CBM Frac Seminar 2011

Hydraulic Fracturing

Emphasis on Coal Bed Methane Emphasis on Coal Bed Methane (Coal Seam Gas)

A short course by Prof. Michael J. Economides

©2010

Principle of Least Resistance

Least Principal Stress Least Principal Stress

HYDRAULIC FRACTURING •••• PROF. M. J. ECONOMIDES2

Horizontal fracture Vertical fracture

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


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,


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

� Length and width are interdependent through fracture conductivity.

� Optimization is warranted

1-

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


� Multi-branched wells

Longitudinal Vertical

Fracture - Horizontal Well


σσσσH,max

xf

σσσσH,min

σσσσH,min

Transverse Vertical

Fractures - Horizontal Well


σσσσH,max

Hydraulic Fracture

σσσσH,max

D

xf

σσσσH,min

Radial converging flow in frac


Production or Injection

Enhancement

What are we doing?

� Bypass formation damage

� After a successful fracture any damage skin is eliminated


damage skin is eliminated

� Radically modify flow profile into the wellbore

� New pseudoskin; New productivity index

Vertical Well, Fully Penetrating

Vertical Fracture: Performance

wp

h2V


2xf

h2Vfp

Transient Flow Regimes

Vertical Fracture - Vertical Well

Linear Fracture Flow

Elliptical or Transition Flow


Bilinear Flow

Linear Formation Flow Pseudoradial Flow

Pseudoskin Factor, Radial Flow

D

fe

JB

kh

sr

rB

khJ

=

+−

=

µ

π

µ

π 2

75.0]ln[

12

q J p= ∆ sf is pseudoskin factor used after the treatment

to describe the productivity for radial flow


f

w

sr

+− 75.0]ln[

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

Dimensionless Fracture

Conductivity

2 xf

w


Dimensionless

fracture conductivityf

f

fDkx

wkC =

w

fracture conductivity

no name

44

33

44

33

xf/r

w)

+ 0

.5 I

n (

CfD

)

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

Pseudoskin Factor for a Finite

Conductivity Vertical Fracture


22

11

00

22

11

000.1 1000

sf+

In

(xf/r

w),

sf+

In

(x

CfD

sf + In (xf /rw)

CfD, opt

1 10 100

The JD of a Hydraulically Fractured Well

� From Cinco-Ley and Samaniego and simple re-arrangement

( ) ( )DJ =1


( ) ( )fwffe

Dsrxxr

J++−

=/ln75.0/ln

( )fwffD

ff

e

D

srxCkh

Vkr

J

+++

−−

=

/lnln5.0ln5.075.0ln

1

44

33

44

33

xf/r

w)

+ 0

.5 I

n (

CfD

)

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

Pseudoskin Factor for a Finite

Conductivity Vertical Fracture


22

11

00

22

11

000.1 1000

sf+

In

(xf/r

w),

sf+

In

(x

CfD

sf + In (xf /rw)

CfD, opt

1 10 100

Penetration Ratio

Proppant Number

ye = xee

f

xx

xI

2=

wk


2 xf

xe

f

f

fDkx

wkC =

fDx

res

wingf,prop,f

res

wingf,prop,f

prop C)(IkV

Vk

kV

VkN

221 24===

−−

e

ff

fDxprop

kx

wxk

CIN

2

2

4=

=

Proppant Number -

Various Ways to Look at itVarious Ways to Look at it

Nprop= const means


reservoir

proppedwingf

prop

e

proppedwingf

e

kV

VkN

hkx

Vk

kx

,2

2

,1

2

4

−

−

=

=

fixed proppant volume

JD vs CfD (moderate Nprop)


JD vs CfD (large Nprop)


Maximum Achievable PI

( )

1.0 if )(089.0311.0423.0

exp6

1.0 if ln5.0990.0

1

2max

>

−−

−

≤−

=propprop

prop

prop

propD

NNN

NN

NJ


1.0 if )(015.0667.01

)(089.0311.0423.0exp

62

>

++

−−−

prop

propprop

proppropN

NN

NN

π

Optimal Length and Width

2Vfp = 2h wp xf

Competition for propped volume: w and xf

2Vfp = 2h wp xf


fpfp xhwV =

f

pf

fDkx

wkC =

2/1

=

hkC

kVx

fD

ffp

f

2/1

=

f

fpfD

phk

kVCw

Tight Gas and Frac&Pack:

the Extremes

Tight Gas k << 1 md (hard rock)

2/1

6.1

=

f

fp

phk

kVw

2/1

6.1

=

hk

kVx

ffp

f


High permeability k >> 1 md (soft formation)

