Visualization of Salt-Induced Stress Visualization of Salt-Induced Stress PerturbationsPerturbations

Patricia CrossnoPatricia Crossno David H. RogersDavid H. Rogers

Rebecca BrannonRebecca BrannonDavid CoblentzDavid Coblentz

Sandia National LaboratoriesSandia National Laboratories

October 14, 2004October 14, 2004

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy under contract DE-AC04-94AL85000.

Deepwater Gulf of MexicoDeepwater Gulf of Mexico

Gulf of Mexico Salt Formations

salt

Continental Shelf<600’ water depth

Deepwater 600’-5000’

oil

Ultra Deepwater 5000’-10,000’+

ocean

13 to 28 billion barrels of oil

estimated

32 billion barrels known oil in US

in 2002

Salt FormationsSalt Formations

Evolution of a salt diapir

salt (low density)

traps with oil

Salt moves and deforms surrounding sediments creating traps

compacted sediments (denser than salt)

gravitational loading

salt relaxes until vertical stress = horizontal stress (Sv = Sh)

Wellbore DisplacementWellbore Displacement

• Drilling failures result in well abandonment costs of tens of millions of dollars

• We need to:– Plan well locations and

drilling trajectories with respect to loading in and around salt bodies

– Design well casings for loading caused by salt creep

salt flow

sheared well

casing

spherical salt body8,136 elements

salt diapir with tongue10,128 elements

Static SimulationStatic Simulation

Prior Tensor Visualization Approaches

• Glyphs– Ellipsoids – Haber (Haber 1990)– Reynolds (Kriz 1995)– Velocity gradient probes (De Leeuw & van

Wijk 1993)• Features

– Hyperstreamlines (Delmarcelle & Hesselink 1992)

– Topological skeletons (Lavin 1997)• Artistic (Laidlaw 1998; Kirby 1999)

1

2

3

1

2

3

Finite Element Tensors

- shear stress

- normal stress

normal and shear stresses on a plane depend on the orientation of that plane

- shear stress

- normal stress

parametric plot of normal and shear stresses on a plane as a function of the

plane’s orientation angle

tensioncompression

• Developed by Otto Mohr ~100 years ago• 3D symmetric tensors • Eigenvalues (1, 2, 3) at circle intersections• Anisotropy increases with circle size (peak shear)• Compression to left; tension to right• Leveraged user’s mental model

Traditional Mohr Diagrams

tensioncompression

3

2

1 = 2 = 3

2 = 3

1

C

B1

2

3

D

1

A

shear

Modernized Mohr Diagrams

global envelope = anisotropy for entire model

color-coded envelope = subset anisotropy

Mohr’s circle glyph = selected element

Probing

Mohr’s Circle Extrema

• Min / max anisotropy (circle radius)• Min / max stretch (x axis position)

Similarity-based Color Coding

• Select element (highlighted in white)

• New variable created based on difference between eigenvalues of selected element and neighbors

• Elements re-colored by created variable

Filtering

• Select element (highlighted)• Display all elements within 2% of Mohr’s circle

parameters of selected element

Salt Sphere

Salt Daipir

• Filtered to show just elements with high degree of rotation

• Color-coded by degree of rotation

Results

• Stress near salt interface is spatially variable and perturbed from the far field state - including amplification of sheer adjacent to salt bodies.

• Simulations combined with tensor vis tools can successfully quantify stress in and around salt bodies.

• For some geometries, anisotropy in horizontal stress can be induced (up to 35% of far field horizontal stress)

• Principal stress may rotate away from vertical and horizontal planes near interface (up to 20% rotation).

• Geomechanical modeling can improve well path planning to avoid regions of geomechanical instability with respect to salt bodies.

Summary

• Extended color-coding and filtering features of earlier Visual Debugging work to include tensor data.

• Used Mohr’s circles as probe to tap into user’s mental models.

• Extended traditional Mohr’s circles to provide global information and color-coding, along with filtering and brushing.

• Examined geomechanical simulations to isolate regions of low and high stress.

Acknowledgments

• Joanne Fredrich • Work funded by DOE Mathematics,

Information, and Computer Science Office. • Work performed at Sandia National

Laboratories. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.

Questions?

Rotational Information

Two methods of display– Principal direction vectors (eigenvectors)

colored by the eigenvalues

– Axis of rotation colored by the angle of rotation