Research ArticleExperimental Study on the Anisotropic Characteristics andEngineering Application of Tight Sandstone

Yuanlong Wei1 Wei Liu 2 and Zhenkun Hou23

1Guizhou Oil and Gas Exploration and Development Engineering Research Institute Guiyang 553000 Guizhou Province China2State Key Laboratory of Coal Mine Disaster Dynamics and Control Chongqing University Chongqing 400044 China3School of Materials Science and Engineering South China University of Technology Guangzhou 510640 China

Correspondence should be addressed to Wei Liu whrsmliuwei126com

Received 5 August 2020 Revised 27 October 2020 Accepted 19 January 2021 Published 8 February 2021

Academic Editor Sakar Mohan

Copyright copy 2021 YuanlongWei et al-is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-e anisotropy of tight sandstone (a type of unconventional gas reservoirs) is a significant factor influencing the characteristics ofcracks network under hydrofracturing thus it also has a large influence on the final production capacity of the gas reservoirs Toimprove the understanding of anisotropy degree and mechanical properties of the tight sandstone of Xujiahe Formation and thusto provide reliable reference for the establishment of hydrofracture model and parameter designing in fracture field a series ofexperiments including ultrasonic wave velocity and uniaxial and triaxial compression tests of the tight sandstone samples obtainedfrom Xujiahe Formation with different inclination angles (the angle between sample drilling direction and bedding plane) havebeen conducted With the increase of inclination angle the velocity of the longitudinal wave and elastic modulus both show thetendency of decreasing whereas the compressive strength shows a ldquoUrdquo shape varying pattern which is high on sides and low in themiddle region -e values of uniaxial compression strength (UCS) are the lowest of sandstone with the inclination angles of 30degand 45deg -e fracture patterns are dominant by splitting fracture under uniaxial compression tests However shear fracture anddilatancy morphology is the main pattern under triaxial compression test But the local morphology of the failure surfaces behavesdifferent if the inclination angle is changed Combining the mechanic theory of transversely isotropic material the anisotropyparameters of the tight sandstone are analyzed as well as the influence on the hydrofracturing technology for tight sandstone inthe field

1 Introduction

In China under the situation of increasing natural gassupply tight sandstone gas has become one focus ofdeveloping nonconventionalunconventional natural gasdue to its wide distribution and rich reserves [1ndash5]However as a type of reservoirs with low porosity and lowpermeability technological measures of increasing pro-duciton must be taken to achieve an ideal capacity for thetight sandstone gas well [6ndash8] Tight sandstone is a typicalsedimentary rock mass Usually bedding planes arewidely distributed in tight sandstone formations [9] Sothe influences of anisotropy on the physical and me-chanical properties of tight sandstone are significant Ingeneral when the reservoir stratum contains bedding

structure under hydrofracturing cracks are prone toinitiate along the bedding surface and then propagate inthe matrix acting as important impacts on the fracturingfracture network of the stratum as well as the ultimateproduction capacity [10] From the perspective of me-chanical properties such property is named as anisotropy-erefore the anisotropic characteristics of the tightsandstone are a significant foundation and a prerequisitefor the development of hydraulic fracturing

Many theoretical and experimental studies have beencarried out on the anisotropic characteristics of rock Henget al [11] studied the anisotropic characteristics of shale bydirect-shear test and revealed that the general anisotropystrength characteristic curve is U-shaped with the increase ofthe bending angle Zhang et al [12ndash14] studied the

