Affection mechanism research of initiation crack pressure of perforation parameters of horizontal well

Accepted Manuscript Affection Mechanism Research of Initiation Crack Pressure of Perforation Parameters of Horizontal Well Hua Tong, Ningning Wang, Liangliang Dong, Xiaohua Zhu PII:

S2405-6561(16)30066-9

DOI:

10.1016/j.petlm.2016.05.002

Reference:

PETLM 79

To appear in:

Petroleum

Received Date: 11 December 2015 Revised Date:

21 April 2016

Accepted Date: 5 May 2016

Please cite this article as: H. Tong, N. Wang, L. Dong, X. Zhu, Affection Mechanism Research of Initiation Crack Pressure of Perforation Parameters of Horizontal Well, Petroleum (2016), doi: 10.1016/ j.petlm.2016.05.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Affection Mechanism Research of Initiation Crack Pressure of Perforation Parameters of Horizontal Well Hua Tong , Ningning Wang , Liangliang Dong , Xiaohua Zhu School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China

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ABSTRACT Horizontal wells show better affect and higher success rate in low water ratio cement, complex fracture zone, crevice and heavy oil blocks, it is the main measures to expand control area of a single well. Hydraulic fracturing technology is the most financial way to improve the penetration of the reservoir to increase the production. However, compare with the vertical wells, the fracture of Horizontal wells are more complex, and lead to the

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initiation crack pressure is much higher than vertical wells. In this paper, defined the crack judging basis, and established the finite element model which could compute the initial crack pressure, to research the affection

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mechanism of perforation azimuth angle, density, diameter and depth, to provide references of perforation project’s design and optimize. The research of this paper has significances on further understanding the affection mechanism of perforation parameters. Keywords:

horizontal well

perforation parameter

0 Introduction

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Drilling horizontal well is an important measure to reduce exploration and development cost, increase single well productivity and enhance the recovery rate. Especially, it boasts of good application effect and high success rate in terms of the exploration and tapping potentials of oil deposits characterized by low water, complex fault block, crack, heavy oil, etc [1, 2]. The hydraulic fracturing technology is one of the most economic and effective ramping up production measures to innovate permeation reservoir and meet with industrial exploration need [3, 4]. During the hydraulic fracturing, the increase of hydraulic force of fracturing will pose higher requirements on booster equipment and fracturing sling, and significantly raise the hydraulic fracturing cost. In the early 1898, Ljunggren, C. and Amadei, B. researched the method to estimate virgin rock stressed from horizontal hydro-fractures which started the rock cracked pressure prediction research [5]. And then, Hubbert, M. K. et al. studied the hydraulic fracturing mechanics, and developed the first realistic model relating the hydraulic fracturing test variables to the rock stress distribution [6]. Haimson, B. et al.

initiation crack pressure

crack mechanism

researched rocks initial crack and crack extension during hydraulic fractures, their researches invoked the theory of poroelasticity to incorporate the fluid injection effect on the wellbore around rock stress distribution [7]. Hudson, J. A. et al. researched the rock tension strength theory and statistical the approach of rock failure that refer judgment of rock crack theory with rock mechanical properties [8, 9]. Hoek, E. , Bieniawski, Z. T. et al. concluded some strength criterion for rock massed with many rock crack tests and statistical [10, 11] . El Rabaa, W. et al. studied the affection of initial cracked pressure during hydraulic fracture by wellbore geometry from horizontal wells with experimental methods [12]. Soliman, M. Y and Weijers, L. et al. interpreted the affection reason by the hole deviation of horizontal wells of the hydraulic fracture, and concluded some laws of the rock initial crack pressure [13, 14]. Hossain, M. M. et al. researched the hydraulic fracture initiation and propagation of rock with the affection of trajectory, perforation and stress regimes [15]. Djurhuus, J. and Nelson, E. J. studied the way to inverse in situ stress state with fracturing data from oil wells and borehole image logs [16, 17]. Wu, H., Jasarevic, H. et al. observed the hydraulic fracture

