# Presentation: 466680

## 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.

## Deepwater Gulf of Mexico

- 13 to 28 billion barrels of oil estimated

- 32 billion barrels known oil in US in 2002

## Salt Formations

**Evolution of a salt diapir**

**salt relaxes until vertical stress = horizontal stress (S****v**** = S****h****)**

## 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**

## Static Simulation

- spherical salt body
- 8,136 elements

- salt diapir with tongue
- 10,128 elements

**Static 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)**

## Finite Element Tensors

- 

-  - shear stress

-  - normal stress

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

- parametric plot of normal and shear stresses on a plane as a function of the plane’s orientation angle 

## 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 

**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**

## 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**