Well Stimulation
Dr. Le Nguyen Hai Nam
Drilling & Production Engineering Lab
Department of Drilling & Production Engineering
Objective of Stimulation
• Maximize of:
• Increase hydrocarbon production rate
• Increase the reservoir economic life
• Increase reserves recovery
• Reduce, or overcome near wellbore damage
• Stimulation for reservoir management
• Economically efficient drainage of reservoir
• Economically efficient drainage of laminated formations
• Delaying the onset of water production
• Sand control
Well stimulation work process
Step 1: Candidate Selection: Skin
analyses
Step 2: Treatment Selection:
• Tubing Clean-out
• Wellbore Clean-out
• Scale Removal
• Sandstone Acidizing
• Carbonate Acidizing
• Hydraulic Fracturing
Step 3: Fluid Selection:
• Sandstone
• Carbonate
Step 4: Pumping Schedule:
• Pre-flush
• Main flush
• Post flush
• Diversion
Step 5: Pre-treatment Evaluation
Step 6: Job Execution
Step 0: Existing data & experience
Candidate Selection
requirements for successful matrix treaments
• Hydrocarbon saturation
30% or more
Highly depleted wells are
poor acidizing candidates
(from economic of view)
• Water cut
50% or less
Acid will preferentially
stimulate the water zone
• Gross reservoir height
No limit
• Permeability
Gas > 1mD, Oil >10 mD
Low permeability reservoirs need a frac, not acid
• Damage skin
S>2, damage soluble in acid and/or solvent
• Reservoir pressure
Gas: two times the abandonment pressure
Oil: 80% depletion
• Production system & tubing
Current production not more than 80% of maximum
capacity of facilities
Must be able to handle increased production
Fundamental of Hydraulic
Fracturing
Introduction
▪ The objective of hydraulic fracturing is to improve
permeability of the near-wellbore region
▪ Fractures are created by injecting high pressure
fluid from the surface into the wellbore
▪ Solid particles called proppants are injected into the
fractures to keep them open
▪ Hydraulic
fracturing
is
required
for
tight
unconventional reservoirs such as shale gas.
or
Objective: Change in Flow Regime
Pre-Frac
Radial Flow
Post-Frac
Bi-linear
Objective: Bypass Damage
Reservoir Pressure
Bottomhole Flowing
Pressure
8
Objective: Improve Area of Contact
9
Basic Rock Mechanics
The cylindrical rock body shrinks in the axial direction, but
expand s in the radial direction.
Strain in the axial direction is expressed as:
Strain in the radial direction is expressed as:
The Poisson’s ratio is defined as the strain in the unloaded
direction divided by the strain in the loaded direction:
Rock deformation under uniaxial loading (compressional force)
Rock Type
Poisson’s Ratio
Sandstone (Gas)
0.10-0.25
Sandstone
(Liquid)
0.25-0.30
Limestone
0.3-0.35
Shale
0.28-0.43
Young’s Modulus (E)
Young’s modulus (modulus of elasticity)
How much energy it takes to deform rock
𝜎
𝐸=
𝜀
Elastic
Regime
Plastic
Regime
Basic Rock Mechanics
• Two types of deformation for solid materials: elastic and plastic
deformation.
• In elastic deformation, all strain recovers when the applied stress is
removed.
• There exists a linear and unique e relationship between stress and
strain, which is commonly known as Hooke’s Law:
• The linear coefficient E in Hooke’s Law is Young’s modulus of the
material.
Young’s Modulus (E)
Hard Rock
Characteristics
Challenge
Frac Geometry
: tend to transmit stress
: high pump pressure
: long, narrow
Soft Rock
Strain Characteristics
Challenge
Frac Geometry
: tend to deform
: proppant embedment
: short, wide
Stress
High E ( > 3 x 106 psi)
Hard Rock
High E ( < 3 x 106 psi)
Soft Rock
Basic Rock Mechanics
• A shear stress is defined as the component of stress arising from the
force vector component parallel to the cross-section of the material.
• Shear strain is defined as the length of deformation divided by the
perpendicular length in the plane of the force applied.
• The proportionality coefficient between the shear stress and shear
strain is defined as shear modulus.
• In fracture mechanics and fracture modeling, there is another
modulus appearing often in equations, which is named the
plane strain modulus.