HindawiAdvances in Materials Science and EngineeringVolume 2021 Article ID 3580956 12 pageshttpsdoiorg10115520213580956

anisotropic strength characteristics of bedded compositerock and established a Figureure to show the change ofstrength with the bedding inclination Louis et al [15] in-vestigated the microstructural inhomogeneity and me-chanical anisotropy associated with the bedding effect forRothbach sandstone Chen et al [16] studied the anisotropicproperties of low Cambrian black shale at Niutitang theeffects of confining pressure and bedding angle on the blackshale are also demonstrated by triaxial compression testsAnisotropy of the rock reservoirs is also important forunconventional gas exploitation as it is a significant pa-rameter for production in the field Ma et al [17] studied theanisotropy gas permeability and its relationship with frac-ture structure of Longmaxi shale in the laboratory by usinghelium gas as permeate gas and found that the permeabilityparallel to the bedding of shale is about 104 times thatperpendicular to the bedding In addition the anisotropy isalso relative to the stress state Feng et al [18] revealed theanisotropic deformation and stress-dependent directionalpermeability of the coalbed methane reservoirs and sug-gested that the anisotropic properties should be consideredwhen simulating gas flow behavior and predicting theproduction of coalbed methane production

From the above studies many experts pointed out thatthe anisotropy is an important factor for the unconventionalgas reservoirs and the predominant studies focused on theshale rock because shale gas production is a very hot issue inthese years As for the research on tight sandstone anotherhuge resource with great production potential in China therelative research to support the field application is relativelyrare As a type of sedimentary rock tight sandstone also hasobvious anisotropy with bedding angle and this is theprerequisite for the designing of hydrofracturing in reser-voirs So the study on the anisotropy of tight sandstone isalso necessary and significant

In this study the tight sandstone samples are collectedfrom Xujiahe reservoir which is a tight sandstone reservoirin Hubei Province -e samples are prepared with differentbedding angles and uniaxial and triaxial compression testsare carried out to investigate the anisotropy characteristics ofthe tight sandstone from the viewpoint of strength me-chanical parameters and failure characters -e anisotropicindex of the Xujiahe tight sandstone is also analyzed anddiscussed by using the transversely isotropic theory of rockmass -is study can provide effective technical support fordesigning and optimizing hydraulic fracturing in the tightsandstone fields

2 Test Profile

21 Specimen Preparation -e rock core blocks for testingthe same stratum with the tight sandstone reservoirs aspotential exploitation formation are taken from LichuanCity Hubei Province -e lithology of the rock cores ismainly dominated by gray fine sandstone Cylinder samplesare drilled with different angles with the bedding plane in thecore blocks which are respectively 0deg 30deg 45deg 60deg and 90degas shown in Figure 1 According to the test requirements thesamples are processed with the following properties 50mm

in diameter and 100mm in length and the roughness of thetwo end faces of all the samples is within 002mm

22 Test Equipment and Test Methods -e uniaxial andtriaxial compression tests are conducted by using the me-chanical equipment ofMTS-81503 in Chongqing Universityof China -e axial displacement control mode is used forloading all the samples and the corresponding loading rateis minus 0001mms In the process of loading the axial load axialstress axial displacement and the circular displacement areall recorded in time and the stress-strain curves are drawnsynchronously -e used MTS equipment is shown inFigure 2

3 Test Results and Analysis

31 Brittle Characteristics of Tight Sandstone -e mineralcompositions of the tight sandstone cores are measured byusing the equipment of AXS D8-Focus X Bruker Ray Dif-fraction and the testing results are shown in Table 1 In thistable the quartz and feldspar are collected together as brittleminerals and illite and chlorite are collected as clayminerals

-e brittleness of rock is evaluated based on the com-ponents of brittle minerals [19] It is usually demonstratedthat rock with a higher content of quartz and carbonate hasstronger brittleness while for rock containing more clayminerals the brittleness will be weaker

In this study the calculation method for the rockbrittleness index based on mineral composition is asfollows [19]

I WQ + WC1113872 1113873

WT

(1)

where I is the brittleness index of rock WQ is the quartzcontent WC is the carbonate rock content WT is the totalcontent of all minerals

