2009NTCE 07 03 Tech Paper by 1W0mCX

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									                                                                               experience have been carried out till now. The basic idea of increasing
                                                                               fracture gradient is to increase the wellbore hoop stress artificially 3-11.
                                                                               One important application of increasing the wellbore stress is that of
                                                                               the depleted formation. In a depleted formation, pore pressure has
                                                                               dropped due to production, which causes a reduction in the total
  2009 NATIONAL TECHNICAL CONFERENCE & EXHIBITION,                             formation stress. At the same time, the neighboring shale layers may
                NEW ORLEANS, LOUISIANA                                         maintain their pore pressure and not seen a reduction in total formation
                                                                               stress. In such a case, there is often not enough fracture gradient in the
AADE 2009NTCE-07-03: WELLBORE STRENGTHENING:                                   depleted zones to balance the mud weight and not exceed the fracture
THE EFFECT OF PERMEABLE CASE                                                   resistance. The wellbore strengthening method can be used to increase
                                                                               the fracture gradient in those formations.
AUTHOR(S) & AFFILIATIONS:
NEAL B. NAGEL, CONOCOPHILLIPS                                                  A wider mud weight window will give more options for the design of
FRANK MENG, CONOCOPHILLIPS                                                     well trajectory, casing, shoe settlement, mud fluid, and also the wellbore
                                                                               stability. Definitely, the cost will be reduced. Using a wellbore
                                                                               strengthening method, the fracture gradient in a weak zone may be
                                                                               increased. Many field cases show the results for the increased fracture
Abstract                                                                       gradient by using the wellbore strengthening method12-20. Results
                                                                               demonstrate significant increase of the FG. But how fracture geometry,
Wellbore instability, particularly lost circulation, is one of the most        in-situ stress, formation properties and permeable/impermeable
critical challenges affecting drilling and production. The wellbore            formation affect the FG increase value?
strengthening technique, whereby micro-fractures are created and
propped open to increase the tangential stress in the wellbore wall,           In this paper a finite element model is used to analyze the fracture
provides one solution to the problems of lost circulation, drilling            gradient increase behavior under the permeable formation case. The
through depleted formations, and wellbore instability. However,                pressurized fracture, fracture length and width, and propped fracture
formation pore pressure changes near-wellbore can cause changes in the         behaviors were evaluated using the finite element model. Also in this
tangential stress, affect the fracture initiation pressure and affect the      paper, many factors affecting fracture gradient value are analyzed and
amount of wellbore strengthening.                                              their effects are presented. These factors include isotropic and
                                                                               anisotropic stress fields and formation properties. Interesting and
This paper will report the results of a numerical investigation into the       valuable results and findings have been concluded in this paper. The
effect of wellbore strengthening on permeable formations, building             permeable formation case study was compared with impermeable case
upon the results from a previous paper assuming the impermeable case.          in a previous paper21.
In addition, the study will show the breakdown pressure changes under
different stress conditions, formation strength behavior and                   Summary of Previous Paper
impermeable and permeable formation cases. The results of stress and
fracture initiation pressure changes will be quantitatively presented          The previous paper21 presented the results of an analysis of the effect of
considering the cases of a permeable formation.                                a single fracture, both pressurized and propped, on wellbore
                                                                               breakdown. The influence of a pressurized fracture, fracture length and
Introduction                                                                   width and propped fracture behaviors were evaluated using a numerical
                                                                               model and quantitative results were provided.
