Hydraulic Fracture: multiscale processes and moving interfaces

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 InterfacesExperiment, 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
Fracture Energy Breaking rock
Leak-off
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