Frac plug with rod plug

1. A frac plug system for use in a wellbore, comprising:

a frac plug including a slip and a setting cone; and

a plug member configured to be held stationary in the wellbore via a setting rod to constrain axial movement of the slip during setting of the frac plug while allowing axial movement of the setting cone against the slip to set the frac plug in the wellbore, wherein the plug member is releasable from the setting rod once the frac plug is set in the wellbore, wherein once the plug member is released, the plug member is maintained within the frac plug and moves within the frac plug to control a flow of fluid through the frac plug, wherein the plug member comprises a plug seal at a first end for controlling the flow of fluid through the frac plug, the plug seal comprising a frangible connection for coupling the plug member to the setting rod while the frac plug is being deployed in the wellbore.

2. The frac plug system of claim 1 , further comprising a bottom sub coupled to a second end of the plug member, wherein the bottom sub constrains the axial movement of the slip during setting of the frac plug in the wellbore.

3. The frac plug system of claim 2 , wherein, once the plug member is released, the bottom sub limits a motion of the plug member toward the first end during the flow of the fluid through the frac plug from the second end to the first end.

4. The frac plug system of claim 1 , wherein the plug seal has a sealing interface that forms a seal with a ball seat of the frac plug.

5. The frac plug system of claim 1 , wherein the frangible connection is configured to break upon application of a tensile force between the plug member and the setting rod above a rupture threshold of the frangible connection.

6. The frac plug system of claim 1 , wherein a body of the frac plug is coupled to a setting rod via a frangible connection while the frac plug is being deployed in the wellbore.

7. The frac plug system of claim 1 , further comprising a retainer configured to secure the plug member in the frac plug during deployment, the retainer configured to release the plug member from the frac plug when a flow rate of the fluid through the frac plug is above a selected flow rate threshold.

8. The frac plug system of claim 1 , wherein the plug member controls the flow of fluid by performing at least one of: (i) closing a flow path for the flow of fluid in a direction from above the frac plug to below the frac plug; (ii) opening a flow path for the flow of fluid in a direction from below the frac plug to above the frac plug; and (iii) closing the frac plug during the pumping of a frac fluid.

9. A method of controlling a flow of fluid within a wellbore, comprising:

conveying a frac plug system in the wellbore, the frac plug system including a frac plug and a plug member, the frac plug including a slip and a setting cone, the plug member having seal at a first end;

coupling the plug seal to a setting rod via a frangible connection while the frac plug is conveyed into the wellbore;

constraining an axial movement of the slip via the plug member and the setting rod as the setting cone moves against the slip to set the frac plug in the wellbore;

releasing the plug member from the setting rod after the frac plug is set in the wellbore;

maintaining the plug member within the frac plug once the plug member is released while allowing the plug member to move within the frac plug to control a flow of fluid through the frac plug; and

controlling the flow of fluid in a first direction via the plug seal.

10. The method of claim 9 , wherein the plug member is coupled to a bottom sub, further comprising constraining the axial movement of the slip during setting the frac plug via the bottom sub.

11. The method of claim 10 , further comprising limiting a motion of the plug member, once released, toward a first end during the flow of the fluid through the frac plug from a second end to the first end via the bottom sub.

12. The method of claim 9 , wherein the plug seal has a sealing interface that forms a seal with a ball seat of the frac plug.

13. The method of claim 9 , further comprising breaking the frangible connection upon application of a tensile force between the plug member and the setting rod above a rupture threshold of the frangible connection after the frac plug has been set in the wellbore.

14. The method of claim 9 , further comprising coupling a body of the frac plug to the setting rod via a frangible connection while the frac plug is being deployed in the wellbore.

15. The method of claim 9 , further comprising securing the plug member in the frac plug during deployment via a retainer and releasing the plug member from the frac plug via the retainer when a flow rate of the fluid through the frac plug is above a selected flow rate threshold.

16. The method of claim 9 , further comprising controlling the flow of fluid by performing at least one of: (i) closing a flow path for the flow of fluid in a direction from above the frac plug to below the frac plug; (ii) opening a flow path for the flow of fluid in a direction from below the frac plug to above the frac plug; and (iii) closing the frac plug during the pumping of a frac fluid.