2/1

6.1

=

f

fp

phk

kVw

2/1

6.1

=

hk

kVx

ffp

f

Pushing the Limits with

the UFD Approach



Stress and Stress Distribution

Stresses In Formations

σ ρv

H

g dz= ∫0

′ = −σ σ αp

abs


′ = −σ σ αv v p

( )σν

νσ α αh v p p=

−− +

1

eff

abs

Crossover of Minimum Stress

gro

und s

urf

ace,

m

Critical Depth-1000

-500

0

-500

0

Curr

ent

Depth

, m

Ground Surface


80x1060 20x106 40x106 60x106

Stress, Pa

Depth

fro

m o

rigin

algro

und s

urf

ace,

m

-3000

-2500

-2000

-1500

-2500

-2000

-1500

-1000

Curr

ent

Depth

, m

Influence of Lithology on In-Situ

Stress Distribution


Data from hydraulic fracturing

Stress Representation

σzz

τzy

z

y τ

σzz

τθz

τrz

τzr

z

r

θ


y

x

σyy

σxx

τzx

τxz

τyz

τxy

τyx

(b)

σrr

τrθ

σθθ

τzθ

τθr

Fracture Initiation Pressure

� For perfectly vertical well

pbd = 3σH,min- σH,max + To – p


pbd = 3σH,min- σH,max + To – p

� For perfectly horizontal well along σH,max

pbd = 3σH,min- σV + To – p



Rock and Fracture

Mechanics

Linear Elasticity And Rock

Mechanics,

� Stress and Strain Concept

� Linear Elasticity

� Material Properties, Interrelation


� Material Properties, Interrelation� Uniaxial Compression Test

� Plane Stress - Plane strain

� PKN-KGD-Radial

E =Fl

A ∆ ∆ ∆ ∆ l

A

F

∆ ∆ ∆ ∆ l

Uniaxial Loading Test to Obtain

Linear Elastic Parameters


D ∆∆∆∆ lv = -

l ∆∆∆∆ D

∆ ∆ ∆ ∆ D/2

D

l

Interrelations Of Various Elastic

Constants Of An Isotropic Material

Known quantities E, ν G, ν E ,G

Shear modulus:

G( )

E

2 1 + ν G G

Young's modulus: ( )+ ν


Young's modulus:

EE ( )2 1G + ν E

Poisson ratio:

ν ν νE G

G

− 2

2

Plane strain

modulus:

E'

E

1 2−ν

2

1

G

−ν

2

1

G

−ν

Ideal Crack Shapes

� Pressurized Line Crack

� Plane strain

� Net Pressure - Superposition


� Net Pressure - Superposition

� How to apply?� Width equations

� More complex models

Pressurized Line Crack

x

y

cx

σ

Tip


u(x)

p(x)

Tip

r

Line Crack

For constant pressure inside the frac the solution is:

c

x

y


22

0'

4)( xcp

Exw n −=

For constant pressure inside the frac the solution is:

E' is the plane strain modulus (almost same as Young's)

E' = E/(1-v2)

Plane Strain

x

y


x

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


� 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 views

Vertical PlaneStrain Condition


Horizontal PlaneStrain Condition

PKN Width

1 Wellbore width at the end of pumping from the PKN model

41

41

41

57.3512

=

=qxqx

wff µµ


2 Convert wellbore width into average width

0,'

57.3'

512

=

=

E

qx

E

qxw

ff

w

µµ

π

628.055

4

4===

ππγ

Application: Basic 2D Models

0,wPKN ww γ=

hf

PKN

ww,0xf

qi


wKGD ww γ=

wellbore tip

KGDhf

ww

qi

Stress Intensity Factor

weighted pressure at tip

Pa · m1/2

psi - in.1/2

stress distributionat tip

∫−

−

+=

c

c

nI dxxc

xcxp

cK )(

2

1

xc −∝

1


psi - in.1/2

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

−−

cxcc2

x

c

KI : proportionality const

xc −

Fracture toughness, Fracture toughness, KIC

Tip Propagation Pressure

fIctip

xKp

48

π=

Fracture toughness, Fracture toughness, KIC


fx48

x

c

Application:

Fracture Height Prediction

� Height containment: why is it critical?� Fracturing to water or gas


� 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?

Upper tip Far-field Stress

Questions:


Pinch point Up or Down?

Width?

Hydrostatic

pressure?

Height

control?

What can be

measured?

