Hydraulic Fracture

Hydraulic FracturingHydraulic FracturingShort Course, Short Course,

Texas A&M UniversityTexas A&M UniversityCollege StationCollege Station

20052005

Modeling, Monitoring, Post-Job Evaluation, Improvements

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3D3D

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P3D and 3D Models

FracPro (RES, Pinnacle Technologies)

FracCADE (Dowell)

Stimwin (Halliburton) and PredK (Stim-Lab)

TerraFrac

StimPlan

MFrac

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Dimensionless Form of Nordgren Model

204

201w

x t -+

wt

D

D D D

D

D

wx

ii

D

D

04

0

dxdt

wx

fD

D

D

D

43

03

xD = 0 (wellbore) xD = xfD (tip)

D(xfD) : inverse of xfD(tD)

w D0 0

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Propagation Criterion of the Nordgren Model

Net pressure zero at tip

Once the fluid reaches the location, it opens up immediately

Propagation rate is determined by “how fast the fluid can flow

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Other Propagation Criteria

(Apparent) Fracture Toughness

Dilatancy

Statistical Fracture mechanics

Continuum Damage mechanics

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Fracture Toughness Criterion

KI

xf

hf pn

KIC

(Rf)

Stress Intensity Factor KI =pnxf1/2

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CDM

dDdt

= C n

n 1- D

dDdt

= C1- D

What is the time needed for D to start at D = 0 and grow to D = 1 ?

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CDM Propagation Criterion

u =Cl x

l + xwf

H,

2

f

fx=x2

f

2 1 2

min

/

Cl 2Combined Kachanov parameter:

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P3D

Pseudo 3 D Models: Extension of Nordgren’s differential model with height growth

Height criterionEquilibrium height theory

or Assymptotic approach to equilibrium

Plus some “tip” effect

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3D (Finite Element Modeling)

x

ywellbore element

tip element

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Fracture Toughness Criterion

pn

KIC

Fluid flow in 2 DFluid loss according to local opening timePropagation: Jumps

Stress Intensity Factor KI > KIC ?

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Data Need for both P3D and 3D:

Layer dataPermeability, porosity, pressure

Young’s modulus, Poisson ratio, Fracture toughness

Minimum stress

Fluid data

Proppant data

Leakoff calculated from fluid and layer data

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Design Tuning Steps

Step Rate test

Minifrac (Datafrac, Calibration Test)

Run design with obtained min (if needed)

and leakoff coefficient

Adjust pad

Adjust proppant schedule

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Step rate test

Time

Bot

tom

hole

pre

ssur

e

Inje

ctio

n ra

te

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Step rate test

Injection rate

Bot

tom

hole

pre

ssur

e

Propagation pressure

Two straight lines

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Fall-off (minifrac)

1st

injec

tion

cycle

2nD

injec

tion

cycle

flow-backshut-in

1

2

34

5

68

7

Injection rate

Time

Bot

tom

hole

pre

ssur

e

Inje

ctio

n ra

te

3 ISIP

4 Closure

5 Reopening

6 Forced closure

7 Pseudo steady state

8 Rebound

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Pressure fall-off analysis(Nolte)

eLeDpeitt tC2AtgS2AV=Ve

,

eD ttt /

eLDpi

tt tCtgSAVw

e2 ,2-

e

eA

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g-function

where F[a, b; c; z] is the Hypergeometric function, available in the form of tables and computing algorithms

dimensionless shut-in time

area-growth exponent

D

t

AD

DD

D dAdtAt

tgD

D

1

0

1

/1/1

1,

211;1;,2/1124

,1

DDDD

tFtttg

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g-function

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Pressure fall-off

,2-2-/ DeLfpfeifCw tgtCSSSAVSpp

p b m g tw N N D ,

eLeDpeitt tC2AtgS2AV=Ve

,

eD ttt /

,22- e

DeLpi

tt tgtCSAVw

e

wSp fnet Fracture stiffness

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Fracture Stiffness(reciprocal compliance)

Table 5.5 Proportionality constant, Sf and suggested for basic fracture geometries

PKN KGD Radial

4/5 2/3 8/9

Sf 2Ehf

'

Exf

'

316ERf

'

wSp fnet Pa/m

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Shlyapobersky assumption

No spurt-loss

,2-2- DeLfpfe

ifCw tgtCSSS

AVSpp

Ae from intercept

g

pw

bN mN

g=0

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Nolte-Shlyapobersky

PKN KGD Radial

Leakoffcoefficient,

CL

Ne

f mEt

h

'4

Ne

f mEt

x

'2

Ne

f mEt

R

'3

8

FractureExtent CNf

if pbh

VEx

22

CNf

if pbh

VEx

3

83

CN

if pb

VER

FractureWidth

eL

ff

ie

tC

hxV

w

830.2

eL

ff

ie

tC

hxV

w

956.2

eL

f

ie

tC

R

Vw

754.22

2

FluidEfficiency

i

ffee V

hxw

i

ffee V

hxw

i

fe

e V

Rw2

2

Vi: injected into one wing

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7 Calculate

(fluid efficiency)

3 Calculate Rf

(fracture extent -radius)

4 Calculate CLAPP

(apparent leakoff coeff)

5 Calculate wL

(leakoff width)

6 Calculate we

(end-of pumping width)

RE V

b pfi

N C

38

3

CRt E

mLAPPf

eN

83 '

w g C tL LAPP e ( , )089

2

wV

Rwe

i

fL 2 2 /

w

w we

e L

1: g-function plot of pressure2: get parameters bN and mN

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Computer Exercise 3-1 Minifrac analysis

