I've read in one of Smil's books that fuel cells are somehow limited (in what sense I'm not sure anymore but I believe it was power output) by their "active area". I'm having difficulties learning more about this "active area". Can someone maybe expand on that?
I've not worked directly with large-scale fuel cell installations (never heard of one, actually) but I did some undergraduate lab work involving methanol fuel cells which seem to share the same principle. I imagine the limiting factor that probably causes problems with large scale-up is increasing mass transport to and from surface area. Unlike a turbine which acts on volumes of fluid, a fuel cell acts on area fluxes of fluid.
Consider a bizarre branch of history where fuel cells were invented and perfected long before combustion turbines, I imagine engineers would be amazed at how a "combustible" fuel in a turbine can act as its own catalyst once it reaches sufficiently high temperature and pressure. In contrast, fuel cells require careful slow flow of fluid through a fragile membrane which acts as a sort of two-dimensional catalyst that facilitates the proton-stripping reaction. Fuel cell membranes can't be cut up and dissolved into the fluid bulk to facilitate the reaction; the membrane must form a perfect electrically-conductive seal to prevent mixing of the electron-donating fuel and the electron-accepting oxidizer fluids.
Since each unit of energy produced requires one unit volume of fuel fluid pass through two stagnant boundary layers on both sides of the membrane, the amount of energy lost to friction in the supporting piping is significant no matter how large the array of membranes. In contrast, a unit of fluid passing through a gas turbine has a lower probability of passing near a surface film of a pipe wall or turbine blade the more the turbine machinery and its supporting piping is enlarged.