Lower tip

Height Map

400

600

800

1000 300

200

100

Tip Location

[m]

Tip

Location

[ft]


-1200

-1000

-800

-600

-400

-200

0

200

400

3000 3100 3200 3300 3400 3500 3600 3700 3800

-300

0

21 26

psi

MPa

100

-100

-200

Treating Pressure

Material Balance

Leakoff Delineation

Geometry Evolution (History)


Geometry Evolution (History)

During Pumping

During Shut-in

Bulk Fluid Loss, Detailed

Leakoff, Material Balance

� Material Balance

� Leakoff as Material


� Leakoff as Material Property

� Formal Material Balance

� Power-Law Assumption

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 t A S+ +κ 2A

Less than 2


( ) ( )V = V 2A C t A Si L e p+ +κ 2

peL St2Cw

w

2++=

κη

2A=AL :here

A

eitq

peLi St2Cw=

A

V2++ κ

κ is about 1.5

Nolte’s Power Law

Assumption

α

α

τ /1

D

DD

A

tA

=

=A A AD e= / t t tD e= /

V


( ) ( )( )2/3

0+Γ

Γ==

α

ααπακ g

dAdt-t

C=V

e eA t

LLoffe ∫ ∫0

12

ττ ( ) eLe

Loffe

tCA

V

2=κ

peL St2Cgw

w

2)(0 ++=

αη

Max 2


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

22

1

1

22

122

2222

1

0,'

14.2198.315.9

+−

++

++

+×

nf

n

f

n

inn

n

n

n

nw

E

xhqK

n

n=w

628.0 ww =

Pumping Time, Fluid Volume


3 Assume a κ = 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

0,628.0 we ww =

( ) 022 =+−−

)Sw(tκ C t

xh

qpeL

ff

i

eii tqV =

i

eff

i

fe

eV

wxh

V

V= =η

Adjustment for κ

� Several ways…see page 111 in UFD

� One way, according to Nolte


κ = 1.33ηe+ 1.57 (1 - ηe )

Nolte’s Power Law Proppant

Schedule:

C/Ce

1

y = ξεεεε

εε

+=∫ 1

11

0

dxx

ε+−=

1

1)1( padfArea


fpad1 V/Vi0

slurry

0 1

ξ

ε

ε

+

−××=

1

1ie VcM

ε

ε

+

−=

1

1Area

Nolte's proposition:

select fpad=ε

ie VcM ××= η

η

ηε

+

−=

1

1

1 Calculate the Nolte exponent of the proppant concentration curve

2 Calculate the pad volume and the time needed to

pump it

e

e

η

ηε

+

−=

1

1

ipad VV ε=

epad tt ε=

Proppant schedule


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)

ε

−

−=

pade

pad

ett

ttcc

ie

eV

Mc

η=

propp

added c

cc

ρ−

=

1

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 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

Equilibrium height:

Stress intensity factors at vertical tips equal to fracture toughness of layers where both fracture tips take place.

Fracture Height Calculation

1

yD


1

-1

hg

Δhu

Δhd

yu

yd

σtop

σmid

σbot

Simonson et al. model

( )

( )

+

−×

−==

−

+×

−==

∫

∫

−

−

1

1botI,botIC,

1

1topI,topIC,

1

1

)(KK

1

1

)(KK

D

D

DD

du

g

D

D

DD

du

g

dyy

yyp

yy

h

dyy

yyp

yy

h

π

π


Ddu

∆+∆+

∆+−=

∆+∆+

∆−=

dug

dd

dug

uu

hhh

hy

hhh

hy

21

21

dugf hhhh ∆+∆+=

Finally, fracture height is:

Net Pressure Distribution

(in Vertical Direction)

Pressure @ center of the crack:Minimum In-situ Stress at interested location.( )0,00 wfmidnwmid wSpk +=+= σσ


( ) )(100 DDD yykkyp σ−+=

Pressure gradient in fracture:

D

du

g

D yyy

hgyk

−−= ρ1


Incorporating Rigorous

Fracture Height Calculation

into UFD (p-3D UFD)

p-3D UFD Logic

2D UFD & Design Procedure:

Offers optimum fracture half-length and width based on given amount of proppants and assumed fracture height. EOJ net pressure can be derived from the hydraulic fracture width and max. proppant


the hydraulic fracture width and max. proppant concentration can be derived from the hydraulic fracture volume.

Equilibrium Height:

Gives the fracture height. It requires EOJ net pressure and concentration for calculation.

