tan thesis defense 0814 final

7/29/2019 Tan Thesis Defense 0814 Final

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Two Dimensional Hydraulic Fracture

Simulations Using FRANC2D


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Vapor extraction well intersecting horizontal

hydraulic fracture, from Bradner (2002)

kfrx/k

10 100 1000 100001

10


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Importance of 2-D


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Objective

Develop and apply a model for predicting the

forms of curving hydraulic fractures in twodimensions


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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


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Hydraulic Fracture Design

Vertical Fractures

a

Qh

X

Y

Z Horizontal Fractures

(a)

(d)(c)

(b)

a

Qd

Z

r

Q

a

d

Z

r

Y

Z

Q

h

X

a


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Previous Models

Pressure

Length

Aperture

time

time

time

1

1CtfP

2

2

Ctfa

3

3

Ctf

)],,,([ 3,2,1 QKEff

)2.05.0( 1 C

)44.025.0(2C

)5.011.0(3C


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Simulate Hydraulic Fracture

Fracture apertureanalyze as elastic

displacements due to fluid pressure

Fluid pressureanalyze as flow in

deforming fracture

Propagation

require stress intensity to

equal critical value


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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 automaticregridding around fracture


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FRANC2D

2-D stress and displacement

Developed for structural

fracture mechanicsapplications

Auto regrid around

fracture Fluid flow within

fracture not included


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Fracture with Fluid Flow-

Coupled Approach

Modify FRANC2D to perform mechanical analysis,then calculate geometry of fracture, caused by fluidpressure, and other loadings

Fluid flow analysis adjust fluid pressure due to theshape changes of fracture, coupled with mechanicalanalysis

Propagation criterion:

is decided by fracture geometry and fluid

pressure

ICIKK

IK


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Flow and Deformation Coupling

Aperture

From 1-D implicit solution; flow bc at well, head bc at tip

From FEM elasticity solution

x

x


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Propagation

KI=Stress intensity factor

KI=KIc for propagation

KIC is material property, calledfracture toughness.


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How to ensure KI=KIc?

Pressu

re

Ptip

KI

Ptip

KIc

x


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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


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Automatic Propagation Subroutine

ICIKK

Fluid flow and mechanical analysis

coupling to decide pressure and geometry

Propagation criterion: KI=KIC

Auto-remesh around fracture tip


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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


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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


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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


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Verification

Uniform Pressure: Model Setting

PInfinite elastic

media

Uniform

pressure

Radialsymmetric

a

z

r


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Verification-Driving Pressure

5

10

0 5 10 15

Time(min)

P

ressure(KPa)


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Verification (II): Fracture Length

1

3

5

0 5 10 15Time(min)

Length(m)


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Verification (III): Fracture Aperture

0.5

1.0

1.5

0 5 10 15

Time(min)

Aperture

(mm)


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Error Analysis

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

1 2 3 4 5

Length (m)

Relative

Error

Error PError aError d


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Applications

Hydraulic fracture in shallow soil:

- Gravity

- Fluid injection

Soil with under-lying softer material

Soil with high lateral residual stress


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Forms of Hydraulic Fractures

in the Field


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Field Data Adoption

Four cross-sectionselection

Each cross-section

starts from center of

fracture to the edge ofit, perpendicular with

each other

Fracture path, uplift,and sand extent data

are adopted

0 5 10 15feet

0.1

0.3

0.5

0.7

N

0.9

Cross 1

Cross 4

Cross 3

Cross 2


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General case-Model Setting

Depth

0 m

-2 m

12 m

-5 m

Distance from well0 m

frx-1.6 m


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Vertical Stress During Propagation


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Pressure Log

0

10

20

30

40

50

60

0 2 4 6 8

Time (minutes)

Pressure

(psi)

Measured

Simulated


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Fracture Form

-1.8

-1.5

-1.2

-0.9

0 1 2

Distance from center of fracture (m)

Depthbelow

grou

ndsurface

(m)

simulated

Well H Cross-s 1Well H Cross-s 2

Well H Cross-s 3

Well H Cross-s 4


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Aperture and Uplift

0.00

0.02

0 1 2 3 4

distance from center (m)

Uplift

fromf

ield,orsimulated

apertu

re

simulated

Well H cross 1

Well H cross 2

Well H cross 3

Well H cross 4

Average radial

extent of sand

(m)


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Effects of Layering

-2

-1.5

-1

-0.5

0

0 1 2 3 4 5

E2=2000psi, E1 = 5000psi

E1=E2=5000psi

E2=3000psi, E1=5000psi

E2=4000psi, E1=5000psi

Richardson


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Effects of Lateral compression

-1.8

-1.2

-0.6

0 1 2 3 4 5 6 7

Distance from Wellbore m

De

pth(m)

Fracture Path from lowresidual area

Fracture path from high

residual compressionregion

v

h

v


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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 analyticalsolutions, error within a few percent


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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.

tan thesis defense 0814 final

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