty in converging to numerical solutions is generally caused by the existence of multiple solid phases and of liquid occlusions in the solid streams.Occlusions add to the magnitude of the off-diagonal terms in the material balance matrices and make the matrices more ill-conditoned. In the extreme, the multistage system becomes a single back-mixed stage with singular matrices. For a system with multiple solid phases, it is necessary to include only equations of existing phases. This may be accomplished either by an enumeration of all possible phases or by using phase equations that degenerate automatically to only those required (Chien and Larsen, 1974). A review is given in papers by Gautam and Seider (1979).These numerical problems inherent in the crystallization simulation have not been solved successfully. In this work, a new approach has been found to avoid these problems.Most multistage crystallizers have relatively few stages.A simple approach to avoid singular matrices is to simulate each stage rigorously and then to use either recycle convergence methods or the stage-by-stage method suggested by Lewis and Matheson (1932) for multistage problems. This approach has been successful in this study in solving multistage crystallizer simulation problems. The simulation of a single stage crystallizer is described in this section, followed by a discussion of multistage simulations.A new method has also been developed to provide solutions to systems with multiple pure solid phases. It is much simpler than the enumeration method. Since the dimensionality of the problem has been k...

Particle size improvement by a countercurrent tower crystallizer

“…Mathematical development of simulation models for countercurrent column melt crystallizers has been presented by Player (1969), and more recently by Chien (1984). However, these examples do not deal directly with product CSD.…”