Inventions are disclosed that generate osmotic pressure that can be used to remove fluids from a patient. One embodiment involves implanting a reservoir that has a semipermeable membrane sidewall. The reservoir contains trapped osmotic solutes that can not pass out through the membrane. But fluid from the patient can flow in. The osmotic pressure from the trapped solutes in the reservoir draws fluid from the patient across the semipermeable membrane and into the device. The reservoir may optionally be recharged from time to time and/or replaced by a new reservoir.