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the strata initiation fracture pressure. A good many scholars [31-33] have conducted empirical study on the calculation of initiation fracture pressure, and drawn some rules on the impact on initiation fracture pressure by the perforation parameters, and Zhu, X.et al. research the parameter control methods for the pumping tool string composed of perforating gun and fracturing plug in a horizontal well, and the results show that, with increasing well head pressure, the grease injection rate should be increased to improve sealing pressure, and the minimum weight of tool string should also increase, which show the difficulty of pressure increase[34]. However, the literature above doesn't illustrate in detail the mechanism of impact on the initiation fracture pressure of the strata by the perforation parameters. A basis for perforation hole fracture judgment is put forward herein. Besides, the impact on the initiation fracture pressure of the strata by the perforation azimuth angle, diameter, depth and density is studied through the establishment of the finite element model for calculating the initiation fracture pressure of the strata.

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initiation and propagation with simulation experiment [18, 19] . Jiang, H. et al. researched the impact of oriented perforation on hydraulic fracture initiation and propagation [20]. Huang, J. et al. referred that the magnitude of the most tensile strength in the wellbore wall should always be compared with the tensile strength of the rock to predict hydraulic fracture initiation based on elastic theory, and some special cases have been found in which the most tensile principle stress reaches the tensile strength of the rock simultaneously at all point on the circumference of the wellbore [21]. Lecampion, B. et al. researched the hydraulic fracture initiation from an open-hole, the affection of wellbore size, pressurization rate and fluid-solid coupling of the fluid and wellbore [22]. Finite element method used widely with the fast speed developing of computing methods. Smart, K. J. et al. established the geomechanical model of hydraulic fracture initiation and propagation in a mechanically stratified geologic system [23]. Zhu, H. et al. in combination with the tensile failure criterion, a prediction model for the hydraulic fracture initiation pressure in the shale gas reservoirs is put forward, and the study provides a reference for the hydraulic fracturing design in shale gas wells [24]. Fan, T. et al. researched the impact of cleats on hydraulic fracture initiation and propagation in coal seams with experiments [25]. Stanchits, S. et al. onset of hydraulic fracture initiation monitored by acoustic emission and volumetric deformation, and three experiments were conducted on a low permeability sandstone block, loaded in a poly-axial test frame, to representative effective in situ stress conditions [26]. Lei, X. et al. researched the impact of perforation on hydraulic fracture initiation and extension in Tight Natural Gas reservoirs. Jeffrey, R. G. measured and analyzed the Full-Scale hydraulic fracture initiation and reorientation [27]. Dehghan, A. N. et al. using a tri-axial hydraulic fracturing test system studied the mechanism of fracture initiation and propagation in naturally fractured reservoirs [28]. Fatahi, H. et al. using distinct element method studied the determination of hydraulic fracture initiation and breakdown pressure by numerical simulation [29]. Zhao, X. et al. researched the impact of hydraulic perforation on fracture initiation and propagation in shale rocks [30]. Also, perforation parameters are an important

1 Mathematic Model and Perforation Hole Fracture Judgment Basis 1.1 Main Stress of Shaft Acted by the crustal stress, the stress state in the perimeter of the shaft is one of the important factors affecting the initiation fracture pressure. The main stress σ 1 , σ 2 , σ 3 in three directions are separately[35] :

  σ1 = σ r  1  2 σ 2 =  (σ θ + σ zz ) + (σ θ − σ zz + 4τ θ z  2  1  2   σ 3 = 2  (σ θ + σ zz ) − (σ θ − σ zz + 4τ θ z  Where:

1

σ r radial stress, σ θ circumferential stress,

positive stress in the axial direction of shaft,

τθ z

tangential stress in the perimeter of well wall. 1.2 Perforation Hole Fracture Judgment Basis Based on the state of load imposed in the

