fraccourse 2007.ppt

Hydraulic Fracturing

©2007

Hydraulic Fracturing For Production Enhancement

Worldwide massive application 90% of gas wells 70% of oil wells

Historically, for low-permeability reservoirs skin effect less than -6

No longer true - high perm. is common

High-Permeability Fracturing

Stimulation Skin effect from -4 to 0 or even slightly

positive

Originally an offshoot of sand production control (with skins as high as +30). Prevents fines de-consolidation

Hydraulic Fracturing Implementation

Complex operation Requires knowledge and high

competence in a number of areas of engineering and science

Large up-front investment in people, equipment and capabilities

“Massification” is crucial

Basic Principles

Injection of fracturing fluids Formation “breaks down” Fracture propagates, perpendicular

to least resistance “Proppants” are used to keep

fracture open

Principle of Least Resistance

Horizontal fracture Vertical fracture

Least Principal Stress Least Principal Stress

Production Stimulation

Long path of large permeability contrast with the reservoir is created

Flow is from the reservoir into the fracture and then along the fracture into the well

There is virtually no flow into the well from outside the fracture. If there is, the fracture should be considered as unsuccessful

A Road Analogy

Optimal Fracture Length and ConductivityLow Permeability CaseWhen there’s only one-lane roads, better buildat least one two-lane road as far as possibleDrivers will seek the better road

Assuming a fixed amount of paving material, do I build a long, two-lane road or a short multi-lane road to the wellbore, I mean, city?

Optimal Fracture Length and ConductivityHigh Permeability CaseWhen there’s already a network of two-lanes and lot of traffic,You’d better focus many lanes near the hub

Length Vs. Width

Low-permeability reservoirs require long fractures, width is secondary

High-permeability require wide fracture, length is secondary. Tip Screenout (TSO)

Length and width are interdependent through fracture conductivity.

Optimization is warranted

1-

Tip Screenout (TSO) for High-Permeability Reservoirs

Arrest of lateral growth Fracture inflation Leakoff control is another major

benefit of TSO

Vertical Fracture - Vertical Well

Bypass damage

Original skin disappears

Change streamlines

Radial flow disappears

Increased PI is the

result

p or q pJq post

Complex Fracturing

Horizontal wells Transverse vs. longitudinal

Multi-branched wells

Longitudinal Vertical Fracture - Horizontal Well

H,max

xf

H,min

H,min

Transverse Vertical Fractures - Horizontal Well

H,max

Hydraulic Fracture

H,max

D

xf

H,min

Radial converging flow in frac

Multibranch Well withFractured Vertical Branches(Horizontal "Parent" Well isDrilled above the Reservoir)

Horizontal Well with MultipleTransverse Fractures

Multibranch, Multiple-fracture Configurations for Horizontal Wells


Production or Injection Enhancement

What are we doing?

Bypass formation damage After a successful fracture any

damage skin is eliminated Radically modify flow profile into

the wellbore New pseudoskin; New

productivity index

Complementary Roles

Control of sand deconsolidation Reduce fines migration and

asphaltene production Reduce bottom water coning Improve communication between

reservoir and wellbore

Fracturing Role Expanded

Permeability Gas Oil

Low k <0.5 md k <5 md

Moderate 0.5< k <5 md 5< k <50 md

High k >5 md k >50 md

Pseudosteady State Productivity Index

pJq

pJB

khq D

2

srr

J

w

e

D

43

ln

1

Circular:

Production rate is proportional to drawdown, defined as average pressure in the reservoir minus wellbore flowing pressure

Dimensionless Productivity Index

Drawdown


Production Mechanism

Vertical Well, Fully Penetrating Vertical Fracture: Performance

wp

2xf

h2Vfp

Transient Flow Regimes Vertical Fracture - Vertical Well

Linear Fracture Flow

Bilinear Flow

Linear Formation Flow

Elliptical or Transition Flow

Pseudoradial Flow

Pseudoskin Factor, Radial Flow

D

fw

e

JB

kh

sr

rB

khJ

2

75.0]ln[

12

q J p

sf is a function of what?•half-length, •dimensionless fracture conductivity•wellbore radius, rw

JD is a function of what?•half-length, •dimensionless fracture conductivity•Drainage radius, re

sf is pseudoskin factor used after the treatment

to describe the productivity for radial flow

Dimensionless Productivity Index, sf and f and r’w

fx

r

r

xs

xr

J

f

e

w

ff

f

e

D

472.0

ln

1

ln472.0

ln

1

fw

eD

sr

rJ

472.0ln

1

)( fDCf

w

eD

rr

J

'472.0ln

1or

Prats

Cinco-Ley

Dimensionless Fracture Conductivity

Dimensionless fracture conductivity

f

ffD kx

wkC

2 xf

w

fracture conductivity

no name

Cinco-Ley and Samaniego

0

1

2

3

4

0.1 1 10 100 1000CfD

f

fD

fD

Cuu.+u.u+.+

u.u+.-.Cf

ln where005006401801

11603280651)(

32

2

use f = ln(2) for CfD > 1000

The JD of a Hydraulically Fractured Well

From Cinco-Ley and Samaniego and simple re-arrangement

fwffeD srxxr

J

/ln75.0/ln

1

fwffDff

e

D

srxCkh

Vkr

J

/lnln5.0ln5.075.0ln

1

44

33

22

11

00

44

33

22

11

00 0.1 1000

s f +

In(x

f /r w

), s

f + In

(x f

/rw)

+ 0

.5 In

(C

fD)

CfD

sf + In (xf /rw)

sf + In (xf /rw) + 0.5 In (CfD)

CfD, opt

1 10 100

Pseudoskin Factor for a Finite Conductivity Vertical Fracture

Penetration Ratio Proppant Number

2 xf

ye = xe

xe

e

fx x

xI

2

f

ffD kx

wkC

fDxres

wingf,prop,f

res

wingf,prop,fprop C)(I

kV

Vk

kV

VkN 221 24

reservoir

proppedwingfprop

e

proppedwingf

e

ff

fDxprop

kV

VkN

hkx

Vk

kx

wxk

CIN

,2

2

,1

2

2

2

4

4

Proppant Number - Various Ways to Look at itVarious Ways to Look at it

Nprop= const means

fixed proppant volume

JD vs CfD (moderate Nprop)

JD vs CfD (large Nprop)

Maximum Achievable PI

1.0 if

)(015.0667.01

)(089.0311.0423.0exp

6

1.0 if ln5.0990.0

1

2

2max

prop

propprop

propprop

prop

prop

propD

NNN

NN

NN

NJ

Optimal Length and Width

2Vfp = 2h wp xf

Competition for propped volume: w and xf

fpfp xhwV

f

pffD kx

wkC

2/1

hkC

kVx

fD

ffpf

2/1

f

fpfDp hk

kVCw

2Vfp = 2h wp xf

Tight Gas and Frac&Pack: the Extremes

Tight Gas k << 1 md (hard rock)

High permeability k >> 1 md (soft formation)

2/16.1

f

fpp hk

kVw

2/1

6.1

hk

kVx ffp

f

2/16.1

f

fpp hk

kVw

2/1

6.1

hk

kVx ffp

f

PI in Irregular ShapesPI in Irregular Shapes

Reservoir Volume now defined as

hyxV eeres

e

efDx

ef

ef

ee

ff

res

pfp y

xCI

xx

xx

hykx

whxk

kV

VkN 2

42

Proppant Number becomes,

Results for Results for NNpp <0.1 <0.1

Np=0.0001

Np=0.0003

Np=0.0006

Np=0.001

Np=0.003

Np=0.006

Np=0.01

Np=0.03

Np=0.06

Np=0.1

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.1 1 10 100 1000

CfD

JD

yyee/x/xee=0.5 =0.5

yyee

xxee

22xxff

N p J D

0.1 0.4330.0001 0.174

Np=0.0001

Np=0.0003

Np=0.0006

Np=0.001

Np=0.003

Np=0.006

Np=0.01

Np=0.03

Np=0.06

Np=0.1

0.10

0.15

0.20

0.25

0.30

0.35

0.1 1 10 100 1000

CfD

J D

N p J D

0.1 0.3360.0001 0.155


yyee/x/xee=0.25 =0.25

yyee

xxee

22xxff


0.10

0.20

0.30

0.40

0.50

0.1 1 10 100 1000

CfD

JD

ye/xe=1

ye/xe=0.5

ye/xe=0.25

ye/xe=0.2

ye/xe=0.1

Example:Example:

