A Scaling Analysis of the Effects of Natural Convection, when Sal’nikov's Reaction: P→A→B Occurs, Together With Diffusion and Heat Transfer in a Batch Reactor

A comparison of measured temperatures with those calculated numerically and analytically for an exothermic chemical reaction inside a spherical batch reactor with natural convection

“…diffusion or natural convection) and the timescale for reaction. This is similar to the results derived in a previous scaling analysis by Campbell et al (2005aCampbell et al ( , 2006 for Sal'nikov's reaction scheme. The constants applied to the scaling expressions were found to be of similar order in both works.…”

“…It is also interesting to note that the same deviation from linearity seen in Fig. 2, was also evident in the numerical results of Campbell et al (2005aCampbell et al ( , 2006, where in that case, the deviation from linearity was due to the transition from the slow reaction regime, to an oscillatory regime with much larger temperature rises. The deviation from linearity was observed in simulations both with very weak natural convection and in the complete absence of convection.…”

“…In the linear regime, the temperature rises are small enough for the exponential term to be ~ 1; however, when τ diffusion / τ reactio n is increased, the larger temperature rises that result, mean that the magnitude of the exponential increases and becomes significant, eventually leading to explosion. The agreement between the coefficients calculated in this work and that of Campbell et al (2005aCampbell et al ( , 2006 for the case when natural convection is significant is also rather good. The agreement for the two different reactions is expected, given that the constants should depend on the geometry of the system and not the order of the reaction.…”

“…2 and 3 with another scaling analysis by Campbell et al (2005aCampbell et al ( , 2006, for Sal'nikov's kinetic scheme, consisting of two, consecutive first-order reactions. In the purely diffusive case, it was shown by Campbell et al (2005aCampbell et al ( , 2006) that the dimensionless temperature rise for the slow reaction regime was also proportional to τ diffusion / τ reaction . The numerical coefficient calculated from the numerical results was of similar order to that derived above from the experimental measurements of Archer (1977).…”

“…Recent numerical studies of exothermic reactions occurring under the influence of natural convection (Campbell et al, 2005a, b;Campbell et al, 2006;Cardoso et al, 2004a, b) have considered a more complex reaction, namely that proposed by Sal'nikov (1949), consisting of two consecutive first-order steps. The concentration fields occurring during the course of this reaction are far more complex than those produced using the pseudo-zeroth-order approximation.…”