Curved flapper with angle variant seat for a subsurface safety valve

A subsurface safety valve for controlling fluid flow in a well bore. In one embodiment, the subsurface safety valve includes a tubular member having a longitudinal bore extending therethrough, a curved flapper removably connected to the tubular member. The curved flapper is configured to pivot against the tubular member between an open position and a closed position. The subsurface safety valve further includes a hard seat positioned inside the tubular member, in which the hard seat defines a seating surface configured to receive a sealing surface defined on a bottom periphery portion of the curved flapper to form a sealing interface having a slope that varies along the sealing interface.