(427c) Dynamics and Control of Axially Dispersed Chemical Reactors

Axially dispersed reactors with simultaneous convection, dispersion and reaction are a common type of reactors that may be used to approximate real reactors. While the steady-state solution to an axially dispersed reactor is well described in the literature, its dynamic behavior is not often discussed. Studying this problem (generally described by partial differential equations (PDEs) with moving boundary conditions) helps to answer a class of industrial concentration transition problems, such as the product transition in a glass melting furnace where one glass product is gradually replaced by another with a different composition. In this work, the dynamics in an axially dispersed reactor is explored following a state-space approach. The state-space models can be constructed either analytically or numerically. In the analytical approach, a continuous state-space model is derived from eigenfunction expansion followed by solving a Sturm-Liouville problem. In the numerical approach, a high-dimensional discrete state-space model is formulated by discretization of the process PDE using the implicit finite difference scheme. Proper orthogonal decomposition is then used to reduce the order of the state-space model. In either case, an optimal control trajectory to achieve a concentration transition with input constraints is solved based on the derived state-space model using quadratic programming. Computer simulations are used to compare these two formulations and to illustrate the effectiveness of proposed optimization methods.