As shown in Table 1 the clay minerals in the tightsandstone are mainly illite which has a content of 2367-e brittle minerals in tight sandstone samples are mainlyquartz and feldspar with a total content of 7633 con-sisting of 6240 of quartz and 1393 of carbonateAccording to equation (1) it can be calculated that thebrittleness index I of the tight sandstone in this study equals076 According to the discriminant standard of brittlenessdegree [19] it can be known that the brittleness of tightsandstone samples is relatively dense so the tight sandstonestudied here belongs to high brittle-fracturing tight sand-stone reservoir -e greater the brittleness is the easier it isto form a complex fracture network after hydraulic frac-turing and thus a better ideal production may be obtainedduring the process of gas exploitation

32 Stress-Strain Curves -e results of the uniaxial andtriaxial compression tests of tight sandstone samples withdifferent dip angles and different confining pressure areshown in Table 2 20 samples are tested in total Under each

2 Advances in Materials Science and Engineering

confining pressure (0 15MPa 30MPa and 45MPa) fivesamples are used with dip angles of 0deg 30deg 45deg 60deg and 90degrespectively -e stress-strain curves of samples with thesame confining pressure and different angles are listed inFigures 3 and 4 Figure 3(a) shows the strain-stress curves ofthe tight sandstone samples with the same dip angle of 0degunder different confining pressure Figure 3(a) shows thestrain-stress curves of the tight sandstone samples with thesame dip angle of 0deg under different confining pressure Bycomparing these two pictures the influence of dip angle canbe revealed Figure 4(a) and Figure 4(b) show the stress-strain curves of the tight sandstone samples under the sameconfining pressure with different dip angles By these two

pictures the influence of dip angle can be observed moreobviously

By analyzing the data and curves in Table 2 and Figures 3and 4 the main summaries can be made as follows

(1) Under the same conditions the shape and defor-mation characteristics of the stress-strain curves areaffected by the confining pressure and bedding angleIt can be indicated from Table 2 that for the samplewith the same dip angle with the increase in con-fining pressure the peak strength and elastic mod-ulus of tight sandstone are significantly increased Sothe confining pressure is a significant factor to in-fluence the strength of tight sandstone

(2) It can be seen from Figures 3 and 4 that under thecondition with the same confining pressure obviousyield deformation appears in front of all the dipangles of the stress-strain curve For the samplesunder confining pressure of 45MPa with a dip angleof 0deg 30deg 45deg and 60deg the stress-strain curve ofsamples immediately drops after reaching the topintensity While this angle is 90deg the curves ofsamples present an obvious yield platform when it isclose to the peak point and after reaching the peakpoint it does not drop but shows a ductility char-acteristic -e reason is that when the dip angle α is0deg 30deg 45deg and 60deg the samples present shear slipdamage after reaching the peak point While the dipangle α is 90deg the samples happen to shear ex-pansion damage after reaching the peak point with achubby middle and no obvious slip lines so thesamples still have a strong bearing capacity

33 Anisotropy Characteristics Analysis

331 Wave Velocity Anisotropy -e anisotropy in wavevelocity is another important factor to reflect the anisotropiccharacteristics of rock mass [20] So in this study we alsoapply this method to study the anisotropic characteristics oftight sandstone Five groups of the samples are divided Four

x-axis

z-axis

y-axis

xy-plane

z-axis

α

0

90deg 60deg 45deg30deg

0deg

30deg 15deg

15deg30deg

Figure 1 Schematic diagram of the five sampling angles with bedding plane (dip angle a is the inclination angle between the bedding planeand sample drilling direction which is 0deg 30deg 45deg 60deg and 90deg respectively)

Figure 2 -e MTS-815 system of Chongqing University

Table 1 Mineral composition of tight sandstone

Number of samplesBrittle minerals () Clay minerals

()Quartz Feldspar Illite Chlorite

1 5985 1480 2200 3352 6938 1211 1560 2913 5798 1488 2307 408Average value 6240 1393 2022 345Gross 7633 2367

