Research ArticleStudy on Wellbore Stability and Failure Regions of Shaleconsidering the Anisotropy of Wellbore Seepage

Fan Zhang ,1 Houbin Liu,2 Yingfeng Meng,2 Shuai Cui,2 and Haifeng Ye3

1Shaanxi Key Laboratory of Advanced Stimulation Technology for Oil & Gas Reservoirs, Xi’an Shiyou University,Xi’an 710065, China2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China3Geological Exploration & Development Research Institute, CNPC Chuanqing Drilling Engineering Co. Ltd., Chengdu 610051, China

Correspondence should be addressed to Fan Zhang; fanz@xsyu.edu.cn

Received 16 November 2020; Revised 29 November 2020; Accepted 14 December 2020; Published 18 January 2021

Academic Editor: Chun Zhu

Copyright © 2021 Fan Zhang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The hard and brittle shale formation is prone to collapse and instability, and the penetration of drilling fluid along the beddingreduces the mechanical properties of rock near the borehole wall, resulting in serious downhole accidents. Therefore, in thispaper, the geomechanical parameters of the reservoir in the Longmaxi formation of Jiaoshiba were determined by field hydraulicfracturing and laboratory experiments. Then, the stress distribution model of borehole wall under the condition of underbalancedseepage flow is established based on the experimental results obtained by mechanical experiments on underground cores. Theinstability zone of borehole wall under the condition of underbalance is calculated and analyzed. The results show that the two-way horizontal ground stress of the Longmaxi formation is higher than 2.2MPa/100m, and the original ground stress is high.Moreover, the mechanical parameters of the stratified shale stratum matrix and weak surface are significantly different. Thecohesion (4.7MPa) and the angle of internal friction (26.9°) of bedding plane are significantly lower than that of the matrix(7.77MPa) and the angle of internal friction (46.7°). Hard and brittle shale is easy to be destroyed along the stratification. Underthe condition of underbalanced seepage, the mechanical properties of borehole shale can be stable. It is found that when theborehole axis is vertically stratified, the collapse pressure is the lowest, while in other drilling directions, the drilling fluid densityneeds to be increased by 0.5 g/cm3 to maintain the borehole stability. With the increase of the inclination angle of beddingplane, the wall failure area increases. The results of this study can provide guidance and suggestions for drilling in Jiaoshibablock and other permeable hard and brittle shale formations.

1. Introduction

Unconventional oil and gas resources account for about 80%of the world’s oil and gas resources, among which shale oiland gas reservoirs account for a large proportion [1]. There-fore, the effective development of shale oil and gas reservoirsis particularly important. Shale accounts for more than 75%of the world’s drilling, and most of them cause wellboreinstability, resulting in drilling costs of more than $5 billionper year [2]. The drilling test and production results showthat the collapse of the shale section of the Longmaxi forma-tion is very serious in China’s Changning-Weiyuan and Ful-

ing shale gas demonstration areas [3], so it is necessary tostudy the wellbore stability of the shale formation in Fulingarea. After analysis, the factors affecting wellbore stability ofstratified shale mainly include hydration mechanical proper-ties, pore pressure, and in situ stress [4]. Meanwhile, thestrength of shale decreases with the time of mud exposure[5, 6], especially in the Shale area of the Longmaxi formation[7, 8]. Moreover, in situ stress is very important for safe dril-ling [9], and the stress concentration is different from that ofisotropic formations on the borehole wall of stratified shale[10]. Among them, the maximum horizontal ground stresshas the greatest influence on the stability of shale formation

HindawiGeofluidsVolume 2021, Article ID 6694689, 13 pageshttps://doi.org/10.1155/2021/6694689

[11]. In addition, anisotropic seepage will cause changes inthe stress field near the shaft wall [12, 13], which will affectthe accurate calculation of shaft wall collapse pressure.

Bradley [14] has studied borehole wall instability basedon the linear elasticity hypothesis of homogeneous rocks.Subsequently, the problem of borehole wall instability hasattracted the attention of researchers all over the world. Theinfluence of strength anisotropy on wellbore stability is notconsidered in previous models. However, shale contains nat-ural bedding surface, and experimental studies have shownthat the failure form of shale with certain stress state is signif-icantly different from that of homogeneous rock [15–20].Based on the special experimental phenomena of shale, vari-ous mathematical models are established to study the insta-bility of shale formation. Hikweon [21] considered theanisotropic strength of shale, converted in situ stress to bed-ding plane, and the results showed that compared with iso-tropic formation, the critical collapse pressure of shaleformation increased significantly. At the same time, addi-tional stress is generated due to the influence of temperaturegradient, and a wellbore stability model with thermal holeelasticity considered is established [22–25].

The influence of anisotropic seepage in shale formationcannot be ignored. The drilling fluid penetrates into the for-mation along the bedding, changing the stress state aroundthe well and reducing the strength of the rock on the shaft wall[26, 27]. The Longmaxi formation belongs to the hard andbrittle shale, where the water absorption and diffusion coeffi-cient and drilling fluid activity have obvious influences onwellbore expansion and strong sensitivity. Then, the drillingfluid immersion causes instability [28]. For the shale of theLongmaxi formation, water absorption and expansion experi-ments were carried out [8], and the results showed that hydra-tion effect permeated along the bedding surface, and shalesamples were stripped and dropped. As the shale water activityis less than the drilling fluid, in addition to the predictedhydraulic gradient, additional fluids will flow into the shaleformation due to the chemical imbalance applied [29]. Thiscreates abnormal pore pressure near the borehole, followedby additional fluid-induced stress, and prolonged exposureto drilling fluid in the wellbore results in reduced strength.