Data Needed for p-3D UFD :

� Layer data

� Permeability, porosity, pressure

� Young’s modulus, Poisson ratio, Fracture toughness, Minimum in-situ stress


toughness, Minimum in-situ stress

� Fluid data

� Proppant data

� Leakoff calculated from fluid and layer data

Sample Calculation using

p-3D UFD approach

Reservoir and Rock Properties

Drainage area, Ad, acre 320

Net pay thickness, hn, ft 50

Reservoir porosity, ϕ 0.2

Reservoir permeability, k, md 1

Min. in-situ stress of target layer, σmid, psi 7,500

Inter-layer stress contrast, ∆σ, psi 1,000


Proppant and Proppant Properties

Mass of proppant, Mprop, lbm 200,000

Proppant pack permeability, kf, md 287,000

Proppant diameter, Dp, inch 0.027

Proppant specific gravity, SGp 3.56

Proppant pack porosity w/o stress, ϕ1 0.43

Proppant pack porosity under stress, ϕ2 0.364

Inter-layer stress contrast, ∆σ, psi 1,000

Fracture toughness of bounding layers, KIC, psi-inch0.5 1,000

Young's modulus, E, psi 1.00E+06

Poisson ratio, ν 0.26

Treatment Fluid & Leak-Off Variables

Injection rate, qi, bpm 30

Rheology consistency index, K', lbf-sn/ft2 0.23

Rheology flow behavior index, n' 0.38

Leak-off coefficient, CL, ft/min0.5 0.005

Spurt loss coefficient, Sp, gal/ft2 0.01

Fracture Height from p-3D

UFD

2D UFD + = p-3D UFD

600

700

800

900

1000

Ne

t P

ress

ure

, pn,

psi

600

700

800

900

1000

Ne

t P

ress

ure

, pn,

psi

Equilibrium Height

600

700

800

900

1000

Ne

t P

ress

ure

, pn,

psi


0

100

200

300

400

500

600

0 50 100 150 200 250 300

Ne

t P

ress

ure

,

Fracture Height, hf, ft

0

100

200

300

400

500

600

0 50 100 150 200 250 300

Ne

t P

ress

ure

,


0

100

200

300

400

500

600

0 50 100 150 200 250 300

Ne

t P

ress

ure

,


≈ 85 ft

p-3D UFD with Bisection

Method

Set upper and lower limit of net pressure (pn,max, pn,min) and max. proppant conc. (ce)

2

min,max,

,

nn

avgn

ppp

+=


Find fracture height (hf ) corresponding to pn,avg and ce using equilibrium height

Calculate new net pressure (pn,calc) and ce corresponding to hf

Update pn,max or pn,min and ce

Until solution converges

Introducing…

pp--3D UFD3D UFD


pp--3D UFD3D UFD

Input Parameters

� Proppant mass for (two wings), Mprop (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, ϕp (e.g. 0.35)

� Proppant pack permeability, k (md)


ϕ

� Proppant pack permeability, kf (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, k (md)� Permeable (leakoff) thickness, hn (ft)� Wellbore Radius, rw (ft)� Well drainage radius, re (ft)

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

� Pre-treatment skin factor


� 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.

� Minimum in-situ stress of formation and adjacent impermeablelayers, σmid , σtop, σbot (psi)

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

� Poisson ratio, ν

� Fracture toughness of adjacent impermeable layers, KIC,top, KIC,bot (psi - in0.5)


� Slurry injection rate (two wings, liq+ prop), qi (bpm)

� Rheology, K' (lbf - secn'/ft2)

� Rheology, n'

� Leakoff coefficient in permeable layer, CL (ft/min0.5)

� The leakoff coefficient outside the permeable layer is considered


� 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.


� 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.


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)

Sensitivity of Fracture

Height from p-3D UFD

130

150

170

190

Fracture Height, h

f, ft

k = 0.1 md, KIC = 500

k = 0.1 md, KIC = 1000

k = 0.1 md, KIC = 1500

k = 1 md, KIC = 500

k = 1 md, KIC = 1000

k = 1 md, KIC = 1500

k = 10 md, KIC = 500


50

70

90

110

130

0 500 1000 1500 2000 2500 3000

Fracture Height,

Stress Contrast, ∆σ, psi

k = 10 md, KIC = 1000

k = 10 md, KIC = 1500


Advanced Concepts

Fracturing High-Rate Gas Wells

� Non-Darcy flow reduces fracture flow capacity substantially

� However, fracturing is a major way to


� 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+

=

ρβ vkN

nf ,=

Effective Fracture

Permeability

Reynolds Number


µ

ρβ vkN

nf ,

Re =Reynolds Number

a

nfk

bx

)()101(

,

8=βa and b are constants

of 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


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

µµµµ(cp) 0.015


T (R) 580

ZZZZ 0.91

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

a 1.541.541.541.54

b 110,470110,470110,470110,470

Design Procedure in UFD

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

maximum possible productivity index maximum possible productivity index maximum possible productivity index maximum possible productivity index JJJJD,maxD,maxD,maxD,max and and and and the optimum dimensionless fracture the optimum dimensionless fracture the optimum dimensionless fracture the optimum dimensionless fracture


