C8 hydraulic fracturing

5/9/2014

Designed & Presented by
Mr. ĐỖ QUANG KHÁNH, HCMUT

03/2014

Đỗ Quang Khánh – HoChiMinh City University of Technology
Email: or

1

Content & Agenda
Ref:


Recent Advances In Hydraulic Fracturing, John L. Gidley, Stephen A. Holditch, Dale E.
Nierode & Ralph W. Veatch Jr.,1991



Reservoir Stimulation, 3e – Economides & Nolte



Petroleum Production Systems - Economides et al., 1994



Production Operations: Well Completions, Workover, and Stimulation -Thomas O. Allen,
Alan P. Roberts,1984

1


5/9/2014

Introduction
 Objective: to create highly conductive paths some
distance away from the wellbore into the reservoir.
o Execution of a hydraulic fracture involves

the injection of fluids at a pressure sufficiently
high to cause "tensile failure" of the rock.
o At the fracture initiation pressure, often known
as the "breakdown pressure“, the rock opens.
o As additional fluids are injected, the opening

is extended and the fracture propagates.
o A properly executed hydraulic fracture results in a "path," connected to the well,
that has a much higher permeability than the surrounding formation.

Introduction
o Minimum hydraulic fracturing candidate well selection screening criteria

2


5/9/2014

LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT

o Every hydraulic fracture can be characterized by its:
– length ;
– conductivity;
– related equivalent skin effect

o In almost all calculations, the fracture length, which must be the conductive length and not the created
hydraulic length, is assumed to consist of two equal half‐lengths, xf, in each side of the well.
- beside, consider the penetration ratio: Ix = 2 xf / xe.

LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
o The dimensionless fracture conductivity: CfD = kf W / k Xf
= (Ability of fracture to deliver oil/gas to well)/(Ability of formation to deliver gas into the fracture)
> 30 (Infinitely Conductive Fracture)
2 xf
w
o -Related to Prat’s a (called the relative capacity): CfD = л/2a
where:k is the reservoir permeability, k f is the fracture permeability, and w is the propped fracture width.
o Fracture skin effect varying with fracture conductivity
(Cinco-ley and Samaniego, 1981)

3


5/9/2014

LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
o Equivalent skin effect, sf, & Improve Productivity Index J:
o The equivalent skin effect, sf: the result of a hydraulic fracture of a certain length and conductivity
& can be added to the well inflow equations in the usual manner.=> sf is pseudo skin factor
used after the treatment to describe the productivity:

 2kh 
 2kh 
1

 J D
J  
 
 B  ln[ re ]  0.75  s
 B 
f
rw
o Prats (1961): the concept of dimensionless effective wellbore radius r’wD

in a hydraulically fractured well:

LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT

 for small values of a, or high conductivity fractures, the r’wD is equal to 0.5, leading to r’w
= xf /2; which suggests that for these large-conductivity fractures the reservoir drains to a
well with an effective wellbore equal to half of the fracture half-length.
 Since the effective wellbore must be as large as possible, values of ”a” larger than unity m
ust be avoided because the effective wellbore radius decreases rapidly.
=> hydraulic fractures should be designed for a < 1 or CfD > 1.6
 for large values of a, the slope of the curve is equal to 1, implying a linear relationship
between r’w and a that is approximately r’w = kf w/4k; Which suggest that for low
conductivity fractures, the increase in r’w does not depend on fracture length but instead
on fracture permeability-width product,which must be maximized.

4

5/9/2014

LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT

o What length or fracture permeability is desirable in hydraulic fracturing?

 • Low‐permeability reservoirs, leading to high‐conductivity fractures,
would benefit greatly from length.

 • Moderate‐ to high‐permeability reservoirs, naturally leading to
low‐conductivity fractures, require good fracture permeability

(good quality proppant and nondamaging fracturing fluid).

Notation
rw

wellbore radius, m (or ft)

r'w

Prats’ equivalent wellbore radius due to fracture,
m (or ft)

f  s f  ln

xf
rw

Cinco-Ley-Samanieggo factor, dimensionless

sf

the pseudo skin factor due to fracture,
dimensionless

rw
xf

Prats' dimensionless (equivalent) wellbore
radius
But JD is the best

5


5/9/2014

Pseudo-steady state Productivity Index

q  Jp
Production rate is proportional to drawdown, defined as average
pressure in the reservoir minus wellbore flowing pressure

Circular:

 2kh 
 J D p

q  
B




1
JD 
r  3
ln  e    s
 rw  4

Drawdown

Dimensionless
Productivity Index

Pseudo-skin, equivalent radius, f-factor
J

2kh


r
B ln 0.472 e  s f 
rw



J

or

2kh

r 
B ln 0.472 e 
r 'w 


Prats

f (C fD )
J

2πkh
 0.472re 
x 
Bμ ln
  s f  ln f 
xf
rw 





2πkh
 0.472re


Bμ ln
 f
xf


Cinco-Ley

6


5/9/2014

Dimensionless Productivity
Index, sf and f and r’w
JD 

1
ln 0.472

re
 sf
rw

or

1

JD 

ln 0.472

re
r 'w

Prats

f (C fD )

1
1
JD 

0.472re
x 
0.472re 
f
ln
  s f  ln f  ln
x
xf
rw 
f

Cinco-Ley

Factor f

(after Cinco-Ley and Samaniego, 1981)

7

5/9/2014

LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT

oExample:

8


5/9/2014

Proppant placement into formation
 We can use the propping
agent to increase fracture

length or width.

