A seal assembly for a rotary machine is provided. The seal assembly includes multiple sealing device segments disposed circumferentially intermediate to a stationary housing and a rotor. Each of the sealing device segments includes a stator interface element. The sealing device segment also includes a shoe plate having one or more labyrinth teeth facing the rotor and a load-bearing surface region, wherein the shoe plate allows a high pressure fluid to an upstream portion of the forwardmost labyrinth tooth and a low pressure fluid to a downstream portion of the aftmost labyrinth tooth. The sealing device segment further includes a secondary seal in contact with the stator interface element at a radially outer end and in contact with an elevated nose of the shoe plate on a radially inner end; and multiple bellow springs or flexures attached to the shoe plate and to the stator interface element.