Advances in Materials Science and Engineering 3

ones for dip angle are prepared for this test So 20 samplesare used for the measurement of the longitudinal wavevelocity before the mechanical tests as shown in Table 2 Allthe tests are conducted by using the device of NonmetallicUltrasonic Detector JL-IUA6(a) According to the longitu-dinal wave velocity test on the tight sandstone samples theanisotropy properties of tight sandstone can be revealed insome aspects -e experimental results of ultrasonic velocityfor samples are shown in Table 3 -e change regularities oflongitudinal wave velocity with different dip angles of all thesamples are shown in Figure 5

From Table 3 it can be seen that the longitudinal wavevelocity decreases gradually with the dip angleWhen the dipangle equals 0deg the longitudinal wave propagates parallel to

the bedding surface consuming the minimal energy and theshortest penetrating time thus having the greatest wavevelocity But for the samples with the dip angle of 90deg thepropagation direction of the longitudinal wave is perpen-dicular to the bedding planes so the longitudinal wave has topenetrate the bedding layers to spread which causes themaximum energy consumption and the longest travel timeand results in the minimum wave velocity in the process ofspreading So the wave velocity is a factor to reflect theanisotropy of the tight sandstone -e ratio of the wavevelocity of the direction in 0deg and 90deg is 1206 which issomewhat lower than that of the Longmaxi shale [11]-erefore the anisotropy of tight sandstone exists but islower than that of shale

Table 2 Triaxial compression testing results of samples with different strata angles

Confining pressure (MPa) Dipangle (deg)

Peak strength(MPa)

Elastic modulus(GPa)

Poissonrsquosratio

Peakstrain ()

Ruptureangle (deg)

Residual strength(MPa)

0

0 5457 508 016 155 83 mdash30 4184 339 031 148 88 mdash45 4622 438 034 165 82 mdash60 5653 474 035 164 825 mdash90 5268 445 019 152 90 mdash

15

0 18215 925 015 210 705 904630 15803 842 016 191 695 819845 14807 809 021 203 65 579860 15430 780 021 222 635 599790 15490 752 018 215 68 5710

30

0 25550 1112 019 239 715 984030 20599 1058 024 192 60 1019245 21804 988 030 238 625 1006060 23023 949 027 255 695 1126290 22086 822 024 248 62 9900

45

0 33319 1424 017 259 61 1420330 27211 1263 021 206 565 1541545 27582 1194 026 227 57 1298260 28280 1140 023 280 695 1374890 27760 1081 021 296 63 mdash

0

50

100

150

200

250

300

350

0 05 1 15 2 25 3 35 4

Axi

al st

ress

(MPa

)

Axial strain ()

0 MPa15 MPa

30 MPa45 MPa

(a)

Axi

al st

ress

(MPa

)

0

50

100

150

200

250

0 05 1 15 2 25 3 35 4Axial strain ()

0 MPa15 MPa

30 MPa45 MPa

(b)

Figure 3 Typical curves of stress-strain of tight sandstone samples with the same dip angle under different confining pressure (a) Angleα 0deg (b) Angle α 60deg

4 Advances in Materials Science and Engineering

332 Elastic Modulus Anisotropy Elastic modulus is a basicmechanical parameter which is also an important factor toshow the anisotropy of the tight sandstone Based on theuniaxialtriaxial compression tests in the laboratory all the

elastic moduli of the 20 tested samples are calculated -etriaxial compression tests are conducted under the confiningpressures of 15MPa 30MPa and 45MPa Table 4 shows theelastic modulus anisotropy values of the tight sandstonesamples under different confining pressures and dip anglesAs shown in Figure 6 when the confining pressure is 0MPa(which corresponds to the uniaxial compression test) withthe increase of dip angle the change of the elastic modulus isapproximately a U shapeWhen the dip angle is 0deg the elasticmodulus has a maximum value of 508GPa but when thedip angle equals 30deg the elastic modulus has a minimumvalue of 339GPa In addition when the confining pressureis respectively 15MPa 30MPa and 45MPa with the in-crease of the dip angle the elastic modulus decreasesgradually

