Length to diameter ratio of extrudates in catalyst technology I. Modeling catalyst breakage by impulsive forces

Abstract

Natural or forced catalyst extrudate breakage is an important phenomenon during catalyst manufacture. Here, a twoparameter model for predicting the reduction in the length to diameter ratio of catalyst extrudates due to breakage by impulsive forces as experienced in a laboratory drop test is developed. Part II will show how both parameters can be correlated with the strength of the extrudates and the severity of the drop test. For breakage by impulsive forces, the model reveals that extrudates are reduced in length to diameter ratio according to a pseudosecond-order break law. Also, a tie-in exists with the well-known Golden Ratio that is famous for its inherent esthetic value. Applying the model to cases of "severity sequencing" and "severity conditioning" reveals the nonlinear behavior of the length to diameter ratio and yields results that are often nonintuitive and hard to get without this engineering analysis.

Length‐to‐Diameter Ratio of Extrudates in Catalyst Technology: III. Catalyst Breakage in a Fixed Bed

“…To summarize, if a bed of extrudates is loaded in the bulk crush strength test and a stress P is applied, then the extrudates will break throughout the entire bed under the applied stress P to an average value given by Eq. (8). It is clear from the equation of the aspect ratio as a function of Be r that a bed with a starting aspect ratio F 0 has a critical pressure P c it can withstand given by:…”

“…Both the single‐pellet crush strength test and the bulk crush strength test are important aspects in understanding catalyst mechanical properties. When considering practical catalyst breakage, there also exists a need to determine the bending strength of the catalyst, and reference is given to Li et al , Staub et al and Beeckman et al , . The bending strength of the catalyst is characterized by the Euler‐Bernoulli modulus of rupture and is typically obtained in a three‐point bending test.…”

Length to diameter ratio of extrudates in catalyst technology II. Bending strength versus impulsive forces

“…Beeckman has shown that also a second asymptotic aspect ratio exists. It is observed after just one drop, when the starting aspect ratio is sufficiently large.…”

“…The development of the finite difference modeling of the drop test has been described in detail by Beeckman. The authors show that two asymptotic aspect ratios exist for collision against a surface.…”

“…In this follow‐up manuscript, we attempt to relate quantitatively, the parameters and to independently measurable properties of the catalyst extrudates, and also of course with the severity of the impact. For clarification, the authors drop the bolded L notation for aspect ratio used in Beeckman, in favor of the letter to avoid confusion with the notation L for the geometric length of the extrudate used herein.…”