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Multiscale Processes and Moving Interfaces in Hydraulic Fracturing by Anthony Peirce

This presentation will delve into the intricate processes of hydraulic fracturing (HF) at multiple scales, highlighting the theoretical and numerical modeling methods employed to address 1D, 2D, and 3D challenges. Key topics include special solutions for hydraulic fractures, energy loss mechanisms, and boundary conditions. The work will also feature case studies, including well stimulation and block caving, offering insights into the complexities of fracture propagation and interaction with material interfaces. Conclusively, we will examine experimental verifications of the models.

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Multiscale Processes and Moving Interfaces in Hydraulic Fracturing by Anthony Peirce

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  1. Hydraulic Fracture: multiscale processes and moving interfaces Anthony Peirce Department of Mathematics University of British Columbia • Collaborators: • Jose` Adachi (SLB, Houston) • Rachel Kuske (UBC) • Sarah Mitchell (UBC) • Ed Siebrits (SLB, Houston) Nanoscale Material Interfaces:Experiment, Theory and Simulation Singapore 10-14 January 2005

  2. Outline • What is a hydraulic fracture? • Scaling and special solutions for 1D models • Numerical modeling for 2-3D problems • Conclusions

  3. HF Examples - block caving

  4. HF Example – caving (Jeffrey, CSIRO)

  5. HF Examples – well stimulation

  6. An actual hydraulic fracture

  7. HF experiment (Jeffrey et al CSIRO)

  8. 1D model and physical processes Viscous energy loss Leak-off Fracture Energy Breaking rock

  9. Scaling and dimensionless quantities • Rescale: • Dimensionless quantities: • Governing equations become:

  10. Two of the physical processes • Large toughness: • Large viscosity:

  11. Experiment I (Bunger et al 2004) Theory Large toughness: (Spence & Sharp)

  12. Experiment II (Bunger et al 2004) Theory Large viscosity: (Desroches et al)

  13. The coupled EHF equations in 2D • The elasticity equation – balance of forces • The fluid flow equation – mass balance

  14. Boundary & propagation conditions • Boundary conditions • Propagation condition

  15. The elasticity equation

  16. 3 Layer Uniform Asymptotic Solution

  17. Crack cutting an interface

  18. A penny crack cutting 2 interfaces

  19. A crack touching an interface

  20. Eulerian approach & Coupled HF Equations

  21. MG preconditioning of • C coarsening using dual mesh • Localized GS smoother

  22. Performance of MG Preconditioner ~9.5 x

  23. Front evolution via the VOF method 0.75 0.15 1.0 0.78 0.06 1.0 1.0 0.3

  24. Time stepping and front evolution Time step loop: VOF loop: Coupled Solution end next VOF iteration next time step

  25. Radial Solution

  26. Fracture width for modulus contrast Modulus Changes Source

  27. Fracture width for stress jump

  28. Pressure and width evolution

  29. Channel fracture and breakout

  30. Hourglass HF with leakoff

  31. Concluding remarks • Examples of hydraulic fractures • Scaling and physical processes in 1D models • Tip asymptotics: & • Experimental verification • Numerical models of 2-3D hydraulic fractures • The non-local elasticity equation • An Eulerian approach and the coupled equations • FT construction of the elasticity influence matrices • A multigrid algorithm for the coupled problem • Front evolution via the VOF method • Numerical results

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