Fracture gradient, equal to the minimum horizontal in-situ stress, plays a
critical role in mud weight design, wellbore stability evaluations, drilling   In that paper, the potential benefits of wellbore strengthening by
arrangement, and fracturing analyses. Breakdown pressure is also               creating a propped fracture within the formation around the well for
another critical factor that needs to be considered. Simply treating the       breakdown limit or breakdown pressure was described. Due to the
breakdown value as always larger than fracture gradient is not correct.        tangential hoop stresses developed within the wellbore wall as the
Sometimes the breakdown pressure around the wellbore is less than the          wellbore was drilled, the breakdown limit can be several ppg greater
far field minimum horizontal stress. With known in-situ stresses and           than the far-field fracture gradient, the so-called minimum horizontal
pore pressure, the mud weight program can be designed according to             stress. Further, wellbore strengthening does not alter the far-field
the stress range. The lower limit for the mud weight, i.e. the minimum         fracture gradient. Rather, the wellbore strengthening method alters the
mud weight, will be determined to avoid pressure influx, compressive           near-wellbore hoop stresses and the breakdown limit of the well.
failure and well collapse. The upper limit for the mud weight, the
maximum mud weight, needs to be obtained so that tensile failure and           Some conclusions from previous paper are listed below:
loss circulation, i.e. fracturing, does not take place.
                                                                                    a. Difference between FG and Breakdown
Lost circulation is one of the costly problems encountered in drilling a
well. One method to prevent lost circulation is to increase the stress         The pressure necessary to initiate a fracture in intact rock is known as
around the wellbore wall. In early 1990’s, the concept of adding granular      breakdown pressure, or formation fracture pressure (FFP). Formation
particles to the mud to seal fractures around the wellbore was                 breakdown pressure is a function of the tensile strength of the rock, its
presented1,2. After that, lots of research work, testing and field             pore pressure, and the maximum and minimum horizontal stresses.


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Breakdown pressure gradients can range from less than 0.4 to over 1.2             and behaves plastically, the simulation results show that
psi/ft. The breakdown pressure, which is measured at the bore hole,               tension can only be created some distance inside the wellbore
can be affected greatly by borehole conditions.                                   wall, which may or may not offer some strengthening
                                                                                  behavior.
Fracture closure stress or fracture gradient, which is taken to be the
stress at which a fracture closes, is ideally the far field total minimum    5.   For the anisotropic stress/elastic property case, strengthening
horizontal stress.                                                                increases with length up to 8.1ppg (where length is really a
                                                                                  proxy for width). For the anisotropic stress/MohrCoulomb
FG and breakdown can be significant different along the wellbore.                 property and the isotropic stress/MohrCoulomb property
Breakdown stress can be much higher or lower than the value of FG.                cases, rock failure (unless very strong) results in no effective
When FG is considered equal to the near-wellbore hoop stress,                     strengthening. For the isotropic stress/elastic property case,
significant drilling risks are incurred.                                          no strengthening occurs except for very long fractures due to
                                                                                  a lack of stress contrast around the wellbore.
     b. Individual Points
                                                                             6.   For a given frac length, hole size impacts the amount of
     1.   Formation modulus, or rock stiffness, has a large impact on             strengthening with lower strengthening in larger hole sizes.
          the width of a created fracture but not strengthening. An               Wellbore size will impact the increase in breakdown for a
          increase in the formation Young’s modulus reduces fracture              given propped fracture length. For larger wellbores, the
          width, but, all other things being equal, modulus does not              potential increase in breakdown can be reduced by as much
          alter the increase in breakdown after strengthening.                    as 46% over a smaller wellbore. The larger the wellbore, the
                                                                                  less the benefits increasing breakdown due to a given length
     2.   There is a critical importance of created fracture length on            propped fracture. Nonetheless, a significant increase in
          fracture width (though there is little control or knowledge of          breakdown, 5.1ppg for the extra long propped fracture, can
          actual field lengths). Fracture length, as a proxy for fracture         still be achieved even in a larger wellbore.