Underbalanced drilling has high efficiency and low cost. InUBD drilling, the bottom hole is completely compressed [30],which can improve the bottom hole seepage capacity and mini-mize formation damage [31]. In UBD drilling, when consideringfluid seepage, the calculation of collapse pressure is more accu-rate, but the mud density window is narrower [32]. [33, 34] pro-posed a wellbore stability model of anisotropic strengthformation. Before the formation of macroscopic failure surfacein the stratigraphic weak plane, sporadic failure occurs in the rock[35]. Previous wellbore stability models failed to predict the dam-age area around the wellbore. Thus, it is particularly important toaccurately calculate and control the area of minor damage.

Therefore, this paper obtained ground stress data of theLongmaxi formation through field hydraulic fracturing com-bined with laboratory experiments. The mechanical parametersof shale matrix and weak surface were obtained by combiningthe direct shear test and triaxial compression test. Using theseparameters, a wellbore stability model considering anisotropic

seepage under the condition of underbalanced drilling is estab-lished. The collapse pressure and failure area are analyzed, andthe slight failure pattern of wellbore is studied in the same hori-zon at different shale inclination and inclination angle.

2. Stress Distribution Model of Shale Formation

2.1. Coordinate System and Transformation. In the process ofestablishing the anisotropic wellbore stability model, five ref-erence coordinate systems are needed. These five coordinatesystems are called global coordinate systems (GCS), in situstress coordinate system (ICS), borehole coordinate system(BCS), polar coordinate system (PCS), and facture coordi-nate system (FCS). The transformation relationship of thesecoordinate systems is shown in Figures 1 and 2 [36].

In GCS, the positive direction of axis-Xn is defined as thegeographic North Pole, axis-Yn is defined as East, and axis-Zn is perpendicular to the ground. In ICS, this paper stipulatesthat Xo is the horizontal maximum principal stress direction,Yo is the horizontal minimum principal stress direction, andZo is consistent with GCS. It is worth noting that in the studyof [33, 34], it is specified that the positive direction of the x-axis is the direction of the minimum horizontal principalstress, while the positive direction of the y-axis is the directionof the maximum horizontal principal stress. GCS and ICS forthe transformation of the process, according to the right-handrule, first round Zn shaft turn αo, Yn shaft rotate βo again. Therotation matrix for the transformation from GCS to ICS canbe expressed by Equation (1).

MNtO =cos βo 0 −sin βo

0 1 0sin βo 0 cos βo

2664

3775

cos αo sin αo 0−sin αo cos αo 0

0 0 1

2664

3775:ð1Þ

By the same token, GCS and BCS conversion process, αo,βo replace αb, βb, including αb or wellbore azimuth,βb inclina-tion angle, transformation matrix of Equation (2).

MNtB =cos αb cos βb sin αb cos βb −sin βb

−sin αb cos αb 0cos αb sin βb sin αb sin βb cos βb

2664

3775: ð2Þ

In polar coordinates, r is defined as the distance from theborehole axis to the remote formation, and θ is the angle thatrotates counterclockwise from the axis-Xb to the axis-Yb, inthe borehole rectangular coordinate system. Therefore, fromBCS and PCS, you just rotate the BCS about the axis-Zb by θ, the conversion formula of Equation (3).

MBtR =cos θ sin θ 0−sin θ cos θ 00 0 1

2664

3775: ð3Þ

As shown in Figure 2, FCS is based on the direction of the

2 Geofluids

XN (North)

ZN (Down)

YN (East)

Horizontal plane

ICSGCS

CCSBCS(r, 𝜃, z)

(r, 𝜃, z)

XN

YN

ZN

XO

YO

ZO

XB

YB

ZB

XB

YB

ZB

XO

YO

ZO

XB

YB

ZB

αo

αb

𝛽b

𝛽o

σh

𝜎H

θ

Figure 1: The relationship between different coordinate systems.

XN (North)

ZN (Down)

YN (East)

Horizontal plane

ZW

Weak plane

XW

YW

WCS

XW

YW

ZW

𝛽w

𝛼w

Figure 2: The relationship between GCS and WCS.

3Geofluids

weak plane, where Xw determines the tendency of the weakplane and Yw is perpendicular to the weak plane at the azimuthangle of the weak plane. Zw is perpendicular to the weak plane.Therefore, the rotationmatrix of the transformed stress compo-nents from GCS to FCS can be obtained by Equation (4).

MNtW =cos βw sin αw sin βw sin αw cos αw

−sin αw cos βw 0−cos βw cos αw −sin βw cos αw sin αw

2664

3775:

ð4Þ

2.2. Borehole Stress Analysis. As drilling destroys the in situstress state of the shale formation, in situ stress will form a stressconcentration around the wellbore. The conversion process is toconvert in situ stresses into GCS and then convert the stresscomponents in the GCS into different stress components in

the BCS. The above transformation matrix can be used to rep-resent the mutual transformation of ground stress in differentcoordinate systems. Therefore, the ground stress componentin the BCS can be obtained by using Equation (5).

σbcs =MNtB ×MTNtO × σics ×MNtO ×MT

NtB: ð5Þ

Among them, in situ stress is σics = fσH , 0, 0 ; 0, σh, 0 ; 0,0, σvg. MT

NtO and MTNtB are the matrix transpose of MNtO and

MNtB. Based on the stress model around drilling proposed by[14], Equation (6) of elastic isotropic wellbore stress expressionis presented. It is worth noting that in this model, when r = rw,the model can be simplified to the stress model at the previousshaft wall [34]. Since the radius r from borehole axis to deep for-mation is retained in thismodel, the stress state of the formationnear the borehole wall can be calculated by the model.

where rðθ, rÞ, σθðθ, rÞ, σzðθ, rÞ, τrθðθ, rÞ, τrzðθ, rÞ, τθzðθ, rÞ is the normal and tangential stress of the effective stress com-ponents near the wellbore, rw is the borehole radius, and r is thedistance from the borehole axis to the distant formation. Pp isthe formation pressure, which can be affected by formationfluid seepage. α is the Biot’s parameter, and θ is the circumfer-ential angle of the borehole rotation counterclockwise centeredon the borehole axis. Equation (6) is used to obtain the tensor ofeffective stress distribution near the borehole wall, and then, thestress component is converted to the coordinate system FCS inthe weak plane by using the formula in Equation (7) [5, 12, 34].