ACCEPTED MANUSCRIPT Perforation hole

Rock

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perimeter of the perforation hole shown in figure 1, acted by the crustal stress, the rock surrounding the perforation hole is under the pressure state. During the hydraulic fracturing, the acting force of the fracture fluid in the perforation hole is also the pressure. Therefore, the rock surrounding the hole cannot present the tension stress state. However, there is indeed tension stress here. In order to resolve the aforementioned contradiction, the circumferential stress of the hole acted by the crustal stress is taken as the reference herein, and the variation of the circumferential stress of the hole acted by hydraulic fracturing (stress difference) is used as the basis for judging whether the hole is fractured, namely

Fig.1. The stress state of the perforation holes.

2 Finite Element Model

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2.1 Governing equations

σ = σe −σ p

2

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σ e = σ e21 + σ e22 + σ e23 + τ e212 + τ e213 + τ e223

The constitutive equation can be expressed with the modified Hooke’s law[36]

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σ ij' = DTε ij

σ p = σ +σ 2 p1

2 p2

+σ

2 p3

+τ

2 p12

+τ

2 p13

+τ

2 p 23

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Where:

σ e Mises stress value acted by the crustal

stress,

σ e1 , σ e 2 , σ e 3 , τ e12 , τ e13

and

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τ e 23 respectively main stress or shear stress in each

direction acted by the crustal stress, σ p Mises stress value simultaneously acted by the crustal stress and

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fracturing fluid, σ p1 , σ p 2 , σ p 3 , τ p12 , τ p13 and τ p 23

respectively main stress or shear stress in each direction simultaneously acted by the crustal stress and fracturing fluid.

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When σ > 0 , the rock is under pressure; when

σ < 0 , the rock is under tension. When the tension stress is more than the tensile strength of the rock, the strata fracture initiates. Therefore, the basis for judging fracture of the perforation hole may be defined as:

−σ > σ s

6

5

 1  E  h  vhh − E h   vvh − Ev DT =          

Where,

vhh Eh

−

vvh Ev

1 Eh

−

vvh Ev

−

−

vvh Ev

               2(1 + vhh )   Eh 

1 Ev 1 Gvh 1 Gvh

Ev

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is the elasticity modulus in the

perpendicular direction; Eh is the elasticity modulus in horizontal direction; vv is the Poisson’s ratio of the horizontal strain when vertical strain is applied;

vh is the Poisson’s ratio of the horizontal strain when horizontal normal strain is applied; Gv is the shear modulus in the vertical plane; Gh is the shear

Where: σ s tensile strength of rock.

modulus in the horizontal plane

[36]

. Assume that the

rock is isotropic in the horizontal direction, Gh and

Gv can be shown below

ACCEPTED MANUSCRIPT  1 8 ϕ1' ( z1 ) = E ' µ2 − D ' )  ( 2∆ ( µ1 cos θ − sin θ ) 

1 2(1 + vh ) = Gh Eh

The elasticity matrix given above is defined in the local coordinate system in the bedding plane, whereas in the wellbore stability analysis, the stress and deformation occur under the well coordinate system. Therefore, the elasticity matrix under the bedding plane coordinate system needs to be transformed into the well coordinate system [24]. The elasticity matrix D under the cylindrical coordinate is

D=qDTq 0

sin 2 α

0

−2sin α cos α

1

0

0

0

0

cos α

0

2sin α cos α

0

0

cos α

0

0

cos 2 α − sin 2 α

− sin α

0

2

0 − sin α cos α 0

0

0   0  0   sin α  0   cos α 

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TE D 12

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  D = ( Pw − σ 1,0 ) cos θ − τ 12,0 sin θ   − i ( Pw − σ 1,0 ) sin θ − iτ 12,0 cos θ   ' E = − ( Pw − σ 2,0 ) sin θ − τ 12,0 cos θ   − i ( Pw − σ 2,0 ) cos θ  ' F = −τ 13,0 cos θ − τ 13,0 sin θ − iτ 13,0 cos θ  '

