Introductory Course in Hydraulic Fracturing

1. James A. Craig

2.  Introduction
 Job Procedures
 Hydraulic Fracturing Materials
 In-situ Stresses
 Fracture Initiation
 Fracture Geometry
 PKN Model
 KGD Model
 Conductivity & Equivalent Skin Factor

3.  Hydraulic fracturing occurs when the well pressure
gets high enough to split the surrounding formation
apart.
 Unintentional fracturing leads to:
 Lost circulation
 Hydrostatic pressure loss in the well
 Blowout
 Intentional fracturing (well stimulation):
 Pumping fluid and solids (proppants)
 To increase permeability of the reservoir.

5.  Heavy equipment involved in hydraulic fracturing jobs
include:
 Truck-mounted pumps
 Blenders
 Fluid tanks
 Proppant tanks

7.  A hydraulic fracturing job is divided into 2 stages:
 Pad stage
 Slurry stage

8. Fracturing fluid only is injected to break down the
formation & create a pad.
Pad Stage

9. 1/2"
Open fracture
during job
Fracture tends to close
once the pressure has
been released
Fracture
width

10. Fracturing fluid is mixed with sand/proppant in
a blender & the mixture is injected into the fracture.
Slurry Stage

11. Propped Fracture Acid Fracture
Proppant/sand is
used to keep the frac
open
Acid etched in
the walls keep
the frac open

12. After filling the fracture with proppant, the
fracturing job is over & the pump is shut down.

13.  Base fluid systems
 Chemical additives
 Proppants

14. Slickwater Applications
 Low Friction
 Low Viscosity (<5cp)
 Low Residue, less
damaging
 Low Proppant Transport
capabilities
Linear Gel Applications
 Mild Friction Pressures
 Adjustable Viscosity
(10<x<60cp)
 High Residue, more
damaging

15. Crosslinked Applications
 High Friction
 High Viscosity (>100cp)
 Excellent Proppant
Transport capabilities
 High Residue, more
damaging
 Expensive
 Complex Chemical
Systems
 pH & Temperature
dependent
Energized Fluid
Applications
 Carbon Dioxide
 Nitrogen
 Water Sensitive
Formations
 Depleted Under
pressured wells
 Low Permeable Gas
Formations
 High Proppant
Transport capabilities
 Gelled Oil Fluids
 Acidizing Services

16.  Gelling Agents
 Friction Reducers
 Crosslinker Control
 pH Adjusting Agents
 Clay Control
 Breakers
 Scale Inhibitors
 Corrosion Inhibitors
 Bactericide
 Oxygen Scavengers
 Surfactants
 Recovery Agents
 Foaming Agents
 Acids
 Anti-Sludge Agents
 Emulsifiers
 Fluid Loss Agents
 Resin Activator

17. Frac Sand (<6,000 psi)
 Jordan
 Ottawa
 Brady
Resin-Coated Frac Sand
(<8,000 psi)
 Santrol
 Cureable
 Borden
 Precured
17
Intermediate Strentgh
Ceramics (<10,000 psi)
 Carbo Ceramics
 Norton-Alcoa
High Strength Ceramics
(<15,000 psi)
 Carbo Ceramics
 Sintex

18. Strength
comparison of
various types of
proppants

19. Ceramic Proppants Ultra Light-Weight
Proppants

20.  There are always 3 mutually orthogonal principal
stresses. Rock stresses within the earth also follow this
basic rule.
 The 3 stresses within the earth are:
 Vertical stress
 Pore pressure
 Horizontal stresses
 These stresses are normally compressive, anisotropy,
and non-homogeneous.

21.  The magnitude and direction of the principal stresses
are important because:
 They control the pressure required to create & propagate
a fracture.
 The shape & vertical extent of the fracture
 The direction of the fracture..
 The stresses trying to crush and/or embed the propping
agent during production.

22.  At some depth gravity has a main control on the stress
state.
 Vertical stress is a principal stress
 Vertical stress is given by the weight of overburden.
 
D
 v   z gdz
0
v    gD

23.  ρ = density of the material
 g = acceleration due to gravity
 D = depth in z-axis pointing vertically downward.
 Average overburden density ≈ 15 – 19.2 ppg.
 Note:
  f  z
 It increases slightly with depth (≈ 1 psi/ft).
 Upper sediments have high porosity, hence low density
 At greater depth, density is high because porosity is
reduced by compaction and diagenesis.
 σv or σ1 represents vertical stress.

24.  Pore pressure is derived from the pore fluid trapped in
the void spaces of rocks.
 The pore fluid carries part of the total stresses applied
to the system, while the matrix carries the rest.
 Pore pressure can be normal or abnormal.
f ,n f P   gD
 ρf = density of the fluid
 Average pore fluid density for brine ≈ 8.76 ppg.
 Normal pore pressure ranges from ≈ 0.447 – 0.465 psi/ft.
 It averages 0.0105 MPa/m.

