A crude oil demulsification system includes a vessel. A cyclonic separator is disposed outside the vessel. The cyclonic separator is configured to receive and separate phases of a multi-phase fluid stream into a gaseous stream and a liquid stream that includes a first liquid phase and a second liquid phase by inducing cyclonic flow. A heat exchanger is fluidically connected to the cyclonic separator. The heat exchanger is disposed outside the vessel, and is configured to receive the liquid stream and to heat the liquid stream by exchanging heat with a heating medium flowed through the heat exchanger. An electrostatic coalescer is fluidically connected to the heat exchanger and is disposed inside the vessel. The electrostatic coalescer is configured to receive the liquid stream heated by the heat exchanger and to demulsify the liquid stream by causing coalescence of liquid droplets of one of the first or second liquid phases.