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Where Pw is the pressure of the fluid column in

Where α is the azimuth angle. The analytical model for the stresses around wellbore of the bedding shale reservoir could be obtained from boundary conditions.  σ 1 =σ 1,0 + 2 Re {µ12ϕ1' z1 ) + µ 22ϕ 2' z2 )}   σ 2 = σ 2,0 + 2 Re {ϕ1' z1 ) + ϕ 2' z2 )}    a  µ 2ϕ ' z ) + µ22ϕ 2' z 2 )    σ = σ − 2 Re  31  1 1 1  a33 3,0  3 ' '  + a32 ϕ1 z1 ) + ϕ 2 z 2 )     τ 12 = τ 12,0 − 2 Re {µ1ϕ1' z1 ) + µ2ϕ 2' z2 )}   τ 13 = τ 13,0 + 2 Re {µ3ϕ3' z3 )}   τ 23 = τ 23,0 − 2 Re {ϕ3' z3 )} 

∆ =µ 2 − µ1

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Where

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13

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v 1 1 1 = + +2 v Gh Eh Ev Ev

 cos 2 α  0   sin 2 α q=  0  sin α cos α  0 

 1 D ' − E ' µ1 )  ( 2∆ ( µ 2 cos θ − sin θ )   1 ϕ3' ( z3 ) = F ' µ 2 − µ1 )  ( 2∆ ( µ3 cos θ − sin θ ) 

ϕ 2' ( z2 ) =

Where z k = x + µ k y ( k = 1, 2,3) , µk is the characteristic root of the characteristic equation corresponding to the equation of strain compatibility, and the analytical function ϕ k ( z k ) is determined by the boundary conditions. It can be expressed below

the wellbore; a31 , a32 and a33 are the elements in the flexibility coefficient matrix A. This model can be used to solve for the stress distribution around wellbore in anisotropic strata with any well deviation angle, well azimuth angle, principal stress field, stratum dip angle, etc. The crack pressure judge see section 1.2. 2.2 Computed Model With respect to the horizontal well, the shaft axial direction is usually perpendicular to the direction of the minimal horizontal main stress. Therefore, the physical model is established herein by taking the shaft axial direction as the horizontal symmetry center. In order to reduce unit quantity and save calculation time, the model is reasonably dissected. C3D8R hexahedron unit is used to make grid classification, and the perforation hole perimeter undergoes unit segmentation so as to reduce impact on the calculation result by the grid accuracy, shown in figure 2. So as to facilitate analysis on the distribution state of the circumferential stress of the shaft, assumptions below are made: 1) the strata rock represents the homogeneous isotropic elastic porous medium, 2) the physical and chemical action of the rock and fracturing fluid is not taken into account, 3) the perforation hole axis and shaft axis are

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perpendicular and well connected, 4) the pressure of fluid inside the perforation hole is constant.

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Experimental results Computed results

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25 0

25

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Fracture pressure

Shaft

50

75

100

Azimuth angle

Perforation hole

Fig.3. Comparison of the experimental results and the computed results

Fig.2. Mesh model

2.3 Basic Parameters

Change the angle (hereinafter referred to as the azimuth angle) of the perforation axis and the maximum main stress in vertical shaft direction (overburden pressure here), perforation hole diameter, depth and density, and analyze reasons for and rules of impact on the initiation fracture pressure by each element. In order to better extract the stress value in the perimeter of the perforation hole acted by the load, the calculation assumes that the rock will not be fractured under infinite pressure. Besides, make artificial judgment on whether there is fracture by comparison.

2.4 Model Validation

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A certain oil field block is taken as an example herein, the vertical depth in the horizontal section 1,400m, shaft diameter 5-7/8, rock's young modulus 17 796MPa, Poisson ratio 0.2, tensile strength of rock 8MPa. The average value of the overburden pressure experienced by the strata is 52MPa, minimum horizontal main stress 36.5MPa, maximum horizontal main stress 46MPa.

