A comparison between the insensitive Runge—Kutta, the semi—implicit extrapolation and the backward differencing methods in solving the ODE systems which describe the radical hydrocarbons pyrolysis

Abstract

The performances of the insensitive Runge—Kutta, the semi-implicit extrapolation and the backward differencing methods in solving the ODE systems which describe the free radical mechanism of heavy hydrocarbons pyrolysis are presented. From the free radical pyrolysis mechanisms proposed we select the Sundaram and Froment ( Ind. Engng Chem. Fundam 17, 174, 1978) variant. Instead of a pure kinetic system, the nonisothermal and nonisobaric reactor (Sundaram and Froment, 1978) is simulated. To offer more information, the Jacobian's eigenvalues are computed at a few points of the reactor using the EISPACK code (Smith et al. Lecture Notes in Computer Sience, 2nd Edns, Springer, New York 1976). Our results confirm the assumptions found in the literature, i.e. the extrapolation and the backward differencing methods perform better for large systems with n > 10.