7/18/2019 A New Approach to Modeling Hydraulic Fractures in Consolidated Sands http://slidepdf.com/reader/full/a-new-approach-to-modeling-hydraulic-fractures-in-consolidated-sands 1/14 Copyright 2005, Society of Petroleum Engineers This paper was prepared for presentation at the 2005 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, U.S.A., 9 – 12 October 2005. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.Abstract Field data show that fracturing in poorly-consolidated rocks is not adequately represented by traditional models for brittle, linear-elastic rocks. This is not unexpected since unconsolidated sands do not exhibit brittle- elastic behavior. In addition, sands have very low tensile and shear strengths. A model is presented for the propagation of “fractures” in unconsolidated sands. The model departs radically from current models in that brittle fracture mechanics is not used. Instead the propagation of pore pressure is computed and the porosity and permeability of the sand is specified as a function of the effective stress. This results in the creation of an anisotropic zone of increased porosity and permeability along the plane of maximum in-situ stress (normal faulting stress regime) or at a certain angle to it (strike slip faulting regime). This region of enhanced porosity defines a “fracture” in unconsolidated sands. The physics of creation and propagation of this oriented, high permeability zone, is modeled for the first time. It is shown that in-situ stress anisotropy and shear failure play a very important role in determining the dimensions of this fracture zone. In addition, the permeability anisotropy generated due to the stress anisotropy in the sand is the critical driving force behind the creation of the oriented “fracture”. During the hydraulic fracturing of an unconsolidated formation, a high permeability zone (channel or fracture) will form in response to the difference in situ horizontal stresses and the decrease in the net effective stress near wellbore. To correctly model the fluid distribution, the fluid flow behavior must be coupled to the mechanical behavior of the sands. Based on the coupled geo-mechanics and reservoir simulation (model, iterative-coupled 2-D finite difference software is developed to simulate the strain, stress change due to the injection. Based on the constitutive relationship of permeability and porosity, we modeled permeability and porosity as a function of effective stress. Introduction Sand control is a growing concern in most offshore wells in the Gulf of Mexico, Western Canada, and Brazil. The application of fracpacks in these poorly consolidated reservoirs has been an effective method for preventing sanding problems. In conventional hydraulic fracture simulations, to which linear elastic fracture mechanics (LEFM) is applied [1] fracture initiation and propagation is governed by in-situ stresses, fracture toughness, tip dilatancy, and the process zone. Unlike competent formations, unconsolidated sand beds have little or no tensile strength. LEFM is adequate for hard rocks, but the fracture geometry predictions fall short when applied to fracturing soft rocks. For example, it has been reported that millions of barrels of solid waste slurry can easily be injected into soft formations over a period of several years [2] . To accommodate such a large volume of solids fracture lengths of several miles would be required, even with fractures that are several centimeters wide when using classical fracture models for simulating this process. Some experimental and simulation work [2-9] has been done to identify the mechanisms of fracture propagation and initiation in unconsolidated sand formations. Khodaverdian and McElfresh’s experiments [2] show that fracture tip propagation in unconsolidated sand is dominated by fluid invasion and shear failure within a process zone ahead of the tip. In addition, sub-parallel fractures form and contribute to the post-stimulation skin since these fractures are not expected to be propped open during frac-pack operations. Di Lullo and Curtis [3] provide an alternative mechanism for the initiation and propagation of the shear-failure zones based on their experiments. They postulate that fluid leakoff into the matrix pressurizes and fluidizes the visco-plastic formation matrix As the pressure surpasses the yield stress, the formation “parts” (or deforms) forming a channel, allowing sand-laden slurry to penetrate and propagate. Wang and Sharma [4 measured the mechanical properties of poorly consolidated sands. Their data indicate that unconsolidated sands do not show classic failure modes in compression. Instead, a region of elasto-plasticity is observed as stresses are increased resulting in ductile failure over an extended range of stresses. Settari [5] [6] proposed a non-elastic injection model by coupling fluid flow and soil mechanics behavior for unconsolidated sands. The non-linearity of the compressibility and shear failure were thought of as the principle mechanisms controlling the injectivity in oil sands. In addition, dilatan failure behavior increases porosity and permeability Numerical methods for coupling fluid flow and gemechanic SPE 96246 A New Approach to Modeling Hydraulic Fractures in Unconsolidated Sands Z. Zhai, SPE, and M.M. Sharma, SPE, U. of Texas at Austin
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7/18/2019 A New Approach to Modeling Hydraulic Fractures in Consolidated Sands
This paper was prepared for presentation at the 2005 SPE Annual Technical Conference andExhibition held in Dallas, Texas, U.S.A., 9 – 12 October 2005.