σFCS =MNtW ×MTNtB ×MT

BtR

×

σr θ, rð Þ τrθ θ, rð Þ τrz θ, rð Þτrθ θ, rð Þ σθ θ, rð Þ τθz θ, rð Þτrz θ, rð Þ τθz θ, rð Þ σz θ, rð Þ

0BBB@

1CCCA

×MBtR ×MNtB ×MTNtW :

ð7Þ

In the stress component tensor σFCS, the normal and shearstresses in the near-wellbore range can be obtained by Equation(8).

σnw θ, rð Þ = σz θ, rð Þτw θ, rð Þ =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiτ2xz θ, rð Þ + τ2yz θ, rð Þ

q8<: , ð8Þ

f θ, rð Þ = 0: ð9ÞEquation (9) can be established to distinguish rock failure

by strength criterion. When Equation (9) is equal to 0, undera certain drilling fluid density, the value r of borehole circumfer-ence radius can be determined when damage occurs at anyborehole circumference angle near the borehole wall, and then,the morphological characteristics of borehole wall caving undera certain drilling fluid density can be obtained. For the mostpart, models were simplified by r = rw, bringing the stress ofthe sidewall into strength criterion to judge whether the rockdamage, unable to determine whether wall surrounding rock

σr θ, rð Þ = σx + σy

2 1 − r2wr2

� �+

σx − σy2 cos 2θ + τxy sin 2θ

� �1 − 4 r

2w

r2+ 3 r

4w

r4

� �cos 2θ + r2w

r2pw − αpp

σθ θ, rð Þ = σx + σy2 1 + r2w

r2

� �−

σx − σy

2 cos 2θ + τxy sin 2θ� �

1 + 3 r4w

r4

� �cos 2θ − r2w

r2pw − αpp

σz θ, rð Þ = σv − 2μ r2w

r2σx − σy� �

cos 2θ + 2τxy sin 2θ� �

− αpp

τrθ θ, rð Þ = −σx − σy

2 sin 2θ − τxy cos 2θ� �

1 + 2 r2w

r2− 3 r

4w

r4

� �

τrz θ, rð Þ = σxz cos θ + σyz sin θ� �

1 − r2wr2

� �

τθz θ, rð Þ = σyz cos θ − σxz sin θ� �

1 + r2wr2

� �

8>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>:

, ð6Þ

4 Geofluids

damage due to stress concentration. However, in this model,both the well circumference angle and the distance from theborehole axis radius r are unknown, so the stress state of therock around the borehole wall can be directly brought into thestrength criterion to determine the failure location of the rockaround the borehole wall, and then, the failure area and shapeof the rock can be obtained.

2.3. Failure Criteria. Most of the existing mechanisms ofborehole wall instability are based on the elastic mechanicstheory of porous media and rock stability in continuousmedia is mainly controlled by borehole stress and rockstrength. In fractured rock mass, the existence of discontinu-ous fractures changes the mechanical properties of rock to alarge extent, which not only reduces the strength of rockbut also reduces the overall cohesion and internal frictionangle [18]. It also changes the stress distribution during bore-hole formation, making surrounding rock more vulnerable todamage. Except for obvious loose or plastic formations, theweak plane criterion is effective in predicting wellbore failure[37]. The weak plane criterion can be expressed as Equation(10).

σθ − σr =2 Cw + tgϕw ⋅ σr − α ⋅ pp

1 − tgϕw cot βð Þ sin 2β , ð10Þ

where σθ, σr are the circumferential stress and the radialstress of borehole wall (MPa), CW , ϕW are cohesion (MPa)and internal friction angle (°) of weak plane, PP is pore for-mation stress (MPa), β is the included angle between the nor-mal direction of fracture surface and the maximum principalstress (°), and c, ϕ are cohesion (MPa) and internal frictionangle (°) of the sample matrix.

According to Equation (7), the maximum and minimumprincipal stresses of borehole wall are substituted into theformula of weak surface strength criterion (Equation (10)).According to Equation (11), it can be judged whether theshale has shear failure in the rock matrix or sliding failurealong the soft surface. The wellbore failure area and failurepattern flow are shown in Figure 3.

β1 =φw

2 + 12 arcsin σ1 + σ3 + 2Cw cot φwð Þ sin φw

σ1 − σ3

� �

β2 =π

2 + φw

2 −12 arcsin σ1 + σ3 + 2Cw cot φwð Þ sin φw

σ1 − σ3

� �2β1 ≤ 2β ≤ 2β2

8>>>>>><>>>>>>:

:

ð11Þ

3. The Influence of Underbalanced DrillingSeepage Effect

During UBD operation, the effective fluid column pressure islower than the formation pore fluid pressure, which meansthat the fluid flows into the wellbore. Previous studiesignored the influence of fluid seepage. However, the fluidpenetrates into the wellbore from the formation and causes

additional stress, which affects the wellbore stability to a cer-tain extent.

3.1. Isotropic Seepage Model. Mody [38] first proposed themethod of using equivalent pore pressure to evaluate thephysical and chemical interaction between mud shale anddrilling fluid. Considering the mud shale as isotropic semi-permeable membrane, the permeable flow of water in themud shale is the result of the joint action of pressure potentialand chemical potential. The seepage under chemical poten-tial difference can be equivalent to seepage under a certainpressure gradient, and the chemical potential is equivalentto pore pressure (as shown in Equation (12)) [32].

