In a pump system, a process fluid is directed into inlet chambers of a pump casing at an inlet pressure, and a plurality of rotors disposed inside the pump casing are rotated to pump the process fluid from the inlet chambers to an outlet chamber located between the inlet chambers, wherein the process fluid in the outlet chambers is at an outlet pressure. The process fluid is directed from the outlet chamber to a separator configured to separate particulate matter from the process fluid, and a portion of separated process fluid is directed from the separator to a gear chamber of the pump. Pump bearings are lubricated with the portion of separated process fluid from the gear chamber. Some of the portion of the separated process fluid from the pump bearing is leaked to the inlet chambers via rotor shrouds to reduce accumulation of particulate matter in the inlet chambers.