          width, plays a significant role in the magnitude of increase of
          breakdown pressure due to wellbore strengthening. The              7.   In order to see the benefit of a propped fracture on
          longer the propped length, the greater the potential increase           breakdown, the fracture must be propped at the wellbore
          in breakdown pressure for the wellbore. Longer fractures                wall. If the fracture is propped some distance into the
          allow greater fracture width and it is the increase in fracture         formation and away from the wellbore wall, there may be no
          width that actually creates the greater increase in breakdown           increase in breakdown due to the presence of the propped
          pressure.                                                               fracture. In the event that the propping agent gets pushed
                                                                                  further into the fracture or gets dislodged from the mouth of
     3.   Stress contrast (SHmax<>Shmin) plays an important role in               the fracture due to drilling operations, the simulation suggests
          strengthening. The horizontal stress anisotropy plays a                 that this can completely eliminate any benefit from creating a
          significant role in the magnitude of increase of breakdown              propped fracture in the wellbore wall. Consequently, the
          pressure. The closer the magnitude of the two horizontal                wellbore strengthening treatment must be designed to prop
          principle stresses, the less the potential increase in breakdown        the fracture at the wellbore wall and remain there through
          pressure. In fact, for the shorted propped fracture lengths             subsequent drilling operations.
          and isotropic horizontal stresses, there is no benefit to
          creating a propped fracture. This strongly suggests that in        c. Summary Points
          order to properly design a wellbore strengthening operations,
          both the minimum and maximum horizontal stresses must be           1.   It is important to know the formation modulus in order to
          known.                                                                  estimate the fracture width – which is needed to size the
                                                                                  plugging material.
     4.   There is a critical importance of rock strength/failure. While
          assuming elastic rock behavior shows encouraging results for       2.   There is a critical need for an accurate estimate of fracture
          wellbore strengthening, the influence of shear failure in weak          length to estimate width – which, again, is needed to size
          rocks may significantly affect the ability to increase                  plugging material AND determines the amount of
          breakdown. If the formation is very strong, relative to the             strengthening. Basically, if the rock is strong enough, you get
          stresses created around the wellbore due to drilling and the            more strengthening with a wider fracture, which comes with
          creation of a propped fracture, then the elastic results are            longer fractures.
          appropriate. However, if the rock is not strong and shear
          failure occurs in association with the effort to increase the      3.   It is important to know the stress contrast around the
          breakdown pressure of the well, then the simulation results             wellbore. If the stress conditions around the wellbore are at
          raise a number of uncertainties. First, at least some of shear          or near isotropic, only very long fractures will provide
          zones are likely to completely fail and create cuttings in the          strengthening.
          wellbore. This will alter the cylindrical shape of the wellbore
          and reduce the ability to increase the tangential stress within    4.   In weak formations, rock failure will occur and little or no
          the wellbore wall. If the shear-failed material remains intact          strengthening is likely.
Permeability Effects
                                                                              Table 2 shows the fracture width changes with different fracture
The first paper dealt with the perfectly impermeable case; that is, even      lengths, stress conditions, and formation strength behaviors. The
as mud pressure exceeded the formation pressure, the formation                fracture length changes from 2in to 15.7in in both impermeable and
pressure did not increase. So, the influence of formation permeability        permeable cases.
and filtrate leak-off was also not reviewed in that study.
                                                                              In the permeable case, fracture widths are at least an order of magnitude
In the permeable case (our case is the perfectly permeable case where         narrower than in the impermeable case. This is due to the breakdown
near wellbore pressure matches the increase in mud pressure), the             pressure being relatively smaller and closer to the far-field stress.
increasing formation pore pressure reduces the effective stresses on          Admittedly, since this does not account for fracture toughness effects,
formation and reduces the breakdown limit. This filtrate invasion will        the widths may be larger. However, for such narrow, transient fractures,
increase the chance of formation shear failure, and in turn, would alter      it is difficult to estimate the increase in width due to fracture toughness.
the ability to increase the tangential stress in the wellbore wall. This is
well known.                                                                   These narrow widths also are due to complete leakoff into the
                                                                              formation. Logically, the drilling fluid will have some wall-building
Simulations of Strengthening                                                  effect, which will increase the pressure drop in these small fractures and
                                                                              increase the width. Again, it is difficult to estimate this due to the very
The effect of permeable case in wellbore strengthening for breakdown          transient nature of these fractures.
