A seal assembly for a rotary machine is provided. The seal assembly includes a plurality of seal segments disposed circumferentially intermediate to a stationary housing and a rotor, where each of the plurality of seal segments includes a stator interface element and a shoe plate movably supported by the stator interface element. The shoe plate includes one or more labyrinth teeth, a load-bearing surface, and one or more supply ports for facilitating supply of high pressure fluid toward the rotor. In one embodiment, the shoe plate also includes a radially extending portion that is in contact with a portion of the ring movably supported into the stator interface element. In another embodiment, each of the plurality of seal segments includes a plurality of overlapping spring-loaded leaf seal plates in contact with the stator interface element and the radially extending portion. Method of operating the seal segment is also disclosed.
