Centrifugal compressors have three important pluses; first, they mate to very powerful (and compact) gas turbines; second, they can move staggeringly large volumes of gas; and third, they don't require lubrication to be added to the gas stream. The big minus is that each stage can only do 1.5-2.5 compression ratios. For a booster station, that needs to boost an 800 psig stream to 1300 psig all day every day with no significant variability in either suction or discharge pressure they are ideal.
In locations where conditions change (like a wellsite) they are much less applicable. Where the controlling factor is energy density (e.g. on a offshore platform), then people accept the limited flexibility. On offshore applications, the compressors have throttling suction controllers to keep the suction pressure in a very narrow band (usually at the cost of having a significant dP across the suction controller and holding considerable back pressure on the wells--which leads to premature abandonment).
I like them in applications like the discharge of Amine plants, or pipeline booster stations. I don't recommend them for plant inlet, gathering system booster stations, or onshore wellsite use. I've seen a couple of sites with dynamic compressors (like centrifugals) installed in parallel with positive displacement compressors (like recips or flooded screws) and the result is never pretty.
In answer to your basic question, there are hundreds of thousands of centrifugal compressors in use around the world. This is a very mature technology with a pretty limited number of unknowns. The GPSA Field Data Book has a pretty good section on Centrifugal and Axial Compressors.
David