RTV

ln αshaleαmud

� �= P − P0: ð12Þ

Here, R is the perfect gas constant, T is the absolute tem-perature (K),V is the partial molar volume of water (1/mole),αshale is the activity of water for pore fluid, αmud is the activityof water for drilling mud, P is pore pressure (MPa), and P0 isthe original pore pressure (MPa).

3.2. Anisotropic Seepage Model. The permeability of stratifiedshale is different between vertical stratification and alongstratification. Therefore, the effect of anisotropic seepage onpore pressure is different from that of isotropic formationand, thus, affects the stress field near the borehole wall [39].On the basis of isotropic seepage research, the Darcy formulacan be expressed as Equation (13) when considering theseepage anisotropy of stratified strata.

qx = −1μ

kxx∂p∂x

+ kxy∂p∂y

+ kxz∂p∂z

� �

qy = −1μ

kyx∂p∂x

+ kyy∂p∂y

+ kyx∂p∂z

� �

qz = −1μ

kzx∂p∂x

+ kzx∂p∂y

+ kzz∂p∂z

� �

8>>>>>>>><>>>>>>>>:

, ð13Þ

where qx , qy, qz is the seepage velocity (m/s), kii is perme-ability in all directions (D), μ is fluid viscosity (mPa·s), and pis formation pressure (MPa). Therefore, anisotropic perme-ability can be expressed as tensor from Equation (14).

k =kxx kxy kxz

kyx kyy kyz

kzx kzy kzz

2664

3775: ð14Þ

It can be seen that the permeability tensor has a similarexpression form to the stress tensor and is also a symmetrictensor. The permeability tensor has properties similar tothose of the stress tensor and can be expressed as an assertion

5Geofluids

in relation to the principal stress form of the stress. The per-meability assertion is expressed as follows Equation (15).

k =kx 0 00 ky 00 0 kz

2664

3775: ð15Þ

When the local layer contains obvious bedding, the maindirection of penetration can be expressed as the permeabilityalong the bedding and perpendicular to the bedding. Therelationship between the permeability and the bedding struc-ture is shown in Figure 4.

In particular, for stratified strata, the same flow charac-teristics are often found within the same bedding plane.Therefore, the pressure transfer around the well can be

Input base parameters (depth, in-situ stress,weaksurface, mechanical parameters, biot’s coefficient)

Taking a well inclination and azimuths

Coordinate transformation of the original in-situ stress

Increase mud weight from 0 to X

Calculate the stress componentcaused by seepage effect

Calculate the stress distributionaround the well

Maximum andminimum

principal stresses

�e critical drilling fluid density of a stable hole

Weak planeshear stress,

normal stress

Shear failureacross intactrock matrix?

Slippagefailure in weak

planes?

�e drilling fluid density within a certain caving rangeis brought in

Get failure regions for a given mud weight

Expansion rate and wall caving shape

No No

Yes Yes

Go to nextmud weight

Go to nextmud weight

Figure 3: Flow chart of the borehole wall and surrounding instability area.

y

x

Beddingplane

13

k33 k110

𝜃

Figure 4: Schematic diagram of the relationship between the maindirection of penetration and stratification.

6 Geofluids

regarded as a plane problem. Therefore, Darcy’s two-dimensional anisotropy formula can be expressed as Equa-tion (16).

qx = −1μ

kxx∂p∂x

+ kxy∂p∂y

� �

qy = −1μ

kyx∂p∂x

+ kyy∂p∂y

� �8>>><>>>:

: ð16Þ

When the permeability spindle coincides with the coordi-nate axis, the permeability tensor can be written as Equation(17).

k =k11 00 k33

" #: ð17Þ

According to the measurement of vertical bedding andpermeability along the bedding, the additional stress on theformation under different borehole conditions can beobtained by Equation (18).

Pij = Pw + Pp − Pw

� �erf

rkij4ΦμCtt

� �, ð18Þ

where Pij is the pore pressure of any well trajectory(MPa), Φ is porosity (%), r is distance from borehole centerto far sidewall (m), μ is the viscosity of the pore fluid (D),Ct is fluid compressibility, and t is time (s).

4. Borehole Stability and Caving underUnderbalanced Condition

The in situ stress state of the Longmaxi formation was deter-mined by on-site hydraulic fracturing and laboratory experi-ment, and the downhole core was subjected to triaxialcompression experiment to obtain the mechanical parame-ters of shale matrix. The layered shale was subjected to directshear test, and the cohesion and internal friction angle of theshale weak surface were obtained by using the mole line [39].On this basis, the minimum mud density and the unstableregion under different bedding distribution considering theseepage effect are studied.

4.1. Geological Mechanics and Rock Mechanics Parameters ofthe Longmaxi Formation. Horizontal in situ stress values arecalculated using hydraulic fracturing data. Hydraulic pres-sure method calculates ground stress according to hole’sstress state and fracture mechanism. The hydraulic pressureovercomes the ultimate tensile strength of the formationand causes it to break, causing fractures. Fracturing fluidenters the formation and causes a sudden drop in pressure.When the fracture extends beyond the wellbore stress con-centration area, the pump is stopped instantaneously, andthe pressure value is the minimum horizontal ground stress.The maximum horizontal ground stress is calculated byopening the fracture again by opening the pump. And thelaboratory in situ stress experiment measured the horizontal

maximum and horizontal minimum in situ stress throughthe Kaiser effect of the rock. Through field test of hydraulicfracturing in the formation of the Longmaxi formation andlaboratory experiment, horizontal ground stress in this areais obtained (as shown in Table 1).

