Visualization of Salt-Induced Stress Perturbations Patricia Crossno David H. Rogers Rebecca Brannon...
Transcript of Visualization of Salt-Induced Stress Perturbations Patricia Crossno David H. Rogers Rebecca Brannon...
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