maximum possible productivity index maximum possible productivity index maximum possible productivity index maximum possible productivity index JJJJD,maxD,maxD,maxD,max and and and and the optimum dimensionless fracture the optimum dimensionless fracture the optimum dimensionless fracture the optimum dimensionless fracture conductivity, conductivity, conductivity, conductivity, CCCCfD,optfD,optfD,optfD,opt . Determine fracture . Determine fracture . Determine fracture . Determine fracture dimensions. dimensions. dimensions. dimensions.

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

Design Iteration 1

Proppant Number, Nprop 1.288

Dimensionless PI, JD, opt 1.06

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


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

Design Iteration 1

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

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

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

1424

)( 2222

=−

=−

= D

wfaveJ

ZT

ppkhq

µ


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

ρρρρ = 0.076 γγγγg/Bg lbm/ft3 = 1.22 γγγγg/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

Design Iteration 1

==a

fk

b

)(108β 75,800 1/m

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


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

Design Iteration 2




Optimal dimensionless fracture cond, 1.6



1.6



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

Design Iteration 3




Optimal dimensionless fracture cond, 1.6



1.6



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

Design Pumped

Efficiency, ηηηη, % 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

20

25

30

Liq

uid

in

jec

tio

n r

ate

, b

pm

6

7

8

9

10

ca

, lb

m p

rop

ad

de

d t

o

ga

llo

n l

iqu

id


0

5

10

15

0 10 20 30 40 50 60

Pumping time, min

Liq

uid

in

jec

tio

n r

ate

, b

pm

0

1

2

3

4

5

ca

, lb

m p

rop

ad

de

d t

o

ga

llo

n l

iqu

id

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


� 10 to 20 1.34 27,539

� 20 to 40 1.54 110,470

� 40 to 60 1.60 69,405

Advanced Issues with Natural

Gas Well Fracture Designs

� Effects of Turbulence and its Remediation by Fracturing

� Net Pressure Constraint


� Net Pressure Constraint

� The Use of High-Quality Proppants

Natural Gas Well FOI vs Permeability

8

10

12

Fra

c)

Vertical Oil Well Vertical Gas Well


Fracture width determined from optimum values of JD and CfD [kP = 150,000 md]

0

2

4

6

8

0.01 0.1 1 10 100

FO

I of

JD

(Fra

c/N

o-F

rac)

Reservoir Permeability k, md


8

10

12

Fra

c)

Vertical Oil Well Vertical Gas Well ADJUSTED Vertical Gas Well not adjusted


Fracture width constrained by net pressure of 1,000 psi [kP = 150,000 md]

0

2

4

6

0.01 0.1 1 10 100

FO

I of

JD

(Fra

c/N

o-F

rac)



8

10

12

14

(Fra

c/N

o-F

rac)

Vertical Oil Well Vertical Gas Well ADJUSTED Vertical Gas Well not adjusted


Fracture width constrained by net pressure of 1,000 psi [kP = 500,000 md]

0

2

4

6

8

0.01 0.1 1 10 100

FO

I of

JD

(Fra

c/N

o



Production Forecast for

Hydraulically Fractured

Coalbed Methane (CBM)

Adsorption capacity

� Defined as the volume of gas adsorbed per unit mass of coal usually expressed in scf /ton of coal. The range is usually between 100-800 scf /ton for most coal


between 100-800 scf /ton for most coal deposits.

Langmuir Isotherm

� Langmuir Isotherm

� A curve representing the methane desorption process


� Langmuir volume constant (VL)

� Maximum gas content (at infinite pressure)

� Langmuir pressure constant (CL)

� The pressure at which half of gas is adsorbed on a coal

Langmuir Isotherm

pp

pVC

L

Lg

+=

250

300

350

400A

dso

rptio

n C

ap

acity,

scf/

ton


0

50

100

150

200

0 1000 2000 3000 4000 5000

Ad

so

rptio

n C

ap

acity,

scf/

ton

Pressure, psi

� Example:

� VL = 400 scf/ton

� CL = 500 psi

� At reservoir pressure 5,000 psi, adsorbed gas in-place is 364 scf/ton.