In order to obtain more practical mechanical propertiesof layered strata, triaxial rock mechanics experiment anddirect shear test were carried out with the research object ofunderground shale and surface outcrop in the Longmaxi for-mation. At the same time, according to the field logging data,the main parameters required by the model are obtained (asshown in Table 2).

4.2. Underbalanced Drilling Collapse Pressure. Under thecondition of underbalanced drilling, the stress around thewell has changed. Although the permeability of shale forma-tion is low, it is not a nonpermeable formation. When con-sidering both the weak plane of bedding and the conditionof underbalance, the collapse pressure of the Longmaxi for-mation block has been studied.

By comparing and analyzing the distribution law of thecollapse pressure around the well with different beddinginclination angles of 30° and 60°, it is found that along thedirection of bedding inclination or its relative direction, thecollapse pressure is generally low, while on the direction withan included angle of 90° with the bedding inclination, the col-lapse pressure generally reaches its maximum. In addition,the distribution law of collapse pressure is also different fordifferent beddings. In the direction of bedding inclination,the minimum value is generally obtained at the position ofinclination angle corresponding to the bedding inclinationangle. While drilling horizontal wells in other directions,the drilling fluid density is usually increased by more than0.5 g/cm3 to maintain borehole stability (as shown inFigures 5 and 6).

The above figure shows that different bedding plane pro-files have a significant influence on the collapse pressure den-sity. When the inclination angle of bedding plane is 30° andthe inclination direction is 0°, the collapse pressure of theshaft wall is the largest when the inclination angle of boreholeis 0-10°, so it is necessary to pay attention to prevent collapsein drilling straight wells under this condition. With theincrease of the inclination angle of borehole, the law of col-lapse pressure on different azimuth angles of borehole is dif-ferent. When the azimuth angle of borehole is 90° and 270°,the collapse occurs always in high pressure, above1.7 g/cm3. The collapse pressure decreases gradually withthe increase of well inclination angle in the range of azimuth330-30° and 150-210°. In this range, when the inclinationangle of borehole exceeds 20°, the collapse pressure willdecrease significantly, with an average decrease of 0.2-0.3.Special attention is paid to the fact that the minimum col-lapse pressure is 1.2 g/cm3 when the azimuth angle of bore-hole is 15° and the inclination angle of borehole is 30°.When the inclination angle of bedding plane is 30° and theinclination direction is 30°, the collapse pressure distributionhas changed significantly. In the same way, the azimuth angleof borehole 90° and 270° direction to achieve maximumvalue, but the area where the collapse pressure is decreasing

7Geofluids

expands. Directional wells with a certain angle can be drilledwithin the azimuth range of 320-70° and 140-250°. In partic-ular, in the azimuth angle of borehole of 30° and 210°, the col-lapse pressure first decreases, then increases, and thendecreases. The minimum value of collapse pressure is1.1 g/cm3 when the inclination angle of borehole is about30°. When the inclination angle of bedding plane is 30° andthe inclination direction is 60°, the collapse pressure is rela-

tively low in the range of azimuth angle of borehole of 30-75° and 210-255°, and the well inclination angle is lower than60°. While in other directions, the collapse pressure is higher,averaging around 1.6 g/cm3. At the inclination angle of bed-ding plane of 30° and the inclination direction of 90°, the col-lapse pressure along the azimuth angle of borehole of 90° and270° is small, but when the well inclination angle exceeds 60°,the collapse pressure will increase significantly. While in the

Table 1: The horizontal ground stress was determined by field and laboratory experiments.

Parameters Field hydraulic fracturing Laboratory experiment Average value

Maximum horizontal stress gradient (g/cm3) 2.73 2.87 2.80

Minimum horizontal stress gradient (g/cm3) 2.24 2.18 2.21

Table 2: Mechanical parameters of stratigraphic foundation of the Longmaxi formation.

Parameters Value Parameters Value

Depth (m) 2450 Cohesion of rock matrix (MPa) 7.77

Vertical stress gradient (g/cm3) 2.61 Friction angle of rock matrix (Deg) 46.7

Pore formation stress gradient (g/cm3) 1.15 Cohesion of shale bedding (MPa) 4.7

Biot’s coefficient 0.45 Friction angle of shale bedding (Deg) 26.9

Elastic modulus (GPa) 22.0 Poisson’s ratio 0.21

Wellbore azimuth (°)

80

60

40

20

0

20

40

60

80

Incli

natio

n an

gle (

°)

030

60

90

120

150180

210

240

270

300

330

Wellbore azimuth (°)

ECD (g/cm3)

1.100

1.150

1.200

1.250

1.300

1.350

1.400

1.450

1.500

1.550

1.600

1.650

1.700

80

60

40

20

0

20

40

60

80

Incli

natio

n an

gle (

°)

030

60

90

120

150180

210

240

270

300

330

Wellbore azimuth (°)

ECD (g/cm3)

1.100

1.150

1.200

1.250

1.300

1.350

1.400

1.450

1.500

1.550

1.600

1.650

1.700

030

60

90

120

150180

210

240

270

300

33080

60

40

20

0

20

40

60

80

Incli

natio

n an

gle (

°)

ECD (g/cm3)

1.100

1.150

1.200

1.250

1.300

1.350

1.400

1.450

1.500

1.550

1.600

1.650

1.700

Incli

natio

n an

gle (

°)

80

60

40

20

0

20

40

60

80

90

030

60

120

150180

210

240

270

300

330

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Inclination direction (𝛼) = 60° Inclination direction (𝛼) = 90°

Inclination direction (𝛼) = 30°

Figure 5: The inclination angle of bedding plane is 30°.

8 Geofluids

azimuth angle of borehole of 0° and 180°, the maximum col-lapse pressure is more than 1.7 g/cm3.