• Rock exhibits tensile and compressive strengths.
• The strength of a rock sample obtained with uniaxial stress
testing is called the uniaxial compressive strength (UCS).
• The tensile strengths of rocks are generally much lower than
their compressive strengths.
Fracture Modes and Fracture Tougness
Principal Stresses
Hooke’s Law
Overburden, Horizontal and Effective
Stresses
• The overburden stress is caused by the weight of all the rocks
above the point of interest and is always in the vertical direction.
• For a reservoir rock at depth H with variable density ρ, the
overburden stress σv is calculated as
σv is in psi, ρ is in lb/ft3, and H is in ft.
• In geological formations, the overburden stress is often the
maximum principal stress.
• The other two principal stresses in the horizontal directions,
often denoted as σh,max and σh,min.
• In order to derive a relationship between the horizontal and
overburden stresses, elastic deformation in a homogenous and
isotropic reservoir without tectonic influences from the outside is
assumed.
• To take the fluid pressure into
consideration, the effective
stress σ’ is calculated as:
where α is Biot’s poroelastic constant from 0
to 1.
• The poroelastic constant
describes how effectively the
fluid pressure counteracts the
total applied stress.
Faults and Tectonic Stresses
Minimum Horizontal Stress
Principal Stress
• 𝜎𝑚𝑎𝑥 ≥ 𝜎𝑖𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 ≥ 𝜎𝑚𝑖𝑛
• Hydraulic fracture will initiate and propagate with the least
energy.
• Hydraulic fracture propagates perpendicular to the direction of
the minimum principal stress
18/04/2023
Dr. Mai Cao Lan, Dept. of Drilling & Production Engineering, GEOPET, HCMUT
23
Principal Stress
sv
Overburden Stress
Maximum Horizontal Stress
sH
sh
Minimum Horizontal Stress
Fracture opens up
perpendicular to minimum
stress
Or in the direction of the
maximum stress
Fracture Direction
Overburden Stress (Least Principle Stress)
Minimum Horizontal Stress
Maximum Horizontal Stress
(Maximum Principle Stress)
Fracture will propagate on the direction of the smax and perpendicular to smin
Principle of least resistance
Least
Principal
Stress
Horizontal fracture
Least Principal Stress
Vertical fracture
Effect of Wellbore Direction on Hydraulic
Fracture Propagation
Hydraulic Fracture Geometry Overview
Type A represents an ideal fracture
developed in a homogenous
reservoir. In high-permeability
reservoirs with high porosity and
very low Young’s modulus, smaller
fractures are usually required to
bypass near wellbore damage or
to mitigate sand production.
Hydraulic Fracture Geometry Overview
Type B represents the scenario that
a single hydraulic fracture is
developed with natural fractures
activated in a direction perpendicular
to the hydraulic fracture.
Hydraulic Fracture Geometry Overview
Type C represents the scenario that
the orientations of hydraulic and
natural fractures are about the same
so that multiple hydraulic fractures
may propagate along the orientation
of the preexisting natural fractures.
Hydraulic Fracture Geometry Overview
Type D represents the scenario
that a complex fracture network is
developed in reservoirs having two
orthogonal sets of natural fractures
Coupled fluid-driven fracture problem
sh
y
x
x
y
q(x)
sh
hf
xf
pf
xf
Hydraulic Fracture Models
• The process of hydraulic fracturing involves fracture initiation
and propagation, rock deformation, fluid flow in the fracture,
fluid loss into the formation, and proppant transport, etc.
• Hydraulic fracture models are:
• (1) predicting the fracture geometry and proppant placement achieved
by a specified treatment design;
• (2) conducting sensitivity analysis of the effects of rock/reservoir
properties and treatment design parameters such as fluid type,
treatment size, and pumping rate, etc.;
• (3) performing treatment optimization with costs, production
performance and economics taking into considerations.
• Hydraulic fracture models can be generally classified into three
categories:
• 2D fracture models,
• 3D fracture models, and unconventional fracture models.
• Net pres sure, which is defined as the pressure inside the
fracture minus the rock closure stress (i.e., the minimum stress
against which the fracture opens) :
where pnet, is the net pressure, pf is the fluid pressure inside the
fracture, and σmin is the minimum stress.
