Designing a wellbore cement sheath in compacting or subsiding formations

1. A method, comprising:

performing a field scale analysis on a formation surrounding a wellbore to output boundary conditions comprising:

a pore pressure of the formation; and

a three-dimensional movement of the formation, wherein the field scale analysis is performed on the formation within a 5 km radius of the wellbore;

performing a wellbore scale analysis based on the boundary conditions, a wellbore scale model, wellbore conditions, and cement material properties to output an indication of stress applied over time to a cement sheath within the wellbore, wherein the wellbore scale analysis is performed on the formation within a wellbore scale radius of the wellbore that is 50 times a wellbore radius of the wellbore;

determining cement material properties of the cement sheath to withstand the stress applied over time outputted by the wellbore scale analysis; and

installing the cement sheath within the wellbore, the cement sheath comprising a cement mixture that includes the cement material properties.

2. The method of claim 1 , wherein the three-dimensional movement of the formation comprises an axial movement of the formation, a lateral movement of the formation, or both.

3. The method of claim 1 , wherein the field scale analysis is based on a field scale model and formation material properties, and wherein the field scale model is based on field geometry and production loads, injection loads, or fracturing loads at the wellbore and a neighboring well.

4. The method of claim 1 , wherein the field scale analysis uses a Cam-Clay type model to represent formation layers that exhibit pore compaction.

5. The method of claim 1 , wherein the wellbore conditions comprise wellbore geometry and wellbore construction and completion loads.

6. The method of claim 1 , wherein the wellbore scale analysis is further based on casing material properties.

7. The method of claim 1 , further comprising:

designing the cement mixture of the cement sheath based on the cement material properties.

8. The method of claim 1 , wherein the pore pressure and the three-dimensional movement of the formation are variable over time based on expected production loads, injection loads, or fracturing loads of the wellbore.

9. A non-transitory computer-readable medium that includes instructions that are executable by a processing device to perform operations comprising:

performing a field scale analysis on a formation surrounding a wellbore to output boundary conditions comprising:

a pore pressure of the formation; and

a three-dimensional movement of the formation, wherein the field scale analysis is performed on the formation within a 5 km radius of the wellbore;

performing a wellbore scale analysis based on the boundary conditions, a wellbore scale model, and cement material properties to output an indication of stress applied over time to a cement sheath within the wellbore, wherein the wellbore scale analysis is performed on the formation within a wellbore scale radius of the wellbore that is 50 times a wellbore radius of the wellbore;

calibrating the cement material properties of the cement sheath to withstand the stress applied over time outputted by the wellbore scale analysis; and

outputting the calibrated cement material properties usable to design a cement mixture for the cement sheath.

10. The non-transitory computer-readable medium of claim 9 , wherein the wellbore scale analysis is performed on a single layer of the formation.

11. The non-transitory computer-readable medium of claim 9 , wherein the field scale analysis uses a Cam-Clay type model to represent porous formation layers that exhibit pore compaction and a Mohr-Coulomb model or a Drucker-Prager model to represent nonporous formation layers that exhibit volume conservation.

12. The non-transitory computer-readable medium of claim 9 , wherein calibrating the cement material properties of the cement sheath to withstand the stress applied over time comprises calibrating the cement material properties to withstand the stress applied over a production lifespan of the wellbore.

13. The non-transitory computer-readable medium of claim 9 , wherein the wellbore scale model is based on wellbore geometry and wellbore construction and completion loads.

14. The non-transitory computer-readable medium of claim 9 , wherein the field scale analysis is based on a field scale model and formation material properties, and wherein the formation material properties comprise tensile strength of the formation, compressive strength of the formation, Young's modulus of the formation, Poisson's ratio of the formation, or any combination thereof.

15. A computing system, the computing system comprising:

a processing device; and

a memory device in which instructions are stored that are executable by the processing device for causing the processing device to:

perform a field scale analysis on formation layers of a formation surrounding a wellbore to output boundary conditions of the formation layers comprising:

a pore pressure of the formation layers; and

a three-dimensional movement of the formation layers, wherein the field scale analysis is performed on the formation within a 5 km radius of the wellbore;

perform a wellbore scale analysis based on the boundary conditions, a wellbore scale model, and cement material properties to output an indication of stress applied over time to a cement sheath within the wellbore, wherein the wellbore scale analysis is performed on the formation within a wellbore scale radius of the wellbore that is 50 times a wellbore radius of the wellbore;

calibrate the cement material properties of the cement sheath to withstand the stress applied over time outputted by the wellbore scale analysis; and

output the calibrated cement material properties usable to design a cement mixture for the cement sheath.

16. The computing system of claim 15 , wherein the formation layers are determined based on logging while drilling operations, measurement while drilling operations, or both.

17. The computing system of claim 15 , wherein the pore pressure of the formation layers and the three-dimensional movement of the formation layers vary over time based on production loads of the wellbore.

18. The computing system of claim 15 , wherein the field scale analysis uses a Cam-Clay type model to represent porous formation layers that exhibit pore compaction and a Mohr-Coulomb model or a Drucker-Prager model to represent nonporous formation layers that exhibit volume conservation.

19. The computing system of claim 15 , wherein the field scale analysis is based on a field scale model and formation material properties, and wherein the wellbore scale model is based on wellbore geometry and wellbore construction and completion loads.