This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in a proposal submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to a proposal of not more than 300words; illustrations may not be copied. The proposal must contain conspicuous
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract Field data show that fracturing in poorly-consolidated rocks isnot adequately represented by traditional models for brittle,
linear-elastic rocks. This is not unexpected sinceunconsolidated sands do not exhibit brittle- elastic behavior.
In addition, sands have very low tensile and shear strengths.
A model is presented for the propagation of “fractures” in
unconsolidated sands. The model departs radically fromcurrent models in that brittle fracture mechanics is not used.
Instead the propagation of pore pressure is computed and the
porosity and permeability of the sand is specified as a functionof the effective stress. This results in the creation of an
anisotropic zone of increased porosity and permeability along
the plane of maximum in-situ stress (normal faulting stressregime) or at a certain angle to it (strike slip faulting regime).
This region of enhanced porosity defines a “fracture” in
unconsolidated sands. The physics of creation and propagation of this oriented, high permeability zone, is
modeled for the first time.
It is shown that in-situ stress anisotropy and shear failure play a very important role in determining the dimensions of
this fracture zone. In addition, the permeability anisotropy
generated due to the stress anisotropy in the sand is the criticaldriving force behind the creation of the oriented “fracture”.
During the hydraulic fracturing of an unconsolidatedformation, a high permeability zone (channel or fracture) willform in response to the difference in situ horizontal stresses
and the decrease in the net effective stress near wellbore. To
correctly model the fluid distribution, the fluid flow behavior
must be coupled to the mechanical behavior of the sands.Based on the coupled geo-mechanics and reservoir simulation
(model, iterative-coupled 2-D finite difference software isdeveloped to simulate the strain, stress change due to the
injection. Based on the constitutive relationship of
permeability and porosity, we modeled permeability and
porosity as a function of effective stress.
IntroductionSand control is a growing concern in most offshore wells in
the Gulf of Mexico, Western Canada, and Brazil. The
application of fracpacks in these poorly consolidatedreservoirs has been an effective method for preventing sanding
problems.In conventional hydraulic fracture simulations, to which
linear elastic fracture mechanics (LEFM) is applied [1]
fracture initiation and propagation is governed by in-situ
stresses, fracture toughness, tip dilatancy, and the processzone. Unlike competent formations, unconsolidated sand beds
have little or no tensile strength. LEFM is adequate for hardrocks, but the fracture geometry predictions fall short when
applied to fracturing soft rocks. For example, it has been
reported that millions of barrels of solid waste slurry can
easily be injected into soft formations over a period of severalyears [2]. To accommodate such a large volume of solids
fracture lengths of several miles would be required, even withfractures that are several centimeters wide when using
classical fracture models for simulating this process.
Some experimental and simulation work [2-9] has been done
to identify the mechanisms of fracture propagation and
initiation in unconsolidated sand formations. Khodaverdianand McElfresh’s experiments [2] show that fracture tip
propagation in unconsolidated sand is dominated by fluid
invasion and shear failure within a process zone ahead of the
tip. In addition, sub-parallel fractures form and contribute to
the post-stimulation skin since these fractures are not expectedto be propped open during frac-pack operations. Di Lullo and
Curtis [3] provide an alternative mechanism for the initiation
and propagation of the shear-failure zones based on theirexperiments. They postulate that fluid leakoff into the matrix
pressurizes and fluidizes the visco-plastic formation matrix
As the pressure surpasses the yield stress, the formation“parts” (or deforms) forming a channel, allowing sand-laden
slurry to penetrate and propagate. Wang and Sharma
[4
measured the mechanical properties of poorly consolidatedsands. Their data indicate that unconsolidated sands do not
show classic failure modes in compression. Instead, a region
of elasto-plasticity is observed as stresses are increasedresulting in ductile failure over an extended range of stresses.
Settari [5] [6] proposed a non-elastic injection model by
coupling fluid flow and soil mechanics behavior for
unconsolidated sands. The non-linearity of the compressibilityand shear failure were thought of as the principle mechanisms
controlling the injectivity in oil sands. In addition, dilatanfailure behavior increases porosity and permeability
Numerical methods for coupling fluid flow and gemechanic
SPE 96246
A New Approach to Modeling Hydraulic Fractures in Unconsolidated SandsZ. Zhai, SPE, and M.M. Sharma, SPE, U. of Texas at Austin
7/18/2019 A New Approach to Modeling Hydraulic Fractures in Consolidated Sands
were introduced. Chin and Montgomery [7] developed a model
for solids injection and compared their results with field data.