2-D Fracture Models
• There are three types of 2D fracture models, namely, the radial,
Perkins-Kern-Nordgren (PKN) and Klerk fracture model (KGD)
models.
• Both the KGD and PKN models assume a fixed fracture height
and predict the fracture width and length. General assumptions
of these 2D fracture models include:
• (1) the formation is homogeneous and isotropic;
• (2) the deformation of the formation during fracture propagation is
based on the linear elastic stress-strain relations;
• (3) fluid flow in the fracture is laminar;
• (4) gravity effects are neglected
Radial Models
The fracture width at the wellbore can be approximated
by:
where ww is fracture width in in. at the wellbore, μ is fluid
viscosity in cP, qi is pumping rate in bbl/min, and R is
fracture radius in ft, and E is Young’s modulus in psi
PKN model
• Fixed fracture height
• Eliptical cross section
• Eliptical shape
• Xf ≥ 3hf
The maximum fracture width at the wellbore (x = 0) in oilfield units is as follows:
where ww is the maximum fracture width at the wellbore in in.,
μ is in cP, qi in bbl/min, L is in ft, ν is Poisson’s ratio, and E is in psi
The average width in the entire fracture is given by
The storage-dominated approximation without
leakoff effects
The high-leakoff approximations
where xf is the fracture half-length in ft,
where xf is the fracture half-length in ft, qi is in bbl/min,
ww is the maximum fracture width at the wellbore in in. Ct is in ft/min1/2, hf is the fracture height in ft,
E is in psi, qi in bbl/min, μ is in cP,
t is the pumping time in min,
t is the pumping time in min
ww is the maximum fracture width at the wellbore in in.,
μ is in cP, and E is in psi
Consider an oil reservoir with the following properties: Poisson’s ratio of 0.2, Young’s
modulus of 3.0x106 psi, pay zone depth of 5000 ft, pore pressure gradient of 0.45 psi/ft,
minimum stress gradient of 0.6 psi/ft, permeability of 0.01 Darcy (or 10 md), porosity of 0.2,
pore fluid viscosity of 1.0 cP, total compressibility of 1.0E-5 psi-1. A fracturing fluid with a
viscosity of 500 cP is pumped at 50 bbl/min for 60 minutes with an average net pressure of
250 psi during the treatment. Assume that a fixed fracture height equals 150 ft and that the
leakoff mechanisms due to filtercake buildup and filtrate invasion are neglected. Calculate
the fracture half-length and the fracture width at the wellbore using Nordgren’s PKN model
for both no-leakoff (storage dominated) and high-leakoff cases.Ct is the leakoff coefficient
as
𝑘𝑐𝑡 𝜙
𝐶𝑡 = 0.0374
∆𝑝𝑐
𝜇
where Ct is in ft/min1/2, k is in Darcy, ct is in psi-1, f is in fraction, Δpc is in psi, and μ is in cP
The KGD model
• Fixed fracture height
• Rectangular cross-section
• Elliptical shape
• hf>>xf
The fracture width at the wellbore
where ww is in in., μ is in cP, qi is in bbl/min,
L is in ft, E is in psi, and hf is in ft
The average width in the fracture
The no-leakoff solution of the KGD model in
oilfield units
where xf is the fracture half-length in ft,
ww is the fracture width at the wellbore in in.,
μ is in cP, qi is in bbl/min, E is in psi, and hf is in ft.
For the case of high-leakoff, the approximation to
calculate the fracture half-length from the PKN model
expressed in also applies to the KGD model
where xf is the fracture half-length in ft, qi is in bbl/min,
Ct is in ft/min1/2, hf is the fracture height in ft,
t is the pumping time in min,
ww is the maximum fracture width at the wellbore in in.,
μ is in cP, and E is in psi
• Consider an oil reservoir with the following properties: Poisson’s ratio
of 0.2, Young’s modulus of 1.0x106 psi, pay zone depth of 5000 ft,
pore pressure gradient of 0.45 psi/ft, minimum stress gradient of 0.6
psi/ft, permeability of 0.01 Darcy, porosity of 0.2, pore fluid viscosity
of 1.0 cP, total compressibility of 1.0E-5 psi21. A fracturing fluid with
a viscosity of 500 cP is pumped at 25 bbl/min for 15 minutes with an
average net pressure of 250 psi during the treatment. Assume that a
fixed fracture height equals 200 ft and that the leakoff mechanisms
due to filtercake buildup and filtrate invasion are neglected. Calculate
the fracture half-length and the fracture width at the wellbore using
the KGD model for both the no-leakoff and high-leakoff cases.