pressure and tangential hoop stress was evaluated with the finite
difference software FLAC3DTM. For the model description, mechanical                c. Breakdown after the strengthening treatment
properties, boundary conditions, initial conditions, model verification
and fracture simulations, the previous paper21 gave detailed information.     Table 3 shows the breakdown pressure changes with the wellbore
                                                                              strengthening treatment. The results in the tables come from the
    a. Breakdown limits                                                       original paper and shows the potential strengthening associated with the
                                                                              various cases. In the impermeable cases, there was no strengthening
Table 1 shows the breakdown limit from model evaluation for both              with any case. This was due solely to the very narrow created fracture
impermeable and permeable cases. The results are based on the                 widths.
combinations of isotropic stress, anisotropic stress, elastic formation
behavior and Mohr-Coulomb type behavior.                                           d. Breakdown IF the impermeable case fracture
                                                                                      widths were achieved
For both the AE and AMC cases, breakdown occurred at less than the
far-field Shmin value. This is typically a ballooning-type event. 11.8 ppg    Table 4 shows the breakdown pressure changes under the permeable
and 11.9 ppg of breakdown values are reported in Table 1 for AE and           case if the impermeable case fracture widths were achieved.
AMC in permeable case. The far field minimum horizontal stress is
12.51 ppg. “Ballooning” originally implied that the wellbore diameter         If either or both fracture toughness effects or wall-building effects allow
expands when circulation is started due to the additional ECD and             for greater fracture width, the likely upper limit would be the fracture
contracted when circulation was stopped. It seems more likely that the        widths from the impermeable case. Table 4 shows a comparison of
phenomenon is due to fractures being opened and closed by the                 potential strengthening from the original impermeable simulations and
breakdown pressure and far field fracture gradient. Mud losses while          the new permeable cases. Note, again, that these are only possible with
circulating are required for ballooning to occur but these are partial and    additional delta pressure down the fractures.
not total. Small losses that are continuous while drilling ahead may not
easily be detected but can accumulate to a sizeable volume over a long        The cases with Mohr Coulomb failure are not shown because, just as in
drilling time. The losses must be into fractures that are contained within    the impermeable case, no real strengthening was possible due to rock
a limited fracture network. When the pumps are stopped, the annular           failure along the wellbore wall.
pressure will fall and mud lost to these fractures will flow back into the
well bore. Such returns are more noticeable than the losses since the         Discussion
return occurs rapidly and during a period when no flow is expected.
                                                                              Based on the previous paper and the current study, there are some
In the IE and IMC cases, breakdown occurred at roughly the same               points to address:
value of far-field Shmin shown in Table 1.
                                                                                   a.   The permeable case is admittedly a worse-case scenario where
The ballooning situation for the AE and AMC cases means that care                       there is essentially no wall-building capacity within the mud-
must be used during the strengthening treatment design. Typically, the                  system. It also requires something akin to a very high-
treatment is run to some small pressure beyond the inflection point in a                permeability sandstone.
pressure vs. volume plot. However, this may mean only micro-fractures
are created as an additional 0.6 to 0.7 ppg is required to just reach the          b.   Less important than the magnitude of potential strengthening
far-field Shmin value.                                                                  due to fracture creation in the impermeable case (a maximum
                                                                                        of 4.2 ppg in the anisotropic elastic case with a long fracture),
     b. Fracture Width                                                                  is the importance of the potential ‘strengthening’ that is
         achieved simply by preventing pore pressure buildup in the        5.    Wang, H., Towler, B.F. and Soliman, M.Y. 2007:
         formation around the wellbore. Comparing the initial                    “Fractured Wellbore Stress Analysis – Can Sealing
                                                                                 Micro-cracks Really Strengthen a Wellbore?” paper
         breakdown between the impermeable and permeable cases,                  SPE/IADC 104947 presented at SPE/IADC Drilling
         breakdown in the anisotropic case is increased 3.1 ppg (from            Conference, Amsterdam, The Netherlands, 20-22
         11.9 to 15.0) simply by preventing pressure buildup in the              February.