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Example

Permeable (leakoff) thickness, ft, 42

Plane strain modulus, E' (psi), 2.0E+6

Closure Pressure, psi, 5850

21.8 9.9 0.0 1 0

21.95 0.0 7550.62 0 0

22.15 0.0 7330.59 0 0

Time, min

BH Injection rate, bpm

BH Pressure, psi

Include into inj volume

Include into g-func fit

0.0 9.9 0.0 1 0

1.0 9.9 0.0 1 0

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Output

Slope, psi -4417

Intercept, psi 13151

Injected volume, gallon 9044

Frac radius, ft 39.60

Average width, inch 0.49205

Fluid efficiency 0.16708

Apparent leakoff coefficient (for total area), ft/min^0.5

0.01592

Leakoff coefficient in permeable layer, ft/min^0.5 0.02479

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From "apparent" to "real“ (radial)

64.0)arcsin()1(2

53.06.39*2

422

5.02

xxxr

Rh

x

p

f

p

ft/min 0.024 ft/min 0.640.015 m/s

0.2141085.5

ft/min 0.015 m/s1085.5

0.50.50.55

,

0.50.55,

TrueL

AppL

C

C

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Redesign

Run the design with new leakoff

coefficient

(That is why we do minifrac analysis)

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Monitoring

Calculate proppant concentration at bottom (shift)

Calculate bottomhole injection pressure, net pressure

Calculate proppant in formation, proppant in well

Later: Add and synchronize gauge pressure

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Nolte-Smith plot

Log net pressure

Log injection time

Normal frac propagation

Tip screenout

Wellbore screenout

Unconfined

height growth

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Post-Job Logging

Tracer Log

Temperature Log

Production Log

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Radius of penetration

Available Techniques for Width and Height

Measured Directly Formation Micro Scanner Borehole Televiewer

Based on Inference Temperature Logging Isotopes (fluid, proppant) Seismic Methods, Noise Logging Tiltmeter techniques Spinner survey

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ScSb Ir

Tracerlog

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Tiltmeter Results after Economides at al. Petroleum Well Construction

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0 100 200 300 400

Fracture Half-Length (ft)

< 0.00.00.0 - 2.02.0 - 4.04.0 - 6.06.0 - 8.08.0 - 10.010.0 - 12.012.0 - 14.0> 14.0

FracCADE

*Mark of Schlumberger

EOJ Fracture Profile and Proppant Concentration

Texaco E&POCS-G 10752 #D-12Actual05-23-1997

-0.45 -0.30 -0.15 0 0.15 0.30 0.45

Wellbore Hydraulic Width(in)

5600 6400 7200

Stress(psi)

7300

7350

7400

7450

7500

Pressure Match with 3D Simulation

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3D Simulation

0 50 100 150 200 250Fracture Half-Length - ft

0

0.05

0.10

0.15

0.20

0.25P

ropp

ed W

idth

- in

0

1000

2000

3000

4000

5000

Conductivity (K

fw) - m

d.ftPropped Width (ACL)

Conductivity - Kfw

FracCADE

*Mark of Schlumberger

Flow Capacity Profiles

Texaco E&POCS-G 10752 #D-12

Actual05-23-1997

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Well Testing: The quest for flow regimes

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Design Improvement in a Field Program

Sizing Pad volume for “generic” design More aggressive or defensive proppant

schedule Proppant change (resin coated, high strength

etc.) Fluid system modification (crosslinked, foam)

Proppant carrying capacity Leakoff

Perforation strategy changes Forced closure, Resin coating, Fiber

reinforcement, Deformable particle

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Example: Tortuous Flow Path

Analysis of the injection rate dependent element of the treating pressure

Does proppant slug help?

Does limited entry help?

Does oriented perforation help?

Extreme: reconsidering well orientation:

e.g. S shaped

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Misalignment

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Fracture Orientation: Perforation Strategy after Dees J M, SPE 30342

max max

From overbalanced perforation

From underbalanced perforation

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High Viscosity slugs

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Proppant Slugs

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Forcheimer Equation

Cornell & Katz

Case Study: Effect of Non-Darcy Flow

2vkv

Lp

2avkv

Lp

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Non-Darcy Flow

Dimensionless Proppant Number is the most important parameter in UFD

res

propfprop V

Vkk

N2

Effective ProppantPack Permeability

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Non-Darcy Flow

Effective Permeability

Reynolds Number

Re1 Nkk nom

eff

vkN nomRe

keff is determined through an iterative processDrawdown is needed to calculate velocity

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Non-Darcy Flow Coefficient

Several equations have been developed mostly from lab measurements (empirical equations)

General form of equation

where is 1/m and k is md

cbfk

ax

8101

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SPE 90195

Optimum FractureTreatment Design Minimizes the Impact of Non-Darcy Flow Effects

Henry D. Lopez-Hernandez, SPE, Texas A&M University, Peter. P. Valko, SPE, Texas A&M University, Thai T. Pham, SPE, El Paso Production

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Case Study: Reynolds number

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Case Study: Proppant number

Comparison for 20/40 Norton Proppants

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Prop

pant

Num

ber

Naplite® Interprop® Sintered Bauxite

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Case Study: Max possible JD

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Case Study: Optimum frac length

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Case Study: Optimum frac width

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Summary

Increasing role of evaluation

Integration of reservoir engineering, production engineering and treatment information

Cost matters

Expensive 3D model does not substitute thinking

Still what we want to do is increasing JD