For the condition with different confining pressure thecalculation method of the elastic modulus anisotropy [21] isas follows

RE Emax

Emin (2)

where RE is the anisotropy degree of elastic modulus Emax isthe maximum elastic modulus of the sample which

0

10

20

30

40

50

60

70

0 05 1 15 2 25

Axi

al st

ress

(MPa

)

Axial strain ()

0deg30deg45deg

60deg90deg

(a)

0deg30deg45deg

60deg90deg

0

50

100

150

200

250

300

0 05 1 15 2 25 3 35 4

Axi

al st

ress

(MPa

)

Axial strain ()

(b)

Figure 4 Typical curves of stress-strain of tight sandstone samples with different dip angle under the same confining pressure (a) Confiningpressure σ3 0MPa (b) Confining pressure σ3 45MPa

Table 3 Longitudinal wave velocity of tight sandstone samples with different dip angle

Dip angle (deg) Longitudinal wave velocity (ms) Average velocity (ms)

0 2331 2331 2272 2259 23162254 2354 2311 2419

30 2156 2176 2028 2261 21562155 2111 2092 2270

45 2068 2088 1973 1919 20302022 2072 2065 mdash

60 2036 2015 1981 1873 19912097 1937 1981 2008

90 1994 1944 1878 1906 19211966 1803 1959 mdash

1750

2000

2250

2500

2750

0 15 30 45 60 75 90 105

Vel

ocity

of l

ongi

tudi

nal w

ave

(m

s)

Dip angle αdeg

Velocity of longitudinal waveAverage velocity

Figure 5 Longitudinal wave velocity of tight sandstone sampleswith different dip angles

Advances in Materials Science and Engineering 5

corresponds to the dip angle of 0deg and Emin is the minimumelastic modulus

According to equation (2) the anisotropy degree of theelastic modulus was calculated as shown in Table 4 For thesamples under the confining pressure of 0MPa the elasticmodulus of the tight sandstone is of obvious anisotropy -eanisotropy degree of RE equals 164 For the samples underthe confining pressure of 15MPa 30MPa and 45MPa theanisotropy degree (RE) of the elastic modulus becomes lowerthan that under the confining pressure of 0MPa rangingbetween 125 and 136 -erefore the existence of confiningpressure has decreased the anisotropy of the tight sandstoneof Xujiahe Formation which causes the anisotropy of elasticmodulus to become much weaker As for the laboratory testof hydraulic fracturing of tight sandstone samples the hy-draulic fracturing calculation model and the numericalsimulation of the Xujiahe tight sandstone considering thatthe anisotropy degree of elastic modulus is much weakerwhen subjected to three-directional stress state the elasticmodulus in an isotropic plane and vertical plane isotropicelastic modulus can be taken as the average elastic modulusfor a rough estimation But for an accurate calculation it isstill suggested that the anisotropy influence of elasticmodulus cannot be neglected

333 Compressive Strength Anisotropy Figure 7 shows theanisotropy curves of triaxial compressive strength forsamples with different dip angles under different confiningpressures Under the same confining pressure for thesamples with the dip angles of 0deg and 90deg (the dip angle of 0deg

corresponds to the maximum strength) the compressivestrength of samples is relatively high For samples with thedip angles of 30deg and 45deg the compressive strength ofsamples is relatively low -e overall evolution of thecompression strength performs a U shape which is high atboth sides and low in the middle location Under thecondition of different confining pressures the calculationmethod for the anisotropy degree of the compressivestrength anisotropy of RP [21] is as follows

RP σmax

σmin (3)

where RP is the anisotropy degree of compressive strength σ(max) is the maximum compressive strength of sampleswhich corresponds to the dip angle of 0deg and σmin is theminimum compressive strength

