Well system cementing plug

1. A wellbore cementing plug, comprising:

a plug element comprising a polymer, the polymer comprising a viscoelastic polyurethane, a viscoelastic phenolic resin or a viscoelastic epoxy resin, wherein the polymer has:

a glass transition temperature in a range from about 78 to 156° C.,

a ratio of Moduli of Glassy to Rubbery State log ((E′ g )/(E′ r )) in a range from 0.5 to 2, wherein E′ g is a glassy modulus of the polymer and E′ r is a rubbery modulus of the polymer,

a loss modulus in a range from greater than about 80 MPa to 240 MPa for a tan δpeak equal to 0.2, and

a storage modulus in a range from greater than about 400 to 1200 MPa;

the polymer deformable at a first stiffness when subjected to a first strain rate to allow the plug element to pass through a wellbore while sealing against passage of cement past the plug element, and

the polymer resists deformation at a second, higher stiffness when subjected to a second, higher strain rate to resist allowing the plug element to pass through the wellbore while sealing against passage of cement past the plug element.

2. The wellbore cementing plug of claim 1 , where the stiffness of the polymer is responsive to a tubing pressure in the wellbore to have the first stiffness when subjected to the first strain rate and the second, higher stiffness when subjected to the second, higher strain rate.

3. The wellbore cementing plug of claim 1 , where the plug element comprises a plurality of discrete polymer elements that stick together.

4. The wellbore cementing plug of claim 1 , where the plug element comprises a single mass of the polymer, a cross-section of the single mass of the polymer in an initial, sealing state being equal to or larger than a cross-section of the wellbore.

5. The wellbore cementing plug of claim 1 , where the plug element comprises a core and fins extending radially from the core to walls of the wellbore, the fins or the core or both comprising the polymer.

6. The wellbore cementing plug of claim 5 , where the core element is cylindrical and the fins are disc-shaped fins about the core.

7. The wellbore cementing plug of claim 5 , where the core element comprises a material selected from the group consisting of metal, plastic, and fiber composite.

8. The wellbore cementing plug of claim 5 , further comprising a second plug element in the wellbore, the second plug element comprising the polymer and sealing against passage of cement past the second plug element, the cement in the wellbore between the first mentioned plug element and the second plug element.

9. A method, comprising:

deforming a polymer of a well plug element having a first stiffness in response to a first strain rate of the polymer to allow the well plug element and cement in a wellbore to pass through the wellbore while sealing against passage of cement past the well plug element, the polymer comprising a viscoelastic polyurethane, a viscoelastic phenolic resin or a viscoelastic epoxy resin, wherein the polymer has:

a glass transition temperature in a range from about 78 to 156° C.,

a ratio of Moduli of Glassy to Rubbery State log ((E′ g )/(E′ r )) in a range from 0.5 to 2, wherein E′ g is a glassy modulus of the polymer and E′ r is a rubbery modulus of the polymer,

a loss modulus in a range from greater than about 80 MPa to 240 MPa for a tan δpeak equal to 0.2, and

a storage modulus in a range from greater than about 400 to 1200 MPa; and

gripping with the polymer of the well plug element having a second, higher stiffness against movement of the well plug element through the wellbore in response to a second, higher strain rate of the polymer while sealing against passage of cement past the well plug element.

10. The method of claim 9 , where the first strain rate and the second, higher strain rate depend on a fluid characteristic of a fluid in the wellbore, the fluid characteristic selected from the group consisting of pressure, flow rate, temperature, and fluid density.

11. The method of claim 9 , further comprising:

deforming the polymer of a second well plug element having the first stiffness in response to the first strain rate of the polymer to allow the second well plug element and cement in the wellbore between the first mentioned well plug element and the second well plug element

to pass through the wellbore while sealing against passage of cement past the second well plug element; and

gripping with the polymer of the second well plug element having the second, higher stiffness against movement of the second well plug element through the wellbore in response to the second, higher strain rate of the polymer while sealing against passage of cement past the second well plug element.

12. The method of claim 9 , where sealing against passage of cement pass the well plug element includes resisting fluidic communication between the cement and fluid in the wellbore on an opposite side of the well plug element.

13. The method of claim 9 , where gripping the polymer of the well plug element having a second, higher stiffness against movement of the well plug element through the wellbore in response to a second, higher strain rate of the polymer includes activating a well tool in the wellbore with the well plug element.

14. The method of claim 9 , where deforming a polymer of a well plug element having a first stiffness in response to a first strain rate of the polymer to allow the well plug element and cement in the wellbore to pass through the wellbore while sealing against passage of cement past the well plug element includes deforming polymer fins of a cement wiper.

15. The method of claim 9 , where sealing against passage of cement past the well plug element includes sealing against passage of cement past a plurality of discrete polymer elements of the well plug element by allowing the plurality of discrete polymer elements to stick together and seal the wellbore.

16. The method of claim 9 , further comprising activating a well tool in the wellbore due to a pressure increase in the wellbore while gripping with the polymer of the well plug element against movement of the well plug element through the wellbore.

17. A wellbore plug, comprising:

a plug element comprising a viscoelastic polymer deformable at a first stiffness in response to a first strain rate to allow the plug element to pass through a wellbore and seal against passage of cement past the plug element, and the polymer resists deformation at a second, higher stiffness in response to a second, higher strain rate to allow the plug element to seal the wellbore against passage of cement past the plug element and resist movement of the plug element and cement through the wellbore, wherein the viscoelastic polymer comprises a polyurethane, a viscoelastic phenolic resin or a viscoelastic epoxy resin, wherein the polymer has:

a glass transition temperature in a range from about 78 to 156° C.,

a ratio of Moduli of Glassy to Rubbery State log ((E′ g )/(E′ r )) in a range from 0.5 to 2, wherein E′ g is a glassy modulus of the polymer and E′ r is a rubbery modulus of the polymer,

a loss modulus in a range from greater than about 80 MPa to 240 MPa for a tan δpeak equal to 0.2, and

a storage modulus in a range from greater than about 400 to 1200 MPa.

18. The wellbore plug of claim 17 , where the plug element is a cement wiper comprising a composite core and fins comprising the polymer.

19. The wellbore plug of claim 17 , where the plug element is a spherical mass of the polymer with an initial, sealing shape diameter greater than a diameter of the wellbore or a diameter of a restriction in the wellbore.

20. The wellbore plug of claim 17 , where the plug element is a plurality of discrete polymer elements that stick together.