THREE-PHASE MATHEMATICAL MODEL OF THE PROCESS OF DEHYDRATION AND GRANULATION IN THE FLUIDIZED BED

Abstract

A mathematical model is developed which takes into account the hydrodynamics of a fluidized bed, the contact of droplets with particles and their adhesion to the surface, as well as the kinetics of drying the solution on the surface of the particles. In developing the model, the following assumptions were made: the change in the parameters of the fluidized bed occurs in time, without taking into account the radial component and changes in height; heat exchange between air, particles and droplets is convective; particles are monodispersed, non-porous, agglomeration is absent. The intensity of the mixing of particles between the layers is described by the coefficient of the axial dispersion r, which depends on the velocity of the gas phase, as well as the properties of the particles. The droplets obtained with the pneumatic nozzle have a narrow size distribution, which allows them to be considered as a mono-dispersed phase. Between the drops there are no collisions and sticking, no sticking on the walls of the device. The droplets move through the fluidized bed, aligned with the air flow. When creating the model, the process of dehydration and granulation in the fluidized bed is considered as a heterogeneous three-phase process, during which they interact with three separate phases: the particles are the centers of granulation, the source material is ammonium sulfate in the form of droplets and the carrier - air. The system of equations is designed taking into account the empirical correlations for calculating the specific drying rate, the specific speed of droplet settling on the particles as a result of adhesion, the coefficient of the axial dispersion of the particles, the coefficients of heat transfer, the ratios for calculating the material losses and the thickness of the coating layer, as well as the initial conditions. To get the dynamic characteristics of the developed system, the Simulink library of the Matlab software package is used. Using the built-in library elements, we obtain a scheme of differential equations describing the model of the control object. In order to maintain the stable operation of devices with a fluidized bed and the necessary hydrodynamic regime inside the apparatus, it is necessary to develop an efficient system for controlling dewatering and granulation processes. The quality of management of the developed system directly depends on the accuracy of the object model. The results of the research allow to specify the model of the control object and become a reliable ground for developing an effective control system.