Modeling and Simulation of Vertical Continuous Cooling Crystallizers for the Sugar Industry

Abstract

Vertical continuous cooling crystallizers (VCCC) are commonly used in the sugar industry for the economically important final recovery of sucrose from the mother liquor present in the massecuite obtained at the end of the vacuum evaporative crystallization stages. In this work, a steady-state one-dimensional distributed model is formulated to simulate well-designed VCCC in which the massecuite follows approximately an ideal plug-flow pattern. The model consists of seven ordinary differential equations comprising mass, energy, and crystal population balances. The model describes the changes (along the crystallizer height) of the massecuite weight fraction of crystals, mother liquor dry substance content, mother liquor purity, crystal average size, crystal size coefficient of variation, massecuite temperature, and cooling water temperature. Simulation of the model yields a very accurate description of the reported performance of a VCCC [with vertically oscillating horizontal cooling coils (OVCC system)] from a beet sugar factory in Germany.

Digital Twin for Monitoring of Industrial Multi-Effect Evaporation

“…As desired brix values for each tank are defined by the operation crew, these values were used as references for calculation of the initial conditions and for corrections performed by the numerical state observer (Equation 7). The specific gravity and thermodynamic properties of the juice were calculated as described by Llano-Restrepo (2005) [22], Rein (2016) [20] and Hugot (1986) [23], considering effects of sugar content, sugar purity and temperature. The thermodynamic properties of vapor streams, such as specific weight and enthalpies, were calculated as described by Smith et al (2001) [24].…”

Librería de Modelos Orientada a Objetos para la Simulación del Cuarto de Azúcar: Cristalizador Continuo por Evaporación al Vacío

“…Existen varios trabajos previos sobre modelado de tachas continuas por evaporación al vacío para la industria azucarera, así se tienen por ejemplo las contribuciones de Broadfoot (1980), Hoekstra (1985), Love (1991) y más recientemente un muy completo tratamiento del tema por Hassani, Saidi y Bounahmidi (2001). La contribución de Llano-Restrepo (2005), aunque específicamente dedicada a los cristalizadores verticales por enfriamiento, merece ser citada en este contexto. Cualquier esfuerzo de modelado en esta área, además, se beneficia del aporte de un conjunto importante de literatura técnica sobre el proceso de fabricación de azúcar (ver Van der Poel et al, 1998 y las referencias ahí contenidas), en particular en lo que concierne a la cinética de la cristalización (Heffels, 1986;Ekelhof y Schliephake, 1995).…”

“…La determinación de los valores de k s , k R y c ns en función de la temperatura y de la concentración de impurezas puede ser seguido en el artículo original y también en Llano-Restrepo, (2005). La expresión original para el crecimiento ha sido modificada mediante la multiplicación de un factor, f b (cc) para tener en cuenta la influencia de la presencia de la masa de azúcar ya cristalizada en la suspensión.…”

Operating Strategy for Continuous Multistage Mixed Suspension and Mixed Product Removal (MSMPR) Crystallization Processes Depending on Crystallization Kinetic Parameters

“…19,20 The PBE have been applied for estimating and modeling various crystallization systems. 11,12,[21][22][23][24] However, PBE containing breakage and agglomeration terms, which are commonly expressed as integral functions, are so complex that analytic solution of the PBE could not be obtained. 18 Although solutions of the PBE could be obtained by several numerical methods, such as the method of moments, 25,26 the method of characteristics, 27 discretized population balances, [28][29][30] and weighted residuals, 31 the computation time for model solving is significantly long and it is too difficult to estimate the parameters required for expressing the breakage and agglomeration phenomena.…”

“…These crystallization systems are usually modeled by utilizing population balance equations (PBEs), as a well-designed mathematical framework for describing the growth, nucleation, breakage, and agglomeration of crystals . The PBE was extended to crystallization by including expressions for nucleation and growth. , The PBEs have been applied for estimating and modeling various crystallization systems. ,,− However, PBE containing breakage and agglomeration terms, which are commonly expressed as integral functions, are so complex that analytic solution of the PBE could not be obtained . Although solutions of the PBE could be obtained by several numerical methods, such as the method of moments, , the method of characteristics, discretized population balances, − and weighted residuals, the computation time for model solving is significantly long and it is too difficult to estimate the parameters required for expressing the breakage and agglomeration phenomena.…”