Total Gas In-Place

Calculation

� Free gas in pore space

Adsorbed gas

)1(, wnHCp SAhV −= φ gHCpfreeg Vm ρ×= ,,


� Adsorbed gas

� Total gas in-place

))1((, φρ −×== nRgRgAdsg AhCVCV scgAdsgAdsg Vm ,,, ρ×=

Adsgfreeginplaceg mmm ,,, +=sc

sc

airg

inplaceg

scgp

RT

M

mV

γ,

, =

Material Balance (CBM)

Total gas in-place at time t

= Remaining gas in-place after producing for Δt

+ total producing gas for Δt


where

[ ] [ ] [ ]ttmtmtm inplacegprodginplaceg ∆++∆= ,,,

[ ] [ ]ttVtqtV scgscgscg ∆++∆×= ,,,

Convert all terms into volume in standard condition

( ) ( )( )wftt

sc

scDnscg pmpm

Tp

TkJhq −= ∆+π,

Material Balance (CBM)

[ ] [ ]ttVtqtV scgscgscg ∆++∆×= ,,,

Function of pt Function of p


Function of pt Function of pt+Δt

Where pt is initial pressure at time tpt+Δt is pressure after producing for Δt

Solve for pt+Δt !!! qsc can be calculated

Sample Calculation (CBM)

Reservoir and Rock Properties

Drainage area, Ad, acre 320

Net pay thickness, hn, ft 100

Reservoir porosity, ϕ 0.1

Water saturation, Sw 0.7

Reservoir permeability, k, md 1

Reservoir pressure, pR, psi 5,000


Reservoir pressure, pR, psi 5,000

Reservoir temperature, T, ˚F 200

Gas Specific Gravity (ɤg) 0.7

N2 Mole Fraction 0.00

H2S Mole Fraction 0.00

CO2 Mole Fraction 0.00

Langmuir Parameters

Rock Specific Gravity (ɤR) 2.65

Langmuir Volume (VL), scf/ton 400

Langmuir Pressure (pL), psi 500

Production Forecast (CBM)

At 5000 psi,

initial gas in pores: 11.147 Bscf

initial adsorbed gas: 39.904 Bscf


Total initial gas in-place: 51.051 Bscf

Performing production forecast for 3 years with 100 time steps.


(1st time step)

Δt = 11 days


By solving material balance equation:


Pressure at 11th day: 4,791 psi

Remaining gas in-place: 50.597 Bscf

Flow rate at 11th day: 41.371 MMscf

Cumulative production: 0.454 Bscf


(2nd time step)

Δt = 22 days


By solving material balance equation:


Pressure at 22nd day: 4,607 psi

Remaining gas in-place: 50.174 Bscf

Flow rate at 22nd day: 38.659 MMscf

Cumulative production: 0.876 Bscf

Pressure Decline (CBM)

(3 years)

4,000

4,500

5,000

5,500

Re

se

rvo

ir P

ressu

re, p

si

Reservoir Pressure

Abandonment Pressure


1,500

2,000

2,500

3,000

3,500

0 365 730 1095

Re

se

rvo

ir P

ressu

re, p

si

Time, days

Production Rate (CBM)

(3 years)

30

35

40

45

50

Flo

w R

ate

, M

Mscfd


0

5

10

15

20

25

0 365 730 1095

Flo

w R

ate

, M

Mscfd

Time, days

Cumulative Production (CBM)

(3 years)

8

10

12

14

Cu

mu

lative

Pro

du

ctio

n, B

scf


0

2

4

6

8

0 365 730 1095

Cu

mu

lative

Pro

du

ctio

n, B

scf

Time, days

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


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


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

2

2 ==e

ff

fDxkx

wxkCI

r

pf

pe

pff

e

ff

fDxpropkV

Vk

hkx

whxk

kx

wxkCIN

24422

2 ====


Elongated Drainage

hyxV eeres =

e

e

fDx

ef

ef

ee

ff

res

pf

py

xCI

xx

xx

hykx

whxk

kV

VkN

242

=×==

88.30

A

ppe

CNN =

Fluid Flow For Transversely

Fractured Horizontal Well

rw 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(π

−=wf

cr

h

wk

khs


c

DV

DTH

sJ

J

+

=

)1

(

1

Multiple Transverse Fractures

Intersecting a Horizontal Well

σσσσmin σσσσmaxσσσσmin σσσσmaxσσσσmin σσσσmax


W

rw

W

rw

W

rw

Vertical vs Horizontal

Performance ComparisonProppant

Mass, lbsx 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 x (ft) y (ft) N C x (ft) J