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3 Calculation Results and Analysis

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In order to validate the correctness of finite element module established herein for calculating the initiation fracture pressure of the horizontal well strata and the initial fracture pressure judgment method, the hydraulic fracturing calculation model under the work condition mentioned in references[7]. Comparison of the experimental results and the computed results is shown in figure 3: It can be seen in figure 3, computed results and experimental results basically match and the error is within the allowed scope. Therefore, the finite element calculation model established hereinto may be used to calculate initiation fracture pressure and study the initiation fracture mechanism.

3.1 Impact of Azimuth Angle In figure 4, the direction at 0°and 180°represents the shaft axial direction, namely: the acting direction of the minimum horizontal main stress. It may be seen in the figure that the stress difference perpendicular to the minimum horizontal main stress direction is obviously lower than the one parallel to the minimum horizontal main stress direction. The direction perpendicular to the minimum horizontal main stress is under tension first, namely the initiation fracture position during fracturing; with the increase of azimuth angle, the tension stress experienced in this direction gradually reduces, and the initiation fracture pressure rises accordingly.

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30

330 2 -2

60

300 -6 -10 270

90

-10 -6 120

240 -2

azimuth angle 30° tension strength

2 150

210 180

azimuth angle 60° azimuth angle 70° azimuth angle 90° tension strength

0 330

30

6 2 300

initiation fracture pressure is the smallest when the azimuth angle is 0. In the meantime, it can be seen from the formula, when the difference of the maximum main stress and minimum main stress perpendicular to the shaft direction is relatively small, the impact on the initiation fracture pressure by the azimuth angle accordingly reduces. In the curved or horizontal section, try to reduce the angle of the perforation hole direction and maximum main stress direction of the strata. Fmin

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-2 -6 -10 270

In case of α ≠ 0 , F < Fα . Therefore, the

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0

F

90

Shaft

240

120

2 6 210

150 180

Fig.4. Stress difference of the perforation holes while the pressure is 40MPa.

F = Fmin

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The change on azimuth angle actually means the change on the acting direction of the crustal force relative to the perforation hole. The main stress parallel to the perforation hole direction has relatively small impact on the initiation fracture pressure. However, the crustal force crossing to perpendicular to the perforation hole direction shows a bigger impact on the initiation fracture pressure of the perforation hole. The force-bearing schematics are given in figure 5 and figure 6. When the azimuth angle is 0, the clamping force of the perforation hole is: 15

The clamping force of perforation hole is:

Fα = Fmin cos α + Fmax sin α

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Where: Fmin minimum main stress in vertical shaft direction; Fmax maximum main stress in vertical

Fmax

-2

Fmin

Fig.5. Force analysis of the perforation holes of different azimuth angle is 0°.

Fmin Fα Shaft

α Fmax

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Fmin

Fig.6. Force analysis of the perforation holes of different azimuth angle is α.

3.2 Impact of Hole Diameter Based on the maximum tension stress experienced by the hole of different parameters shown in figure 7, when the tensile strength of the rock is very low, the tension stress state is presented in the perimeter of the perforation hole with smaller diameter under the very low hydraulic fracturing force. Conversely, the bigger the hole diameter, the quicker the increase of the tension stress in the hole perimeter.

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Tension stress/MPa

Therefore, during the fracturing process design, when the tensile strength of the of the strata rock is lower than 1.5MPa, the smaller perforation hole diameter is recommended; conversely, based on the construction condition, try to select bigger perforation hole diameter.

-4

-2

-6

2mm 3mm 5mm 10mm 16mm 24mm 30mm

0 15

-15

-2

30

40

50

-9

-6

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Fracturing fluid pressure/MPa

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-12

20

45

Depth 800mm Depth 1000mm Depth 1500mm Depth 2000mm Depth 5000mm Depth 10000mm

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0 10

30

Fracturing fluid pressure/MPa

Tension stress/MPa

Tension stress/MPa

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diameter diameter diameter diameter diameter diameter diameter

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Fig.7. The maximum tension stress of the perforation holes in different diameters.

