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