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WELL STIMULATION TECHNIQUES
CHAPTER 4 HYDRAULIC FRACTURING 1
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LESSON OUTCOME
At the end of this section, the students will be able to :
Understand different fracturing fluids.
Design hydraulic fracturing treatment.
Identify selection criteria for fracturing.
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MECHANICS OF FRACTURING
Naturally occuring underground stresses resist wellbore
fracturing.
The general stress condition underground can be defined
in terms of the effective stresses, z, along the vertical Zaxis and xand yalong the horizontalXandYaxes.
In the absence of external forces, the stress at any point is
due to the weight of the overburden.
Using an average density rock to be 144 lbm per cu ft, thevertical stress at any point is expressed by the equation
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WhereDis the depth in feet.
Under the influence of this vertical stress, the rock tends
to expand laterally but is prevented from doing so by the
surrounding rock.
In the elastic zones of the earths crust, since no horizontal
movement has occured.
According to Hookes law, thehorizontal strainis expressed
(4.1)
(4.2)
MECHANICS OF FRACTURING
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Where E is Youngs modulus.
For rock in compression, xis essentially zero and since the
lateral stress xequals the lateral stress y,
(4.3)
Where his the horizontal stress in general.
SincePoissons ratio for consolidated sedimentary rocks
ranges from 0.18 to 0.27, the horizontal compressive stressis between 0.22 and 0.37 psi per ft of depth.
In the absence of external forces the horizontal stress is
always less than the vertical stress.
MECHANICS OF FRACTURING
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If fluid pressure is applied within rocks and increased until
parting of the rocks occurs that plane along which fracture
or parting may first occur is the one perpendicular to the
least principal stress (Fig 4.1).
When a well is drilled the preexisting stress field in the
rock is distorted.
An approximate calculation of this distortion has beenmade by assuming the rock to be elastic, the borehole
smooth and cylindrical, and the borehole axis vertical.
MECHANICS OF FRACTURING
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MECHANICS OF FRACTURING
Using0 to 500 psi as the range of tensile strenghts for
competent sandstones and limestones, the pressure
necessary to induce vertical fracturing should lie between
and
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MECHANICS OF FRACTURING
Once a fracture has been started, the pressure is applied
to the walls of the fracture.
According to Hubbert and Willis, the minimum down-the-
hole injection pressure requried to hold open and extend a
fracture isslightly in excess of the original stress normal to
the plane of the fracture.
Loss of fluid slightly decreases the pressure required toproduce vertical fractures.
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MECHANICS OF FRACTURING
In the case of horizontal fractures, the confining stress
holding the fracture planes together is equal to the
effective overburdenat the depth of the fracture.
In the case of vertical fractures, the confining stress
holding the planes together is some function of the
effective overburden.
In the lower limiting case, horizontal fracturing can take
place when
(4.5)
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MECHANICS OF FRACTURING
The approximate maximum depth at which horizontal
fracturingshould occur, can be determined from Eqn (4.4)
and (4.5) by assuming
(4.6)
Using a vertical stress (overburden) gradient of 1.0 psi perft, a Poissons ratio of 0.25, and a tensile strength of 1000
psi, the maximum depth for horizontal fracture is found to
be 3000 ft.
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PRODUCTION INCREASE FROM FRACTURING
Reasons for production increases from fracturing are:
1. new zones exposed,
2. reduced permeability zone is bypassed, and
3. flow pattern in reservoir changed from radial to
linear.
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New Zones Exposed
In a carbonate formationwhere productivity depends on
porosity or
in a fractured zonewhere primary flow capacity is related
to the fracture system or
in a deltaic sand formationwhere permeability is related
to regional depositional geometry,
the possibility of increasing well productivity by fracturinginto a new zone may be significant.
In some situation, however, the new zone might be
water or gas.
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By-passed Damage
Production increase from bypassing reduced permeability
zone is afunction ofthedepth of the damaged zoneand
theratio of damaged to undamaged permeability.
Production increase can be estimated more effectively
from transient pressure tests.
Only a short fracture is needed to bypass most damagezones, but it is very important to prop the fracture in the
area near the well-bore to provide a highly conductive
path through the damaged zone. 15
Radial Flow pat tern changed to Linear Pat tern
Production increase from changing the flow pattern results
from creation of a high conductivity fracture (relative to
the formation), extending a long distance from the well-
bore.