Compared with the inclination angle of bedding plane of30°, when the bedding dip angle is 60°, the distribution law ofcollapse pressure will change significantly. When the beddingtendency is 0°, in the azimuth range of 120-180° and 300-360°, the collapse pressure density is relatively low, and thedirectional hole with the drilling inclination angle less than80° is relatively stable. In the azimuth angle of borehole of45° and 225°, the collapse pressure is relatively large, gener-ally above 1.6 g/cm3. When the bedding tendency is 30° andthe azimuth angle is 30° and 210°, the collapse pressure isabove 1.6 g/cm3 with a small inclination angle of borehole.With the increase of the well inclination angle, the collapsepressure will gradually decrease. When the inclination angleof borehole is 60°, the collapse pressure drops to 1.1 g/cm3,a decrease of 0.5 g/cm3. When the bedding tendency is 60°,the collapse pressure is lower in the azimuths of 60° and240°. While in other directions, the collapse pressure is above1.5 g/cm3. When the bedding tendency is 90°, the collapsepressure along the azimuth direction 90° and 270° is lower,and when the inclination angle of the well in this directionexceeds 30°, the borehole is generally stable.

Therefore, the bedding occurrence has a great influenceon the collapse pressure distribution. In the drilling construc-tion process, the distribution of bedding occurrence shouldbe noted to determine the optimal drilling constructionparameters.

4.3. Unbalanced Drilling Wellbore Failure Zone. During dril-ling, the design of collapse pressure density provides a favor-able guarantee. However, when the borehole wall collapseoccurs, the situation of borehole wall instability is oftenunclear. Therefore, based on the results of the abovemen-tioned collapse pressure, the collapse characteristics of thebedding strata in the Longmaxi formation are studied (asshown in Figures 7 and 8).

According to Figure 7, when the dip angle of the weaksurface is 30°, the caving patterns of shaft walls with differentazimuths are greatly different. When the tendency of beddingsurface is 30°, if the borehole wall collapses or brittle cavingoccur, the diameter will be expanded along the well circum-ference angles of 75°, 165°, 255°, and 345°, and the degree ofcaving along the four directions will be roughly equal. Whenthe bedding azimuth angle is 45°, the caving point will rotateclockwise, and the amount of caving along the directions of 0°

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Figure 6: The inclination angle of bedding plane is 60°.

9Geofluids

and 180° will exceed the other two directions. When theinclined azimuth angle of bedding plane is 60°, the shapecharacteristics of shaft wall caving will change further. Thedegree of caving will decrease in the direction of 15° and195°, and the degree of caving will increase in the directionof 90° and 180°. When the bedding inclination azimuth is90°, the sidewall will collapse along the perimeter, in whichcase the sidewall will expand along the perimeter. It can beseen from Figure 8 that when the bedding inclination angleis 60°, when the inclination azimuth of the bedding plane is30°, 45°, and 60°, the shaft wall will collapse along the fourperpendicular directions, and the collapse scale is roughlythe same. With the increase of the bedding inclination azi-muth angle, the collapse direction will rotate clockwise.When the bedding tendency is 90°, the shaft wall will collapsealong the directions of 45°, 135°, 225°, and 315°, and theamount of collapse is basically the same. On the whole, thecaving is more regular when the bedding surface dip angleis 60° than 30°. It can be concluded that the anisotropy ofbedding has a great influence on the shape characteristics ofshaft wall caving, and the shape of shaft wall caving shouldbe analyzed according to the specific formation conditions.

5. Conclusion

In order to solve the prominent problem of borehole insta-bility in shale formation in the Jiaoshiba area, a collapsepressure calculation model and a model of well cycle insta-bility area are proposed, which take into account theunderbalanced seepage flow condition and anisotropy ofrock strength. According to the depth of the unstable sec-tion of the shaft wall, the in situ stress parameters of theLongmaxi formation were obtained by hydraulic fracturingand laboratory test. It is generally considered that highground stress is greater than 2MPa/100m. The resultsshow that the two-way horizontal ground stress is higherthan 2.2MPa/100m, so the original ground stress of therational stratum of the Longmaxi formation is in a stateof high stress.

Through downhole core mechanics experiments, themechanical parameters of the shale matrix and the weak sur-face of the bedding were obtained, indicating that the cohe-sion and internal friction angle of the bedding surface(4.7MPa, 26.9°) were significantly lower than that of the rockbody (7.77MPa, 46.7°). Combined with the site, the

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Inclination direction (𝛼) = 45Inclination direction (𝛼) = 30

Inclination direction (𝛼) = 90Inclination direction (𝛼) = 60

Figure 7: Characteristic shape of wellbore caving at 30° inclination angle of bedding plane.

10 Geofluids

stratigraphy of the Longmaxi Formation is developed, whichis prone to loss during drilling, and the permeability of shalematrix is low. Therefore, it is believed that the drilling fluidmainly intruded along the stratigraphy. At the same time,the mechanical parameters of bedding surface are obviouslylower than that of rock matrix, which further affects the sta-bility of wellbore. It is considered that underbalanced drillingcan reduce the damage of drilling fluid to near-wellbore for-mation and improve the stability.

For horizontal wells, the collapse pressure law of differentbedding occurrences (inclination angle and tendency) isstudied. Generally, the minimum value is obtained at theinclined angle position of the well corresponding to the bed-ding inclination angle, that is, when the borehole axis is per-pendicular to the bedding plane. Otherwise, the drilling fluiddensity is often increased by 0.5 g/cm3 in other directions tomaintain borehole stability. The bedding occurrence has agreat influence on the collapse pressure distribution. Duringdrilling construction, the distribution of bedding occurrencemust be noted to determine the most accurate drilling con-struction parameters.