Fracture Operation
Equipment Setup
Equipment Setup
Candidate well selection
Some of the reservoir characteristics suitable for hydraulic fracturing
include:
• Unconventional shale or coalbed methane reservoirs
• Low-permeability formations, or pay zones that have been damaged
• Undepleted reservoirs with medium to high reservoir pressure
• Good stress barriers to minimize fracture growth out of pay zones
• Relatively thick pay zone(s) with enough hydrocarbons in place
Reservoirs that are poor candidates for hydraulic fracturing are
basically those that lack the above characteristics.
Proppant Selection Considerations
• Natural sands are cheaper than resin-coated sands, and much
cheaper than ceramic proppants and resin coated ceramic
proppants.
• A major consideration in proppant selection is conductivity
σe is the effective closure stress on
proppant,
σh,min is the minimum horizontal stress in
the payzone,
pwf is the flowing bottom-hole pressure
during production
Grain size of proppants
• Mesh Scale System
• 12/18, 12/20, 20/40,40/70, etc
20: Can pass through by 20 mesh
40: Will be filtered by 40 mesh
Size distribution
Roundness
&
Sphericity
1 Size Distribution
Uneven Distribution
f = 45%
f<30%
K = thousands md
K = hundreds md
Fracturing Fluid Selection Considerations
• Fluid creates the desired fracture geometry and controls the
efficiencies of carrying proppant.
• Fluid viscosity: the ability to suspend and transport proppants;
• Fluid loss: hinder fracture propagation or growth
• Considerations:
• Safe to use and friendly to the environment
• Cost effective
• Cross-linking requirement
• Compatible with reservoir rocks and fluids
• Damage to the reservoir
• Pumping pressures
• Fluid loss control
Base Fluid
Oil-based
Water-based
Pros
- Less damaging to clays
- Low interfacial tension
Pros
Cons
- Expensive
Cons
- Difficult to handle in operation
- Not friendly environmental
- Safe
- Available
- Economical
- Damaging to clays
Polymer
Gelling Agent
Cross-linker
Guar Gum
Borate
Water
Linear Gel
<50cP
Crosslinked Gel
>100 cP
Collection and Validation of Reservoir
Properties
The most critical parameters for hydraulic fracturing:
• The description of reservoir lithology versus depth
• Basic reservoir properties, including effective reservoir permeability, porosity,
pressure,
• Temperature, reservoir fluid viscosity, reservoir rock/fluid compressibility
• Rock mechanical properties such as Young’s modulus, Poisson’s ratio, and
fracture toughness
• The in-situ stress distribution, namely the minimum horizontal stress value in
each formation layer
• Well configuration (tubing/casing size and grade, perforations, and wellbore
trajectory
• Wellhead equipment specifications
Mechanical Earth Model (1D MEM)
𝑉𝑐 ∆𝑡𝑠
𝑅𝑣 = =
𝑉𝑠 ∆𝑡𝑐
1010 𝜌𝑏
𝐺 = 1.34
∆𝑡𝑠2
Sonic Log
Shear Modulus
Dynamic Young Modulus
Density Log
Poisson’s Ratio
𝜌𝑏
0.5𝑅𝜈2 − 1
𝜈=
𝑅𝜈2 − 1
𝐸 = 𝐺(1 + 𝜈)
(log-based)
𝜎𝑣 = 𝑔𝑜𝑏 𝐻
Overburden
Pressure
Static Young
Modulus
𝐸𝑠𝑡𝑎 = 0.4145𝐸𝑑𝑦𝑛 − 1.0593
𝐸𝑠𝑡𝑎 = 𝐸𝑑𝑦𝑛 −2.21𝜙 + 0.963
(core-based)
𝜈
𝜎ℎ =
1−𝜈
𝐸𝑠𝑡𝑎
𝜎𝑣 − 𝛼𝑃𝑝 + 𝛼𝑃𝑝 +
(𝜀 + 𝜈𝜀𝑦 )
1 − 𝜈2 𝑥
Minimum
Horizontal Stress
Pore Pressure
𝑃𝑝 = 𝑔𝑝𝑜𝑟𝑒 𝐻
Calibration
1D MEM from sonic log data must be calibrated using the fracture closure data obtained from minifrac
Treatment Procedure and Schedule
Treatment procedure including prepad, pad, proppant stage(s),
displacement, and shut-in.