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0

15

3.3 Impact of Hole Depth

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Based on the maximum tension stress experienced by the hole of different depth shown in figure 8, when the hole depth is smaller, the tension stress state is presented under the very low hydraulic fracturing force; however, when the hole depth is lower than 200mm, with the increase of the hydraulic fracturing force, the tension stress increases slowly; when the hole depth reaches more than 1,500mm, the increase rate of the tension stress basically doesn't change. However, with the increase of the hole depth, acted by the lower hydraulic fracturing force, the hole perimeter is only presented with the pressure stress state. Therefore, during the perforation parameters design, it's recommended that the perforation depth

shall be in between 200∼1500mm. In case the tensile strength of the strata rock is relatively low, the smaller hole depth within such scope is recommended. When the tensile strength of the rock is relatively big, bigger hole depth within such scope shall be adopted.

30

45

60

75

Fracture fluid pressure/MPa

Fig.8. The maximum tension stress of the perforation holes in different depths.

3.4 Impact of Hole Density Based on the computed result of circumferential tension stress of perforation hole with different hole density shown in figure 9, acted by the same hydraulic fracturing force, the tension stress state presented in the perimeter of hole at 3 pores/m, 4 pores/m and 5 pores/m is obviously higher than that with hole density at 1 pore/m, 2 pores/m, 6 pores/m and 7 pores/m. During the process when the hole density increases from 1 pore/m to 3 pores/m, acted by the same hydraulic fracturing force, the tension stress presented increases gradually. During the process when the hole density increases from 3 pores/m to 7 pores/m, acted by the same hydraulic fracturing force, the tension stress presented decreases gradually. Force analysis of the rock in oriented perforating is given in figure 10. Take the direction along the shaft as an example, the crustal force experienced by holes on both ends is relatively big; the blockage of the force transmission by holes on both ends reduces the pressure stress experienced by holes in the middle;

ACCEPTED MANUSCRIPT the maximum main stress of the strata direction both

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Acknowledgements

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This research is supported by the Natural Science Fund for Outstanding Youth Science Fund (Grant No. 51222406), New Century Excellent Talents in University of China (NCET-12-1061), Scientific Research Innovation Team Project of Sichuan Colleges and Universities (12TD007), the key projects of academic and technical leaders cultivate fund in Sichuan Province, China(2011-441-zxh), and Sichuan Science and Technology Innovation Talent Project (20132057).

20

25

30

35

Fracturing fluid pressure/MPa

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Tension stress/MPa

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1hole/m 2hole/m 3hole/m 4hole/m 5hole/m 6hole/m 7hole/m

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-8

in the curved section and horizontal section. When the tensile strength of the strata rock is relatively low, smaller perforation diameter and hole depth shall be used; when the tensile strength of the strata rock is relatively high, bigger perforation diameter and hole depth shall be used. When the perforation density is too big or small, the initiation fracture pressure of the strata rock will increase, and it shall be thus controlled in between 3 pores/m ~5 pores/m.

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however, the action of the fracturing fluid pressure on the neighboring hole will offset the pressure of the fracturing fluid pressure of the neighboring hole so that the hole will not be fractured. Thus, the over big perforation hole density will increase the initiation fracture force thereof. During the perforation parameter design, try to control the perforation density in between 3∼5 pore/m.

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Fig.9. The maximum tension stress of the perforation holes in different densities.

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References

perforation hole

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shaft

Fig.10. Force analysis of the rock in oriented perforating.

