1. Visualization of Salt-Induced Stress Perturbations Patricia Crossno David H. Rogers Rebecca Brannon David Coblentz Sandia National Laboratories October 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.

2. Deepwater 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

3. Salt 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 (S v = S h )

4. Wellbore 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

5. spherical salt body 8,136 elements salt diapir with tongue 10,128 elements Static Simulation

6. 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

7. 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

8. 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

9. Modernized Mohr Diagrams global envelope = anisotropy for entire model color-coded envelope = subset anisotropy Mohr’s circle glyph = selected element

10. Probing

11. Mohr’s Circle Extrema Min / max anisotropy (circle radius) Min / max stretch (x axis position)

12. 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

13. Filtering Select element (highlighted) Display all elements within 2% of Mohr’s circle parameters of selected element

14. Salt Sphere

15. Salt Daipir Filtered to show just elements with high degree of rotation Color-coded by degree of rotation

16. 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.

17. 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.

18. 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.

19. Questions?

20. Rotational Information Two methods of display –Principal direction vectors (eigenvectors) colored by the eigenvalues –Axis of rotation colored by the angle of rotation