MATHEMATICAL-MODELS OF COCURRENT SPRAY-DRYING

A steady state mathematical model for a cocurrent spray dryer-is developed. The model includes the mass, momentum, and energy balances for a single drying droplet as well as the total energy and mass balances of the drying medium. A log normal droplet size distribution is assumed to hold at the exit of the twin-fluid atomizer located at the top of the drying chamber. The discretization of this log normal distribution with a certain number of bins yields a system of nonlinear coupled first-order differential equations as a function of the axial distance of the drying chamber. This system of equations is used to compute the axial changes in droplet diameter, density, velocity, moisture, and temperature for the droplets at each representative bin. Furthermore, the distributions of important process parameters such as droplet moisture content, diameter, density, and temperature are also obtainable along the length of the chamber. On the basis of the developed model, a constrained nonlinear optimization problem is solved, where the exit particle moisture content is minimized with respect to the process inputs subjected to a fixed mean particle diameter at the chamber exit. Response surface studies based on empirical models are also performed to illustrate the effectiveness of these techniques in achieving the optimal solution when an a priori model is not available. The structure of empirical models obtained from the model is shown to be in agreement with the structure of the empirical models obtained from the experimental studies.