C8 hydraulic fracturing

 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.

Đỗ Quang Khánh – HoChiMinh City University of Technology

Email: dqkhanh@hcmut.edu.vn or doquangkhanh@yahoo.com

Designed & Presented by

Mr ĐỖ QUANG KHÁNH, HCMUT

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

Introduction

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

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)

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)

2 xf

w

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:

o Prats (1961): the concept of dimensionless effective wellbore radius r’wD

in a hydraulically fractured well:

D f

w e

J B

kh s

r

r B

1 2

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

= x f /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 C fD > 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 = k f 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

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)

Cinco-Ley-Samanieggo factor, dimensionless

sf the pseudo skin factor due to fracture,

dimensionless Prats' dimensionless (equivalent) wellbore radius

r

x s

f   ln

But JD is the best

Pseudo-steady state Productivity Index

p J

p J B

r J

w e

1

Circular:

Production rate is proportional to drawdown, defined as average

pressure in the reservoir minus wellbore flowing pressure

Dimensionless Productivity Index Drawdown

Pseudo-skin, equivalent radius, f-factor

) ( CfDf

kh J

' 472 0 ln

r

r B

kh J

472

r Bμ

πkh r

x s x

r Bμ

πkh J

f e w

f f f

ln

2 ln

472 0 ln

2

Dimensionless Productivity

Index, s f and f and r’ w

f x

r r

x s

x

r J

f e

w

f f

1 ln

s r r

w e D

r r J

' 472 0 ln

LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT

Proppant placement into formation

 We can use the propping

agent to increase fracture

the optimum CfD,opt = 1.6 is a given constant for any reservoir

and any fixed amount of proppant

Optimum fracture dimensions

 Once we know the volume of proppant that can be placed into one wing of the fracture, V f, we can

calculate the optimum fracture dimensions as

 Moreover, since

 and yopt - 0.75 = 0.869, we obtain

Fracture Orientation & In situ stress

Horizontal fracture Vertical fracture

Least Principal Stress Least Principal Stress

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

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:

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

Other elasticity constants

E 4G

4G 2



Poroelasticity and Biot’s constant

Force Pore Fluid Grains

a ~ 0.7 Biot’s constant

Total Stress = Effective Stress + σ  σ   αpa[Pore Pressure]

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

Crossover of Minimum Stress

Frac gradient

horizontal stress line 0.4 - 0.9 psi/ft

Overburden gradient gradient

Slope of the Vertical Stress line  1.1 psi/ft

Stress Gradients

STRESS

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 step- rate test

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:

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;

Fluid Loss in Lab

=

A

V

L p

L

Lost 

mm

s m

m

or s

m : unit C

p

2 3 L

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

Description of leakoff through flow in porous

media and/or filtercake build-up

VL  2 L

t C A

2 / 1/

s

s m s

m



m m

m   Where are those “twos” coming from?

What is the physical meaning?

Definition of injection rate, fracture area

and permeable height

Width Equations

Perkins-Kern-Nordgren (PKN) Kristianovich-Zheltov-Geertsma-DeKlerk (KGD)

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

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)

Water blockage-control agents

Proppant Pack Permeability & Fracture Conductivity

 Be capable of holding the fracture faces apart

 must be long lasting

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

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

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

characteristic dimension (half length or half height)

Two approximations:

 Vertical plane strain

 characteristic half-length ( c ) is half height, h/2

 elliptic cross section

 Horizontal plane strain

 characteristic half length ( c ) is xf

 rectangular cross section

Width Equations (consistent units)

Perkins-Kern-Nordgren PKN

4 / 1

0 ,

' 27

3    q E x   

=

ww  i f

0 ,

628

0 ww

w 

Kristianovich-Zheltov Geertsma-De-Klerk KGD

4 / 1 2

' 22

h E

x q

=

Vf f f

PKN Power-Law Width Equation

maximum width at the wellbore is:

2 2 1 1

2 2 1 2 2 2

2 2

2 1 0

,

'

14 2 1 98 3 15 9

n n

w

E

x h q K n

n

=

w

0 ,

w

w

Power Law fluid K: Consistency (lbf/ft2)·sn

n: Flow behavior index

Material balance +Width Equation

q i 2q i

A

V i = q i t e

xf

Average w(xf)

hf

) x (h w

=

Vf f f

A w

Pumping time, fluid volume, proppant schedule:

Design of frac treatments

 Pumping time and fluid volume:

• Injected = contained in frac + lost

• length 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

Pumping time, slurry volume (1 wing)

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 k = 1 5 and solve the mat balance for inj time, (selecting sqrt time as the new unknown)

4 Calculate injected volume

5 Calculate fluid efficiency

2 2 1 1 2 2 1 2 2 2

2 2 2 1 0 ,

'14

.2198.315.9

n n

w

E x h q K n

n

= w

0 ,

628

κ C

t x h

q

p e L f

f i

e i

i q t

V 

i

e f f i

fe e

V

w x h V

V



Proppant schedule calculation

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”

i pad V

V 

e pad t

i e e

V

M c

pad e

t t t t c c

propp added c

c c

hf