•NNp p =Constant = 0.03=Constant = 0.03 unadjusted

•Conclusion:Conclusion: CCfD,optfD,opt = 1.6= 1.6 maintained`

Equivalent Proppant NumberEquivalent Proppant Number

88.30A

ppe

CNN

NNpp = Proppant NumberNNpe pe = Equivalent Proppant NumberCCAA = Dietz Shape Factor

)ln(5.099.0

1max,

peD N

J

Shape FactorsShape Factors

Dietz shape factors have been used to relate the production rate with the pressure distribution within a shaped drainage volume

y e /x e C A

0.1 0.0250.2 2.36

0.25 5.380.3 90.4 16.170.5 21.840.6 25.80.7 28.360.8 29.890.9 30.661 30.88

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ye / xe

CA

Results for Results for NNpp ≥≥0.10.1

1.0,1.0, 1.0

100

100fDp

fDeDfD,opt CN

CyC

e

eeD x

yy

25.00.1 If 52.04.5

0.251 If 6.1

1.0,

eDeD

eD

fD

yy

y

C

Where,Where,

and,and,

Results for Results for NNpp ≥≥0.1 (cont.)0.1 (cont.)

Np=0.1

Np=0.3

Np=0.6

Np=1

Np=3

Np=6

Np=10

Np=30

Np=60

Np=100

Ix=1

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.1 1 10 100 1000

CfD

JD

JJD,maxD,max = 1.9 at NNpp=100

yyee/x/xee=1 =1

yyee

xxee

22xxff


JJD,maxD,max = 5.81 at NNpp=100

yyee/x/xee=0.25 =0.25

yyee

xxee

22xxff

Np=0.1

Np=0.3Np=0.6

Np=1

Np=3

Np=6

Np=10

Np=30

Np=60

Np=100

Ix=1

0.10

1.00

10.00

0.1 1 10 100 1000CfD

JD


0.1

1

10

0.1 1 10 100Np

J D

,max

ye=xe

1.43ye=xe

2ye=xe

4ye=xe

5ye=xe

10ye=xe

Inverse behavior:Inverse behavior:

• JJD,maxD,max of a rectangle (ye<xe) surpasses that of a square (ye=xe) at a specific Proppant Number

•Linear behavior starts to dominate the flow regime

•Occurs at largerProppant Numbers due to the elongation of the drainage

F F -function at Opt. Values-function at Opt. Values

New function needed since past solutions are not valid after NNpp>0.1

Transition from pseudo-radial to linear

This function describes maximum dimensionless productivity index (JJD,maxD,max) as a function of optimum conductivity (CCfD,optfD,opt)

F F -function at Opt. Values (cont.)-function at Opt. Values (cont.)

1

2

3

4

5

6

0.1 1 10 100 1000 10000CfD

F

0.1 0.30.6 13 610 3060 100F,opt

FFoptopt - Line

yyee/x/xee=1 =1

yyee

xxee

22xxff

optpD FN

J

)ln(5.063.0

1max,


1

2

3

4

5

6

7

8

9

0.01 0.1 1 10 100 1000 10000CfD

F

0.1 0.30.6 13 610 3060 100F,opt

yyee/x/xee=0.1 =0.1

yyee

xxee

22xxff

FFoptopt - Line

optpD FN

J

)ln(5.063.0

1max,


1

2

3

4

5

6

0.1 1 10 100CfD,opt

F ,opt

xe=ye 1.43ye=xe

2ye=xe 4ye=xe5ye=xe 10ye=xe

ExampleExample

1 Fracture 4 Fractures2 Fractures

Reservoir permeability, kk = 10 md

100,000 lb of 20/40 ceramic areinjected per treatmentkkf f = 150,000 md

• Multiple fractures with same type of treatmentMultiple fractures with same type of treatment• Reservoir is split, and calculations done in one of the divisionsReservoir is split, and calculations done in one of the divisions• JJDD is then multiplied by number of fractures for cumulative value is then multiplied by number of fractures for cumulative value

Example (cont.)Example (cont.)

Volume

(ft 3 )Number of fractures

x e (ft) y e (ft) y e /x e N p

1.74E+08 1 1,867 1,867 1 0.0898.71E+07 2 1,867 933 0.5 0.1784.36E+07 4 1,867 467 0.25 0.356

Number of fractures

y e /x e C fD,opt I x x f (ft) w (in)

1 1 1.60 0.236 220.1 0.2822 0.5 1.64 0.233 217.6 0.2854 0.25 1.44 0.249 232.4 0.267

Fracture Dimensions Fracture Dimensions

Drainage area and Proppant NumberDrainage area and Proppant Number

Example (cont.)Example (cont.)

Number of fractures

y e /x e F opt

1 1 1.6422 0.5 1.7864 0.25 2.377

optpD FN

J

)ln(5.063.0

1max,

Number of fractures

y e /x ePer-Well

J D,max

Cumm. J D,max

1 1 0.46 0.462 0.5 0.50 0.994 0.25 0.44 1.77


Stress and Stress Distribution

Stresses In Formations

v

H

g dz 0

v v p

h v p p

1

abs

eff

abs

Crossover of Minimum Stress

80x1060 20x106 40x106 60x106

Stress, Pa

Dep

th f

rom

orig

inal

gro

und

surf

ace,

m

Original Vertical Stress

True Vertical Stress

Minim

um H

orizontal Stress

Critical Depth

-3000

-2500

-2000

-1500

-1000

-500

0

-2500

-2000

-1500

-1000

-500

0

Cur

rent

Dep

th ,

m

Ground Surface

Influence of Lithology on In-Situ Stress Distribution

Data from hydraulic fracturing

Stress Representation

zz

zy

z

y

x

yy

xx

zx

xz

yz

xy

yx

(b)

zz

z

rz

zr

rr

r

z

z

r

r

Fracture Initiation Pressure

For perfectly vertical well

pbd = 3H,min- H,max + To - p


Rock and Fracture Mechanics

Linear Elasticity And Rock Mechanics,

Stress and Strain Concept Linear Elasticity Material Properties,

Interrelation Uniaxial Compression Test

Plane Stress - Plane strain PKN-KGD-Radial

E =Fl

A l

D lv = - l D

D/2

D

A

F

l

l

Uniaxial Loading Test to Obtain Linear Elastic Parameters

Interrelations Of Various Elastic Constants Of An Isotropic Material

Ideal Crack Shapes

Pressurized Line Crack Plane strain Net Pressure - Superposition How to apply?

Width equations More complex models

Pressurized Line Crack

x

y

c

u(x)

p(x)

x

Tip

r

Line Crack

220'

4)( xcp

Exw n

For constant pressure inside the frac the solution is:

c

x

y

E' is the plane strain modulus (almost same as Young's)E' = E/(1-v2)

Plane Strain

x

y

All strains remain on this plane

Notions of Plane Strain

Stress and resulting strain remain on a plane which can be repeated infinite times

Vertical and horizontal plane options Vertical plane strain is for fractures

whose length is considerably larger than the height

Horizontal plane strain, repeated many times, is for fractures whose height is much larger than their length

Plane strain viewsVertical PlaneStrain Condition

Horizontal PlaneStrain Condition

w0(x=0)

Application: Basic 2D Models

0,wPKN ww

wKGDww

wellbore tip

hf

PKN

KGDhf

ww,0

ww

xf

qi

qi

Stress Intensity Factor

weighted pressure at tip

Pa · m1/2

psi - in.1/2

Weighting function: the nearer to tip, the more important the pressure value

stress distributionat tip

c

c

nI dxxc

xcxp

cK )(

2

1

xc

KI : proportionality const

xc

1

Fracture toughness, Fracture toughness, KIC

Tip Propagation Pressure

fIctip x

Kp48

xc

Fracture toughness, Fracture toughness, KIC

Application: Fracture Height Prediction

Height containment: why is it critical? Fracturing to water or gas Wasting proppant and fluid

Can it be controlled? Passive: safety limit on injection pressure Active: proppant (light and heavy)

Height and Width in Layered Formation

Pinch point

Contained?Breakthrough?Run-away?Up or Down?Width?Hydrostatic pressure?Height control?What can be measured?