For vertical fractures the productivity increase dependsprimarily upon the formation permeability.
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PRODUCTIVITY RATIO
Productivity ratio is the ratio of the productivity index of
the well after fracturing to that of the well before
fracturing,Jf/J.
For thecase of a horizontal fracture (fracture gradient
1.0 psi per ft), an equation for the productivity ratio can be
obtained provided it is assumed that there is zero vertical
permeabilityin the fracture zone.
It has been shown that
(4.7)
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PRODUCTIVITY RATIO
where
kavgis the average permeability of thefractured formation
kis thepermeability of the unfracturedformation
From Fig. (1.5) that the average permeability of the
fracture zone is equal to the average permeability
predicted for radial flow in parallelbeds.
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PRODUCTIVITY RATIO
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Fig.1.5
PRODUCTIVITY RATIO
Where
kfzis the average permeability of the fracture zone
kf
is the permeability of the fracture
Wis the thickness of the fracture
k is the formation permeability
(4.8)
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PRODUCTIVITY RATIO
The average permeability of the fractured formation,kavg,is equal to the average permeability predicted for series
beds in radial flow:
(4.9)
Where
re
is the drainage radius of the well
rwis the wellbore radius
rfis the radius of the fracture21
PRODUCTIVITY RATIO
(4.10)
Substituting Eq (4.8) to Eq (4.9), and into Eq (4.7), and
multiplying numerator and denominator byh,
Factoring,
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PRODUCTIVITY RATIO
To facilitate rapid calculation of the productivity ratio of
horizontal fractures, Fig (4.6) was constructed with the use
of Eqn (4.10).
The correlation between Fig. (4.6) and Eq (4.10) is shown
in Example (4.1).
Fig (4.7) shows the permeability of commonly usedfracture sands.
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MECHANICS OF FRACTURING
Fig. 4.6
Estimated
productivity
ratio after
fracturing
(horizontal
fractures)
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MECHANICS OF FRACTURING
Fig. Estimated
productivity
ratio after
fracturing
(vertical
fracture)
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MECHANICS OF FRACTURING
Fig. 4.7 Effect of
pressure on
frac-sand
permeability
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Example (4.1)
Calculate the productivity ratio for a horizontal fracture,
given:
Fracture width = 0.1 in
Net pay thickness = 50 ft
Permeability of propping agent (10 20 mesh) = 32500 md
Horizontal permeability of formation = 0.54 md
re/ rw = 2000
Fracture penetration rf/ re = 0.40
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Example (4.1)
Solution
The value ofkfW/k his
The term ln (re/ rw)in Eq (4.10) can be expressed as
Then substituting in Eq (4.10),
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Example (4.1)
In Fig (4.6), the PR is 5.0
It is also desirable to estimate the productivity ratio for the
vertical fractures (fracture gradient0.7 psi per ft).
The Mobile Oil Company correlated productivity ratios for
various fracture penetrations with the factor C= kfW/ k,
as shown in Fig (4.8), whereWis the fracture width in feetand kfand k are the effective fracture and horizontalformation permeability in milli-darcies respectively.
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PROPPING THE FRACTURE
The object of propping is to maintain desired fracture
conductivity economically.
Fracture conductivity depends upon a number of
interrelated factors: type, size, and uniformity of the
proppant; degree of embedment, crushing, and/or
deformation; and amount of proppant and the manner of
placement. Commonly used proppant types and size ranges are:
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PROPPING THE FRACTURE
Commonly used proppant types and size ranges are:
Placement of propping agent in a fracture (either vertical or
horizontal) in any pattern other than a packed condition isdifficult to achieve with low viscosity fluids.
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PROPPANT HAS TO
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Not to crush at formation closure stress
and temperature
Keep desired conductivity over time
Be smaller than perforations
Not to flow back from the fracture
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PROPPANT SELECTION
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3. Review Proppant Database finding proppants matchingrequired mesh sizes, formation closure stress and temperature
1. Calculate optimal fracture half-lengthand conductivity
4. Select proppants with required conductivity
5. Sort selected proppants by price;Select proppant flowback control additives
2. Determine applicable proppant mesh sizes
PROPPING THE FRACTURE
1. First portions of sand entering fracture drop out to the
bottom of the fracture near the wellbore. Jetting action
through perforation tends to wash sand back several feet
from borehole.