Vertical Well


Number of

Fracsx 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

Fracsx 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

Horizontal Well100,000 lbs

Horizontal Well300,000 lbs

Production Forecast

10000

12000

14000

16000

, S

TB

/day

Vertical

Horizontal - 4 fracs

10000

12000

14000

16000

, S

TB

/day

Vertical

Horizontal - 4 fracs


0

2000

4000

6000

8000

0 50 100 150 200 250 300

t , days

q, S

TB

/day

0

2000

4000

6000

8000

0 50 100 150 200 250 300

t , days

q, S

TB

/day

Artificial lift required

Transversely Fractured Horizontal

Oil Well: FOI vs Permeability


[kP = 150,000 md]


Gas Well: FOI vs Permeability


[kP = 150,000 md]




[kP = 150,000 md]




[kP = 500,000 md]

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


� 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 4 holes radially disposed, 90° phased

Abrasive Jet Cutter


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

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


� 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-Up

Execution Procedure


3. 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.

1) 1) Fracture isolationFracture isolation

2) 2) Fracture PlacementFracture PlacementMinifrac

(Diagnostic Fracturing Tests)Fracturing Job

Hydraulically Setting BP + Pressure Test

Abrasive Cutting1) 1) Fracture isolationFracture isolation



Hydraulically Setting BP + Pressure Test

Abrasive Cutting

Execution Procedure(Pump through hydraulically set bridge plug)


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 CT

Well Test of the Commingle Multi-Fractured Horizontal Drain

Clean-Up Fracturing Fluids









Dummy Run

With CT




Electr. Setting BP + Pressure Test

Abrasive CuttingDummy

RunWith CT




Electr. Setting BP + Pressure Test

Abrasive Cutting

Execution Procedure(Electrically set bridge plug)


















Shale Gas

Exploitation of a New ResourceExploitation of a New ResourceProf. Michael J. Economides

©2010

Resource Triangle (From Holditch)

Conventional ReservoirsSmall volumes that areeasy to develop

Unconventional

Imp

roved

tech

no

log

y

Incre

ased

pri

cin

g

HYDRAULIC FRACTURING •••• PROF. M. J. ECONOMIDES

UnconventionalLarge volumes difficult to develop Im

pro

ved

tech

no

log

y

Incre

ased

pri

cin

g

Basin Analog – The idea…

conventionalconventional

unconventionalunconventional

knownknown

knownknown

conventionalconventional

unconventionalunconventional

knownknown

unknownunknown

Basin

Analogs


US Basins

(Reference)International/Frontier Basin

(Target)

(modified from Singh, 2007)

Shale Gas Plays in the US

MARCELLUS

SO HOW BIG IS IT???

DateDateDateDate Agency or AuthorAgency or AuthorAgency or AuthorAgency or Author Recoverable (TCF) Recoverable (TCF) Recoverable (TCF) Recoverable (TCF)

2009200920092009 Hiscock & BarclayHiscock & BarclayHiscock & BarclayHiscock & Barclay 516516516516

2008200820082008 IOGA of NYIOGA of NYIOGA of NYIOGA of NY 500500500500

Wrightstone 2010

2009200920092009 EngelderEngelderEngelderEngelder 489489489489

2008200820082008 DOEDOEDOEDOE 262262262262

2007200720072007 Engelder & LashEngelder & LashEngelder & LashEngelder & Lash 168168168168

2008200820082008 NCINCINCINCI 34.234.234.234.2

2006200620062006 USGSUSGSUSGSUSGS 31313131

2002200220022002 USGSUSGSUSGSUSGS 0.8 to 30.70.8 to 30.70.8 to 30.70.8 to 30.7

2005200520052005 USGSUSGSUSGSUSGS 1.31.31.31.3

Courtesy Greg Wrightstone, 2010

THE OTHERS

HOW BIG ARE THEY???

DateDateDateDate Agency or AuthorAgency or AuthorAgency or AuthorAgency or Author Recoverable (Tcf) Recoverable (Tcf) Recoverable (Tcf) Recoverable (Tcf)

FAYETEVILLEFAYETEVILLEFAYETEVILLEFAYETEVILLE

2009200920092009 ChesapeakeChesapeakeChesapeakeChesapeake 20202020

Wrightstone 2010

BarnettBarnettBarnettBarnett

2008200820082008 NPRNPRNPRNPR 30303030

HaynesvilleHaynesvilleHaynesvilleHaynesville

2010201020102010 ChesapeakeChesapeakeChesapeakeChesapeake 300300300300

US SHALE IN THE WORLD

How Do the Marcellus and Haynesville Compare to Other GAS

Fields World-wide?

