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BASIC HYDRAULIC
FRACTURING
James A. Craig
IntroductionJob ProceduresHydraulic Fracturing Materials In-situ StressesFracture InitiationFracture Geometry
PKN ModelKGD Model
Conductivity & Equivalent Skin Factor
Hydraulic fracturing occurs when the well pressure gets high enough to split the surrounding formation apart.
Unintentional fracturing leads to:Lost circulationHydrostatic pressure loss in the wellBlowout
Intentional fracturing (well stimulation):Pumping fluid and solids (proppants)To increase permeability of the reservoir.
INTRODUCTION
Heavy equipment involved in hydraulic fracturing jobs include:
Truck-mounted pumpsBlendersFluid tanksProppant tanks
A hydraulic fracturing job is divided into 2 stages:
Pad stageSlurry stage
OPERATION PROCEDURES
Fracturing fluid only is injected to break down the
formation & create a pad.Pad Stage
1 /2 "
Open fracture during job
Fracture tends to closeonce the pressure has been released
Fracture width
Fracturing fluid is mixed with sand/proppant in a blender & the mixture is injected into the
fracture. Slurry Stage
Proppant/sand is used to keep the frac open
Acid etched in the walls keep the frac open
Propped Fracture
Acid Fracture
1 /2 "
After filling the fracture with proppant, the fracturing job is over & the pump is shut down.
Base fluid systems
Chemical additives
Proppants
HYDRAULIC FRACTURING MATERIALS
Base Fluid SystemsSlickwater
ApplicationsLow FrictionLow Viscosity
(<5cp)Low Residue, less
damagingLow Proppant
Transport capabilities
Linear Gel ApplicationsMild Friction
PressuresAdjustable Viscosity
(10<x<60cp)High Residue, more
damaging
Crosslinked ApplicationsHigh FrictionHigh Viscosity
(>100cp)Excellent Proppant
Transport capabilities
High Residue, more damaging
Expensive Complex Chemical
SystemspH & Temperature
dependent
Energized FluidApplications
Carbon DioxideNitrogenWater Sensitive
FormationsDepleted Under
pressured wellsLow Permeable Gas
FormationsHigh Proppant
Transport capabilities
Gelled Oil Fluids
Acidizing Services
Chemical AdditivesGelling AgentsFriction ReducersCrosslinker ControlpH Adjusting AgentsClay Control BreakersScale InhibitorsCorrosion InhibitorsBactericide
Oxygen ScavengersSurfactantsRecovery AgentsFoaming AgentsAcidsAnti-Sludge AgentsEmulsifiersFluid Loss AgentsResin Activator
17
Frac Sand (<6,000 psi)Jordan OttawaBrady
Resin-Coated Frac Sand
(<8,000 psi)Santrol
CureableBorden
Precured
ProppantsIntermediate Strentgh Ceramics (<10,000
psi)Carbo CeramicsNorton-Alcoa
High Strength Ceramics
(<15,000 psi)Carbo CeramicsSintex
Strength comparison of various types of proppants
Ceramic Proppants Ultra Light-Weight Proppants
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 stressPore pressureHorizontal stresses
These stresses are normally compressive, anisotropy, and non-homogeneous.
IN-SITU STRESSES
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 fractureThe direction of the fracture..The stresses trying to crush and/or embed the
propping agent during production.
At some depth gravity has a main control on the stress state.
Vertical stress is a principal stressVertical stress is given by the weight of
overburden.
Vertical Stress
0
D
v z gdz
v gD
ρ = density of the materialg = acceleration due to gravityD = depth in z-axis pointing vertically
downward.
Average overburden density ≈ 15 – 19.2 ppg.
Note:It increases slightly with depth (≈ 1 psi/ft).Upper sediments have high porosity, hence low
densityAt greater depth, density is high because
porosity is reduced by compaction and diagenesis.
σv or σ1 represents vertical stress.
f z
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.
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.
Pore Pressure
,f n fP gD
Gullfaks field in Statfjord
Valhall field in Ekofisk
They are to some extent also caused by gravity.
In the ocean, horizontal stress equals vertical stressOcean 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.
Horizontal Stresses
H h tect
σv >σH > σh
σH or σ2
σh or σ3
σv or σ1
Models
Hooke’s law
Should be used with extreme caution! Or not used at all!!!
v = Poisson ratio α = Biot’s poroelastic constantPf = Pore pressure
1h V
h h fP v v fP
Breckels and van Eekelen (1982)
D < 3,500 m:
D > 3,500 m:
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.
1.145,0.0053 0.46h f f nD P P
,0.0264 31.7 0.46h f f nD P P
Effects of Plate TectonicsIn general, σH > σh because of plate tectonics
and structural heterogeneities.Plate tectonics include:
Spreading ridgeSubduction zoneTransform fault
Vertical stress (ρ = 2.1 g/cm3)
Horizontal stress (from Breckels
and van Eekelen)
Pore pressure (ρf = 1.05 g/cm3)
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.
Vertical well
Vertical fracture
Conditions:A vertical boreholePoroelastic theory Hooke’s law of linear elasticity is obey
FRACTURE INITIATION
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)
:
To = tensile strength of the rock
Upper Limit
, 3w frac h H f oP P T
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)
:
Lower Limit
,
3
2h H
w fracP
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-NordgrenKGD Model – Kristianovitch-Geertsma-de Klerk
Newtonian fluid only is considered.2-D only is considered.
FRACTURE GEOMETRY
Fracture height is constant and independent of the fracture length.
Appropriate when xf/hf > 1.Commonly used in conventional hydraulic
fracture modeling.
PKN Model
Maximum width of the fracture, wm is:
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:
141
0.3 fm
Q xw
G
0.59m mw w
2f f f mV x h w
wm = maximum width of the fracture, in.Q = pumping rate, barrels/minμ = fluid viscosity, cpL = fracture half length, ftν = Poisson’s ratio (dimensionless)G = Shear modulus, psi
E = Young’s modulus, psiVm = volume of fracture, ft3
2 1
EG
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.
KGD Model
Maximum width of the fracture, wm is:
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
2 410.29 f
mf
Q xw
Gh
0.79m mw w
2f mV L H w
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.
CONDUCTIVITY AND EQUIVALENT SKIN
FACTOR
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.
f fCD
e f
k wF
k x
ke
kf
xf
Damage
wf
kf = Fracture permeability
ke = Formation permeability
xf = Fracture half-length
wf = Fracture width
In hydraulic fracturing, damage is not an issue.
Cinco-Ley & Samaniego Chart
Sf = equivalent skin factor
The Cinco-Ley chart is converted into a correlation as follows:
Where
2
2 3
1.65 0.328 0.116ln
1 0.18 0.064 0.05f
fw
x u uS
r u u u
ln CDu F
The inflow equation is given as:
The fold of increase is given as:
Jf = PI of fractured well, STB/D/psiJ = PI of non-fractured well, STB/D/psi
141.2 ln
e wf
eo o f
w
kh P Pq
rB S
r
ln
ln
e
f w
ef
w
rJ r
J rS
r