Upper tip Far-field Stress

Lower tip

Questions:

Height Map

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

3000 3100 3200 3300 3400 3500 3600 3700 3800

300

-300

0

21 26

psi

MPa

200

100

-100

-200

Tip Location

[m]

Tip Location

[ft]

Treating Pressure

Rheology, Fluid Flow in Fractures, Proppant Transport

Stress - Shear Rate Material Properties Flow Geometries Foam

Plastic

Pseudoplastic

Newtonian

Dilatant

Sh

ear

Str

ess,

Shear Rate, .

Yield Pseudoplastic

Idealized Rheological Behavior of Fluids

Rheological Constitutive Equations

Apparent Viscosity

Sh

ear

stre

ss,

Shear rate,

a

.

Parallel Plates (Slot Flow)

w

L

h

Flow

Limiting Elliptic Cross Section

Flow

L

w0

h

Application: Pressure drop in the fracture

Material Balance

Leakoff Delineation

Geometry Evolution (History)

During Pumping

During Shut-in

Bulk Fluid Loss, Detailed Leakoff, Material Balance

Material Balance Leakoff as Material

Property Formal Material

Balance Power-Law

Assumption

Filtercake, Invaded Zone, Reservoir And Pressures For Fluid Leak-Off

Invaded Zone

Filtercake

p

pi

pface

pres

Open Fracture

Invaded zone

Filtercake

UninvadedReservoir

pfpf

pi

Open Fracture

Carter Leakoff Model (Bulk Fluid Loss Concept)

y = 0.0024 + 0.000069x

0 10 20 30 40 50 60

Square root time, t1/2 (s1/2)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Lost

vol

ume

per

unit

surf

ace,

VL/A

L (

m)

m/sin velocity""

t

Cv L

L

S+t2C=A

VpL

L

Lost

mmm

AL

s

mCL in

2CLSp

i

2i

A

Material balance variables

Formal Material Balance for One Wing

V = 2A C t + A SL L L L pCarter I Equation in lab:

Opening-Time Distribution Factor

V =V 2A C t A Si L e p 2

peL St2Cw

w

2

2A=AL :here

A

Less than 2

eitq

peLi St2Cw=

A

V2

is about 1.5

Nolte’s Power Law Assumption

/1D

DD

A

tA

A A AD e / t t tD e /

2/30

g

dAdt-t

C=Ve eA t

LLoffe 0

12

eLe

Loffe

tCA

V

2

peL St2Cgw

w

2)(0

Max 2

g0 Function

0.0

0.5

1.0

1.5

2.0

0 0.5 1 1.5

g0

4/3

/2

Nolte range

Apparent and "True" Leakoff: rp

qi

qL/2

2qi

Rf

hp

qL/2

rp Factor for Radial Fracture

xh

Rp

f

2

h p

R f

21arcsin2

xxxr p

F o r c i r c u l a r

f

pp h

hr :rrectangulaFor

Coupling Of Elasticity, Flow And Material Balance

Width PK KGD No-Leakoff

Derivation of the Original Perkins-Kern Width Equation

Assumptions Height is constant Elasticity: Vertical plane strain (but decoupled) Flow in limiting ellipsoid cross section Newtonian fluid Net pressure is zero at tip No leakoff

Perkins-Kern Width Equation

Elasticity: Rheology: '

20 E

phxw nf

fhw

q

L

p3

0

64

34

3'8

nf

n

ph

iE

dx

dp

4

344

,

'320

f

fwn h

ixEp

41

41

41

0, '57.3

'

512

E

ix

E

ixw ff

w

41

0,0 xxwxw fw 628.055

4

4

PKN Constant Injection - No Leakoff

41

4541

4541

3

'24.2

'625

512

E

hix

E

hixhxwit ffff

ff

54

51

4

351

3

'

512

625t

h

Eix

ff

5

15

125

1

20, '

2560t

hE

iw

fw

51

51

6

2441

2,

'80t

h

iEp

fwn

KGD

'

4

E

pxw nf

w fhw

q

L

p3

12

41

241

241

'22.3

'

336

f

f

f

fw hE

ix

hE

ixw

www 785.04

For 2xf<hf the horizontal plane strain assumption (KGD) is more appropriate

For 2xf>hf the vertical plane strain assumption (PK) is physically more acceptable

Comparison Of Width Equations

w

w

x

h

x

hGK

PK

f

f

f

f

21 625

32 512

20 95

21 4 1 4 1 4/ / /

.


Design Procedure

Pumping Time, Fluid Volume, Proppant Schedule: Design of Frac Treatments

Pumping time and fluid volume: Injected = contained in frac + lostlength reached, width created

Proppant schedule: End-of-pumping concentration is uniform, mass is the required

Given: Mass of proppant, target length, frac height, inj rate, rheology, elasticity modulus, leakoff coeff, max-possible-proppant-added-conc

1 Calculate the wellbore width at the end of pumping from the PKN (Power Law version)

2 Convert max wellbore width into average width

3 Assume a = 1. 5 and solve the material balance for injection time, (selecting sqrt time as the new unknown)

4 Calculate injected volume

5 Calculate fluid efficiency

22

11

22

122

2222

1

0, '

14.2198.315.9

n

fn

fn

inn

n

n

n

nw E

xhqK

n

n=w

0,628.0 we ww

022

)Sw(tκ C t

xh

qpeL

ff

i

eii tqV

i

eff

i

fee V

wxh

V

V=

Pumping Time, Fluid Volume

Adjustment for

Several ways…see page 111 in UFD One way, according to Nolte

= 1.33e + 1.57 (1 - e )

Nolte’s Power Law Proppant Schedule:

fpad1 V/Vi0

C/C e

1

slurry

y =

0 1

1

1ie VcM

1

11

0

dxx

1

1)1( padfArea

1

1Area

Nolte's proposition:select fpad=

ie VcM

1

1

1 Calculate the Nolte exponent of the proppant concentration curve

2 Calculate the pad volume and the time needed to

pump it

3 The required max proppant concentration, ce

should be (mass/slurry-volume)

4 The required proppant concentration

(mass/slurry-volume) curve

5 Convert it to “added proppant mass to volume of

clean fluid” (mass/clean-fluid-volume)

e

e

1

1

ipad VV

epad tt

pade

pade tt

ttcc

iee V

Mc

propp

added cc

c

1

Proppant schedule

Design Logic Specify available proppant, volume and kf

Know your k and h

Assume frac height and fraction of proppant reaching the pay layer

Determine proppant number

Determine optimum CfD

Determine optimum length and propped width

Given the target length, find pumping time and slurry efficiency

Create proppant schedule providing uniform distribution of proppant in the fracture at the moment of shut-in

If necessary, iterate on frac height

Introducing…

HF2DPKNHF2DPKN

Input Parameters Proppant mass for (two wings), lbm

This is the single most important decision variable of the design procedure

Sp gravity of proppant material (from 2.6 to 3.5) Porosity of proppant pack (e.g. 0.35) Proppant pack permeability, md

One of the most important design parameters. Retained permeability including fluid residue and closure stress effects, might be reduced by a factor as large as 10 in case of non-Darcy flow in the frac Realistic proppant pack permeability would be in the range from 10,000 to 100,000 md for in-situ flow conditions. Values provided by manufacturers such, as 500,000 md for a “high strength” proppant should be considered with caution.

Max prop diameter, Dpmax, inch From mesh size, for 20/40 mesh sand it is 0.035 in.

Input Parameters (cont.) Formation permeability, md Permeable (leakoff) thickness, ft Wellbore Radius, ft Well drainage radius, ft

Needed for optimum design. (Do not underestimate the importance of this parameter!)

Pre-treatment skin factor Can be set zero, it does not influence the design. It affects

only the "folds of increase" in productivity, because it is used as basis.

Fracture height, ft Usually greater than the permeable height. One of the

most critical design parameters. Might come from lithology information, or can be adjusted iteratively related to the frac length.

Plane strain modulus, E' (psi) Hard rock: about 106 psi, soft rock 105 psi or less.

Input Parameters (cont.)

