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Two Dimensional Hydraulic Fracture Simulations Using FRANC2D. Qingfeng Tan. Flow Index. 10. 1. 10. 100. 1000. 10000. k. /. k. frx. Vapor extraction well intersecting horizontal hydraulic fracture, from Bradner (2002). Importance of 2-D. Objective.

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vapor extraction well intersecting horizontal hydraulic fracture from bradner 2002

Flow Index

10

1

10

100

1000

10000

k

/

k

frx

Vapor extraction well intersecting horizontal hydraulic fracture, from Bradner (2002)
objective
Objective

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

overview
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
hydraulic fracture design

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)

previous models
Previous Models

Pressure

time

Length

time

Aperture

time

simulate hydraulic fracture
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
problem with analysis in 2 d
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

franc2d
FRANC2D
  • 2-D stress and displacement
  • Developed for structural fracture mechanics applications
  • Auto regrid around

fracture

  • Fluid flow within

fracture not included

fracture with fluid flow coupled approach
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

propagation
Propagation
  • KI=Stress intensity factor
  • KI=KIc for propagation
  • KIC is material property, called fracture toughness.
how to ensure k i k ic
How to ensure KI=KIc?

Pressure

Ptip

x

KI

KIc

Ptip

code development
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

automatic propagation subroutine
Automatic Propagation Subroutine
  • Fluid flow and mechanical analysis coupling to decide pressure and geometry
  • Propagation criterion: KI=KIC
  • Auto-remesh around fracture tip
fracture form calculation
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
fluid flow and aperture subroutine
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
propagation subroutine
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
verification uniform pressure model setting

a

VerificationUniform Pressure: Model Setting

P

  • Infinite elastic media
  • Uniform pressure
  • Radial symmetric
applications
Applications
  • Hydraulic fracture in shallow soil:
      • Gravity
      • Fluid injection
  • Soil with under-lying softer material
  • Soil with high lateral residual stress
field data adoption
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

general case model setting
General case-Model Setting

Depth

0 m

-1.6 m

-2 m

frx

-5 m

0 m

12 m

Distance from well

aperture and uplift
Aperture and Uplift

(m)

Average radial extent of sand

effects of layering
Effects of Layering

observed

Richardson

Simulated

conclusions
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
conclusions applications
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.