In this paper, the characteristics of wellbore instability inbedding strata are studied. When the bedding dip angle islow, during the rotation of the bedding tendency from thedirection of maximum horizontal ground stress to the direc-tion of minimum horizontal ground stress, the shaft wall col-lapse pattern begins with several specific directions and thencollapses uniformly around the well. With the increase ofbedding angle, the diameter expansion rate also increasesgradually. Therefore, it is necessary to understand thecollapse state more clearly when the wellbore collapses inthe stratified formation, so as to provide the basis for safeproduction and accident treatment.

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

�e angle of the borehole circumference

�e angle of the borehole circumference

�e angle of the borehole circumferenceInclination direction (𝛼) = 45Inclination direction (𝛼) = 30

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Figure 8: Characteristic shape of wellbore caving at 60° inclination angle of bedding plane.

11Geofluids

Acknowledgments

The authors are grateful to Dr. Shuai Cui and anonymousreviewers for their constructive comments that substantiallyimproved the manuscript. This research was financially sup-ported by the Open Fund of Shaanxi Key Laboratory ofAdvanced Stimulation Technology for Oil & Gas Reservoirs,grant number 20JS120; Young science and Technology Tal-ents Foundation of Shaanxi province, grant number2019KJXX-054; and National Natural Science Foundationof China, grant numbers (41702146, 51934005, 51874242).

References

[1] C. Zou, Z. Guangming, G. Zhang et al., “Formation, distribu-tion, potential and prediction of global conventional andunconventional hydrocarbon resources,” Petroleum Explora-tion and Development, vol. 42, no. 1, pp. 14–28, 2015.

[2] K. Duan and C. Y. Kwok, “Evolution of stress-induced bore-hole breakout in inherently anisotropic rock: insights from dis-crete element modeling,” Journal of Geophysical Research:Solid Earth, vol. 121, no. 4, pp. 2361–2381, 2016.

[3] L. Houbin, Z. Fan, M. Yingfeng, L. Gao, and C. Yunhai,“Experimental study on wellbore stability of shale gas reservoirfor horizontal well in Jiaoshiba area,” Chinese Journal ofUnderground Space and Engineering, vol. 13, no. 6, pp. 1531–1536, 2017.

[4] L. Ding, Z. Wang, B. Liu, J. Lv, and Y. Wang, “Borehole stabil-ity analysis: a new model considering the effects of anisotropicpermeability in bedding formation based on poroelastic the-ory,” Journal of Natural Gas Science and Engineering, vol. 69,article 102932, 2019.

[5] T. Ma and P. Chen, “A wellbore stability analysis model withchemical-mechanical coupling for shale gas reservoirs,” Jour-nal of Natural Gas Science and Engineering, vol. 26, pp. 72–98, 2015.

[6] Y. I. Ding, P. Luo, X. Liu, and L. Liang, “Wellbore stabilitymodel for horizontal wells in shale formations with multipleplanes of weakness,” Journal of Natural Gas Science and Engi-neering, vol. 52, pp. 334–347, 2018.

[7] X. Li, X. Yan, and Y. Kang, “Investigation of drill-in fluidsdamage and its impact on wellbore stability in Longmaxi shalereservoir,” Journal of Petroleum Science and Engineering,vol. 159, pp. 702–709, 2017.

[8] L. Liang, J. Xiong, and X. Liu, “Experimental study on crackpropagation in shale formations considering hydration andwettability,” Journal of Natural Gas Science and Engineering,vol. 23, pp. 492–499, 2015.

[9] R. Gholami, M. Rabiei, V. Rasouli, B. Aadnoy, and N. Fakhari,“Application of quantitative risk assessment in wellbore stabil-ity analysis,” Journal of Petroleum Science and Engineering,vol. 135, pp. 185–200, 2015.

[10] R. Weijermars, J. Wang, and R. Nelson, “Stress concentrationsand failure modes in horizontal wells accounting for elasticanisotropy of shale formations,” Earth-Science Reviews,vol. 200, article 102957, 2020.

[11] A. Abdollahipour, H. Soltanian, Y. Pourmazaheri,E. Kazemzadeh, and M. Fatehi-Marji, “Sensitivity analysis ofgeomechanical parameters affecting a wellbore stability,” Jour-nal of Central South University, vol. 26, no. 3, pp. 768–778,2019.

[12] J. Zhou, S. He, M. Tang et al., “Analysis of wellbore stabilityconsidering the effects of bedding planes and anisotropic seep-age during drilling horizontal wells in the laminated forma-tion,” Journal of Petroleum Science and Engineering, vol. 170,pp. 507–524, 2018.

[13] X. Li, H. Jaffal, Y. Feng, C. el Mohtar, and K. E. Gray, “Wellborebreakouts: Mohr-Coulomb plastic rock deformation, fluid seep-age, and time-dependent mudcake buildup,” Journal of NaturalGas Science and Engineering, vol. 52, pp. 515–528, 2018.

[14] W. B. Bradley, “Failure of Inclined Boreholes,” Journal ofEnergy Resources Technology, vol. 101, no. 4, pp. 232–239,1979.

[15] S. Heng, X. Li, X. Liu, and Y. Chen, “Experimental study on themechanical properties of bedding planes in shale,” Journal ofNatural Gas Science and Engineering, vol. 76, article 103161,2020.

[16] J. Zuo, J. Lu, R. Ghandriz et al., “Mesoscale Fracture Behaviorof Longmaxi Outcrop Shale with Different Bedding Angles:Experimental and Numerical Investigations,” Journal of RockMechanics and Geotechnical Engineering, vol. 12, no. 2,pp. 297–309, 2020.

[17] Y. Suo, Z. Chen, S. S. Rahman, and X. Chen, “Experimentalstudy on mechanical and anisotropic properties of shale andestimation of uniaxial compressive strength,” Energy Sources,Part A: Recovery, Utilization, and Environmental Effects, pp.1–11, 2020.

