Incertitude induced by testing a small number of catalytic pellets in fixed beds

Heterogeneous catalyst pellets evaluation is performed in smaller and smaller reactors with the main objective of reducing catalyst development costs. Downscaling raises the question: is there a lower limit to the number of pellets that ought to be tested in a reactor so that the results do not depend on which pellets are sampled? Major sources of variability among a catalyst pellet population are dimensions and many parameters that can be grouped as "intrinsic kinetic activity" (porosity, tortuosity, active phase repartition and availability).In this paper, we present a methodology to estimate the incertitude induced by variability on size and kinetics on the evaluation of the apparent kinetic constant in a fixed bed reactor. Analytical expressions are presented to predict this incertitude for sphere and cylinder shaped pellets, with a first order kinetic law in two limiting cases: the absence of mass transfer limitations and presence of severe internal mass transfer limitations. The predicted incertitude scales as the square root of sample population: downsizing increases the incertitude. We propose criteria to evaluate the minimum number of pellets to sample, so that sampling induced variability is lower than an acceptable incertitude, expressed in °C. This acceptable incertitude could be for example a fraction of the experimental temperature incertitude.