Systems and methods for separating multi-phase compositions

Separators for separating a multi-phase composition include a separator casing defining a chamber and a permeate outlet, at least one hydrocyclone within the separator casing, and at least one ceramic membrane. Each hydrocyclone includes a hydrocyclone inlet, a tapered section downstream of the hydrocyclone inlet, an accepted outlet, and a reject outlet. The ceramic membrane may be disposed within the separator casing and downstream of the accepted outlet of the hydrocyclone or may be disposed within at least a portion of the tapered section of the hydrocyclone. The ceramic membrane includes a retentate side and a permeate side, where the permeate side is in fluid communication with the chamber. Systems and methods for separating a multi-phase composition into a lesser-density fluid, a greater-density fluid, and a medium-density fluid using the separators are also disclosed.