Slurry injection rate (two wings, liq+ prop), bpm Rheology, K' (lbf - secn'/ft2) Rheology, n' Leakoff coefficient in permeable layer, ft/min0.5

The leakoff coefficient outside the permeable layer is considered zero. If the frac height to permeable layer ratio is high, the apparent leakoff coefficient calculated from this input will be much lower than the input for this parameter. If the leakoff is significant outside the net pay, you may want to adjust this parameter when you adjust fracture height.

Spurt loss coefficient, Sp, gal/ft2

The spurt loss in the permeable layer. Outside the permeable layer the spurt loss is considered zero. See the remark above.

Input Parameters (cont.)

Max possible added proppant concentration, lbm/gallon fluid (ppga) The most important equipment constraint. Some current mixers

can provide more than 15 lbm/gal neat fluid. Often it is not necessary to go up to the maximum technically possible concentration.

Multiply optimum length by factor This design parameter can be used for sub-optimal design. Play!

Multiply pad by factor Play (if necessary)!

(More input for TSO, Continuum Damage Mechanics)

Computer Exercise: Medium Perm Design Example

Computer Exercise: Tight Gas Design Example

Computer Exercise: High- Perm (Frac&Pack) Example

3D (Finite Element Modeling)

x

ywellbore element

tip element

Data Need for Both P3D and 3D:

Layer data Permeability, porosity, pressure Young’s modulus, Poisson ratio, Fracture

toughness Minimum stress

Fluid data Proppant data Leakoff calculated from fluid and layer data

The Value of Information The available data are never enough

(“data hunger”) Input accuracy is always in question The models may behave “strange” Sensitivity the value of

information What is the uncertainty? How much difference does it make at the

bottomline? (“We do not do fracs for Poisson ratio”)

What is the cost to improve accuracy of the data?


High-Permeability Fracturing

Early “frac packs” viewed primarily as an extension to gravel packing Sand exclusion Sand deconsolidation control

HPF has replaced gravel packs in many petroleum producing areas New PI (bpd/psi) allocated to larger rate or lower

drawdown, or any combination

Transition towards hydraulic fracturing 40/60 gravel --> 20/40 or larger proppant HEC fluid --> Crosslinked fracturing fluids

Advent Of High Permeability Fracturing (HPF)

HPF In View Of Gravel Packing

Progressive deterioration of gravel-pack permeability (increased skin)

Leads to decline in well production Counteracting decline with increased

pressure drawdown Results in accelerated pore-level

deconsolidation and additional sand production

The Gravel Pack Scenario

Assume k=50 md, h=100 ft, B=1.1, =0.75 cp and ln re /rw=8.5

Calculate PI and q for 1000 psi drawdown Ideal (undamaged) 5 bpd/psi or 5,000 bpd Some damage (s=10) 2.3 bpd/psi or 2,300 bpd Gravel pack (s=30) 1.1 bpd/psi or 1,100 bpd

s

rr

B

kh

pp

qJ

w

ewfe 472.0ln2.141

From CfD vs. sf graph, sf = -3 Fracture conductivity, CfD = 1 Fracture length, xf = 50 ft

Calculate PI and q for 1000 psi drawdown Ideal (undamaged) 5 bpd/psi or 5,000 bpd Some damage (s=10) 2.3 bpd/psi or 2,300 bpd Gravel pack (s=30) 1.1 bpd/psi or 1,100

bpd HPF (s=-3) 7.7 bpd/psi or 7,000 bpd HPF (s=-1) 5.6 bpd/psi or 5,600 bpd

vs. The HPF Scenario

HPF In View Of Competing Technologies

Production from high-rate water packs reported to deteriorate with time.

Production may progressively improve during the first several months following a HPF job.

Skin Values Reported by Tiner et al. (1996)

Gravel Pack High-Rate Water Pack HPF

+5 to +10 excellent +2 to +5 reported 0 to +2 normally

+40 and higher reported 0 to -3 in some reports

Key Issues In HPF

Tip screenout concept Net pressure and fluid leakoff

Soft formations, low elastic modulus values Fluid volumes relatively small, potential for

high leakoff rates

Fundamentals of leakoff in HPF Carter leakoff (modified) Mayerhofer (filtercake based) Fan and Economides (series resistance)

Tip-Screenout

Fracture Inflation

Packed Fracture

Width Inflation With the Tip-Screenout Technique

Comparison of Conventional and HPF Design Concepts

- End of Job for Conventional Design -

BHP

Tip-Screenout

Injection Rate

Time

Injected SlurryConcentration

Fracture Creation(Conventional)

TSO

Fracture Inflationand Packing

Fracturing Fluid and Proppant Concentrations in Fracture:

Pad Injection

Slurry Injection

At TSO

After FIP

CÑ + FRACTURA

B-5

-X.5

2

Fracturing a High-Permeability Well in Venezuela

Fracturing Pressure Record and Match

GEOMETRIA DE LA FRACTURA REALIZADA


Fracturing Fluids and Proppants

Fracturing Fluids

Oil-basedWater-based Mixtures of oil and water called emulsions Water-based containing nitrogen and/or carbon dioxide gasOil-based containing nitrogen and/or carbon dioxide gas

Exclusively oil-based in the 1950’sMore than 90% water-based in the 1990’s

Nitrogen and carbon dioxide systems in water-based fluids are used in about 50% of treatments

CMHPG Guar HPG

40 #/Mgal Hydration Curves - Recent Samples

0

5

10

15

20

25

30

35

40

45

0.1 1 10 100 1000 10000

Time, t (min)

Vis

cosi

ty a

t 51

1 1/

sec,

(cP

)

Guar- New

CMHPG

Guar - Old

HPG

Crosslinked Fracturing Fluids

Crosslinker Gelling Agent pH range ApplicationTemp. Deg. F

B, non-delayed guar, HPG 8-12 70-300B, delayed guar, HPG 8-12 70-300Zr, delayed guar 7-10 150-300Zr, delayed guar 5-8 70-250Zr, delayed CMHPG, HPG 9-11 200-400Zr-a, delayed CMHPG 3-6 70-275Ti, non-delayed guar, HPG,

CMHPG7-9 100-325

Ti, delayed G, HPG, CMHPG 7-9 100-325

LIQUID DELAYED BORATE

LIQUID FAST BORATE

SOLID FAST BORATE

40# gel not crosslinkedWith 4#per gal sand

40# crosslinked gelWith 4#per gal sand

KEROSENE DIESEL BLACK OIL

Phosphate Ester

Phosphonate Ester

Phosphinic Acid

Iron Activator

Aluminum activator

Additives

Breakers Causas de daño:

Flido, overdisplac., start pdn

Time

Viscosity

Minimum Proppant Transport Threshold Total Pump

Time

Proppant Transport Drives Breaker Packages and Schedules

Added Breakers and Imperfect Delay

Mechanisms Necessitate Extra Fluid Viscosity

Fluid Testing

Compatibility RheologyFluid LossProppant carrying capacityResidue in the proppant packFilter-cake residueBreaking

Plot Viscos vs T

Proppant Selection

Strength Size Sphericity Quality

Brady 12/20

Ottawa 20/40

Oglebay 30/50

Ceramic 3 20/40

Ceramic 2 20/40

Ceramic 1 20/40

16/20

20/40

Resin –Coated Proppants

16/20

Types of Proppant

d

Stress on Proppant and Fatigue


Injection Test Interpretation

Step rate test

Time

Bot

tom

hole

pre

ssur

e

Inje

ctio

n ra

te

Step rate test

Injection rate

Bot

tom

hole

pre

ssur

e

Propagation pressure

Two straight lines

Fall-off (minifrac)

1st

inje

ctio

n cy

cle

2nD

inje

ctio

n cy

cle

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

Pressure Fall-off Analysis (Nolte)

eLeDpeitt tC2AtgS2AV=Ve

,

eD ttt /

eLDpi

tt tCtgSA

Vw

e2 ,2-

e

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

A

D

DD

D dAdtAt

tgD

D

1

0

1

/1/1

1,

21

1;1;,2/1124,

1

DDDD

tFtttg

g-function

Pressure Fall-off

,2-2-/ DeLfpfeifCw tgtCSSSAVSpp

p b m g tw N N D ,

eLeDpeitt tC2AtgS2AV=Ve

,

eD ttt /

,22- e

DeLpi

tt tgtCSA

Vw

e

wSp fnet Fracture stiffness

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 2E

hf

'

E

xf

'

3

16

ERf

'

wSp fnet Pa/m

Shlyapobersky Assumption

No spurt-loss ,2-2- DeLfpf

e

ifCw tgtCSSS

A

VSpp

Ae from intercept

g

pw

bN mN

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

pbhVE

x

2

2 CNf

if

pbhVE

x

38

3

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

hxwi

ffee V

hxw

i

fe

e V

Rw2

2

Vi: injected into one wing

Example

In a minifrac test 39.75 m3 (10,500 gal) fluid was injected

into one fracture wing during 20 minutes. Estimate the

leakoff coefficient, if E’ = 16.9 GPa, the closure pressure

is pC = 22.1 MPa (3200 psi), the permeable height is

9.75 m (32 ft)

Use the Radial model for analysis.

