7 papanastasiou p hydraulic fracturing

8/11/2019 7 Papanastasiou P Hydraulic Fracturing

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Hydraulic Fracturing:Basic Concepts and Numerical Modelling

Panos Papanastasiou

Department of Civil and Environmental Engineering University of

Cyprus

1991-2002 in Schlumberger Cambridge Research


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2 Initials11/9/2006

Hydraulic fracturing

Petroleum engineering

stimulate oil and gas reservoirs,

cuttings re-injection

Environmental engineering

waste disposal in shallow formations,

cleaning up contaminated sites

Geotechnical engineering

injection of grout, dam construction


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3 Initials11/9/2006

Outline

Basic fracturing theory: controlling parameters fracture opening, propagation, modes, initiation, closure

Perforating for fracturing

Fracture geometry

deviated and horizontal wellbores

tortuosityand multiple fractures

Hydraulic fracturing modeling

physical processes, geometrical models, height growth, net-pressure

Fracturing weak formations

elastoplastic modeling, experiments on soft rocks (DelFrac)


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4 Initials11/9/2006

Why hydraulic fracturing in Petroleum engineering?

Bypass near-wellbore formation

damage

drilling induced, fines invasion-migration,

chemical incompatibility

Extend a conductive path deep into

the formation

increase area exposure to flow

Reservoir management tool

change flow, fewer wells, wellplacement, IVF, frac&pack, screen-less

completion

h

packer

packer

hydraulicfracture

water

gas

Oil


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5 Initials11/9/2006

Fracture Openingmin

pf w

2L x

y

min

yy

Fracture opens if the net pressure

pnet=pf - min >0

Fracture opening

w(x)=4 pnet (L2-x2)1/2/E

E=E/(1-2) is the plane strain modulus

maximum width for x=0

for constant height: W=4 pnet L/E

for radial fracture: W=8 pnet R/ ( E)

singular stress at the crack tip, for x=L

yy=pnet [x/(x2-L2)1/2-1]


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6 Initials11/9/2006

Fracture Propagation The stresses ahead of the crack tip are singular

characterized by the stress intensity factor KI

ij= [KI / (2 r )1/2] f() + ...

example: an elliptical crack, KI = pnet L 1/2

A crack will propagate if

KI = KIC

KIC is a material parameter called fracture toughness.

Typical values for rocks are 0.1 - 2 MPa m1/2

ij

r

pnet

L


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7 Initials11/9/2006

Fracture Modes

p p

p

p p p

I. opening mode II. sliding mode III. tearing mode

tensile fractureshydraulic fractures

drilling induced

faultsshear fractures andturning of fracturesnear wellbore

splitting of thecrack front,multiple fractures


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8 Initials11/9/2006

Fracture Initiation in Open Holes

Fracture initiation at lower pressures

large contrast between insitu stresses

high pore pressure, e.g. eject at low rates prior pressurization

preexisting flaws and natural fractures

h

H

breakout

Pb = 3h

-H

-p+T

p is the formation pressureT is the tensile strength


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9 Initials11/9/2006

Breakdown pressure

Pb = 3h-H-p+T

p is the formation pressure

T is the tensile strength

no fluid penetration, upper bound

Closure stress

ISIP in low permeability formations

2ndcycle

time

BHP breakdown pressure

ISIP

closure stress

Pore pressure

tensile strength

flow rate

open

valves

Pressure vs Time Analysis

Fracture Initiation and Closure


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10 Initials11/9/2006

Perforated Cased Holes


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weak rocks

1. reduce multiples2. risk of sanding

h

H preferentialdirection

1. low breakdown pressures

h

Hpreferentialdirection

strong rocks


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Near Wellbore Fracture Geometry

h

H preferential direction

High flow rates and viscosityresults in high breakdownand smooth fracture paths

Low flow rates and bad cementbond results in breakdownpressures:multiple fractures and tortuosity


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13 Initials

Experiments in Delft Fracturing Consortium (1997)

Deviated and Horizontal Wells


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Fracture Tortuosity

Gradual or sharp fracture re-orientation to the preferred plane resultsin width restriction near the well

Tortuosityoccurs

in high differential stress fields

in deviated wells

in long perforated intervals and in phased perforations

in reservoirs with natural fractures

Problems near-wellbore friction resulting in pressure drop

premature screen-out due to proppant bridging

H

h

Multiple Fractures


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Propagation of multiple fractures away from the wellbore area

Multiples occur

in multiple or long perforated intervals with phased perforations

in deviated wells where the separation between fractures is large compared to the

fracture height

in reservoirs with natural fractures

Problems

increase treating net-pressure

reduced fracture widths: increase screenout potential

increased leakoff: lower efficiency

Reduced fracture length

Multiple Fractures

h

L


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surface

reservoir

v

axial fracturestransverse fractures

wellbore drilled // tomaximum horizontal stress

wellbore drilled // tominimum horizontal stress

overburden

h

Horizontal Wellbores


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Modelling Hydraulic Fracture Propagation

Optimize the treatment (pumping schedule, proppant stages)

increase well production

reduce cost

Control where the fracture is growing

avoid fracturing near layers with different content: oil, gas, water

create long fractures in some layers

Predict the response during treatment

Post-evaluation of the treatment


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Physical Processes in Hydraulic Fracturing

Viscous fluid flow in the fracture

Fluid leakoff in the formation

Rock deformation

Fracture propagation

Proppant transport

pw

vl

wp

net

v vpf

KI=KIC

vs


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Pressure Loading on Fracture Surfaces