25. Gullfaks field in
Statfjord
Valhall field in
Ekofisk

26.  They are to some extent also caused by gravity.
 In the ocean, horizontal stress equals vertical stress
 Ocean consists of only fluid and no shear stress (no
rigidity).
 In a formation (with a certain rigidity), horizontal
stress is different from vertical stress.
 σH or σ2 represents maximum horizontal stress.
 σh or σ3 represents minimum horizontal stress.
 σtect represents tectonic stress.
 H  h  tect

27. σv >σH > σh
σH or σ2
σh or σ3
σv or σ1

28.  Hooke’s law

  
 
h 1 

V
h h f     P
v v f     P
 Should be used with extreme caution! Or not used at
all!!!
 v = Poisson ratio
 α = Biot’s poroelastic constant
 Pf = Pore pressure

29.  Breckels and van Eekelen (1982)
 D < 3,500 m:
 D > 3,500 m:
  1.145
 h  0.0053D  0.46 Pf  Pf ,n
  , 0.0264 31.7 0.46 h f f n   D  P  P
 Derived from fracture (leak-off test) data in GoM (Gulf
of Mexico) region.
 Often used in tectonically relaxed areas like the North
Sea.
 Abnormal pore pressure taken into account.

30.  In general, σH > σh because of plate tectonics and
structural heterogeneities.
 Plate tectonics include:
 Spreading ridge
 Subduction zone
 Transform fault

31. Vertical stress (ρ = 2.1 g/cm3)
Horizontal stress
(from Breckels and
van Eekelen)
Pore pressure (ρf =
1.05 g/cm3)

32.  Fractures develop in the direction perpendicular to the
least principal stress.
 This is the direction of least resistance.
 Smallest principal stress is horizontal stress.
 Therefore, resulting fractures will be vertical.

33. Vertical well
Vertical
fracture

35.  Conditions:
 A vertical borehole
 Poroelastic theory
 Hooke’s law of linear elasticity is obey

36.  Also called Fast Pressurization limit.
 Formation is assumed to be impermeable.
 Pore pressure is constant and unaffected by the well
pressure.
 Initiation/Breakdown Pressure(assume α = 1) :
Pw, frac  3 h  H  Pf To
 To = tensile strength of the rock

37.  Also called Slow Pressurization (to ensure steady state
during pumping) limit.
 Formation is assumed to be permeable.
 Pore pressure near the borehole and the well pressure
are equal.
 Initiation/Breakdown Pressure(assume α = 1) :
 
,
3
h H
2
w frac P
 


38.  Fracture geometry include width, length and height of
the fracture.
 The information is necessary in stimulation design in
order to know what volume of fluid to pump.
 The 2 classical models are:
 PKN Model – Perkins-Kern-Nordgren
 KGD Model – Kristianovitch-Geertsma-de Klerk
 Newtonian fluid only is considered.
 2-D only is considered.

39.  Fracture height is constant and independent of the
fracture length.
 Appropriate when xf/hf > 1.
 Commonly used in conventional hydraulic fracture
modeling.

41.  Maximum width of the fracture, wm is:
1
4 1
   
  
 The rectangular shape of a cross section further from the
well has a smaller width, decreasing to zero at the
fracture length L, so assuming an elliptical shape, the
average width is:
 Volume of fracture:
 
0.3 f
m
Q x
w
G
 
0.59 m m w  w
2 f f f m V   x  h w

42.  wm = maximum width of the fracture, in.
 Q = pumping rate, barrels/min
 μ = fluid viscosity, cp
 L = fracture half length, ft
 ν = Poisson’s ratio (dimensionless)
 G = Shear modulus, psi
E
21 
G



 E = Young’s modulus, psi
 Vm = volume of fracture, ft3

43.  Fracture height is constant and independent of the
fracture length.
 Appropriate when xf/hf < 1.
 Commonly used in open hole stress tests.
 Not interesting from a production point of view.

45.  Maximum width of the fracture, wm is:
 Q   x

  
 The rectangular shape of a cross section further from the
well has a smaller width, decreasing to zero at the
fracture length L, so assuming an elliptical shape, the
average width is:
 Volume of fracture:
 
1
2 4 1
0.29 f
m
f
w
Gh
 
0.79 m m w  w
2 f m V   LH w

46.  Hydraulic fracturing does not change the permeability
of the given formation.
 It creates a permeable channel for reservoir fluids to
contact the wellbore.
 The primary purpose of hydraulic fracturing is to
increase the effective wellbore area by creating a
fracture of given geometry, whose conductivity is
greater than the formation.

47.  Productivity of fractured wells depends on 2 steps:
 Receiving fluids from formation.
 Transporting the received fluid to the wellbore.
 The efficiency of the first step depends on fracture
dimension (length & height)
 The efficiency of the second step depends on fracture
permeability.
 Fracture conductivity is given as:
 FCD of 10 – 30 is considered optimal.
k w
f f
CD
e f
F
k x


48. ke
kf
Damage
xf
wf
 kf = Fracture permeability
 ke = Formation permeability
 xf = Fracture half-length
 wf = Fracture width
 In hydraulic fracturing,
damage is not an issue.

50.  Sf = equivalent skin factor
 The Cinco-Ley chart is converted into a correlation as
follows:
 Where
2
x u u
  1.65  0.328 
0.116
2 3
 ln
  
1 0.18 0.064 0.05
f
f
w
S
r u u u
    
ln  CD u  F

51.  The inflow equation is given as:
 
kh P 
P
e wf
   
    
   
B S
141.2 ln
r
e

o o f
r
w
q

 The fold of increase is given as:
ln
 r

 
 
J r
J r
f w
ln
e
 
e
  
 
f
r
w
S

 Jf = PI of fractured well, STB/D/psi
 J = PI of non-fractured well, STB/D/psi