1 – plot 2 – get slope and intercept

,8/9ΔtgMPa 1.4 -MPa 32.54p D

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

3

83

CR

t EmLAPP

f

eN

8

3 '

w g C tL LAPP e ( , )08

92

wV

Rwe

i

fL 2 2 /

w

w we

e L

Analysis of Injection Test Example

Created Fracture Radius,Apparent Leakoff Coefficient

ft 94.7m 28.91021.210254.38

75.391069.13

8

'33

77

10

3

CN

if pb

VER

ft/min 0.0015 m/s1085.5

1069.112003

)104.1(8.288)(

'3

8

0.50.55

10

6

,

N

e

fAPPL m

Et

RC

Since only hp = 9.75 m is permeable ,

the ratio of permeable to total surface

rp is less than 1

From “Apparent" to “Real"

214.0)arcsin()1(2

1687.02

5.02

xxxr

R

hx

p

f

p

ft/min 0.0070 m/s 107.2

ft/min 0.214

0.0015 m/s

0.214

1085.5

0.50.54

0.50.55

L

L

C

C

Computer Exercise Minifrac Analysis

Redesign

Run the design with new leakoff

coefficient

(That is why we do minifrac analysis)

Treatment Execution

Pump schedule Proppant schedule Treatment flowback and forced

closure


Fracture Propagation

Fracture Propagation

Elasticity

Friction

Material balance

Propagation criterion

Elementary Material Balance

Ac(x)

w(x)

h(x)

x+x

x

q(x)

q(x+ x)

w0

A w hc f4 0

Differential Models: Nordgren

E w

x

h C

t -+ h

w

tf L

f

'

128

8204

20

+Wellbore Boundary +Tip Boundary

q = -w h

64

p

xf n

03

Pressure Loss in Limiting Ellipsoid Flow

p

x

E

h

w

xn

f

'

20

Linear Elasticityvertical plane strain

q

x+

2h C

t - x+

h w

t= 0

f L f

0

4

Material Balance

Dimensionless Variables Of The Nordgren Model

x c x

t c t

w c w

p c w

D

D

D

n D

1

2

0 3 0

4 0

ci

C E hc

i

C h E

ci

C E hc

E i

C h

1/ 3

L f4

2/ 3

L5

f

1/ 3

L2

f

1/ 3

L2

f4

1

5

8 22

2

3

2

4

2 2

128 16

32 4

' '

'

'

Other Propagation Criteria

Fracture toughness

Dilatancy

Statistical fracture mechanics

Continuum damage mechanics

CDM

dD

dt= C n

n 1- D

dD

dt= C

1- D

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

CDM Propagation Criterion

u =Cl x

l + xwf

H,

2

f

f

x=x2

f

2 1 2

min

/

Cl 2Combined Kachanov parameter:

xfD

10-4

10-3

10-2

10-1

100

101

102

103

10-3 10-1 101 103 105 107

tD

C lD D

2

0.01

1

0.1

0.001

0.0001

Fracture Propagation With CDM

10-1

100

101

102

10-3 10-1 101 103 105 107

tD

wD

, p D

0.0001

0.001

0.1

1

C lD D

2

0.01

C lD D

2


10-3 10-1 101 103 105 107

10-2

10-1

100

10-2

tD

C lD D

2

0.0001

0.001

0.010.1

1


Real-Time 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

Nolte-Smith Plot

Log net pressure

Log injection time

Normal frac propagation

Tip screenout

Wellbore screenout

Unconfined

height growth

Evaluating the effectiveness of the treatment

Estimating the subsequent production behavior of the well, and

Checking the accuracy of fracture design and fracture height models used to predict fracture geometry

Fracture Height Measurements

Radius of penetra

tion

Available Techniques

Measured Directly Formation Micro Scanner

Borehole Televiewer

Based on Inference Temperature Logging

Isotopes (fluid, proppant)

Seismic Methods, Noise Logging

Tiltmeter techniques

Spinner survey

ScSb Ir

Tracerlog

Tiltmeter Resultsafter Economides at al. “Petroleum Well Construction”

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 P3D Simulation

P3D Simulation

0 50 100 150 200 250

Fracture Half-Length - ft

0

0.05

0.10

0.15

0.20

0.25

Pro

pp

ed

Wid

th -

in

0

1000

2000

3000

4000

5000

Co

nd

uctivity (K

fw) - m

d.ft

Propped Width (ACL)

Conductivity - Kfw

FracCADE

*Mark of Schlumberger

Flow Capacity Profiles

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

3D (Finite Element)

x

ywellbore element

tip element


Execution of High-Permeability Fractures

Generalized Job Sequence For HPF

Perforate Run the gravel-pack screen assembly Spot/soak acid to clean up perforations Perform and interpret pre-treatment

diagnostic tests Design TSO pumping schedule based

on design variables from diagnostic tests(cont.)

Perforations For HPF

12 shots per foot with “big hole” charges Limited number of 0o or 180o phased

perforations in heart of pay interval Clean formation breakdown Near-well tortuosity Prevent unpacked perforations

Arguments for and against overbalanced and underbalanced perforating

Screenless And Rigless HPF Completions

Reduces $$ and simplifies treatments Paves the way for multiple-zone HPF

completions and thru-tubing recompletions Resin-coated tails to control proppant

flowback; success reported (Kirby et al., 1996)

Rigless coiled tubing completions

Treatment Flowback and “Forced Closure”

Flow fracture fluids back out of well immediately after end of pumping at 10 gpm to 2-3 bpm (requires flowback manifold)

Think of as “reverse gravel packing” rather than causing rapid fracture closure

Supercharged fluids assist fracture/well cleanup

Reduces proppant settling Reduces proppant flowback, a

counter-intuitive result


Fracturing Equipment andField Practices

Fracturing Equipment

Hydration unit Blender Chemical additives system Proppant transport Frac pumps Hi/Lo Pressure manifold Monitoring and control van QA/QC van

Hydration Unit

Blender

100 bpm-35,000 lbpm sand2 dry/3 liquid chemical feeders

Chemical Additives System

Proppant Transport

Frac Pump

2400 bhp frac pump

Hi/LO Pressure Manifold

Monitoring And Control Van

Batch Mixed

control vanQA/QCvanproppant

transports

frac

pum

ps

frac

tank

s

wellbl

ende

r

treating line

pop-off valve

valve

pressure relief line

plug valve

check valve

pressure transducers

conveyor belt

Real Time Mixing With Pit Suction Manifold

control van

frac

pum

ps

well

treating line

pop-off valve

valve


plug valve

check valve


proppanttransports

pit s

ucti

onm

anif

old bl

ende

r

conveyor belt

QA/QCvan

hydr

atio

n un

it

Real Time Mixing

proppanttransports

frac

tank

s

blen

der

conveyor belt

control van

frac

pum

ps

well

trea

ting

line pop-off valve

valve


plug valvescheck valve


QA/QCvan

hydr

atio

n un

it

HI/LO pressuremanifold

Quality Control Philosophy

Start of quality control (QC) was motivated 20 years ago by poor service quality

Producing companies began to exercise various forms of “quality control”

Today QA/QC represents a broad swath of self-policing quality control schemes Checklist, filled out in the field Incentive-ized marketing strategy Latest avante garde business psychology

Quality Control

Fracture treatment should, and can, be carried out as it was designed Pre-treatment planning Well maintained and functioning equipment Trained, conscientious and well-informed

personnel Intense tracking of each fracturing material

and critical treatment parameters Post-treatment evaluation

Quality Control For HPF

Many early treatments failed because of equipment problems and lack of QC on fluids and proppants

Adoption of intense quality control measures common to MHF was slow for HPF

Slowed introduction of HPF Now common for producing company to

supply consultant or in-house specialist to oversee quality control

Standard Fracturing QA Procedures

Pre-job Testing Prior to pumping, each frac tank is strapped and

tested for specific gravity, pH and temperature. A sample is taken from each tank and tested with gelling agent for viscosity and crosslink time. A composite fluid sample is tested with chemicals from location.