Many of the above studies rely on classical brittle fracturemechanics and in some cases do not account for shear failure.
Permeability anisotropy induced by in-situ stresses is notconsidered.
In this paper, we present a new approach to modeling the
mechanical behavior of unconsolidated sands that aresubjected to injection of water –based slurries.
Model for Stress Distribution around an Injection Well
To study fracture initiation and propagation, we need to obtain
the effective stress distribution around the well and then
update the permeability and porosity in accordance with theappropriate constitutive relationships.
The stresses around the wellbore can be divided into three
parts (Figure 1):1. Stresses induced by far-field, in-situ stresses.2. Stresses induced by the wellbore pressure.3. Flow induced stresses (poro-elastic stresses).Based on the stress distribution, we can determine the
anisotropic stress tensor as well as where and when tensile or
shear failure occurs. This approach has been widely applied to
wellbore stability problems for homogeneous, isotropic rocks
[4]. In this paper we couple the stress distribution with the pore
pressure and apply the model to hydraulic fracturing problems
in unconsolidated sands.
Stress Distribution due to In-situ Stresses. Thestresses around a wellbore in a cylindrical coordinate system
(r, θ, and z) due to the principal in-situ stresses are given by,
2
2
2 4
2 4
(1 )2
(1 4 3 ) cos 22
xx yywrr
xx yyw w
r
r
r r
r r
σ σ σ
σ σ θ
′ ′+′ = −
′ ′−+ − +
2
2
4
4
(1 )2
(1 3 ) cos 22
xx yyw
xx yyw
r
r
r
r
θθ
σ σ σ
σ σ θ
′ ′+′ = +
′ ′−− +
2 4
2 4(1 2 3 ) sin 2
2
xx yyw wr
r r
r r θ
σ σ σ θ
′ ′−′ = − + −
(1)
The Flow-induced Stresses. The flow-induced stresses can be
obtained by coupling the fluid flow equation and the geo-
flow chart for the computer implementation is shown in Figure
4.
Results and DiscussionThe model and equations presented in the previous section
have been solved using a fully-implicit, finite-difference
variable-grid simulation. Results are presented for a typical
base case to demonstrate the main results obtained from thesimulations. The formation of “fractures” or zones of failure
(as postulated in this paper) in unconsolidated sands dependsvery much on the in-situ state of stress. Under stress regimes
that favor normal faulting, the vertical stress is the maximum
principal stress and the minimum and maximum horizontal
stresses are 0.6 to 0.9 of the vertical stress. An example of thisstress regime is the Gulf of Mexico (Ref 17). Strike-slip faults
form when the vertical stress is smaller than the maximum
horizontal stress. Examples of this stress regime include the
North Sea and Western Canada (Ref 18). Both cases are
considered below.
Fracture Growth in a Normal Faulting Stress Regime. InCase 1 and Case 2, we will discuss how the fracture forms and
propagates under a normal faulting stress regime.
Base Case. An injection well is placed in the middle of
homogeneous reservoir on 40-acre spacing. All formation
properties are assumed to be isotropic. The vertical stress isassumed to be 10,000 psi. The minimum and maximum in-situ
stresses are 5,000 psi and 6,000 psi respectively. Water is
injected into the well at a bottom-hole pressure of 9,500 psi.
The initial reservoir pressure is assumed to be 1,500 psi.Details of the input data used are provided in Table 1.
As clearly seen in Figure 5 (map view of the formation), the
injection of water results in the formation of a high permeability zone oriented in the direction of intermediate
stress (maximum horizontal in-situ stress). This high permeability zone is created primarily as a result of shear
failure occurring in the direction perpendicular to the
minimum horizontal stress.Figure 6 shows how the pore pressure increases due to fluid
injection. The increase in pore pressure is anisotropic because
the in-situ effective stresses are anisotropic, giving rise to ananisotropic permeability distribution. This effect becomes
more pronounced when shear failure occurs. At failure, a
significant increase in the permeability along the failure planeoccurs due to dilation (Figure 2). The permeability
perpendicular to the failure plane does not change appreciably.