         formation. In the isotropic case, this is 3.9 ppg (from 12.6 to   6.    Wang, H., Towler, B.F. and Soliman, M.Y. 2007. Near
         16.5 ppg). As should be well known, this ‘strengthening’ is             Wellbore Stress Analysis and Wellbore Strengthening for
                                                                                 Drilling Depleted Formations. Paper SPE 102719
         achieved without any elaborate strengthening treatment but by
                                                                                 presented at the SPE Rocky Mountain Oil & Gas
         simply improving the mud system.                                        Technology Symposium, Denver, Colorado, U.S.A., 16–
                                                                                 18 April.
    c.   If the initial breakdown does reflect the permeable case before   7.    Wang, H. 2007. Near Wellbore Stress Analysis for Wellbore
         wall-building occurs, note the amount of strengthening can              Strengthening. Ph.D. Dissertation, University of Wyoming,
         become very significant. For example, in the AE case,                   Laramie, Wyoming, 26 March.
                                                                           8.    Wang, H., Towler, B.F. and Soliman, M.Y. 2008.
         breakdown occurs at 11.9 ppg. If an Xlong fracture is created           Investigation of Factors for Strengthening a Wellbore by
         and wall-building occurs (allowing formation pressure to drop           Propping Fractures. Paper IADC/SPE 112629
         back to the far-field pressure – a normal hydrostatic gradient          presented at the IADC/SPE Drilling Conference,
         in this case), then strengthening could be as high as 11.2 ppg          Orlando, Florida, 4–6 March.
         (8.1 ppg plus 3.1 ppg).                                           9.    Wang, H., Soliman, M.Y., Towler, B.F. and Mukai, D.
                                                                                 2008. Avoiding Drilling Problems by Strengthening the
                                                                                 Wellbore while Drilling. Paper ARMA 08-200 presented
                                                                                 at the 42nd US Rock Mechanics Symposium and 2nd
Nomenclature                                                                     U.S.-Canada Rock Mechanics Symposium, San
                                                                                 Francisco, June 29-July 2.
FG = Fracture Gradient                                                     10.   Wang H., Towler B.F., Soliman M.Y., and Shan Z. 2008.
E = Young’s Modulus                                                              Wellbore Strengthening without Propping Fractures:
ν = Poisson’s ratio                                                              Analysis for Strengthening a Wellbore by Sealing
UCS = Unconfined Compressive Strength                                            Fractures Alone. Paper IPTC 12280 presented at the
AE = Anisotropic stress model with elastic behavior                              International Petroleum Technology Conference held in
AMC = Anisotropic stress model with Mohr-Coulomb behavior                        Kuala Lumpur, Malaysia, 3–5 December.
IE = Isotropic stress model with elastic behavior                          11.   Fuh, G-F., Morita, N., Boyd, P.A., and McGoffin, S.J.
IMC = Isotropic stress model with Mohr-Coulomb behavior                          1992. A New Approach to Preventing Lost Circulation
PSA = Analytical plane-strain equation results                                   While Drilling. Paper SPE 24599 presented at the SPE
SB = Small Wellbore                                                              Annual Technical Conference and Exhibition,
LB = Large Wellbore                                                              Washington, D.C., 4-7 October.
LB/HM = Large wellbore with high modulus                                   12.   Aston, M.S. et al. 2004. Drilling Fluids for Wellbore
                                                                                 Strengthening. Paper SPE/IADC 87130 presented at the
                                                                                 IADC/SPE Drilling Conference, Dallas, Texas, 2-4
                                                                                 March.