Proppant Validation Proppant sieve analysis is provided on location. If

proppant does not meet acceptable standards, each compartment is tested individually.


Pre-job Inventory Prior to the start of the job, the Stimulation

Treatment Check List is filled out with beginning volumes of all chemicals and frac fluid on location. Proppant storage is visually inspected and compared to weight tickets.

Job Testing and Recording Fluids and chemicals are physically strapped every

5,000 gallons or as often as possible. Samples of the pad and 2-3 slurry stages are taken along with corresponding proppant samples.


Real-Time QA In addition to normal treatment displays of rate,

pressure, net pressure and sand concentration, the following parameters will be displayed and recorded: pH, fluid temperature, viscosity and all additive rates.

Post-job Reports In addition to the standard treatment outputs, the

treatment report includes the following: Proppant Sieve Analysis and QC Form, Water Quality Control Form, Frac Fluid Blending and QC Form, and Stimulation Real Time Report.


Evaluation Techniques

Fracture Treatment Evaluation

Real-time analysis Fracture height and orientation Well testing Evaluation of HPF treatments--

a unified approach Production results Evaluation of real-time HPF treatment data Post-treatment PTA in HPF

Decision-Making On Site

Big 3 fracturing variables: ct, po, h Prepare crossplots before going to field:

Read Vs directly; %Pad = (1-F.E.) / (1+F.E.) Sensitivity runs on q, E, fluid properties

Vs

po or CDM

F.E.

po or CDM

c t

c t

Start Job Prepad Pad Flush1 2 3 4Sand-laden 20/40

Lo

g

p

Type IV

Type III

Type II

Type I

Log t

Real time pressure response types, indicating increasing risk of screenout

(Nolte-Smith Plot)

Fracture Geometry and Height Growth

A

H,min

1

2 3 4H,max

v

Shale

Shale

0.90.80.70.60.50.40.30.20.1

pnet /

hf /h

C

31 2

hhf

B

Pn

et

Fracture Height And Fracture Orientation

Temperature log R/A tracer survey Seismic imaging, active and passive Tiltmeter arrays, surface and downhole Borehole elongation caliper Oriented core (anelastic strain

relaxation) Empirical observations

Well Testing

Pre-fracture well tests are not possible in low permeability formations

Post-fracture well test intended to obtain permeability and fracture extent, simultaneously

Different combinations of the unknown parameters can give a good fit

In HPF, the permeability is usually known and the primary goal is to evaluate the created fracture

Know What The Analysis Plot Should Look Like

fracture linear bilinear

pseudo-radial

boundary dominated

formation linear

DimensionlessFracture Conductivity CfD

kt

ctxf

2khTsc [m(p)]

qTpsc

2khp

qBµ

Region of Bilinear Flow

Region of Linear Flow

Dimensionless Time, tDxf

Dim

ensi

on

less

Pre

ssu

re,

pD

10-2

10-1

1

10

10-5 10-4 10-3 10-2 10-1 1

0.1

0.5

1

510

50100500

pD = Oil

pD = Gas

tDxf =CfD =kfw

kxf2

Dimensionless Pressure and Pressure Log-Derivative for a Fractured Vertical Well

Well Testing: The Quest for Flow Regimes

Bilinear Flow Analysis Equations

5.0211.44

kcmh

Bqwk

tBf

000708.0

ppqB

khs if

wff ppqB

khs 0

00708.0

Buildup

Drawdown

m=63.8 psi/hr1/4

2600

2650

2700

2750

2800

0 0.5 1 1.5 2

teqB1/4, hrs1/4

pw

s, p

si

Bilinear Flow Analysis

Limitations of Bilinear Flow Analysis

Applicable only to finite-conductivity fractures Bilinear flow may be hidden by wellbore

storage Requires independent estimate of k To estimate xf there is a need for pseudoradial

flow regime

Linear Flow Analysis Equations

000708.0

ppqB

khs if

wff ppqB

khs 0

00708.0

Buildup

Drawdown

21064.4

tLf ckhm

Bqx

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12 14 16 18

taLeq1/2, hrs1/2

pa

ws,

psi

Linear Flow Analysis

Limitations of Linear Flow Analysis

Applicable only to wells with high-conductivity fractures

Wellbore storage may hide linear flow period Long transition period between end of linear flow

(tLfD < 0.016) and beginning of pseudoradial flow (tLfD > 3)

Requires independent estimate of k To estimate wkf there is need for pseudoradial flow

regime

Evaluation Of HPF Treatments--A Unified Approach

Evaluation of real-time HPF treatment data Step-wise approach for evaluation of bottomhole

treating pressures outlined by Valkó et al. (1996): Leakoff coefficient from minifrac using minimum assumptions

(e.g. radial geometry and Nolte-Shlyapobersky method) Almost automatic procedure to estimate created fracture

dimensions (“slopes analysis”) Convert results to equivalent fracture extent and conductivity Conduct for large number of treatments from various

operators to build data bank

Slopes Analysis

HPF treatments often exhibit numerous increasing pressure intervals which are interrupted by anomalous pressure decreases

Slopes analysis provides a simple tool for examining such behavior

Design parameters Minimum user input beyond real treatment data Relatively independent of fracture propagation model Not be a history matching procedure Screening tool based on well-defined (reconstructible)

algorithm

R

2i

qL /2qL /2

qL /2

qL /2

i

iA = (/2)R2

HPF Radial Fracture Geometry

Slopes Analysis Assumptions

Created fracture is vertical with a radial geometry

Fluid leakoff can be described by the Carter leakoff model plus Nolte power-law type area growth

Fracture packing radius may vary with time, being allowed to increase or decrease

Hydraulic fracture radius (which defines leakoff area) cannot decrease, and is the maximum of the packing radius that has occurred up to a given time

(cont.)

Slopes Analysis Assumptions (cont.)

During regular width-inflation periods, the pressure slope is defined by linear elastic rock behavior and fluid material balance with friction effects being negligible

Injected proppant is distributed evenly along the actual packing area during each incremental period of arrested extension/width growth

Slopes Analysis: Restricted Growth Theory

LqiAdt

dw

1

LqiRR

E

dt

dp

2

2

16

3

2

2RA

w

R

Epn 16

3

and

Slopes Analysis: Restricted Growth Theory (cont.)

,12

0

,

DtD

DLtL t

tg

tACq

.911=

9/8,

0

DtD

D

td

tg

91.11

2,t

ACq LtL

Clock Time, hh:mm:ss

3700B

ott

om

ho

le P

ress

ure

, p

si

19:00:00 19:20:00 19:40:003300

3500

Bottomhole Pressure From HPF Treatment

3700

Clock Time, hh:mm:ss

Fil

tere

d B

HP

, p

si

19:00:00 19:20:00 19:40:003300

3500

Bottomhole Pressures Corresponding to Width Inflation Intervals

Determining Packing Radius For A Width Inflation Period

Combining the newly developed basic equations:

Or:

91.11

22

2

16

3 2

2 tC

Ri

RR

Em L

0375.025.223

m

iE

tm

CERR L

Estimated Packing Radius With Interpolation

50

40

30

20

10

0

t, min

R,

ft

Packing Radius

0 10 20 30 40 50

Hydraulic Radius

Determining The Final Areal Proppant Concentration

For every time interval, t, determine the mass of proppant entering the fracture.

Assume this mass to be uniformly distributed inside the packing radius corresponding to the given time step.

Obtain the mass of proppant in a “ring” between radius R1 and R2 by summing up (accumulating) the mass of proppant placed during the whole treatment.

