In this work, we develop a model for a gravity separator, and we use it together with models from the literature to study the control of a subsea separation system that separates oil, gas, and water from well fluids in hydrocarbon production. Our separation system contains a gravity separator, hydrocyclones, and compact flotation units. The main contributions of the paper are 2-fold. First, we present a coalescence based dynamic gravity separator model, which is able to predict oil concentration in the water outlet and water concentration in the oil outlet. Second, we study optimal operation of the overall separation system with an objective of maximizing water removal. We propose a simple control structure that operates the process close to optimally, by rejecting disturbances from upstream flows and maintaining a tight control of the quality of the purified water leaving the system.