Modeling Catalyst Extrudate Breakage by Impulsive Forces

Here we describe the reduction of the average length to diameter ratio of catalyst extrudates by breakage upon collision with a surface. For this, the authors link the flexural strength of the extrudate described by the Euler-Bernoulli modulus of rupture to the impulsive force the extrudate experiences as described by Newton’s second law. This force balance is applied at the asymptotic length to diameter ratio which is reached after many repeated impacts. This approach yields a dimensionless group as the ratio of the rupture force by bending to the impulsive force by collision and shows that the asymptotic length to diameter ratio is directly proportional with the square root of this group. This dimensionless group also allows one to define a severity of the collision via the impact velocity and the time of contact of the collision. Finally, we also show how the effect of operational severity sequencing and severity conditioning on catalyst breakage can be well described by the method presented.