[18] W. Guo, W. Shen, X. Li et al., “Study on mechanical character-istics and damage mechanism of the Longmaxi Formationshale in southern Sichuan Basin, China,” Energy Exploration& Exploitation, vol. 38, no. 2, pp. 454–472, 2020.

[19] D. Parkash and C. Deangeli, “Wellbore stability analysis inanisotropic shale formations,” in SPE/PAPG Pakistan SectionAnnual Technical Symposium and Exhibition, Islamabad,Pakistan, 2019.

[20] T. Ma, N. Peng, Z. Zhu, Q. Zhang, C. Yang, and J. Zhao, “Bra-zilian tensile strength of anisotropic rocks: review and newinsights,” Energies, vol. 11, no. 2, p. 304, 2018.

[21] H. Lee, C. Chang, S. H. Ong, and I. Song, “Effect of anisotropicborehole wall failures when estimating in situ stresses: a casestudy in the Nankai accretionary wedge,” Marine and Petro-leum Geology, vol. 48, pp. 411–422, 2013.

[22] G. Chen, M. E. Chenevert, M. M. Sharma, andM. Yu, “A studyof wellbore stability in shales including poroelastic, chemical,and thermal effects,” Journal of Petroleum Science and Engi-neering, vol. 38, no. 3-4, pp. 167–176, 2003.

[23] A. Ghassemi, Q. Tao, and A. Diek, “Influence of coupledchemo-poro-thermoelastic processes on pore pressure andstress distributions around a wellbore in swelling shale,” Jour-nal of Petroleum Science and Engineering, vol. 67, no. 1-2,pp. 57–64, 2009.

[24] M. Gomar, I. Goodarznia, and S. R. Shadizadeh, “A transientfully coupled thermo-poroelastic finite element analysis ofwellbore stability,” Arabian Journal of Geosciences, vol. 8,no. 6, pp. 3855–3865, 2015.

[25] W. Liu and X. Zhu, “A coupled thermo-poroelastic analysis ofwellbore stability for formations with anisotropic strengths,”Arabian Journal of Geosciences, vol. 11, no. 18, p. 537, 2018.

[26] Q. Wang, Y. Zhou, G. Wang, H. Jiang, and Y. Liu, “A fluid-solid-chemistry coupling model for shale wellbore stability,”Petroleum Exploration and Development, vol. 39, no. 4,pp. 508–513, 2012.

12 Geofluids

[27] C. Liang, M. Chen, Y. Jin, and Y. Lu, “Wellbore stability modelfor shale gas reservoir considering the coupling of multi-weakness planes and porous flow,” Journal of Natural Gas Sci-ence and Engineering, vol. 21, pp. 364–378, 2014.

[28] S. Jia, Z. Xiao, B. Wu, C. Wen, and L. Jia, “Modelling of time-dependent wellbore collapse in hard brittle shale formationunder underbalanced drilling condition,” Geofluids,vol. 2019, 21 pages, 2019.

[29] V. Dokhani, M. Yu, and B. Bloys, “A wellbore stability modelfor shale formations: accounting for strength anisotropy andfluid induced instability,” Journal of Natural Gas Science andEngineering, vol. 32, pp. 174–184, 2016.

[30] R. Zhang, G. Li, and S. Tian, “Stress distribution and itsinfluencing factors of bottom-hole rock in underbalanced dril-ling,” Journal of Central South University, vol. 25, no. 7,pp. 1766–1773, 2018.

[31] S. He, W. Wang, H. Shen, M. Tang, H. Liang, and J.'. Lu, “Fac-tors influencing wellbore stability during underbalanced dril-ling of horizontal wells - when fluid seepage is considered,”Journal of Natural Gas Science and Engineering, vol. 23,pp. 80–89, 2015.

[32] S. He, W. Wang, M. Tang, B. Hu, and W. Xue, “Effects of fluidseepage on wellbore stability of horizontal wells drilled under-balanced,” Journal of Natural Gas Science and Engineering,vol. 21, pp. 338–347, 2014.

[33] H. Lee, S. H. Ong, M. Azeemuddin, and H. Goodman, “A well-bore stability model for formations with anisotropic rockstrengths,” Journal of Petroleum Science and Engineering,vol. 96, pp. 109–119, 2012.

[34] X. Fan, M. Zhang, Q. Zhang, P. Zhao, B. Yao, and D. Lv, “Well-bore stability and failure regions analysis of shale formationaccounting for weak bedding planes in ordos basin,” Journalof Natural Gas Science and Engineering, vol. 77, article103258, 2020.

[35] P. Bautmans, E. Fjær, and P. Horsrud, “The effect of weaknesspatches on wellbore stability in anisotropic media,” Interna-tional Journal of Rock Mechanics and Mining Sciences,vol. 104, pp. 165–173, 2018.

[36] J. Gao, J. Deng, K. Lan, Y. Feng,W. Zhang, and H.Wang, “Por-othermoelastic effect on wellbore stability in transversely iso-tropic medium subjected to local thermal non-equilibrium,”International Journal of Rock Mechanics and Mining Sciences,vol. 96, pp. 66–84, 2017.

[37] M. D. Zoback, Reservoir geomechanics, Cambridge UniversityPress, 2010.

[38] F. K. Mody and A. H. Hale, “Borehole-stability model to cou-ple the mechanics and chemistry of drilling-fluid/shale inter-actions,” Journal of Petroleum Technology, vol. 45, no. 11,pp. 1093–1101, 1993.

[39] M. Meng, P. Chen, and R. Ren, “Statistic evaluation of failurecriteria in wellbore stability with temperature effects,” Fuel,vol. 252, pp. 730–752, 2019.

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