Two Dimensional Hydraulic Fracture Simulations Using FRANC2D

1. Two Dimensional Hydraulic Fracture Simulations Using FRANC2D Qingfeng Tan

2. Flow Index 10 1 10 100 1000 10000 k / k frx Vapor extraction well intersecting horizontal hydraulic fracture, from Bradner (2002)

3. Importance of 2-D

4. Objective Develop and apply a model for predicting the forms of curving hydraulic fractures in two dimensions

5. Overview • Previous work • Vertical and horizontal fracture • Analytical models • Theoretical Analysis • Coupling mechanical and fluid flow analysis • Code Development • Automatic propagation (EXC_AUTO_DRIVER_FLOW) • Fracture form calculation routines • Fluid flow simulation routines • Application • Shallow soil model • Effects of layering and lateral residual compression

6. h X Q h Y Q a X Z a Y Z Q Z Q Z d d r r a a Hydraulic Fracture Design Vertical Fractures (a) (b) Horizontal Fractures (c) (d)

7. Previous Models Pressure time Length time Aperture time

8. Simulate Hydraulic Fracture • Fracture aperture—analyze as elastic displacements due to fluid pressure • Fluid pressure—analyze as flow in deforming fracture • Propagation—require stress intensity to equal critical value

9. Problem with Analysis in 2-D • Fracture curves-- numerical methods for stress analysis required • Fracture propagation-- analyze as a series of quasi static models. Requires many analyses to be conducted. Need FEM method with automatic regridding around fracture

10. FRANC2D • 2-D stress and displacement • Developed for structural fracture mechanics applications • Auto regrid around fracture • Fluid flow within fracture not included

11. Fracture with Fluid Flow-Coupled Approach • Modify FRANC2D to perform mechanical analysis, then calculate geometry of fracture, caused by fluid pressure, and other loadings • Fluid flow analysis adjust fluid pressure due to the shape changes of fracture, coupled with mechanical analysis • Propagation criterion: is decided by fracture geometry and fluid pressure

12. From 1-D implicit solution; flow bc at well, head bc at tip From FEM elasticity solution Flow and Deformation Coupling Pressure x Aperture x

13. Propagation • KI=Stress intensity factor • KI=KIc for propagation • KIC is material property, called fracture toughness.

14. How to ensure KI=KIc? Pressure Ptip x KI KIc Ptip

15. Code Development • Fracture propagation control routine -EXC_AUTO_DRIVER_FLOW • Fracture geometry calculation routines -EXC_LENGTH_FLOW -EXC_APER_FLOW -EXC_VOLU_FLOW • Fluid flow simulation routines -FLUID_FLOW_INIT -FLUID_FLOW_CALC

16. Automatic Propagation Subroutine • Fluid flow and mechanical analysis coupling to decide pressure and geometry • Propagation criterion: KI=KIC • Auto-remesh around fracture tip

17. Fracture Form Calculation • Length – EXC_LENGTH_FLOW • Aperture – EXC_APER_FLOW • Volume – EXC_VOLU_FLOW • Obtain Crack node info • Calculation in each segment, then integral

18. Fluid Flow and Aperture Subroutine • Calculate new heads using initial aperture • Calculate aperture using new head • Calculate heads using new aperture • Repeat and compare heads and apertures between successive iterations • Converge when change is less than tolerance, usually less than 7 iterations

19. Propagation Subroutine • Calculate KI for pressure at tip • Adjust pressure at tip slightly, redo fluid pressure calculations, and calculate new KI • Use two values of KI and pressure tip to interpolate new value of pressure tip that should give KI=KIc • Check KI and revise pressure tip as needed until KI is within tolerance of KIc

20. a VerificationUniform Pressure: Model Setting P • Infinite elastic media • Uniform pressure • Radial symmetric

21. Verification-Driving Pressure

22. Verification (II): Fracture Length

23. Verification (III): Fracture Aperture

24. Error Analysis

25. Applications • Hydraulic fracture in shallow soil: • Gravity • Fluid injection • Soil with under-lying softer material • Soil with high lateral residual stress

26. Forms of Hydraulic Fractures in the Field

27. Field Data Adoption Cross 4 Cross 3 • Four cross-section selection • Each cross-section starts from center of fracture to the edge of it, perpendicular with each other • Fracture path, uplift, and sand extent data are adopted 0.9 0.7 0.5 0.3 Cross 2 0.1 N Cross 1 0 5 10 15 feet

28. General case-Model Setting Depth 0 m -1.6 m -2 m frx -5 m 0 m 12 m Distance from well

29. Vertical Stress During Propagation

30. Pressure Log

31. Fracture Form

32. Aperture and Uplift (m) Average radial extent of sand

33. Effects of Layering observed Richardson Simulated

34. Effects of Lateral compression

35. Conclusions • FRANC2D has been modified to simulate hydro-mechanical coupling conditions during hydraulic fracturing. • A new simulation tool, HFRANC2D?, is available • The model has been verified using analytical solutions, error within a few percent

36. Conclusions, applications • Gentle bowl-like forms of hydraulic fractures in shallow soils can be predicted. • Effects of state of stress and material properties can be predicted and results resemble field observations.