This causes the pore pressure profile to become increasingly
anisotropic. Pore pressure increases are observed to propagatefaster in the direction of the maximum horizontal stress(perpendicular to the direction of the minimum horizontal
stress). This is also the direction of the plane of shear failure.
The change in vertical, radial and tangential stress
distributions with an increase in pore pressure is shown inFigure 7. In this example (Base Case), the initial effective
vertical stress is 8,500 psi. As the injection is initiated, the
hoop stress increases from negative 2,000 psi at the wellboreto a constant 3,500 psi away from wellbore and the radial
stress decreases from 8,000 psi at the wellbore to a constant
4,500 psi away from the wellbore.
The injection of the fluid increases the pore pressure
resulting in a decrease in all the effective stresses in the near-
wellbore region. The vertical effective stress remains themaximum principle stress (Figure 7). This ensures the
propagation of a failure zone in the direction of the maximum
horizontal in-situ stress.
Figure 8 shows the maximum and minimum principle
stresses (σ3 and σ1). In this figure, the dark-shaded regionindicates the shear failure zone and the lightly-shaded region
indicates the tensile failure zone. The arrows indicate thedirection of increasing radius away from the wellbore starting
at 0.4 ft and going to 7 ft away from the wellbore.
From the changes in the stress distribution shown in the
figure, it is clear that the injection process is dominated byshear failure. The shear failure zone expands from about 1 foo
to several tens of feet from the wellbore over the first few
minutes of injection (Figure 8). The shear failure results in an
increase in permeability in this zone resulting in the creation
of a high permeability zone perpendicular to the minimumhorizontal stress.
In summary, a high permeability shear failure zone formsand propagates perpendicular to the direction of the minimum
horizontal stress, due to fluid injection. The creation of this
high permeability zone is caused by shear failure and a
reduction in the effective stress due to injection. The
anisotropic propagation of this high permeability zone iscaused by differences in the in-situ horizontal stresses.
Case 2 (The effect of in-situ stresses). Clearly the behavior
reported above is very sensitive to the anisotropy in the in-situ
stresses. In Case 2 we present results for a simulation in whichthe difference in the maximum and minimum horizontal
stresses is increased. The maximum in-situ stress is increased
from 6,000 psi to 8,000 psi. The minimum in-situ stress is keptthe same.
As in the base case, a high-permeability zone forms and propagates in the direction of the maximum horizontal stress
However, the high permeability zone in this case is narrower
and shorter than that in the base case (Figure 9).Figure 10 shows how the pore pressure propagates along the
high-permeability zone resulting in the formation of an elliptic
region of high pore pressure. When comparing to the basecase, this high-pressure region is narrower and shorter.
The changes in the stresses are shown in Figure 11. The
initial vertical stress is a constant 8,500 psi; the hoop stressincreases from negative 4,000 psi at the wellbore to a constan
3,000 psi away from wellbore region; and the radial stress
decreases from 8,000 psi at the wellbore to a constant 6,000
psi away from wellbore region.As time increases, all the effective stresses decrease in the
near wellbore region. This causes the failure zone to expand
from 0.8 ft to 20 ft over a period of 3 minutes (Figure 12).
Under normal faulting in-situ stress regime conditions in
unconsolidated sands, shear failure is the dominant or maybethe only failure mechanism when a fluid is injected. Tensile
failure may happen when the injection pressure is close to or
higher than the vertical stress (rare). The length and width ofthe high permeability zone will be decreased if the maximum
horizontal stress is increased. An increase in the maximum
horizontal stress has no effect on the failure (intermediate
7/18/2019 A New Approach to Modeling Hydraulic Fractures in Consolidated Sands
stress) but will cause the effective stresses to increase and the
permeability to decrease.
Fracture Growth in a Strike-Slip Stress Regime. In Case 3
and Case 4, we discuss how a zone of high permeability forms
and propagates under a strike-slip stress regime.Case 3. The vertical stress is decreased from 10,000 psi to
5,500 psi from the Base Case. The maximum and minimumhorizontal stresses are kept the same.
As seen in Figure 13, at early time (less than 1 min), a high permeability region caused by tensile failure forms and
propagates in the maximum horizontal stress direction. Then
(after several minutes) the high permeability region propagates
at a certain angle to the maximum horizontal stress due to theshear failure.
Figure 14 shows how the pore pressure increases due to
fluid injection. The high pore pressure zone propagates in
direction of the maximum horizontal stress at the beginning,
and then propagates in a certain angle to the maximumhorizontal stress.
