Description: We consider the steady state operation of wall-cooled, fixed-bed tubular reactors. In these reactors the temperature rise ..delta..T must normally be limited to small fractions of the adiabatic temperature rise ..delta..T/sub ad/, both to avoid runaway and maintain product selectivity. Yet ..delta..T/..delta..T/sub ad/ << 1 can only occur if eta = t/sub dif//t/sub reac/ << 1, where t/sub dif/ is the timescale on which heat escapes the reactor by ''diffusing'' to the cooled walls, and t/sub reac/ is the timescale over which the reaction occurs. So here we use asymptotic methods based on eta << 1 to analyze the 2-d reactor equations, and find the radial concentration and temperature profiles to leading order in eta. We then obtain a 1-d model of the reactor by substituting these asymptotically correct profiles into the reactor equations and averaging over r. This model, the ..cap alpha..-model, is identical to the standard (Beek and Singer) 1-d model, except that the reactor's overall heat transfer coefficient U is a decreasing function of the temperature rise ..delta..T. This occurs because as ..delta..T increases, the reaction becomes increasingly concentrated near r = 0, causing a decreased heat transfer efficiency through the reactor's walls. By comparing it with numerical solutions of the original 2-d reactor equations, we find that the ..cap alpha..-model simulates the 2-d equations very accurately, even for highly sensitive reactors operated near runaway. We also find that a runaway criterion derived from the ..cap alpha..-model predicts the runaway transition of the original 2-d equations accurately, especially for highly sensitive reactors. 19 refs.
Date: January 1, 1987
Creator: Hagan, P.S.; Herskowitz, M. & Pirkle, J.C.
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