Impact of the non-uniform particle size on conversion in fluid–solid reactions with shrinking-core type kinetics

Abstract

The impact of non-uniform particle size on conversion in fluid–solid reactions with shrinking-core kinetics was investigated in the present work. Classical conversion-time equations for film, ash, and chemical reaction control regimes were extended to systems of solid spheres with log-normal particle size distribution (PSD). This PSD is described by the harmonic mean radius and a dispersion parameter that reflects the deviation regarding uniform size. For every controlling regime, small particles exhibit rapid conversion, while larger particles demand longer reaction times. Hence, overall conversion can be calculated as the result of the contribution of the conversion of each particle size weighted by the proportion of that size over the whole distribution. A characteristic reaction time is defined analogously to systems with uniform-sized particles but based on the harmonic mean radius of the PSD. Thus, conversion-dimensionless time curves for uniform and non-uniform sizes coincide at low reaction times but deviate significantly at higher conversions, with lower values of conversions as the dispersion in the PSD increases. These discrepancies negatively affect the reactor design if the dispersion in the particle sizes is ignored. A simple algebraic equation, capable of relating the conversion to the dimensionless reaction time and the dispersion in the particle size distribution for all controlling regimes, was proposed. This formula enables accurate estimation of conversions or dimensionless reaction times, thus providing a practical tool for reactor design or assisting the first steps of optimization algorithms when fluid–solid reactors are fed with solids having variable ranges of particle sizes.