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Modeling and simulation of a complex biological process for the remo®al of nutrients

Mathematical tools for studying panicle m s p o n in rotary drying and cooling processes are developed in this paper. In contran to conventional approaches aimed at deriving empirical or semi-empirical wrrelalions, a rigorous mathematical analysis which employs differential calculus and analytical geometry is emphasised in the current research. These developments allow accurate compufations of solid flowme, retention lime and parlicle holdup in rotary dryers with arbitrary flight configurations. Consequently, optimal dryer configuration design in terms of drum dimension, flight number and geometry can be achieved Lhraugh a better understanding of lhe mathematical insight of rotary dmm performance.Techniques developed using this method are applied to the distributed parameter model established earlier by the authors Wang el al., 1993) to replace out-dated correlations for the determination of retention Lime and solid holdup. As a result of the new developments, thc distributed parameter approach to the dynamics of rotary drying processes becomes more general and more reliable.

Employment of the axial dispersion theory to model chemical or biochemical processes often results in coupled parabolic partial differential equations (PDEs). The classical Danckwerts boundary conditions have been widely used to solve these PDEs despite the fact that artificial suppression of the exit concentration gradient to zero may be physically unrealistic and may cause numerical instability. In this study, a recently developed exit boundary condition is shown to be inapplicable to model processes which demonstrate significant differences in the dynamics of components ± typically found in biochemical processes. Using an activated sludge process and a pilot-scale subsurface flow (SSF) constructed wetland as case studies, we demonstrated in this study that a time-dependent exit boundary condition is more appropriate for use with the Danckwerts inlet boundary condition and the axial dispersion theory to model a biological system operating at near-plug flow conditions. Instead of using steady-state results we found that evaluation of alternative exit boundary condition using dynamic simulation results is more realistic.