According to equation (3) the anisotropy degree of thecompressive strength of the tight sandstone samples in thisstudy can be calculated as shown in Table 5 With an increasein the confining pressure the anisotropy degree of thecompressive strength decreases When the confining pressureis 0MPa the anisotropy degree of the compressive strengthRP is 151 when the confining pressure is 15MPa 30MPaand 45MPa the anisotropy degree of the compressivestrength RP ranges from 124 to 130 -erefore from theviewpoint of compressive strength it has an obvious an-isotropy -e confining pressure has a negligible influence onthe anisotropy degree for the tight sandstone in this study Inthe field reservoir of the tight sandstone of Xujiahe Forma-tion the influences of the anisotropy and the in situ stressstate should both be considered for gas production

Table 4 Anisotropy degree of elastic modulus

Confining pressure (MPa) Max elastic modulus (GPa) Min elastic modulus (GPa) Degree of anisotropy0 524 319 16415 941 750 12530 1115 822 13645 1447 1075 135

0

3

6

9

12

15

18

0 15 30 45 60 75 90 105

Elas

tic m

odul

us (G

Pa)

Dip angle αdeg

0 MPa30 MPa

15 MPa45 MPa

Figure 6 Elastic modulus anisotropy of the tight sandstonesamples with different dip angles when subjected to differentconfining pressure

0

100

200

300

400

0 15 30 45 60 75 90 105

Peak

stre

ngth

(MPa

)Dip angle (deg)

0 MPa30 MPa

15 MPa45 MPa

Figure 7 Triaxial compression strength anisotropy of samples withdifferent strata angles

6 Advances in Materials Science and Engineering

334 Anisotropy of Fracture Morphology Figure 8 showsfailure mode under the conditions of different confiningpressure and different dip angles -e failure modes of thesamples can be mainly divided into three types splittingfailure shear failure and shear-expansion failure

When the confining pressure is 0MPa the predominantfailure mode of all the samples is splitting failure but somedifferences exist among the samples with different dip anglesFor instance the sample with the dip angle of 0deg has a mainsplitting fracture and several secondary fractures and somesecondary fractures are inclined showing shear failure per-formance-is is a reflection that the matrix perpendicular tothe bedding direction has the greatest strength As for thesample with the dip angle of 90deg only one splitting fractureappears on the sample surface parallel to the axial loadingdirection -is indicates that the matrix along the beddingdirection has a low strength For the samples with the dipangles of 30deg 45deg and 60deg the failure fracture is straight in themiddle location and somewhat inclined at each end -isshows that the propagation direction of the failure fracturemay be influenced by the bedding plane So under theuniaxial compression test (confining pressure 0MPa) an-isotropy exists in the review point of failure morphology

Under triaxial compression testing condition (15MPaand 30MPa) the difference in failure morphology remainsexistent for the samples with different dip angles For ex-ample the sample with 0deg dip angle has a steep failuresurface but the failure surface of the sample with dip angle of90deg is much gentler When the dip angle ranges from 30deg to60deg the failure surface has an inclination angle between thecases of 0deg and 90deg but the failure surface is already not aplane surface but a curved one -at is to say due to theexistence of bedding angle it has caused the failure surface tobe a curved surface With respect to the condition of highconfining pressure (45MPa) the failure mode has becomeshear-dilatant state-ere is onemain failure surface but theaperture of this surface is very small and there are numeroussmall fissures around this surface -e middle location of thesample has expanded showing a drum shape Moreoverexcept the cases with dip angles of 0deg and 90deg the failuresurfaces of the samples are all curved surfaces under theconfining pressure of 45MPa

From the above study one can deduce that the existence ofconfining pressure has largely changed the failure modes forthe tight sandstone During the increase process of the con-fining pressure (0MPa⟶ 15MPa⟶ 30MPa⟶ 45MPa)the failure morphology also changes from splitting failure toshear failure and to dilatant failure Combining with the stress-strain curves the greater the confining pressure is the largerstrength and larger deformation both appear So in the processfor gas production in such tight sandstone reservoir the

influence of confining pressure cannot be ignored -e tightsandstone reservoir usually has a large burying depth the insitu stress state of the rock is under three-directional stress stateWhen considering the hydrofracturing for the reservoir theinfluence of stress state on the strength and fracturingmodes ofthe tight sandstone should also be thoroughly considered