4 Conclusions

This paper focus on the problem of horizontal wellbore hydraulic fracture pressure initial crack pressure estimate. Researched the estimate accordance of initial crack pressure and the affection of holes’ conditions. The conclusion can be conclude below. Put forward a method of using the stress to judge whether the strata rock is fractured, and prove the reliability of computed results by comparing with the experimental data. Reduce the angle of the perforation direction and

[1] Y.F. Cheng, G.H. Wang, R.H. Wang, Rock mechanics problems in horizontal well fracturing, Chinese Journal of Rock Mechanics and Engineering. 23 (14) (2004) 2463 2466. [2] T.M. Li, The Analysis of the Fracture Parameters on Horizontal Wells Productivity, Journal of Guangdong University of Petrochemical Technology. 24 (6) (2014) 61

63.

[3] A.G. Hu, P. Xiong, C.Y. Yao, Y.L. Li, STATUS QUO AND PROSPECT OF HORIZONTAL WELLS FRACTURING TECHNOLOGY IN DANIUDI GAS FIELD, DRILLIN & RODUCTION TECHNOLOGY. 35 ( 5) (2012) 59

62.

[4] L. Ren, J.Z. Zhao, Y.Q. Hu, W. Luo, AFFECTING FACTOR ANALYSIS OF PRODUCTIVITY FOR HORIZONTALLY FRACTURED WELLS, Journal of Southwest Petroleum University (Science & Technology Edition).32 (4) (2010) 77 81

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approach to rock failure[Z]. 1969901-914. [9] Bredehoeft J D, Wolff R G, Keys W S, et al. Hydraulic fracturing to determine the regional in situ stress field, Piceance Basin, Colorado[J]. Geological Society of America Bulletin. 1976, 87(2): 250-258. [10] Hoek E, Brown E T. Empirical strength criterion for rock masses[J]. Journal of Geotechnical and Geoenvironmental Engineering. 1980, 106(ASCE 15715). [11] Bieniawski Z T, Bauer J. Discussion of" Empirical Strength Criterion for Rock Masses"[J]. Journal of the Geotechnical Engineering Division. 1982, 108(4): 670-672. [12] El Rabaa W, Others. Experimental study of hydraulic fracture geometry initiated from horizontal wells[Z]. San Antonio: Society of Petroleum Engineers, 1989189-204. [13] Soliman M Y, Others. Interpretation of pressure behavior of fractured, deviated, and horizontal wells[Z]. Society of Petroleum Engineers, 1990. [14] Weijers L, De Pater C J, Owens K A, et al. Geometry of hydraulic fractures induced from horizontal wellbores[J]. SPE Production Facilities. 1994, 9(02): 87-92. [15] Hossain M M, Rahman M K, Rahman S S. Hydraulic fracture initiation and propagation: roles of wellbore trajectory, perforation and stress regimes[J]. Journal of Petroleum Science and Engineering. 2000, 27(3): 129-149. [16] Djurhuus J, Aadn O Y B S. In situ stress state from inversion of fracturing data from oil wells and borehole image logs[J]. Journal of Petroleum Science and Engineering. 2003, 38(3): 121-130. [17] Nelson E J, Meyer J J, Hillis R R, et al. Transverse drilling-induced tensile fractures in

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Weibull ’ s theory and a general statistical

