Bidirectional downhole isolation valve

1. 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; and

a collet pivotable between a first position configured to move the flapper to the closed position and a second position configured to engage the flapper in the closed position, thereby retaining the flapper in the closed position.

2. The valve of claim 1 , wherein the collet includes a base and a plurality of fingers extending longitudinally from the base.

3. The valve of claim 2 , wherein the plurality of fingers include:

a profile for radially moving the flapper toward the closed position; and

an abutment for engaging the flapper in the closed position.

4. The valve of claim 1 , further comprising a biasing member for biasing the collet toward an expanded position.

5. The valve of claim 4 , further comprising a guide profile for receiving the collet in a retracted position.

6. The valve of claim 1 , further comprising a piston attached to the flapper, wherein the piston is configured to move the collet to the retracted position.

7. The valve of claim 1 , further comprising a piston for axially moving the flapper.

8. The valve of claim 1 , further comprising a flow sleeve for retaining the flapper in the open position.

9. 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.

10. The valve of claim 9 , wherein the collet is pivotable between a first position configured to move the flapper to the closed position and a second position configured to engage the flapper in the closed position.

11. 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.

12. The method of claim 11 , wherein closing the flapper comprises urging the flapper against a kickoff profile of the collet.

13. The method of claim 11 , wherein moving the collet to the retracted position comprises compressing a biasing member configured to bias the collet in the expanded position.

14. The method of claim 11 , wherein contacting the flapper in the closed position with the collet comprises contacting the flapper with an abutment of the collet.

15. The method of claim 11 , wherein moving the collet to the retracted position comprises moving the collet and a sleeve attached to the collet.

16. The method of claim 15 , further comprising engaging a receiver profile of the collet with an upper end of the sleeve.

17. The method of claim 16 , wherein moving the collet to the retracted position further comprises pivoting the collet relative to the sleeve.

18. The method of claim 11 , wherein moving the collet to the retracted position comprises moving the collet into a guide profile.

19. The method of claim 11 , wherein closing the flapper comprises axially moving the flapper against the collet.

20. The method of claim 19 , further comprising using a piston to axially move the flapper.