On the other hand under the triaxial compression condi-tion the application of confining pressure has decreased theanisotropy degree from viewpoints of the strength and me-chanical parameters but the anisotropy performances of thefailure morphology still cannot be neglected For instance theinclination angle between the axial loading direction and thefailure surface is different when the samples have different dipangle and so is themorphology of the failure surface-e samplewith a dip angle of 0deg has a plane failure surface and there arecurved surfaces for the samples with dip angles of 30deg and 45degand numerous small fissures also appear around the failuresurface for the samples with dip angles of 60deg and 90deg -at is tosay even so the confining pressure is high due to the anisotropyof the tight sandstone the difference in failure morphologyremains existent How will such a character influence the crack-net propagation of the tight sandstone under hydrofractureremains unknown so further investigation is still needed

4 Application

41 Material Parameters of Approximate Isotropic MaterialModels From the above study we can find that the tightsandstone of Xujiahe Formation has a certain degree of an-isotropy but the anisotropy will be low when subjected toconfining pressure In addition by observing the samplemorphology and analyzing the mechanical testing results thetight sandstone in this study can be regarded as a type oftransversely isotropic material and the stress-strain relationship(flexibility matrix) of this material can be expressed as [21 22]

εx

εy

εz

cxy

cyz

czx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1E

minusυE

minusυprimeE

0 0 0

minusυE

1E

minusυprimeE

0 0 0

minus minusυprimeE

minusυprimeE

1Eprime

0 0 0

0 0 01G

0 0

0 0 0 01

Gprime0

0 0 0 0 01

Gprime

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

σx

σy

σz

σxy

σyz

σzx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Table 5 Triaxial compression strength anisotropy of tight sandstone samples

Confining pressure (MPa) Max strength (MPa) Min strength (MPa) Anisotropy degree of compressive strength0 6057 4005 15115 18892 14509 13030 26044 20124 12945 33503 27116 124

Advances in Materials Science and Engineering 7

where E and Eprime are elastic moduli of the isotropic plane andthe plane perpendicular to the isotropic plane respectivelyG and Gprime are shear moduli of the isotropic plane and theplane perpendicular to the isotropic plane respectively v

and vprime both are Poissonrsquos ratio and they represent lateralstrain reduction of each isotropic plane which is caused bytensile stress in the same plane and lateral strain reduction ofeach isotropic plane that is caused by tensile stress which isperpendicular to this plane

From the above study we find that the elastic moduluschanges with the dip angle -at is when the axial directionof the sample has a different dip angle its elastic modulusalso changes In reality we concern not only the elasticmodulus of the isotropic plane and its perpendicular planebut also want to know the modulus of the plane that has aninclination angle with the isotropic plane

-emodulus of one plane which has an inclination angleof α can be expressed as [23]

1Eα

sin4α

E+

1Gprime

minus2]E

1113874 1113875cos2αsin

2α +

cos4α

Eprime (5)

where E is the elastic modulus of the isotropic plane(corresponding to the sample with a dip angle of 90deg) and Eprimeand Gprime are the elastic modulus and shear modulus of theplane perpendicular to the isotropic plane (corresponding tothe sample with a dip angle of 0deg)

By a transformation for equation (5) one obtains

1Eα

1 + 2]

Eminus

2Gprime

+1Eprime

1113874 1113875sin α4

+1

Gprimeminus2]E

minus2Eprime

1113874 1113875sin α2

+1Eprime

(6)

0 MPa 15 MPa 30 MPa 45 MPa

(a)

0 MPa 15 MPa 30 MPa 45 MPa

(b)

0 MPa 15 MPa 30 MPa 45 MPa

(c)

0 MPa 15 MPa 30 MPa 45 MPa

(d)

