Solution of Ill-Posed Problems on the Prediction of Nonstationary Regimes of Work of a Reactor for Fischer–Tropsch Synthesis

Abstract

On the basis of analysis of experimental data on the temperature in a reactor for Fischer–Tropsch synthesis, a method for prediction of loss in thermal stability of such a reactor by extrapolating the reactor temperature in time with the use of the first-order and second-order time derivatives of experimental data on this temperature has been developed. Since, in this case, the calculation of derivatives is an incorrect procedure because of the rapid changes in the reactor temperature and the accidental errors in its measurement, this problem was solved using the Tikhonov stabilizing-functional method. An integro-differential equation of calculating the first-order and second-order time derivatives of experimental temperatures of the reactor, providing a minimum of the stabilizing functional, has been derived. The possibility of predicting the behavior of the temperature in a reactor under the conditions of loss in its thermal stability was demonstrated through the comparison of calculation and experimental data on the reactor temperature. The method proposed can be used for development of an automated system for control over the working conditions of a reactor for Fischer–Tropsch synthesis for prevention of its thermal explosion.