A turbomachine and a method of operating the turbomachine are disclosed. The turbomachine includes a stator, a rotor including a rotor bearing face, a face seal assembly, a first pressure cavity, and a second pressure cavity. The face seal assembly includes a seal ring including a seal bearing face, a first pressure cavity, and a plurality of isolated hydrostatic ports extending from the first pressure cavity to the seal bearing face. The face seal assembly is slidably coupled to the stator and defines a face seal clearance between the rotor and seal bearing faces. The second and third pressure cavities are defined by the stator, the rotor, and the face seal assembly. The third pressure cavity is disposed downstream of the second pressure cavity with reference to flow of a process fluid along the stator and rotor. The first pressure cavity is isolated from the second and third pressure cavities.