Well is ready
Thin fluid is pumped down the well
Start Pumping
Thin fluid is pumped down the well
Pad Stage
Fluid: Thin fluid (slickwater, linear gel)
Objective:
• Initiate fracture
• Reduce friction
• Cool down hot formation (keep fracture fluid viscosity high)
Pad Stage
Fluid: Thin fluid (slickwater, linear gel)
Objectives:
• Enhance fracture dimension (height, width, length)
• Fracture continue growing and propagating
Proppant/ Slurry Stage
Fluid: Crosslinked gel fluid (with proppant)
Objectives:
• Staged from low to high proppant concentration
• Place proppant as per pumping schedule to obtain desired conductivity
Final Slurry Stage
Fluid: Crosslinked gel fluid (with proppant)
Objective:
• Staged from low to high proppant concentration
• Place proppant as per pumping schedule to obtain desired conductivity
Final Slurry Stage
Fluid: Crosslinked gel fluid (with proppant)
Objective:
• Staged from low to high proppant concentration
• Place proppant as per pumping schedule to obtain desired conductivity
Flush
Fluid: water, KCl water, slickwater, or a low gel-loading fluid
Objectives:
• Displace propane from wellbore to fracture
• Under displace to keep frac conductivity at perforation face
Shut-in
Objectives:
• Allow fracture to close due to gel break and fluid leak-off
• Breaker is set to break 2-3 hours after fracturing job
• Closure is fully close around 3 hours after job
• Required shut in time of 5-6hours
Clean-up
Objectives:
• Recover polymer to avoid formation damage
• Initiate production (small rate and then ramp up)
• Clean-up wellbore
Pad Stage
Slurry stage
Flush
Shut in
Pressure Response Mode
Nolte & Smith Analysis
Net pressure = Pressure in fracture – close pressure
Final Fracture Geometry
Fractured Well Productivity
• The productivity of a fractured is affected by two simultaneous
processes: the influx of fluid into the fracture from the
reservoir, and the influx of fluid into the wellbore from the
fracture.
qr : flow rate from the reservoir into the fracture
h : pay zone height
xf : fracture half-length
kr : reservoir permeability
m : viscosity of the reservoir fluid
Dpy : pressure drop from the reservoir boundary to the fracture face
Dy : distance from the reservoir boundary to the fracture face
Note: 2 fracture faces are accounted for.
h
x
Dy
Average fluid Influx from the fracture into the wellbore
Dx = xf
qf : the flow rate at the wellbore,
h : the payzone height, w is the fracture width,
kf : the fracture permeability,
μ : the viscosity of the reservoir fluid,
Δpx :the pressure drop from the fracture tip to the wellbore,
Δx is the distance from the fracture tip to the wellbore
Dimensionless fracture conductivity
𝑘𝑓 𝑤
𝐹𝐶𝐷 =
𝑘𝑥𝑓
which provides a comparison of the flow
capacity of the fracture that transmits the fluid
into the wellbore with the flow capacity of the
reservoir that delivers the fluid into the fracture
Fcd >> 30: infinitely conductive, as the pressure
drop along the fracture during production
becomes very small.
1< Fcd<10 : usually obtained in fracture design
Fcd > 10 : in extreme low-permeability reservoirs
Fcd < 1: in high-permeability reservoirs
2xf
k
kf
w
Inflow equation
Sf is the equivalent skin factor
The fold of increase:
f
J = productivity of fractured well, stb/day-psi
Jo = productivity of nonfractured well, stb/day-psi
Low permeability
Low Permeability
High Permeability
• A gas reservoir has a permeability of 1 md. A vertical well of
0.328-ft radius draws the reservoir from the center of an area of
160 acres. If the well is hydraulically fractured to create a 1500ft long, 0.12-in. wide fracture of 150,000 md permeability around
the center of the drainage area, what would be the fold of
increase in well productivity?