Methods and systems for disconnecting casing

1. A detachable tool comprising:

an upper sub-assembly with an adjuster sleeve and a support sleeve, the adjuster sleeve including an upper body, a shaft, and a distal end, the upper body being positioned above the support sleeve, the support sleeve including a first outcrop and a second outcrop, wherein the shaft extends from the distal end to the upper body across the first outcrop;

a lower sub-assembly, wherein the lower sub-assembly is temporarily coupled with the upper-sub assembly;

a housing configured to restrict outward radial movement of the shaft and the distal end when the adjuster sleeve is coupled to the support sleeve at a first location, the housing being directly coupled to the lower sub-assembly;

a rupture disc positioned within a passageway of the lower sub-assembly positioned below a coupling point of the housing and the lower sub-assembly, the passageway extending from an inner diameter of the lower sub-assembly to an outer diameter of the lower sub-assembly, the upper sub-assembly being detachable from the lower sub-assembly and the housing after the adjuster sleeve is sheared from the support sleeve based on pressure.

2. The detachable tool of claim 1 , wherein the upper sub-assembly includes:

a temporary coupling mechanism configured to selectively couple the adjuster sleeve and the support sleeve at a first location, wherein responsive to the temporary coupling mechanism no longer coupling the adjuster sleeve and the support sleeve the adjuster sleeve and support sleeve may be coupled together at a second location.

3. The detachable tool of claim 2 , further including:

a seat positioned on an inner diameter of the support sleeve, the seat being configured to receive an object to isolate a first area above the seat and a second area below the seat, wherein the temporary coupling mechanism is configured to be sheared responsive to increasing a pressure in the first area.

4. The detachable tool of claim 3 , wherein responsive to increasing the pressure in the first area the support sleeve moves downhole while the adjuster sleeve remains fixed in place.

5. The detachable tool of claim 2 , wherein the housing is configured to restrict the movement of the adjuster sleeve when the adjuster sleeve is coupled to the support sleeve at the first location.

6. The detachable tool of claim 2 , wherein the distal end of the adjuster sleeve is a collet, the collet being configured to collapse towards a central axis of the detachable tool, wherein the upper sub-assembly and the lower sub-assembly are configured to be detachable from each other responsive to the collet collapsing.

7. The detachable tool of claim 2 , wherein the support sleeve is configured to move parallel to the axis based on hydraulic pressure while the adjuster sleeve remains fixed in place, and the support sleeve and the adjuster sleeve are configured to simultaneously move up hole based on an upward mechanical force applied to the upper body of the adjuster sleeve.

8. The detachable tool of claim 7 , wherein the support sleeve and the adjuster sleeve are configured to decouple from the bottom sub-assembly based on the mechanical force.

9. The detachable tool of claim 2 , wherein the support sleeve has a weak point, the weak point on the support sleeve being configured to allow the support sleeve to detach from the adjuster sleeve at a location that is remote from the temporary coupling mechanism, the weak point a recess within the support sleeve being a secondary coupling mechanism configured to be mechanically or chemically cut allowing the support sleeve to detach from the adjuster sleeve.

10. The detachable tool of claim 2 , wherein in a first mode of operation an inner projection of the distal end of the adjuster sleeve is positioned adjacent to an outer diameter of the first outcrop and in a second mode of operation the inner projection is positioned between the first outcrop and second outcrop.

11. The detachable tool of claim 1 , wherein the upper sub-assembly and the lower sub-assembly are run in hole together as a single piece, and the passageway extending from an inner diameter of the lower sub-assembly to an outer diameter of the lower sub-assembly is configured to allow for circulation of excess cement after the rupture disc ruptures, wherein the rupture disc is configured to rupture by applying a predetermined amount of pressure across the rupture disc.

12. The detachable tool of claim 1 , wherein the upper sub-assembly is configured to be removed in a single trip while the bottom sub-assembly remain down hole, wherein the bottom sub-assembly has an inner diameter that is greater than or equal to that of casing, and an outer diameter of the bottom sub-assembly and housing are positioned within the casing.

13. A method associated with a detachable tool comprising:

temporarily coupling an upper sub-assembly with a lower sub-assembly, the upper sub-assembly including with an adjuster sleeve and a support sleeve, the adjuster sleeve including an upper body, a shaft, and a distal end, the upper body being positioned above the support sleeve, the support sleeve including a first outcrop and a second outcrop, wherein the shaft extends from the distal end to the upper body across the first outcrop;

directly coupling a housing with the lower sub-assembly, the housing restricting outward radial movement of the shaft and the distal end when the adjuster sleeve is coupled to the support sleeve at a first location;

positioning a rupture disc within a passageway of the lower sub-assembly positioned below a coupling point of the housing and the lower sub-assembly, the passageway extending from an inner diameter of the lower sub-assembly to an outer diameter of the lower sub-assembly;

detaching the upper sub-assembly from the lower sub-assembly and the housing after the adjuster sleeve is sheared from the support sleeve based on pressure.

14. The method of claim 13 , further comprising:

temporarily coupling the adjuster sleeve the support sleeve on the upper sub-assembly at the first location via a temporary coupling mechanism;

shearing the temporary coupling mechanism;

coupling the adjuster sleeve and the support sleeve at a second location, the distal end of the adjuster sleeve being a collet, the collet being configured to collapse towards a central axis of the detachable tool, wherein the upper sub-assembly and the lower sub-assembly are configured to be detachable from each other responsive to the collet collapsing.

15. The method of claim 14 , further including:

positioning an object on a seat positioned on an inner diameter of the support sleeve;

isolating a first area above the seat and a second area below the seat, wherein the temporary coupling mechanism is configured to be sheared responsive to increasing a pressure in the first area.

16. The method of claim 15 , further comprising:

increasing the pressure in the first area the support sleeve moves downhole while the adjuster sleeve remains fixed in place.

17. The method of claim 14 , further comprising:

restricting the movement of the adjuster sleeve via a housing when the adjuster sleeve is coupled to the support sleeve at the first location.

18. The method of claim 14 , further comprising:

moving the support sleeve in parallel to the axis based on hydraulic pressure while the adjuster sleeve remains fixed in place;

applying an upward mechanical force to the upper body of the adjuster sleeve;

simultaneously moving up hole the support sleeve and the adjuster sleeve a based on the mechanical force.

19. The detachable tool of claim 18 , further comprising:

decoupling the support sleeve and the adjuster sleeve from the bottom sub-assembly based on the mechanical pressure.

20. A detachable tool comprising:

an upper sub-assembly with a ball seat, the upper sub-assembly including an adjust sleeve and a support sleeve, the adjuster sleeve including an upper body, a shaft, and a distal end, the upper body being positioned above the support sleeve, the support sleeve including a first outcrop and a second outcrop, wherein the shaft extends from the distal end to the upper body across the first outcrop, wherein a support sleeve within the detachable tool is configured to move axially;

a lower sub-assembly, wherein the lower sub-assembly is temporarily coupled with the upper-sub assembly;

a housing configured to restrict outward radial movement of the shaft and the distal end when the adjuster sleeve is coupled to the support sleeve at a first location, the housing being directly coupled to the lower sub-assembly;

a rupture disc positioned within a passageway of the lower sub-assembly positioned below a coupling point of the housing and the lower sub-assembly, the passageway extending from an inner diameter of the lower sub-assembly to an outer diameter of the lower sub-assembly and housing, wherein the upper sub-assembly is detachable from the lower sub-assembly after the adjuster sleeve is sheared from the support sleeve based on pressure.