Undulating transverse interface for curved flapper seal

In a valve for use in controlling flow in a fluid transmission conduit in a subterranean well, said valve comprising a valve flapper with an upstream face rotatable between open and closed positions for controlling the flow in the fluid transmission conduit;

• a flapper hinge about which the valve flapper rotates;
• a valve seat to hold pressure exerted on the upstream face of the valve flapper in the closed position, the improvement comprising:
• said valve positioned in said fluid transmission conduit and comprising a first sealing surface with a circular cross-section around the periphery of said seat defining longitudinal axis at the center of said first sealing surface, said first sealing surface, while undulating along its entire length, is itself disposed transverse to said longitudinal axis at a constant slope such that every two points along the entire first sealing surface spaced radially from each other with respect to the longitudinal axis forms a line that intersects the longitudinal axis at a substantially 90.degree. angle, relative to the longitudinal axis, wherein the substantially 90.degree. angle is constant throughout the entire first sealing surface;
• said flapper comprising a second sealing surface substantially conforming to said first sealing surface.