| CPC E21B 34/105 (2013.01) [E21B 34/08 (2013.01); E21B 34/106 (2013.01); E21B 2200/05 (2020.05)] | 20 Claims |

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1. An insert valve installed, at least partially, in a safety valve, comprising:
a flow port disposed on an exterior of the insert valve;
a poppet configured to control a fluid flow through the flow port, wherein the poppet comprises a convex tapered wall facing in an uphole direction;
a piston rod, disposed uphole from the poppet, configured to move the poppet past at least part of the flow port, wherein the piston rod is partially retained with respect to the poppet; and
a hydraulic control port configured to control movement of the piston rod.
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