The changes in the stresses are shown in Figure 15. Theinitial effective vertical stress is 4,000 psi. As the injection isinitiated, the hoop stress increases from negative 2,000 psi at
the wellbore to a constant 3,500 psi away from wellbore and
the radial stress decreases from 8,000 psi at the wellbore to aconstant 4,500 psi away from the wellbore. The injection of
the fluid increases the pore pressure resulting in a decrease in
all the effective stresses in the near-wellbore region. The
radial stress remains the maximum principal stress and thehoop stress remains the minimum principal stress (Figure 15).
This ensures the propagation of a failure zone at a certain
angle to the maximum horizontal in-situ stress (if only shear
failure happens).
Figure 16 shows how the maximum and minimum principlestresses (σ3 and σ1) change with time. In this figure, we can see
that in the near wellbore region, only tensile failure occurs
(lightly shaded region), which explains the propagation in thedirection of the maximum horizontal stress. Away from the
wellbore, shear failure occurs and the failure zone extends
from 0.6ft to 5.3ft within the first minute.Case 4. In Case 4 we present results for a simulation in
which the difference in the maximum and minimum horizontal
stresses is increased from Case 3. The maximum in-situ stress
is increased from 6,000 psi to 7,000 psi. The minimum in-situ
stress is kept the same.As in Case 3, a high-permeability zone forms and
propagates at a certain angle to the maximum horizontal stress
direction. However, the high permeability zone in this case islonger and narrower than that in the Case 3 (Figure 17). The
shear failure zone increases. Furthermore, same as in Case 3,
the high permeability zone propagates in direction of the
maximum horizontal stress at the very beginning (less than 1
min) and then propagates at a certain angle to the maximumhorizontal stress.
From Figure 18, we can see that the pore pressure
propagates along the high permeability zone and the high-
pressure zone is longer and narrower than Case 3.Figure 19 shows the stresses change with time and location.
The initial effective vertical stress is a constant 4,000 psi,
while the initial effective hoop stress and radial stress change
with the location. The initial effective hoop stress increases
from negative 3,000 psi at the wellbore to a constant 3,500 psaway from wellbore and the initial effective radial stress
decreases from 8,000 psi at the wellbore to a constant 5,500
psi away from the wellbore. The injection of the fluid
increases the pore pressure resulting in a decrease in all the
effective stresses in the near wellbore region. As in Case 3, theradial stress remains the maximum principal stress and the
hoop stress remains the minimum principal stress.From Figure 17, we can see that tensile failure (lightly
shaded region) is dominant in the near wellbore region. While
away from the wellbore region, shear failure occurs. And the
failure zone extends initially from 0.6ft to 2 ft and 5.5ft at 8and 24 seconds respectively.
Under a strike-slip stress state in unconsolidated sands
shear failure is the dominant failure mechanism when the
fluids are injected. Tensile failure happens only in the near
wellbore region where the pore pressure is very large. Thewidth of the high permeability zone decreases while the length
increases with the increase of the maximum horizontal stressThe Increase in the maximum horizontal stress (principa
stress) will increase the shear failure zone, so the permeability
along the shear failure zone will be larger than the other
directions.
Conclusion
Classical models for linear-elastic, brittle fracture mechanicsthat have been traditionally applied to hard rock fracturing are
not applicable for unconsolidated sands.
A new model is presented to describe “fracture” propagation
in unconsolidated sands. It is shown that shear failure is the
dominant failure mechanism when fluids are injected intounconsolidated sands. This is consistent with experimenta
observations reported in the past. Tensile failure happens only
at the near wellbore region under strike-slip stress conditions.
Under normal faulting conditions, as the pore pressureincreases a region of high permeability forms in a direction
perpendicular to the minimum horizontal stress. The width and
length of this region is controlled by the minimum andmaximum horizontal stresses. The high permeability zone is
narrower and shorter if the difference of the in-situ stresses
(increase the maximum horizontal stress) is larger.
Under strike-slip faulting stress condition, as the pore
pressure increases, a high permeability zones forms and propagates in the maximum horizontal stress direction firs
because of tensile failure in the near wellbore region and then
propagates at a certain angle to the maximum horizontal stresdirection because of shear failure. The high permeability zone
is narrower but longer if the difference of the in-situ stresses is
larger.
Acknowledgements
The authors would like to acknowledge valuable comments provided by Dr. Jon Olson and Dr. Mark Mear.
Nomenclature
P = pore pressure
7/18/2019 A New Approach to Modeling Hydraulic Fractures in Consolidated Sands