Fixed Bed Reactor Hot Spot & Runaway Margin Calculator
Assess hot spot temperature rise (ΔT_max) and Barkelew parametric sensitivity boundary in cooled tubular catalytic reactors.
Exothermic Reaction & Heat Transfer
Hot Spot Amplitude & Stability Index
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Parametric Sensitivity & Fixed-Bed Runaway
Exothermic catalytic reactions carried out inside multi-tubular fixed-bed reactors (such as phthalic anhydride synthesis or ethylene epoxidation) generate heat faster at higher temperatures due to Arrhenius exponential dependence. If the rate of reaction heat generation exceeds the rate of radial heat conduction to the tube wall coolant, a localized thermal hot spot develops.
The Barkelew Stability Criterion
Van Welsenaere and Froment established that a fixed-bed reactor enters an uncontrollable runaway regime if the hot spot temperature rise exceeds the characteristic temperature scale: $$\Delta T_{crit} = \frac{R T_w^2}{E_a}$$ Beyond this threshold, a minor $1^\circ\text{C}$ increase in coolant temperature or feed concentration can cause the hot spot to violently spike by hundreds of degrees, sintering catalysts or exploding reactor tubes.