Method and system for controlling differential pressure for an externally pressurized gas bearing apparatus

A method for controlling a differential pressure across a gas bearing, wherein the gas bearing supports a shaft of a compressor for a heat transfer circuit, the heat transfer circuit comprising the compressor, a condenser, an expander, and an evaporator that are fluidly connected together, the method comprising:

• compressing a working fluid received at a suction inlet of the compressor by rotation of the shaft;
• receiving a fluid from a high pressure gas source at a fluid inlet of a bearing housing of the gas bearing, wherein the gas bearing is configured to use the fluid from the high pressure gas source to form a film between a surface of the bearing housing and the shaft;
• venting the fluid from the bearing housing at an outlet of the bearing housing;
• and
• reducing a vent pressure of the fluid vented from the outlet of the bearing housing by controlling a pressure reducer fluidly connected to the outlet of the bearing housing to control and/or maintain a differential pressure across the gas bearing to a determined value to maintain the film to have a clearance between the gas bearing and the shaft.