Interested to know what are the current metering pumps and what are the problems with them.
For lime metering, most of the applications have quite a few dosing points, so a centrifugal pump with recirculation line is often used for the pumping and a pulsation valve at each dosing point is used for the metering. The flow of the pump is normally much higher than the required and a pipe normally 2" or 3" is used since scaling on pipe wall is a concern for lime. The pump is normally sealless such as Wilfley dynamic sealless pump.
For polymer metering, progressive cavity (helical rotor?) pump is often used. progressive cavity is also positive displacement pump.
Hose pumps (peristaltic)are often used for metering purpose. A adverse comment on the hose metering pumps is that the volume per revolution does not repeat well enough after the hose is pressed for a period of time. So you may have to calibrate the pump again if your dosing is required to be accurate. Another thing heard from the site is that some hose was cut by some sharp solids in the fluid, but that must be a special case since many people put a strainer at the suction pipe.