A lumped parameter model for ‘Model IV’ fluid catalytic cracking units

Abstract The state-of-the-art in structure preserving model reduction techniques is restricted to employing linear process descriptions, thereby requiring the linearisation of the original (nonlinear) ‘reference’ model. If a particular model consists of an explicitly time dependent set of DDEs and of position dependent ODE's (which are only implicit functions of time), the linearisation must be preceded by a transformation of the position dependent ODE-s to make their time dependency explicit. The technique presented in this paper is based on the application of the continuity equation to the integral average properties for which the gradient is given in form of position dependent DDEs. This method overcomes the problem of the dramatic increase in the number of states (characteristic of the conventional techniques based on the discretisation of the spatial coordinates), but still retains model accuracy. The use of the technique is demonstrated on the rigorous physico-chemical model of the reactor/regenerator section of a Model IV Fluid Catalytic Cracking Unit (FCCU) developed by McFarlane et al (1990). Open loop and closed loop responses of the original ‘reference’ and ‘lumped’ models are compared. The adequacy of the lumping is demonstrated.