World's 10 Largest Gas Fields

(2005)

Source: IEA 2005

Field Name Tcf

1. North Field-South Pars (Iran) 1,400

2. Urengoy (Russia) 222

3. Yamburg (Russia) 123

4. Hassi R'Med (Algeria) 123

5. Shtokman (Russia) 110

6. Zapolyarnye 95

7. Hugoton 81

8. Groningen 73

9. Bonavenko 70

10. Medvezhye 68

300 -500 Tcf

Multiple Transverse Fractures

Intersecting a Horizontal Well

σσσσmin σσσσmaxσσσσmin σσσσmaxσσσσmin σσσσmax


W

rw

W

rw

W

rw

Horizontal Wells and

Gas Shale Formations

� Large number of transverse fractures

� Treatment placement is important

� Open-hole jetting

� Cased hole perforating/jetting


Planned Often Realized Optimized

From Schlumberger

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

Abrasive Jet Cutter


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

Microseismic Mapping


From Schlumberger

Fractured Well

Performance – Linear Flow

wk

kxmtmp

f

f

lf )151.1

)(3

(π

+∆=∆


2/1

064.4

=

tlf

fchm

qBkx

φ

µ

t

ic

ktx

φµ9482=

Horizontal Well with Multiple

Transverse Fractures

A = 4.106 ft2 (~100 Acre square)

Bo = 1.1 resbbl/STB

µ = 1 cp

Mp = 150,000 lb (for each fracture)

γp = 2.65

φ = 0.38


φp = 0.38

kf = 60,000 md (20/40 mesh sand)

h = 50 ft

hf = 100 ft

Reference w ell

UFD Fracture

Horizontal Well with

5 UFD Fractures

UFD at PSS

Reference w ell

Permeability = 1 md


No Fracture

Suboptimal FractureUFD at PSS

UFD Fracture

Suboptimal

Fracture

Horizontal Well with 5 UFD Fractures

Permeability = 1 md


No Fracture

UFD Fracture

Suboptimal Fracture


5 UFD Fractures

UFD at PSS

Reference w ell

Permeability = 0.1 md


No Fracture

UFD Fracture

Suboptimal

Fracture

Horizontal Well with 5 UFD Fractures

Permeability = 0.1 md


No Fracture

UFD Fracture


10 UFD Fractures

(k = 0.001 md)


10 UFD Fractures

(k = 0.0001 md)

Reference w ell

Gas, Permeability = 0.001 md



10 UFD Fractures

(k = 0.001 md)


10 UFD Fractures

(k = 0.0001 md)

Gas, Permeability = 0.001 md


UFD Fracture

Reservoir Permeability Sensitivity

IR_k=1E-4

IR_k=1E-3

IR_k=1E-2

IR_k=1E-1

IR_k=1

IR_t

1

10

100

103

104

Pressure runs out

Radial flow

Pre

ssu

re [

psi] a

nd

de

riva

tive

, p

si

k = 0.0001

k = 0.001

k = 0.01

k = 0.1

k = 1

Early linear f low, ½ slope

Compound linear f low, ½ slope

No pressure drawdown

Radial f low

Pseudosteady State, Unit slope


10-3 10-2 10-1 101 100 103 104 105 106 107 108 109

10-3

10-2

10-1

1

Time, hr

Early linear flow

Compound linear flow

PseudosteadyState

Pre

ssu

re [

psi] a

nd

de

riva

tive

, p

si

wk

kxmtmp

f

f

lf )151.1

)(3

(π

+∆=∆

,2

1tmp lf ∆=′∆

2/1

064.4

=

tlf

fchm

qBkx

φ

µ

Linear flow to an infinite conductivity fracture Linear flow depth of pressure investigation

t

ic

ktx

φµ9482=

Sensitivity to Horizontal Well Length

for Same Number of Fractures

100

1000

4000 ft

2000 ft

1000 ft

500 ft

Pre

ssu

re c

han

ge a

nd

deri

vati

ve, p

si

4000 ft

2000 ft

1000 ft

500 ft

Departure times


0.1 1 10 100 1000 10000 1E+5 1E+6 1E+70.1

1

10

Time, hr

Pre

ssu

re c

han

ge a

nd

deri

vati

ve, p

si

Departure time from linear flow is predicted by depth of investigation equation for linear flow. t

ic

ktx

φµ9482=

Departure times

from Linear Flow

Trend

Field Data – New Albany

Shale


Interpretation

2/1

064.4

=

tlf

fchm

qBkx

φ

µ= 128 ft- md1/2


==t

xck it

4

9482φµ

0.0013 md with t = 8304 hr

If xf = 9600 ft then k = 0.00018 md

Documents

CBM Frac Seminar 2011