 Tip screenout (TSO)
techniques:


fracture width can be
increased without
increasing the fracture
extent.

How should we select the optimum fracture length
and width under the constraint that the proppant

volume is given?

Fracture half length & CfD,opt

the optimum CfD,opt = 1.6 is a given constant for any reservoir
and any fixed amount of proppant.

9


5/9/2014

Optimum fracture dimensions


Once we know the volume of proppant that can be placed into one wing of the fracture, Vf, we can
calculate the optimum fracture dimensions as



Moreover, since



and yopt - 0.75 = 0.869, we obtain

Fracture Orientation & In situ stress

Least Principal Stress

Horizontal fracture

Least Principal Stress

Vertical fracture

The fracture will be oriented at a 90-degree angle to
the least principal stress.

10


5/9/2014

Fracture Orientation & In situ stress

Role of Formation Properties in Fracturing
The formation properties that are known to influence a fracture’s

growth pattern, including its height, are:
 Young's modulus

 Poisson's ratio
 Tensile strength
 Fracture toughness
 Permeability
 Porosity
 Poroelasticity constant

11

5/9/2014

Rock Properties
Plane Strain Modulus:

Shear modulus:

Rock Properties


Tensile Strength: The maximum stress that a material can tolerate without rupture in a uniaxial tensile experiment is
the tensile stress.



Fracture Toughness: The critical value of the stress intensity factor, or fracture toughness, characterizes a rock’s
resistance to the propagation of an existing fracture.



Permeability: The larger the fluid leakoff, the less driving force is available for fracture growth.



The Poroelastic Constant, , is defined by the relation:

where K is the bulk modulus (ratio of hydrostatic pressure to volumetric strain) of the dry rock material and Ks is the
same measured in a saturated sample.

12


5/9/2014

Other elasticity constants
Required

\

E, 

Known

Shear modulus, G

Young's modulus, E

Poisson ratio, 

Plane strain modulus, E'

E
21  

G, 

G

G

2G 1   

E



E
1  2

E ,G



2G
1 

E

E  2G
2G

4G 2
4G  E

Poroelasticity and Biot’s constant

σ  σ   αp

Total Stress = Effective Stress + a[Pore Pressure]
Grains
Force
Pore Fluid

Biot’s constant

a ~ 0.7

13


5/9/2014

Vertical Profile of Minimum Stress


The effective stress, s’, is the
absolute stress minus the pore

pressure (p) weighted by the
poroelastic constant (a):



minimum effective horizontal stress



total horizontal stress

1) Poisson ratio changes from layer to layer
2) Pore pressure changes in time

0
-500

Ground Surface

Critical Depth
977 m

-1000

0
-500

-1500

-1000

-2000

-1500

-2500

-2000

-3000

0

20x106

40x106
60x106
Stress, Pa

Current Depth , m

Depth from original ground surface, m

Crossover of Minimum Stress

-2500
80x106

14


5/9/2014

Stress Gradients
Overburden gradient gradient
Slope of the Vertical Stress line

 1.1 psi/ft

Frac gradient

 Basically the slope of the minimum
horizontal stress line

0.4 - 0.9 psi/ft

 Extreme value: 1.1 psi/ft or more

STRESS

oExample:

15


5/9/2014

Fracturing Pressure


Fracture Initiation Pressure or breakdown pressure is the peak value of the pressure appearing

when the formation breaks down and a fracture starts to evolve. Usually it is approximated by

where smin is the minimum horizontal stress, smax is the maximum horizontal stress, T is the tensile
stress of the rock material, a is the poroelasticity constant and po is the pore pressure.


Fracture Propagation Pressure is the stabilized value of the injection pressure for a longer period of
time during which the fracture is evolving.

Detection of formation
breakdown from a steprate test

16


5/9/2014

Fracturing Pressure (MiniFrac)


Fracture Closure Pressure. After a fracture calibration treatment, which is carried out without injecting
proppant material, the fracture volume gradually decreases because of leakoff (and also because of
possible back flow, if the injected fluid is flowed back through the well).