Pressure drop: dp/dx=12 q/w3

Net pressure pnet=pf - hgives KI(+)>0

Closure stress over fluid-lag gives KI

(-)


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HF Geometrical Models

h

L

flow

PKN

L

h

o

w

KGD

Planar 3D

flow

Radial

R

flow

Fully 3D

D MODELS

Fracture Profiles in Layered Formations


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Fracture Profiles in Layered Formations

shale 1

shale 2

shale 3

sandstone1

sandstone 2

pay zone

stress profile

verticalwidthprofile

T-shape fracture

Fracture may not penetrate deep to

the optimum length

Fracture may connect several pay

zones separated by shale layers

Fracture may grow in non-productive

layers

Problems with proppant placement

Indirect Vertical Fracturing (IVF) forsand control

F t ti


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Fracture tip

High net-pressures (pnet=pfrac-min)

high apparent fracture toughness: due to scale effect, confining

pressure, heterogeneities and plasticity

flow behaviour near the tip: fluid-lag, rock dilation

underestimation of the closure stress (min

)

3,max

1,min

pfrac

high shear stress:

plastic zonefluid lag

cohesive zone

Elasto plastic HFmodel


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Elasto-plastic HF model

Fluid-flow in the fracture

Newtonian viscous fluid, lubrication theory:

dp/dx=12 q/w3

Rock deformation Mohr-Coulomb flow theory of plasticity


Cohesive model

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 2 4 6 8

fracture length (m)

fracturehalf

-width(m)

Finite element analysis

fully coupled solution, special

continuation algorithm

meshing/remeshing

Fl id fl


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Fluid-flow

Boundary conditions


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Rock deformation

Propagation criterion


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Propagation criterion

I iti l l ti


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Initial solution


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Numerical Implementation

Finite Element Discretization

8 node element 6 node interface elements

Finite Differences for Fluid Flow

Coupling of fluid-flow with rock-deformation

Arc-length algorithm based on volume control

Meshing/ remeshing


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-3.7

-2.7-1.7

-0.7

0.3

1.3

2.3

3.3

4.3

0 0.5 1 1.5 2

fracture length (m)

n

et-pressure(MP

a)

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 0.5 1 1.5 2

fracture length (m)

fra

cturehalf-width

(m)

plasticity

plasticity

elasticity

elasticity

tiptip

Plastic fractures are wider and shorterthan the elastic fractures

Fluid-lag is smaller in the plasticfracture

Apparent fracture toughness


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Apparent fracture toughness

0

1

2

3

4

5

6

7

0.5 1 1.5 2 2.5

fracture length (m)

n

et-pressure(MP

a)

0

1

2

3

4

5

6

7

8

9

10

0 0.05 0.1 0.15 0.2

fractu re extension (m)

apparen

ttoughness(MP

am^0.5

)

elasticity

plasticity plasticity

elasticity

Apparent fracture toughness ishigher for the plastic fracture

Fracture closure


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Fracture closure

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 2 4 6 8

fracture length (m)

fracturehalf-width(m)

-2

-1

0

1

2

3

4

5

6

7

0 2 4 6 8

fracture length (m)

net-pressu

re(MPa)

plasticity propagation

closure

Plastic fracture closes first nearthe tip Fracture is open at zero net-pressureand closes at negative values


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0

2

4

6

8

10

12

14

0 5 10 15

distance from the wellbore (m)

princ

ipalstresses(M

Pa)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15

distance from fracture face (m)

yieldfactorf failure line

S_z

S_h

S_H

Stresses after fracturing

The rock formation is more stable afterfracturing

The closure stress on proppant is lowernear the wellbore

Dislocation model


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Dislocation model

Position and strength of super-

dislocations

zero stress intensity factor at the crack

tip

stresses satisfy Mohr-Coulomb yieldcriterion at dislocations

total crack-opening-displacement is

maximized

Papanastasiou and Atkinson (2000)

Fracturing WeakRocks


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Fracturing Weak Rocks

Rock dilation: narrower fracture near the tip is a wronghypothesis

Plastic yielding: plays a shielding mechanism increasing

the effective fracture toughness

contrast of insitu stresses

effective Youngs modulus, rock strength pumping parameters: flow rate x viscosity

Fractures are wider and shorter, compared with the elastic

model

B k i l i d li d t fl t t f t


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Break in slope in pressure decline does not reflect true fracture

closure, for soft rocks. Closure stress might be underestimated

Use apparent toughness and unloading modulus in the HF

simulators.

Closure stress on proppant

higher near the tip and lower near the wellbore

more uniformly distributed with increasing fracture length

Formation Stability

decrease of stresses after fracturing

reduced risk of formation failure


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Experimental Set-up (DelFrac)

pump

h

pressure

transducer

fracture

c

clamps lvdt

Acoustictransducer


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Rough fracture surface with dry tip

fluid front

fracture tip

Pressure andwidth in plaster experiments


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Pressure and width in plaster experiments

ch , ch ,


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Closure in plaster

confining stress

confining stress

Strong Plaster: Weak Plaster

Delft Fracturing Consortium Results


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Optimum completion configuration

Perforations with 0/180 gave best link-up, but perforation spacing must be very

small for link-up

Fractures at unfavourable perfs propagated only at low stress contrast;

optimum phasing different for high/low stress contrast

Perforation orientation has little impact

Multiple fractures may be induced even for good perforation link-up

Fracture pressure has a strong positive influence on fracture

geometry

Fracturing in the annulus is important in practice. It has a large

impact on pressure and geometry.

7 papanastasiou p hydraulic fracturing

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