Acknowledgements                                                           13.   Alberty, M.W., and Mclean, M.R. 2004. A Physical
                                                                                 Model for Stress Cages. Paper SPE 90493 presented at
The authors acknowledge permission from ConocoPhillips to publish                SPE Annual Technical Conference and Exhibition,
this paper. The opinions presented are those of the authors and do not           Houston, Texas, 26-29 September.
                                                                           14.   Wang, H., Soliman, M.Y., Whitfill, D.L., Towler, B.F.
necessarily represent those of the ConocoPhillips.
                                                                                 2008. Case Histories Show Wellbore Strengthening as a
                                                                                 Cost-Effective Option for Drilling with Narrow Mud
References                                                                       Weight Windows. Paper AADE-08-DF-HO-17
                                                                                 presented at the AADE Fluids Conference and
          1.   Postler, D.P. 1997. Pressure Integrity Test                       Exhibition, Houston, Texas, April 8-9.
               Interpretation. SPE/IADC paper 37589, presented at          15.   Whitfill, D., Jamison, D. E., Wang, H., and Thaemlitz,
               the SPE/IADC Drilling Conference, Amsterdam, The                  C. 2006. New Design Models and Materials Provide
               Netherlands, 4-6 March.                                           Engineered Solutions to Lost Circulation. Paper SPE
          2.   Oort, E.V. and Vargo, R. 2007. Improving Formation                101693 presented at the Russian Oil and Gas Technical
               Strength Tests and Their Interpretation. SPE/IADC                 Conference and Exhibition, Moscow, Russia, 3-6
               paper 105193, presented at the SPE/IADC Drilling                  October.
               Conference, Amsterdam, The Netherlands, 20-22               16.   Whitfill, D., Wang, H., Jamison, D. E., and Angove-
               February.                                                         Rogers, A. 2007. Preventing Lost Circulation Requires
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               Stress Measurements During Drilling Operations. SPE               International Oil Conference and Exhibition, Veracruz,
               paper 24593, presented at the 67th Annual Technical               Mexico, 27-30 June.
               Conference and Exhibition of the Society of Petroleum       17.   Aston, M.S, Alberty, M.W., Duncum, S. Bruton, J.R.,
               Engineers held in Washington, D.C., October 4-7.                  Friedheim, J.E. and Sanders, M.W. 2007. A New
          4.   Okland, D., Gabrielsen, G.K., Gjerde, J., Sinke, K. and           Treatment for Wellbore Strengthening in Shale. SPE
               Williams, E.L. 2002. The Importance of Extended Leak-             paper 110713, presented at the SPE Annual Technical
               Off Test Data for Combating Lost Circulation.                     Conference and Exhibition, Anaheim, California, USA,
               SPE/ISRM paper 78219, presented at the SPE/ISRM                   11-14 November.
               Rock Mechanics Conference held in Irving, Texas, 20-
               23.
       18. Wang, H., Soliman, M.Y. and Shan, Z. 2008.                                   SPE Annual Technical Conference and Exhibition held
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           World Oil, Vol. 229, No. 6, June 2008, 77-81.                            21. Nagel, N. and Meng, F. What Does the Rock Mechanics
       19. Ramirez, M., Diaz, A., Luna, E. and Figueroa Y.                              Say: A Numerical Investigation of “Wellbore
           Successful Application of Synthetic Graphite to                              Strengthening”. AADE-07-NTCE-65, Houston, Texas,
           Overcome Severe lost Circulation Problem in the                              April 10-12, 2007.
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           30, Houston, Texas, April 5-7, 2005.
