Reduced basins of attraction of large dynamical systems for the simulation of chemical reactors

In this work we describe an approach to discriminate among initial conditions leading to different dynamic steady-states. To this aim, we define a class of initial conditions for the vector state by means of a functional form which is, generally, dictated by the physics and operation procedures of the chemical reactor. It is then possible to scan a reduced parameter space and identify the regions pertaining to each attractor of the dynamical system. These regions are the intersections of the basins of attraction with the -dimensional manifold implicitly defined by this particular class of initial conditions, and, to all practical purposes, represent the attraction basins of the sys¬tem. A direct search algorithm is constructed to identify the boundaries of the reduced basins. The proposed procedure is here applied to a PFR, but can be used for a much wider range of applications in which large dynamical systems are used to simulate the dynamics of chemical reactors, in all cases when suitable classes of initial conditions can usefully be defined to represent operation conditions for the start-up.