A valve apparatus, characterized by: a ball segment valve housing; a check valve housing coupled to the ball segment valve housing such that a longitudinal opening is defined through the ball segment valve housing and the check valve housing; a ball segment disposed within the ball segment valve housing, the ball segment operable to be rotated to a closed position wherein a generally curved end of the ball segment is in sealing engagement with a ball segment valve seat disposed within the ball segment valve housing to prevent the flow of a working fluid through an outlet of the longitudinal opening, and operable to be rotated to an open position wherein the generally curved end of the ball segment is at least partially disengaged with the ball segment valve seat to permit flow of the working fluid through the outlet; and at least one flapper door (32, 34) disposed within the check valve housing, the at least one flapper door (32, 34) operable to be rotated to: a closed position wherein the at least one flapper door (32, 34) is in sealing engagement with a flapper valve seat to prevent flow of the working fluid through the longitudinal opening in a first direction, wherein the at least one flapper door (32, 34) is longitudinally spaced from the ball segment when the at least one flapper door (32, 34) and the ball segment are both in their respective closed positions to define an isolated chamber within the longitudinal opening between the at least one flapper door (32, 34) and the ball segment; and an open position wherein the at least one flapper door (32, 34) permits flow of the working fluid through flapper valve seat in a second direction, and wherein the at least one flapper door (32, 34) extends from the check valve housing into the ball segment valve housing such that the at least one flapper door (32, 34) longitudinally overlaps the ball segment when the at least one flapper door (32, 34) and the ball segment are both in their respective open positions. a ball segment valve housing; a check valve housing coupled to the ball segment valve housing such that a longitudinal opening is defined through the ball segment valve housing and the check valve housing; a ball segment disposed within the ball segment valve housing, the ball segment operable to be rotated to a closed position wherein a generally curved end of the ball segment is in sealing engagement with a ball segment valve seat disposed within the ball segment valve housing to prevent the flow of a working fluid through an outlet of the longitudinal opening, and operable to be rotated to an open position wherein the generally curved end of the ball segment is at least partially disengaged with the ball segment valve seat to permit flow of the working fluid through the outlet; and at least one flapper door (32, 34) disposed within the check valve housing, the at least one flapper door (32, 34) operable to be rotated to: a closed position wherein the at least one flapper door (32, 34) is in sealing engagement with a flapper valve seat to prevent flow of the working fluid through the longitudinal opening in a first direction, wherein the at least one flapper door (32, 34) is longitudinally spaced from the ball segment when the at least one flapper door (32, 34) and the ball segment are both in their respective closed positions to define an isolated chamber within the longitudinal opening between the at least one flapper door (32, 34) and the ball segment; and an open position wherein the at least one flapper door (32, 34) permits flow of the working fluid through flapper valve seat in a second direction, and wherein the at least one flapper door (32, 34) extends from the check valve housing into the ball segment valve housing such that the at least one flapper door (32, 34) longitudinally overlaps the ball segment when the at least one flapper door (32, 34) and the ball segment are both in their respective open positions. a closed position wherein the at least one flapper door (32, 34) is in sealing engagement with a flapper valve seat to prevent flow of the working fluid through the longitudinal opening in a first direction, wherein the at least one flapper door (32, 34) is longitudinally spaced from the ball segment when the at least one flapper door (32, 34) and the ball segment are both in their respective closed positions to define an isolated chamber within the longitudinal opening between the at least one flapper door (32, 34) and the ball segment; and an open position wherein the at least one flapper door (32, 34) permits flow of the working fluid through flapper valve seat in a second direction, and wherein the at least one flapper door (32, 34) extends from the check valve housing into the ball segment valve housing such that the at least one flapper door (32, 34) longitudinally overlaps the ball segment when the at least one flapper door (32, 34) and the ball segment are both in their respective open positions.