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Modeling and Nonlinear analysis of Chemical and Biological Reactor-Separator systems
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The primary objective of a design engineer is to ensure a safe, efficient design of equipment to carry out a process. This needs a good understanding of the various processes occurring in the system. The operation of the equipment under varying operating conditions must be analyzed since any process is prone to disturbances. This needs a model which captures all interactions. Such a model can be used for nonlinear analysis and to subsequently develop control strategies and optimize plant operation. The steady state and dynamic behavior is predicted by carrying out nonlinear analysis. This gives us a clear picture of the nature and the number of steady states that exists for different operating conditions. A small perturbation in an operating condition from a stable steady state may lead to a new stable steady state or even periodic solutions (continuous oscillations), which is undesirable as far as the safety of the plant is concerned. To give a better perception of how non-linear analysis is applied, a cybernetic model of a biological reactor is considered and non-linear analysis is carried out. A new numerical methodology is developed to evaluate the steady state solutions of complex cybernetic models. The nonlinear behavior of an activated sludge process (ASP) is analyzed. Earlier efforts have considered an unstructured model for the aerator. In this work, we propose a structured cybernetic model to incorporate the regulatory features of the microorganism in the aerator. These regulatory features control the rate of uptake of the substrates by the cells in the aerator. The model equations governing the system behavior are ordinary differential equations. We compare two modes of sludge withdrawal from the system: (1) from the aerator and (2) from the settler. We observe a shift in the uptake rates of the substrates as we vary the dilution rate. A two parameter continuation is also carried out to investigate the effect of other operating parameters on the non-linear behavior. We propose another detailed model for ASP and discuss the preliminary results of the simulations carried out.

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