Usually crush strength is not the limiting factor. Certainly the crush strength needs to be at least as much as would be required for the bed of catalyst prior to fluidization. Most manufacturers have a tear sheet on their website which lists the crush strength. What usually is much more important is how much attrition occurs from the fluidization process itself. That can be determined in a laboratory setup where a certain amount of the candidate catalyst is fluidized under conditions resembling the commercial reactor as closely as possible (velocity of gas, e.g.), preferably at the same temp. and pressure etc. So a mini-bench unit would be needed to get a definitive answer as to whether the catalyst will hold up in the actual system. A four inch diameter reactor or so would be the minimum size else slugging behavior would skew the results, I should think. The results will differ if the catalyst is a transport reactor catalyst like in a FCC or it is a bubbling bed with minimal elutriation. Just how much attrition could be tolerated would depend on the specifics of the process such as how much of a nuisance are the fines in regard to product separation, whether a hot gas filter or porous metal filter can be used to remove them or if a cyclone is needed or both, do the fines wind up in quench water or do they end up in an incinerator causing particulate pollution etc., and how valuable is th ecatalyst and cost of the makeup catalyst. Also if the fines cause plugging and blockages in exchangers downstream vs. if they will readily flow out to collection. Additionally, standard drop tests are important that emulate the conditions during catalyst loading operations.
The ability of the catalyst to withstand thermal shock, rapid depressurization and similar events will also be important in ensuring viable lifetime.