2. As more sand enters the fracture, height of the pack
increases to some equilibrium point dependent on the
velocity of flow in the fracture, the viscosity of the fracfluid, the difference in density between proppant and
fluid, and the drag characteristics of the proppant.
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PROPPING THE FRACTURE
3. Additional sand is then carried over the pack and
deposited further out in the fracture.
4. Final height of packed fracture after closure may be a
relatively small percentage of the dynamic fracture
height created during injection.
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PROPPING THE FRACTURE
High viscosity fluids which suspend large proppant permit:
1. Use of much larger concentrations of proppant.
2. Placement of multilayers of large proppant throughout a
high percentage of the fracture height, particularly in the
critical area near the wellbore.
3. Placement of proppant much further away from the
wellbore.
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FRACTURE AREA
During the fracturing process, the fracture fluid is injected
at the well head at a constant rateqi.
In the fracture this injection, rate is split up into two
components as shown in Fig (4.8).
Part of the liquid,ql, enters the formation as a result ofthe differential pressure (pi- pe) between the fracture andthe external boundary, and the remainder, qf, increasesthe fracture area, i.e., it increase the volume of the
fracture. An expression for thefracture area at any timemay be
derived by using this basic concept and the following
assumptions: 37
FRACTURE AREA
An expression for the fracture area at any time may be
derived by using this basic concept and the following
assumptions:
1. The fracture is of uniform width.
2. The flow of fracture fluid into the formation is linear
and the direction of flow is perpendicular to the
fracture face Fig (4.8).3. The velocity of flow into the formation at any point on
the fracture face is a function of the time of exposure
of the point to flow.
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2
MECHANICS OF FRACTURING
Fig. 4.8
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FRACTURE AREA
4. The velocity function v = f(t) is the same for everypoint in the formation, but the zero time for any point
is defined as the instant that the fracturing fluid first
reaches it.
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2
FRACTURE AREA
Fracture area can be expressed as follow:
(4.11)
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Thank You
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2
Thank You
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Error Function of X
FRACTURING FLUIDS
Oil or water fluids are used to create, extend, and place
proppant in the fracture.
Two-thirds of fracture treatments use water base fluids
and one-third oil base fluids.
Recent innovations include gelled alcohol, LPG-CO2, or
aerated foam fluids.
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FRACTURING FLUIDS
Generally these comparative statements can be made:
1. Oil fluids are cheap and have inherent viscosity which
makes themadvantageousfor relativelylow injection
rate,shallow to medium depthfracturing. Pressure loss
down the casing and safety consideration are often
limiting factors.
2. Gelled water fluids have special advantages due to
theirhigher density and lower friction loss in deeper
wells, and where higher injection rates are needed.
Where high temperatures are involved reasonable
viscosity can be maintained above 250oF.45
FRACTURING FLUIDS
3. Ultra-highviscosity fluids arecostly and temperature
sensitive, but can provide wide, highly-conductive
fractures needed to stimulate higher permeability
zones or sand carrying capacity needed to prop long
fractures in low permeability zones.
4. Emulsion fluids provide moderate viscosity, andgood
fluid lossandcarrying capacity at a reasonable cost.5. Alcohol, LPG-CO2 and Aerated fluids have limited
application due to cost, safety and/or complexity.
Usefulness is primarily in gas or low permeability zones
where cleanup is paramount.46
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2
FRACTURING FLUIDS
The constant C in Eq (4.11) is the fracturing fluid
coefficient, and for any given type of flow system it
depends upon thecharacteristics of the fracturing fluid,
thereservoir fluids,and the rock.
The fracturing fluid coefficient is the only term which
reflects the properties of the fracturing fluid and is
therefore a measure of their relative effectiveness.
A low fracturing fluid coefficient means low fluid-loss
propertiesand thus a larger fracture area for a given fluidvolume and injection rate.
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FRACTURING FLUIDS
Fracturing fluids fall into three distinct categories:
1. Viscosity-controlled fluids
2. Reservoir-controlled fluids
3. Wall-building fluids.
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Viscosit y-cont rolled Fluids
Theviscosity of the fracture fluid controls the amount of
fluid loss to the formation.
The coefficient for this type of fracturing fluid is expressed
by
(4.12)
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Viscosit y-cont rolled Fluids
Eq (4.12) simply states that for a viscosity-controlled fluid,
therate of leak-off will depend on the permeability, the
porosity, the treating pressure differential, and the
fracture fluid viscosity.
