# US 12,000,264 B2 · Method for quadrimodal fault prediction using strain tensor cyclides

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- Number: US 12,000,264 B2
- Document ID: US12000264B2
- Status: Granted
- Kind: B2
- Application number: 17/644,103
- Filed: 2021-12-14
- Published: 2023-06-15
- Granted: 2024-06-04
- Earliest claimed: 2021-12-14
- Assignees: Saudi Arabian Oil Company
- Applicants: Aramco Services Company
- Inventors: Seth Busetti
- Web page: https://patentgrep.com/patent/US12000264B2

## CPC

- E21B 47/02: Determining slope or direction
- G01V 20/00: Geomodelling in general
- G01V 2210/6242: Elastic parameters, e.g. Young, Lamé or Poisson
- G01V 2210/642: Faults
- G01V 2210/646: Fractures
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)

## Abstract

A method of predicting three-dimensional fracture geometry in a subterranean region of interest is disclosed. The method includes obtaining a strain tensor for the subterranean region of interest, calculating a set of principal strain components from the strain tensor, and determining a strain cyclide from the set of principal strain components. The method further includes calculating a set of quadrimodal fault normal vectors from the strain cyclide and determining an in-plane shear strain magnitude and a shear strain orientation from the set of quadrimodal fault normal vectors.

## Claims

### Claim 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.

### Claim 2 (depends on 1)

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.

### Claim 3 (depends on 1)

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

### Claim 4 (depends on 1)

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.

### Claim 5 (depends on 1)

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.

### Claim 6 (depends on 5)

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.

### Claim 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.

### Claim 8 (depends on 7)

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

### Claim 9 (depends on 7)

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.

### Claim 10 (depends on 7)

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.

### Claim 11 (depends on 10)

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.

### Claim 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.

### Claim 13 (depends on 12)

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

### Claim 14 (depends on 12)

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.

### Claim 15 (depends on 12)

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.

### Claim 16 (depends on 15)

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.

### Claim 17 (depends on 12)

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