(1) breakdown pressure;
(2) fracture propagation pressure;
(3) instantaneous shut-in pressure;
(4) closure pressure;
(5) fracture reopening pressure;
(6) closure pressure from flow-back;
(7) asymptotic reservoir pressure;
(8) rebound pressure

Leakoff
 Fluid leakoff is controlled by a continuous build-up of a thin layer, or filter cake, which

manifests an ever-increasing resistance to flow through the fracture face.
 The leakoff velocity, VL , is given by the Carter equation:

uL 

CL
t

Where CL is the leakoff coefficient (length/time0.5) and t is the time elapsed since the
start of the leakoff process. The ideas behind Carter's leakoff coefficient are that:
o

if a filter-cake wall is building up, it will allow less fluid to pass through a unit area in unit time;
and,

o

the reservoir itself can take less and less fluid if it has been exposed to inflow.

17


5/9/2014

AL

uL 

CL
t

VLost
= S p  2CL t

AL
units :

m  mm

Lost volume per unit surface, m

Fluid Loss in Lab
0.007
0.006
0.005
0.004
0.003
y = 0.0024 + 0.000069x

0.002

Sp

0.001
0

0

CL
Sp

10

2CL

20
30
40
50
60
Square root time, t1/2 (s1/2)

m
s
unit : m

unit :

or

m3
m2 s

Description of leakoff through flow in porous
media and/or filtercake build-up

 Concept of leakoff coefficient

uL 

m m / s1 / 2
 1/ 2
s
s

Where are those “twos” coming from?

 Integrated leakoff volume:

CL
t

VL  2 AC L t

 Leakoff Width

wL 
What is the physical meaning?

VL
 2CL t
AL

m mm

18


5/9/2014

Definition of injection rate, fracture area
and permeable height

Width Equations

Perkins-Kern-Nordgren (PKN)

Kristianovich-Zheltov-Geertsma-DeKlerk (KGD)

19


5/9/2014

Comparison of PKN and KGD width equations


The crossover occurs approximately at
the point at which a "square fracture"

has been created, i.e., when



For the small fracture extent, the
physical assumptions behind the KGD
equation are more realistic.



For the larger fracture extent, the PKN
width equation is physically more
sound.

Radial (Penny-shaped) Width Equation

20


5/9/2014

No-leakoff Behavior of Width Equations
Perkins-Kern-Nordgren model

Geertsma and deKlerk model

Types of Fluids




Water-Base Fluids


natural guar gum (Guar)



hydroxypropyl guar (HPG)



hydroxyethyl cellulose (HEC)



carboxymethyl hydroxyethyl cellulose (CMHEC)

Oil-Base Fluids




Acid-Base Fluids




Used in limestones or dolomitic formations.

Emulsions




Lease oil and gelled oils.

Mixtures of oil and an aqueous material (either water or acid).

Gas/Foam Fluids


Specialized emulsions using nitrogen or carbon dioxide gas as the inner phase of an aqueous mixture.

21

5/9/2014

Fracturing Additives
Bacteria control agents

Gypsum inhibitors

Breakers

N2and CO2 gases

Clay-stabilizing agents

Scale inhibitors

Demulsifying agents

Sequestering agents

Dispersing agents

Sludge inhibitors

Fluid loss additives

Surfactants

Foaming agents

Temperature-stabilizing agents

Friction loss reducers

Water blockage-control agents

Proppant Pack Permeability & Fracture Conductivity
 Proppant duties:
 Be capable of holding the fracture faces apart

 must be long lasting.

 be readily available, safe to handle, and relatively inexpensive.

22


5/9/2014

Types of Proppants
Two major categories:
 Naturally occurring sand
 White Sand ("Ottawa" sand)

 Manufactured proppants
 Sintered Bauxite
 Intermediate Strength Proppants
 Resin Coated Proppants

A typical proppant selection guide

23


5/9/2014

Design Logics
 Height is known (see height map)
 Amount of proppant to place is given (from NPV)

 Target length is given (see opt frac dimensions)
 Fluid leakoff characteristics is known

 Rock properties are known
 Fluid rheology is known
 Injection rate, max proppant concentratrion is given
 How much fluid? How long to pump? How to add proppant?

Key concept: Width Equation
 Fluid flow creates friction
 Friction pressure is balanced by injection pressure

 Net pressure is positive
 Fracture width is determined by net pressure and

characteristic dimension (half length or half height)
 The combination of fluid mechanics and solid mechanics

24

5/9/2014

Two approximations:
 Perkins-Kern-(Nordgren)
 Vertical plane strain
 characteristic half-length ( c ) is half height, h/2
 elliptic cross section

 Kristianovich-Zheltov - (Gertsmaa-deKlerk)
 Horizontal plane strain
 characteristic half length ( c ) is xf

 rectangular cross section

Width Equations (consistent units)
Perkins-Kern-Nordgren PKN

 width: w, wo, wwell,o
 viscosity: 
 inj. rate (1 wing): qi

 half-length: xf
 plain-strain modulus: E'
 height: hf

Vf = w(h f x f )

 qi x f

ww,0 = 3.27
 E'

1/ 4





w  0.628ww,0

Kristianovich-Zheltov
Geertsma-De-Klerk KGD

 qi x 2f
ww = 3.22
 E' h
f

w  0.785ww

1/ 4






25