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2
Example (4.2)
Calculate the fracturing fluid coefficient of an oil, given:
Fracture gradient = 0.7 psi per foot
Depth = 4000 ft
Bottom-hole pressure = 1800 psi
Bottom-hole temperature = 100oF
Porosity = 20 per cent
Permeability perpendicular to fracture face = 10 md
Fracturing fluid viscosity at 100oF = 500 cp
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Example (4.2)
Solution
The differential pressure is
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2
Reservoir-cont rolled Fluids
This group includes those fracturing fluids that have low
viscosity and high fluid-loss characteristics, i.e., physical
properties identical or nearly identical with those of the
reservoir fluid.
Fracturing fluids which fall into this classification are lease
crude and water, which do not contain additives to reduce
fluid loss.
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Reservoir-cont rolled Fluids
The equation for the fluid-loss coefficient is
(4.13)
Noted that quantities and cf
in the above equation are
properties of the reservoir fluidand not ofthe fracturing
fluid. 54
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2
Wall-building Fluids
The use of modern additives to limit fluid loss (asphaltic-
type materials, synthetic gums, and insoluble solids added
to oil or water) creates a third class of fracturing fluids.
These fluids build a temporary filter cake or wall on the
face of the fracture as it is exposed.
While a small amount of fluid leaks through to form the
wall, once formed, the wall presents quite an effective
barrier to further leak-off due to its low permeability.
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Wall-building Fluids
The volume of fluid which has leaked off through the filter
cake at any times is proportional to the volume of the
filter cake at that time, or
(4.14)
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where
V = volume of fluid
Af= cross sectional area of filter cake
L = thickness of filter cakeC = proportional constant
If a standard fluid loss test is run on a fracturing fluid, and
If V is ploed against t, the slope of the curve is m, and it is
expressed as cu cm/min.
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Wall-building Fluids
If a spurt loss is included in the equation above, Vbecomes
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(4.15)
Wall-building Fluids
Consider a fracture of areaAfwith a spurt loss ofVsp.
The volume of the fracture is AfWwhere W is the true
fracture width.
If we define a quantityW'such that the product AfW'isequal to the volume of the fracture without a spurt loss,
then
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Example (4.3)
Solution
Thespurt loss is used in correcting the fracture widthby Eq
(4.17). If the fracture width is 0.2 in. Thecorrected fracturewidth(W)is
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Example (4.3)
Any fracturing fluid is somewhat viscous, and so Cv
mechanism helps retard leak-off.
Also, the reservoircontains a compressible fluid, and thus
theCc
mechanismwill be operative.
Finally,many oils without additives will have a wall-building
effect, and so the Cw
mechanismusually comes into play.
Combined coefficient could be calculated similarly to thecombined conductance of a series of conductors,
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FRACTURE EFFICIENCY
Once fracturing fluid coefficient is calculated, fracture area
can be determined from the basic equation
Solution of this equation is tedious. So, in another form
will be mentioned to facilitate the calculation.
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(4.11)
FRACTURE EFFICIENCY
If we define the efficiency of a fracture job as the volume
of the fracture divided by the volume of fluid pumped,
then
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(4.18)
By substituting Eqn. 4.18 into 4.11,
(4.19)
Now, Efficiency becomes a function of x alone. Then
efficiency vs x can be plotted as shown in Fig. (4.11)
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FRACTURE EFFICIENCY
Fig. 4.11. Plot of
fracturing
efficiency
against its
function
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Example (4.4)
Calculate the fracture efficiency, given:
Solution
The fracture time is
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Example (4.4)
From Table (4.1), erfc (2.67) = 0.00016, so that the
efficiency is
and
Eff = 0.140 (1248 x 0.00016 + 3,01 1) = 31 per cent
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Example (4.4)
The use of Fig. 4.11 and Eq. (4.19) provide a simplified
method of calculating the area of the fracture at any time,
A (t).
For example, if the injection volume is 20,000 gal of fluid
with a coefficient of 2.22 x 10-3 ft/ min, the fracture width
is 0.2 in., and the pumping time is 20 min, then
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Example (4.4)
From Table (4.1), the efficiency is 37%. Then from Eqn.
(4.18), the fracture area is
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Q & A
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Thank You
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