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           Fractured Formations. SPE 101802, presented at the



                                                 Table 1: Breakdown Limits (ppg)
                          Condition         AE Model          AMC Model          IE Model         IMC Model
                         Impermeable             15.0              15.0          16.5                    16.5
                          Permeable              11.8              11.9          12.5                    12.6
                        AE is the anisotropic stress model with elastic behavior
                        AMC is the anisotropic stress model with Mohr-Coulomb behavior
                        IE is the isotropic stress model with elastic behavior
                        IMC is the isotropic stress model with Mohr-Coulomb behavior
                        Iso Stress: SHmax=Shmin=12.51ppg
                        Aniso Stress: SHmax=13.96 ppg; Shmin=12.51 ppg




                                       Table 2: Fracture 1/2 Width - Impermeable (in)
                               Frac Length        AE Model      AMC Model        IE Model     IMC Model
                                 Short (2in)       3.85E-03         4.30E-03      5.10E-03      6.18E-03
                               Medium (3.9in)      6.41E-03         6.98E-03      8.83E-03      1.05E-02
                                Long (7.9in)       1.14E-02         1.25E-02      1.64E-02      2.01E-02
                               Xlong (15.7in)      2.42E-02         3.07E-02      3.59E-02      6.27E-02
                                              Fracture 1/2 Width - Permeable (in)
                               Frac Length        AE Model      AMC Model        IE Model     IMC Model
                                 Short (2in)        5.79E-04       2.80E-04       7.28E-05 6.93E-06
                              Medium (3.9in)        6.93E-04       3.43E-04       1.08E-04 7.48E-06
                                Long (7.9in)        7.32E-04       4.37E-04       2.33E-04 7.68E-06
                               Xlong (15.7in)       1.09E-03       6.14E-04       1.09E-03 7.74E-06
                             AE is the anisotropic stress model with elastic behavior
                             AMC is the anisotropic stress model with Mohr-Coulomb behavior
                             IE is the isotropic stress model with elastic behavior
                             IMC is the isotropic stress model with Mohr-Coulomb behavior


                       Table 3: Change in Breakdown Pressure (ppg, 10000 ft-TVD)
Propped Length        AE Model        Increase      AMC Model         Increase     IE Model    Increase     IMC Model       Increase
      Short (1in)            17.4              2.4         17.7          2.7           16.5        0.0            16.5          0.0
    Medium (2in)             18.8              3.8       ? 19.1 ?         ---          16.5        0.0          ? 16.8 ?        ---
     Long (3.9in)            20.5              5.5       ? 21.5 ?         ---          17.4        0.9          ? 17.9 ?        ---
     Xlong (7.9in)           23.1              8.1       ? 23.9 ?         ---          19.9        3.4          ? 25.9 ?        ---
AE is the anisotropic stress model with elastic behavior
AMC is the anisotropic stress model with Mohr-Coulomb behavior
IE is the isotropic stress model with elastic behavior
IMC is the isotropic stress model with Mohr-Coulomb behavior
Note: Breakdown in anisotropic model was 15.0ppg and 16.5ppg for the isotropic stress model
             Table 4: Change in Breakdown Pressure (ppg, 10000 ft-TVD) - Same Frac Width
                                            Impermeable                                                    Permeable
Propped Length        AE Model        Increase       IE Model       Increase       AE Model      Increase      IE Model   Increase
      Short (1in)            17.4              2.4       16.5           0.0              13.1        1.2         12.6       0.0
    Medium (2in)             18.8              3.8       16.5           0.0              13.8        1.9         12.6       0.0
     Long (3.9in)            20.5              5.5       17.4           0.9              14.8        2.9         13.1       0.5
     Xlong (7.9in)           23.1              8.1       19.9           3.4              16.1        4.2         14.4       1.8
AE is the anisotropic stress model with elastic behavior
AMC is the anisotropic stress model with Mohr-Coulomb behavior
IE is the isotropic stress model with elastic behavior
IMC is the isotropic stress model with Mohr-Coulomb behavior
Note: Breakdown in impermeable anisotropic model was 15.0ppg and 16.5ppg for the isotropic stress model
Note: Breakdown in permeable anisotropic model was 11.9 and 12.6 ppg for the isotropic stress model

								
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