Repeat Step 3 for all rings to obtain the areal proppant concentration as a function of radial location R.

14

12

10

8

6

4

2

0

R, ft

c p, l

b/f

t2

0 10 20 30 40 50

Final Areal Proppant Concentration as a Function of Distance From the Perforations

Design Improvement in a Field Program Sizing Pad volume for “generic” design More aggressive or defensive proppant schedule Proppant change (resin coated, high strength) Fluid system modification (crosslinked, foam)

Proppant carrying capacity Leakoff

Perforation strategy changes Forced closure Fiber reinforcement

Field Analysis of Fractured Wells

Case Study of 1000 wells analyzed in Western Siberia

Evaluation of field-derived productivity indexes with the ones designed

Improvement in design

JD; JDtarget and the JDAttainable vs.

reservoir permeability, all wells

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.01 0.1 1 10 100 1000

Reservoir permeability, md

JD

JD

JDtarget

JDAttainable

2003 and 2004 fracture designs vs. the presumed reservoir permeability

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.1 1 10 100

Presumed reservoir permeability, md

JD

2004 Design

2003 Design

PI vs. presumed permeability

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

Presumed permeability, md

PI,

cu

b.m

/d/a

tm.

2004

2003

Comparison of JDDesign vs. JD from Nprop field-derived JD wells fractured in 2003

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

1 10 100


JD

2003 JD Design

2003 JD Nprop kpr

2003 JD kpr

Comparison of JDDesign vs. JD from Nprop field-derived JD wells fractured in 2004

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

1 10 100


JD

2004 JD Design

2004 JD Nprop kpr

2004 JD kpr

Comparison of JD based on Nprop from

pressure matched frac geometry 2003

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

JD Design

JD

Ix

kp

r

Comparison of JD based on Nprop from pressure matched frac geometry 2004

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

JD Design

JD

Ix

kp

r

JD based on Nprop from pressure

matched geometry for 2003

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.1 1 10 100 1000

CfD

JD

Np=100

Np=60

Np=30

Np=10

Np=6

Np=3

Np=1

Np=0.6

Np=0.3

Np=0.1

Ix=1

Np 0.08-0.2

Np 0.2-0.45

Np 0.45-0.8

JD based on Nprop from pressure matched geometry for 2004

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.1 1 10 100 1000

CfD

JD

Np=100

Np=60

Np=30

Np=10

Np=6

Np=3

Np=1

Np=0.6

Np=0.3

Np=0.1

Ix=1

Np 0.08-0.2

Np 0.2-0.45

Np 0.45-0.8

Np 0.8-2.0

Np2.0-4.5


Deviations from IdealityAdvanced Concepts

Fracturing High-Rate Gas Wells

Non-Darcy flow reduces fracture flow capacity substantially

However, fracturing is a major way to reduce non-Darcy effects in an unfractured wells and provide well stimulation

(Ref. Economides et al. World Oil, Oct., 2002)

Reduction of Fracture Conductivity

Re

,, 1 N

kk nf

ef

vk

N nf ,Re

Effective Fracture Permeability

Reynolds Number

anfk

bx

)()101(

,

8 a and b are constantsof the proppant

Example of Fracture Design for Gas Well

Proppant mass for (two wings), lbm 150,000

Sp grav of proppant material 2.65

Porosity of the proppant pack 0.3

Formation permeability, md 0.5

Permeable (leakoff) thickness, ft 150

Well Radius, ft 0.30

Well drainage radius, ft 800

Pre-treatment skin factor 10.0

Fracture height (gross) , ft 400.0

Nominal (Darcy) proppant pack permeability, md 200,000

Additional Information Needed for Non-Darcy Calculations

Gas Specific Gravity (air=1) 0.71

p avg (psia) 4000

pwf (psia) 1500

(cp) 0.015

T (R) 580

Z 0.91

Coefficients for the Cooke correlation ( 20/40 mesh sand)

a 1.54

b 110,470

Design Procedure in UFD

Assume a Reynolds number Calculate the effective proppant permeability Calculate the Proppant Number. Obtain the

maximum possible productivity index JD,max and the optimum dimensionless fracture conductivity, CfD,opt . Determine fracture dimensions.

From the productivity index and drawdown determine the actual production rate, which in turn is used to obtain the Reynolds number.

Design Iteration 1

Proppant Number, Nprop 1.288

Dimensionless PI, JD, opt 1.06

Optimal dimensionless fracture cond, CfD,opt

3.0

Optimal half length, xf,opt, ft 464

Optimal propped width, wopt, inch 0.042

Post treatment pseudo skin factor, sf -6.20

Assume NRe = 0, thus kf,e = 200,000 md

Design Iteration 1

Bg = 0.0283 (ZT / pfrac) = 0.0283 (0.91) (580) / 1500 = 0.00997 res ft3/SCF

= 0.076 g/Bg lbm/ft3 = 1.22 g/Bg kg/m3 = 86.9 kg/m3

v = (0.00997)(96,960)(1000)/(24)(3600)(400)(0.042/12)(2) = 4 ft/sec = 1.22 m/s

MSCF/d 96,960 (1.06)R) 580cp)(0.91)( 1424(0.015

)psi) (1500psi) ft)[(4000 md)(150 (0.5

1424

)( 2222

Dwfave J

ZT

ppkhq

Design Iteration 1

a

fk

b

)(108 75,800 1/m

NRe = (75,800) (1.97 X 10-10) (1.22)(86.9) / (0.015 X10-3) = 106

Design Iteration 2

Assume NRe = 9, thus kf,e = 20,000 mdProppant Number, Nprop 0.1288



1.6



q = 45,740 MSCF/d, v = 0.25 m/s, NRe = 22

Design Iteration 3

Assume NRe = 15, thus kf,e = 12,500 mdProppant Number, Nprop 0.0756



1.6



q = 41,000 MSCF/d, v = 0.174 m/s, NRe = 15

Design Pumped

Efficiency, , % 44.9

Pumping time, te, min 47.7

Pad pumping time, tpad, min 18.1

Max added proppant concentration, lb per gal clean fluid

10.0

Design Pumped

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Pumping time, min

Liqu

id in

ject

ion

rate

, bpm

012345678910

ca, l

bm p

rop

adde

d to

ga

llon

liqui

d

Constants a and b in Cooke’s correlation

Prop Size a b 8 to 12 1.24 17,423 10 to 20 1.34 27,539 20 to 40 1.54 110,470 40 to 60 1.60 69,405

Applying The Firoozabadi And Katz Correlation for Non-Darcy Flow

k

k c vk

app

1

1 0 2

.

c q

h

c

hq c qa a g

2 2 0

k

k c qwk

app

f

f

1

1 00 2.

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

Misalignment

Proppant Slugs

Well Orientation

S - shaped

Fracture Orientation: Perforation Strategy (After Dees, SPE 30342)

max max

From overbalanced perforation

From underbalanced perforation

Fracture Face Skin Effect

Damaged Zone

xf

ws

kf

ks

Effect of Fracture Face Skin

fs

s

ssf xhk

wqB

kkp

4

11 1

ffsff s

hk

qBp

21

1

2 sf

sff k

k

x

ws

ff

sD

D

sJ

J

0

11

Dimensionless Productivity Index Including Fracture Face Skin Effect

Fracture Choke Skin

xf

Damaged Zone

kf kck

xs

xf xs

kck

Damaged Zone

ws w kf

Effect of Choke Skin

Production Impairment in Gas-Condensate Reservoirs (SPE 64749)

rgMrgIrg kffkk )1(

bc

aN

f/1)(1

1

here a and b are parameters which are 1.6E-3 and 0.324, respectively, and Nc, is the capillary number which is defined by

Weighted average of immiscible and miscible relative permeability curves:

pk

Nc


Acid Fracturing

Acid Fracturing

Acid is injected at a rate high enough to generate the pressure required to fracture the formation.

Differential etching occurs as the acid chemically reacts with the formation face.

Areas where the rock has been removed and kept open are highly conductive to hydrocarbon flow after the fracture closes.

In general: no proppant

(Fracture Acidizing)

As a general guideline, it is used on formations with >80% hydrochloric acid solubility. (??)

Low permeability carbonates (< 20 md) are the best candidates for these treatments because of the differential permeabilities between the "fracture conductivity" and the matrix of the rock.

