Wet shoe system

1. A downhole assembly, comprising:

a float tool configured to be connected to a casing string and including one or more one-way valves configured to permit fluid flow in a downhole direction and to prevent fluid flow in an uphole direction; and

a first wiper plug configured to be deployed into a well via the casing string and engage the float tool, wherein the first wiper plug comprises:

a valve element that is configured to prevent fluid flow through the first wiper plug at least in the uphole direction; and

a rupture disk configured to break at a predetermined pressure, wherein the rupture disk prevents fluid flow through the first wiper plug in both the uphole and downhole directions prior to rupturing.

2. The downhole assembly of claim 1 , wherein the one or more one-way valves of the float tool are configured to receive a cement slurry therethrough, and wherein the valve element of the first wiper plug is configured not to receive the cement slurry therethrough.

3. The downhole assembly of claim 1 , wherein the first wiper plug defines a bore axially therethrough, and wherein the valve element is positioned within the bore and is not separately deployable into the well.

4. The downhole assembly of claim 3 , wherein the valve element comprises a flapper valve positioned in the bore of the first wiper plug.

5. The downhole assembly of claim 4 , wherein the flapper valve is biased toward a closed position in which the flapper valve blocks fluid flow, and wherein fluid flow in the downhole direction forces the flapper valve out of the closed position and into an open position.

6. The downhole assembly of claim 1 , further comprising a second wiper plug that is configured to be deployed into the well and to engage the first wiper plug.

7. The downhole assembly of claim 6 , wherein the second wiper plug is superposed with respect to the first wiper plug, such that the first wiper plug is positioned axially between the second wiper plug and the float tool.

8. The downhole assembly of claim 6 , wherein the second wiper plug comprises a valve element configured to prevent fluid flow through the second wiper plug at least in the uphole direction.

9. The downhole assembly of claim 1 , wherein the valve element comprises a dissolvable disk.

10. The downhole assembly of claim 1 , wherein the float tool comprises a float shoe and a float collar that is connected to the float shoe, the first wiper plug being receivable at least partially in the float collar and configured to latch therein.

11. The downhole assembly of claim 1 , wherein the valve element comprises a flapper valve including a base and a flapper that is pivotally secured to the base, and wherein the flapper is biased toward a closed position in which the flapper extends across the base and prevents fluid flow through the base at least in the uphole direction.

12. The downhole assembly of claim 11 , wherein the valve element further comprises:

a spacer that is coupled to and extends from the base; and

an end ring that is coupled to the spacer, wherein the end ring is positioned in engagement with a shoulder in the first wiper plug.

13. A method for cementing a well, comprising:

deploying a float tool comprising one or more one-way valves into a well as part of a casing string;

pumping cement into the casing string in the well;

deploying a first wiper plug through the casing string down to the float tool so as to displace at least some of the cement from the casing string into an annulus between the casing string and the well;

preventing the cement from flowing in an uphole direction through the first wiper plug using a valve element positioned in the first wiper plug;

pumping fluid through the first wiper plug in a downhole direction after deploying the first wiper plug down to the float tool;

deploying a second wiper plug through the casing string until the second wiper plug engages the first wiper plug; and

rupturing a rupture disk in the second wiper plug by increasing a pressure in the casing string.

14. The method of claim 13 , wherein the valve element comprises a flapper valve configured to permit fluid flow in the downhole direction through the first wiper plug but prevent fluid flow in the uphole direction through the first wiper plug.

15. The method of claim 13 , further comprising rupturing a rupture disk in the first wiper plug by increasing a pressure in the casing string.

16. The method of claim 13 , further comprising dissolving the valve element prior to pumping fluid through the first wiper plug in the downhole direction.

17. A downhole assembly, comprising:

a float shoe comprising two or more one-way valves;

a float collar coupled to the float shoe and comprising one or more one-way valves;

a first wiper plug that is configured to land on the float collar, the first wiper plug including a valve element configured to prevent fluid flow through the first wiper plug at least in an uphole direction; and

a second wiper plug that is configured to land on the first wiper plug, the second wiper plug including a rupture disk configured to block fluid flow through the second wiper plug, wherein, upon rupturing the rupture disk, the second wiper plug permits fluid flow therethrough at least in a downhole direction.

18. The downhole assembly of claim 17 , wherein the valve element comprises a flapper that has an open position and a closed position, wherein, in the open position, the flapper permits fluid flow in the downhole direction through the valve element, and in the closed position, the flapper prevents fluid flow in the uphole direction through the valve element, and wherein the first wiper plug further comprises a rupture disk therein that is configured to rupture at a predetermined pressure.

19. The downhole assembly of claim 17 , wherein the valve element comprises a dissolvable disk configured to dissolve after a predetermined amount of time in a well.