Method for quadrimodal fault prediction using strain tensor cyclides

1. A method of determining three-dimensional fracture geometry in a subterranean region of interest, comprising:

obtaining a strain tensor for the subterranean region of interest;

calculating a set of principal strain components from the strain tensor;

determining a strain cyclide from the set of principal strain components;

calculating a set of quadrimodal fault normal vectors from the strain cyclide;

determining an in-plane shear strain magnitude and a shear strain orientation associated with a quadrimodal fault from the set of quadrimodal fault normal vectors; and

determining a hydrocarbon reservoir development plan based, at least in part, on the in-plane shear strain magnitude and the shear strain orientation,

wherein the hydrocarbon reservoir development plan comprises a wellbore trajectory planned to penetrate a hydrocarbon reservoir within the subterranean region of interest.

2. The method of claim 1 , further comprising:

executing the hydrocarbon reservoir development plan by drilling, using a drilling system, the wellbore trajectory to penetrate the hydrocarbon reservoir.

3. The method of claim 1 , wherein the strain tensor comprises a finite strain tensor obtained from a satellite measurement dataset.

4. The method of claim 1 , wherein determining the strain cyclide comprises:

determining four cyclide parameters based on a plurality of combinations of three principal components of the strain tensor; and

forming a surface in cartesian space, wherein the surface is defined by a function quartic in each cartesian coordinate and by the four cyclide parameters.

5. The method of claim 1 , wherein calculating the set of quadrimodal fault normal vectors comprises predicting a set of fault orientation angles based, at least in part, on the strain cyclide and a plane of no finite linear strain.

6. The method of claim 5 , wherein predicting the set of fault orientation angles comprises determining a set of intersection points of the strain cyclide with the plane of no finite linear strain.

7. A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions comprising functionality for:

obtaining a strain tensor for a subterranean region of interest;

calculating a set of principal strain components from the strain tensor;

determining a strain cyclide from the set of principal strain components;

calculating a set of quadrimodal fault normal vectors from the strain cyclide;

determining an in-plane shear strain magnitude and a shear strain orientation associated with a quadrimodal fault from the set of quadrimodal fault normal vectors; and

determining a hydrocarbon reservoir development plan based, at least in part, on the in-plane shear strain magnitude and the shear strain orientation,

wherein the hydrocarbon reservoir development plan comprises a wellbore trajectory planned to penetrate a hydrocarbon reservoir within the subterranean region of interest.

8. The non-transitory computer readable medium of claim 7 , wherein the strain tensor comprises a finite strain tensor obtained from a satellite measurement dataset.

9. The non-transitory computer readable medium of claim 7 , wherein determining the strain cyclide comprises:

determining four cyclide parameters based on a plurality of combinations of three principle components of the strain tensor; and

forming a surface in cartesian space, wherein the surface is defined by a function quartic in each cartesian coordinate and by the four cyclide parameters.

10. The non-transitory computer readable medium of claim 7 , wherein calculating the set of quadrimodal fault normal vectors comprises predicting a set of fault orientation angles based, at least in part, on the strain cyclide and a plane of no finite linear strain.

11. The non-transitory computer readable medium of claim 10 , wherein predicting the set of fault orientation angles comprises determining a set of intersection points of the strain cyclide with the plane of no finite linear strain.

12. A system for predicting three-dimensional fracture geometry in a subterranean region of interest, comprising:

a wellbore tool configured to measure a strain tensor of the subterranean region of interest; and

a computer system configured to:

receive the strain tensor from the wellbore tool;

calculate a set of principal strain components from the strain tensor;

determine a strain cyclide from the set of principal strain components;

calculate a set of quadrimodal fault normal vectors from the strain cyclide;

determine an in-plane shear strain magnitude and a shear strain orientation associated with a quadrimodal fault from the set of quadrimodal fault normal vectors; and

determine a hydrocarbon reservoir development plan based, at least in part, on the in-plane shear strain magnitude and the shear strain orientation,

wherein the hydrocarbon reservoir development plan comprises a wellbore trajectory planned to penetrate a hydrocarbon reservoir within the subterranean region of interest.

13. The system of claim 12 , wherein the strain tensor comprises an infinitesimal strain tensor obtained from the wellbore tool.

14. The system of claim 12 , wherein determining the strain cyclide comprises:

determining four cyclide parameters based on a plurality of combinations of three principle components of the strain tensor; and

forming a surface in cartesian space, wherein the surface is defined by a function quartic in each cartesian coordinate and by the four cyclide parameters.

15. The system of claim 12 , wherein calculating the set of quadrimodal fault normal vectors from the strain cyclide comprises predicting a set of fault orientation angles based, at least in part, on the strain cyclide and a plane of no finite linear strain.

16. The system of claim 15 , wherein predicting the set of fault orientation angles comprises determining a set of intersection points of the strain cyclide with the plane of no finite linear strain.

17. The system of claim 12 , further comprising a drilling system configured to drill the wellbore trajectory to penetrate the hydrocarbon reservoir.