Fluid loss to the matrix and natural fractures can be better controlled in lower permeability formations.

The Closed Fracture Acidizing (CFA)

Existing fractures in the formation. The fractures can be natural, previously created fractures, or fractures hydraulically induced just prior to the CFA treatment.

Pumping acid at low rates below fracturing pressure into a fractured well. The acid preferentially flows into areas of higher conductivity (fractures) at low rates for extended contact times, resulting in enhanced flow capacity.

Performance Prediction

Fracture conductivity, created dynamic width, created dissolved width

Width from stochiometry and material balance

Etched pattern Stress and strength (Nierode

and Kruk) limit: 5000 psi

Newtonian Flow of Fluid (Slot Flow) Darcy’s Law

2

12

w

u

L

p avg

Darcyu

kL

p

12

3wkw

Equivalent Permeability of Empty Fracture

Equivalent Conductivity of Empty Fracture

12

2wk

Acid Fracturing

“Ideal” width

Ideal permeability (in consistent units)

Realistic kfw from Nierode and Kruk (rock embedment stress)

area Fracture

dissolvedrock of Volumew i

12

wk

2

id

Nierode and Kruk

Input ideal width wi (in.) rock embedment stress Srock (psi) closure stress (psi)

Output kfw in md-ft

psi 20,000 S if 10)ln28.08.3(

psi 20,000 S if 10)ln3.19.13(

1047.1

rock3

2

rock3

2

47.271

12

rock

rock

i

Cf

SC

SC

wC

eCwk

Controlling Fluid Loss

Pumping a high viscosity preflush ahead of the acid solution, or controlling the densities of the preflush, acid, and overflush fluids used in the treatment.

One technique uses nonacid phases containing fluid-loss control additives pumped at intervals during the treatment to re-establish fluid loss control.

Another technique uses a high viscosity preflush ahead of the acid solution.

ACIDS

Hydrochloric (HCl) Acetic (CH3COOH) Formic (HCOOH) Hydrofluoric (HF)

Fracturing Horizontal Wells

Longitudinal Similar to vertical well but with multiple

stages potential increases Transverse

Multiple transverse treatments

Basis of Design

The PI of a fractured vertical well is used to evaluate the attractiveness of the multiple transverse fracture

Unified Fracture Design is adapted with shape factors to account for elongated drainage shapes

Traditional perforating methods if applied will lead to failure. New methods using abrasive jets are preferred

Necessary isolation methods can impact execution time and cost

Design Procedure for Vertical Well, Vertical Fracture

Determine the amount of proppant reaching the target layer

Determine the proppant number and the optimum fracture conductivity

Determine appropriate fracture dimensions

Calculate injection time and proppant schedule to deliver the optimum fracture dimensions.

Np for Elongated Drainage

Square Drainage

Const4

22

e

fffDx kx

wxkCI

r

pf

pe

pff

e

fffDxprop kV

Vk

hkx

whxk

kx

wxkCIN

24422

2

Elongated Drainage

hyxV eeres

e

efDx

ef

ef

ee

ff

res

pfp y

xCI

xx

xx

hykx

whxk

kV

VkN 2

42

88.30A

ppe

CNN

Fluid Flow For Transversely Fractured Horizontal Well

rw

2xf

w

rw

2xf

Fluid flow from reservoir into fracture Fluid flow from fracture into wellbore

PI of Transversely Fractured Horizontal Well

]2

)2

[ln(

wf

c r

h

wk

khs

cDV

DTH

sJ

J

)

1(

1

Multiple Transverse Fractures Intersecting a Horizontal Well

min max

W

rw

min max

W

rw

min max

W

rw

Vertical vs Horizontal Performance Comparison

Proppant Mass, lbs

x e (ft) y e (ft) N p C fD x f (ft) J D

100,000 1640 1640 0.0696 1.60 171 0.43

200,000 1640 1640 0.1391 1.64 239 0.50

300,000 1640 1640 0.2087 1.71 287 0.55

Number of Fracs

x e (ft) y e (ft) N p C fD x f (ft) J DTH

2 1640 820 0.1391 1.62 170 0.65

4 1640 410 0.2782 1.42 182 1.17

5 1640 328 0.3478 1.20 198 1.34

Number of Fracs

x e (ft) y e (ft) N p C fD x f (ft) J DTH

2 1640 820 0.4173 1.75 283 0.94

4 1640 410 0.8347 1.55 301 1.73

5 1640 328 1.0434 1.33 325 2.02

Vertical Well

Horizontal Well100,000 lbs

Horizontal Well300,000 lbs

Production Forecast

0

2000

4000

6000

8000

10000

12000

14000

16000

0 50 100 150 200 250 300

t , days

q, S

TB

/day

Vertical

Horizontal - 4 fracs

0

2000

4000

6000

8000

10000

12000

14000

16000

0 50 100 150 200 250 300

t , days

q, S

TB

/day

Vertical

Horizontal - 4 fracs

Artificial lift required

Planning and Execution Considerations

The notion of fracturing a horizontal well transversely has to be considered BEFORE the well is drilled

Horizontal section must be drilled along the minimum horizontal stress;

Casing, completion and all mechanical elements that go into the well must be able to sustain the pressures and injection rates required for the treatment(s);

Two major decisions need to be taken: a) Method of perforation b) Method of isolation between individual treatments

Method of Perforation

The only suitable method for “perforation” is by abrasive jet cutting tools

It is the only tool that offers large, clean and deep holes and in close spacing.

Traditional guns will require as much as 3 ft to place the required number of perforations for the fracture treatment; this length, in turn, may cause tortuosity or even multiple fracture initiations.

Tortuosity will result in extra fracturing pressure that, many times, might not be available, and the fracture may not initiate.

Example of jet cutter tool with 6 holes longitudinally disposed, 180° phased in a 4” section

Example of jet cutter tool with 4 holes radially disposed, 90° phased

Abrasive Jet Cutter

Method of Isolation Between Individual Treatments

Choices: drillable (composite) coiled tubing conveyed electrically set, or pump-through, hydraulically set bridge plugs. The selection will impact both the operations schedule and the cost.

Using an e-line CT would require first to switch CT reel from the previous pumping operation to an e-line reel. This is the major reason that a pump-through, hydraulically set bridge plug might be preferred.

On the other hand, using an e-line coil tubing allows the operator to also run a CCL locator for greater accuracy for the exact location of the bridge plug.

Four sets of operations to be executed

1. Fracture Isolation2. Fracture Placement3. Fracture Clean-Up4. Post Fracture Flow-Back and Testing

The first three sets are repeated for each additional fracture treatment; the fourth is to be performed after all fracture treatments have been placed.

The isolation method selected will impact both the operations schedule and the cost.

Execution Procedure

1) 1) Fracture isolationFracture isolation

2) 2) Fracture PlacementFracture PlacementMinifrac

(Diagnostic Fracturing Tests)Fracturing Job

3) 3) Fracture CleanFracture Clean--UpUpClean-Up Hole

(+ Possible Lift) With CTWell Test

Each Fracture Placement Requires a Loop of Each Fracture Placement Requires a Loop of these 3 Main Tasks. Besides, the final Taskthese 3 Main Tasks. Besides, the final Task

4) 4) Post Fracturing Post Fracturing Milling-Out BP and

Clean-Up Hole With CTWell Test of the Commingle

Multi-Fractured Horizontal Drain

Hydraulically Setting BP + Pressure Test

Abrasive Cutting

Clean-Up Fracturing Fluids










Hydraulically Setting BP + Pressure Test

Abrasive Cutting


Execution Procedure (Pump through hydraulically set bridge plug)

Dummy Run

With CT










Electr. Setting BP + Pressure Test

Abrasive Cutting


Dummy Run

With CT










Electr. Setting BP + Pressure Test

Abrasive Cutting


Execution Procedure(Electrically set bridge plug)

Summary

Increasing role of evaluation Integration of reservoir engineering,

production engineering and treatment information

Cost matters Expensive 3D and P3D models do not

substitute thinking Still what we want to do is increasing JD

fraccourse 2007.ppt

Documents

successful fracture

fracture openprinciple

fracture conductivity

wide fracture

twolane road

flow profile

high competence

production rate