Bidirectional downhole isolation valve

An isolation valve for use in a wellbore, comprising:

• a housing having a bore;
• a flapper movable between an open position and a closed position, the flapper operable to isolate an upper portion of the bore from a lower portion of the bore when the flapper is in the closed position;
• a sleeve disposed below the flapper;
• a collet connected to and movable with the sleeve, wherein the collet is configured to engage the flapper in the closed position;
• and
• a biasing member disposed between the housing and the sleeve, wherein the biasing member is compressible by movement of the sleeve relative to the housing in response to movement of the flapper relative to the housing.

A method of isolating a string in a wellbore using an isolation valve, comprising:

• closing a flapper of the isolation valve by urging the flapper against a collet in an expanded position;
• moving the collet to a retracted position;
• and
• contacting the flapper in a closed position with the collet in the retracted position.