implications for the in situ stress regime[J]. International journal of rock mechanics and mining sciences. 2005, 42(3): 361-371. [18] Wu H, Golovin E, Shulkin Y, et al. Observations of hydraulic fracture initiation and propagation in a brittle polymer[Z]. American Rock Mechanics Association, 2008. [19] Jasarevic H, Golovin E, Chudnovsky A, et al. Observation and modeling of hydraulic fracture initiation in cohesionless sand[Z]. American Rock Mechanics Association, 2010. [20] Jiang H, Chen M, Zhang G Q, et al. Impact of oriented perforation on hydraulic fracture initiation and propagation[J]. Chinese Journal of Rock Mechanics and Engineering. 2009, 28(7): 1321-1326. [21] Huang J, Griffiths D V, Wong S. Initiation pressure, location and orientation of hydraulic fracture[J]. INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES. 2012, 49: 59-67. [22] Lecampion B, Others. Hydraulic fracture initiation from an open-hole: Wellbore size, pressurization rate and fluid-solid coupling effects[Z]. American Rock Mechanics Association, 2012. [23] Smart K J, Ofoegbu G I, Das K, et al. Geomechanical modeling of hydraulic fracture initiation and propagation in a mechanically stratified geologic system[Z]. American Rock Mechanics Association, 2012. [24] Zhu H, Guo J, Zhao X, et al. Hydraulic fracture initiation pressure of anisotropic shale gas reservoirs[J]. GEOMECHANICS AND ENGINEERING. 2014, 7(4): 403-430. [25] Fan T, Zhang G, Cui J. The impact of cleats on hydraulic fracture initiation and propagation in coal seams[J]. PETROLEUM SCIENCE. 2014, 11(4): 532-539. [26] Stanchits S, Surdi A, Gathogo P, et al. Onset of Hydraulic Fracture Initiation Monitored by Acoustic Emission and Volumetric Deformation Measurements[J]. ROCK MECHANICS AND ROCK ENGINEERING. 2014, 47(5SI): 1521-1532. [27] Jeffrey R G, Chen Z R, Zhang X, et al. Measurement and Analysis of Full-Scale

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[5] Ljunggren C, Amadei B. Estimation of virgin rock stresses from horizontal hydrofractures[J]. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1898, 26: 69-78. [6] Hubbert M K, Willis D G. Mechanics of hydraulic fracturing[J]. Trans AIME. 1957, 210: 239-257. [7] Haimson B, Fairhurst C, Others. Initiation and extension of hydraulic fractures in rocks[J]. Society of Petroleum Engineers Journal. 1967, 7(03): 310-318. [8] Hudson J A, Fairhurst C. Tensile strength,

2011) 1081

1085.

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Hydraulic Fracture Initiation and Reorientation[J]. ROCK MECHANICS AND ROCK ENGINEERING. 2015, 48(6SI): 2497-2512. [28] Dehghan A N, Goshtasbi K, Ahangari K, et al. Mechanism of fracture initiation and propagation using a tri-axial hydraulic fracturing test system in naturally fractured reservoirs[J]. European Journal of Environmental and Civil Engineering. 2015: 1-26. [29] Fatahi H, Hossain M M, Fallahzadeh S H, et al. Numerical simulation for the determination of hydraulic fracture initiation and breakdown pressure using distinct element method[J]. Journal of Natural Gas Science and Engineering. 2016. [30] Zhao X, Ju Y, Yang Y, et al. Impact of hydraulic perforation on fracture initiation and propagation in shale rocks[J]. Science China Technological Sciences. 2016: 1-7. [31] C.G. Jia, M.Z. Li, J.G. Deng, LARGE-SCALE THREE DMENSIONAL SIMULATION TEST FOR DIRECTIONAL PERFORATION AND FRACTUREINGT IN DEFLECTED WELL, Journal of Southwest Petroleum University. 29 (2) (2007) 135-137. [32] H.X. Lin, C.Z. Du, Experimental research on the quasi three-axis hydraulic fracturing of coal, JOURNAL OF CHINA COAL SOCIETY.36 (11)

EP

[33] Z.W. Huang, G.S. Li, Experimental study on effects of hydrau-perforation parameters on initial fracturing pressure, Journal of China

AC C

University of Petroleum. 31 (6) (2007) 48 51 [34] Zhu X, Xue S, Tong X. Parameter control methods for the pumping toolstring composed of perforating gun and fracturing plug in a horizontal well[J]. PETROLEUM EXPLORATION AND DEVELOPMENT. 2013, 40(3): 398-404. [35] X. Liu, C.J. Liu, T.B. Liu, L.Q. Zhao, Q. Wang, Impact of phase angle on the breakdown pressure of deviated wellbore in perforating, Natural Gas Industry. 30 (3) (2010) 55-56. [36] Sayers C M. Seismic anisotropy of shales[J]. Geophysical prospecting. 2005, 53(5): 667-676.