Since it doesn't seem you have a mechanical engineering degree let me try to put it very simply: Probably fail, but here goes.
Sheave size has no bearing on the subject matter under normal conditions unless you purposefully introduce garbage into the bearing/bushing itself. It matters a lot if you are trying to rotate said pulley from an internal torque as in an electric motor. It would appear that whoever wrote that lazy drivel, lifted that information right from a power sheave company literature. Now, I would LOVE to have an electric motor to haul people out of crevasses, but I will let you carry it along with the generator OK? So, all Sheave diameter increases efficiency information for POWERED applications needs to be discarded. We have to go back to basics of what is happening when we are pulling on the rope in question.
Let me explain. A bit convoluted: Assume the small bushing Petzl/DMM,CMI has is sufficient for rope bend considerations. Its diameter is approx 1.5inches. A 9mm has no problems going over this. A 10.2mm I have is a bit stiff. A bearing DMM prussic minding pulley has a diameter of about 2".
The real deciding factor is can the rope/cable in question actually bend easily around said diameter? If all of your "power" is being used to bend the rope/cable, then your "efficiency" will be lower. IE the DMM "revolver" pulley is WAY too small. Yea, it works in a pinch, but a good portion of your work energy is being used to HEAT
the rope due to internal friction of the fibers bending/sliding against one another instead of lift the object. A good rule of thumb is, " If you can easily bend 180 said rope/cable in your hand they any diameter of sheave above this is essentially useless. For this reason, it is better to use 2 identical biners as a pulley than 1 as it creates a larger diameter "pulley" and therefore less inernal heating of the rope.
The difference is maybe 1% between extremely small and a very large sheave under starting conditions and that is only in regards to static friction. Static means the object in question is not moving. Introduce garbage into the bearing and then, yes, Sheave/bearing diameter does matter as you are trying to "crush" rocks. If you are so stupid as to not keep your pully's clean, hey more power to ya. Once the person/object starts moving the efficiency of hauling is no different in regards to sheave size. This is like not cleaning your CAM's. If you are that stupid you deserve everything coming your way and the DARWIN award that ultimately follows.
SO, yes, Petzl can claim higher efficiencies with a larger pulley as technically they are correct though its under 1%. In reality, the static friction inside a bearing/bushing is absurdly small and not even worth contemplating as we are not trying to turn the pulley to create said torque on said rope and lift an object like one does with an electric motor! IE transferring torque from the inside of the sheave through friction to the rope/cable in question. Only when you do this does the diameter (area) of the sheave matter a GREAT DEAL.
PS. Yes, I have read their(Petzle, CMI, BD) reports before and when you practice crevasse rescue you can easily tell the difference between no bearings and bushings. The difference between bushing's and bearings is very small. As far as I am concerned, especially on 2 man rope teams each person must carry 2 pully's that have been at least heavily graphited. A graphited climbers pulley has same efficiency as a greased shielded bearing pulley and for the same weight you can carry nearly double the number of pully's and likewise the money you save can go into buying more gear. If you want the ultimate in efficiecy you use non greased bearings. This grabs you another 5% efficiency. I would use such bearings in my competition engineering projects. You do need to make sure they stay clean.
PPS. The CMI statements are pure drivel as the idiots claim 133% efficient
. Sweet, they create energy...
PPPS. To bring home the Sheave diameter has no bearing, next time you are beside a VERY large crane, you will notice that the DRUM around which the vast majority of the cable is wound is VERY LARGE. WHy? Because the electric/hydraulic motor has to transfer its power to the cable in question. The only way to do this is via friction. Now, look at the block and tackle hoist apparatus coming down and you will notice that its sheaves are much, much, much, smaller than the drum. IE if there was any truth to the matter that one needs a large diameter sheave for higher efficiency you most certainly would see it in large cranes. You do not for the reasons I gave.
Bottom line, Petzl, CMI and whatever idiot wrote their web pages are idiots. Or more likely is that they had to put something on their webpage and technically they can claim what they did. Of course its so insignificant as to be absurd.