FINITE-DIFFERENCE METHODS FOR COMPUTING THE TURNING-POINT OF IGNITIONIN A TUBULAR REACTOR OPERATED ADIABATICALLY

A system of partial differential equations (PDEs) is derived to comput e the point of ignition (with respect to the Damkohler number) in an a diabatically-operated tubular reactor in which a first-order, exotherm ic and irreversible A --> B reaction takes place. The temperature-depe ndent rate constant is assumed to obey the Arrhenius Law. A family of numerical methods using finite-difference approximations is developed to integrate the system of PDEs. The numerical schemes are analysed fo r stability by a linearized von Neumann method. Two numerical methods are selected to compute solutions: the explicit Euler Method in conjun ction with global extrapolation and a novel semi-explicit computation scheme.