0 MPa 15 MPa 30 MPa 45 MPa

(e)

Figure 8 Fracture morphology of tight sandstone samples under different confining pressure (a) Dip angle α 0deg (b) Dip angle α 30deg(c) Dip angle α 45deg (d) Dip angle α 60deg (e) Dip angle α 90deg

8 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

confining pressure (0 15MPa 30MPa and 45MPa) fivesamples are used with dip angles of 0deg 30deg 45deg 60deg and 90degrespectively -e stress-strain curves of samples with thesame confining pressure and different angles are listed inFigures 3 and 4 Figure 3(a) shows the strain-stress curves ofthe tight sandstone samples with the same dip angle of 0degunder different confining pressure Figure 3(a) shows thestrain-stress curves of the tight sandstone samples with thesame dip angle of 0deg under different confining pressure Bycomparing these two pictures the influence of dip angle canbe revealed Figure 4(a) and Figure 4(b) show the stress-strain curves of the tight sandstone samples under the sameconfining pressure with different dip angles By these two

pictures the influence of dip angle can be observed moreobviously

By analyzing the data and curves in Table 2 and Figures 3and 4 the main summaries can be made as follows

(1) Under the same conditions the shape and defor-mation characteristics of the stress-strain curves areaffected by the confining pressure and bedding angleIt can be indicated from Table 2 that for the samplewith the same dip angle with the increase in con-fining pressure the peak strength and elastic mod-ulus of tight sandstone are significantly increased Sothe confining pressure is a significant factor to in-fluence the strength of tight sandstone

(2) It can be seen from Figures 3 and 4 that under thecondition with the same confining pressure obviousyield deformation appears in front of all the dipangles of the stress-strain curve For the samplesunder confining pressure of 45MPa with a dip angleof 0deg 30deg 45deg and 60deg the stress-strain curve ofsamples immediately drops after reaching the topintensity While this angle is 90deg the curves ofsamples present an obvious yield platform when it isclose to the peak point and after reaching the peakpoint it does not drop but shows a ductility char-acteristic -e reason is that when the dip angle α is0deg 30deg 45deg and 60deg the samples present shear slipdamage after reaching the peak point While the dipangle α is 90deg the samples happen to shear ex-pansion damage after reaching the peak point with achubby middle and no obvious slip lines so thesamples still have a strong bearing capacity

33 Anisotropy Characteristics Analysis

331 Wave Velocity Anisotropy -e anisotropy in wavevelocity is another important factor to reflect the anisotropiccharacteristics of rock mass [20] So in this study we alsoapply this method to study the anisotropic characteristics oftight sandstone Five groups of the samples are divided Four

x-axis

z-axis

y-axis

xy-plane

z-axis

α

0

90deg 60deg 45deg30deg

0deg

30deg 15deg

15deg30deg

Figure 1 Schematic diagram of the five sampling angles with bedding plane (dip angle a is the inclination angle between the bedding planeand sample drilling direction which is 0deg 30deg 45deg 60deg and 90deg respectively)

Figure 2 -e MTS-815 system of Chongqing University

Table 1 Mineral composition of tight sandstone

Number of samplesBrittle minerals () Clay minerals

()Quartz Feldspar Illite Chlorite

1 5985 1480 2200 3352 6938 1211 1560 2913 5798 1488 2307 408Average value 6240 1393 2022 345Gross 7633 2367

Advances in Materials Science and Engineering 3

ones for dip angle are prepared for this test So 20 samplesare used for the measurement of the longitudinal wavevelocity before the mechanical tests as shown in Table 2 Allthe tests are conducted by using the device of NonmetallicUltrasonic Detector JL-IUA6(a) According to the longitu-dinal wave velocity test on the tight sandstone samples theanisotropy properties of tight sandstone can be revealed insome aspects -e experimental results of ultrasonic velocityfor samples are shown in Table 3 -e change regularities oflongitudinal wave velocity with different dip angles of all thesamples are shown in Figure 5

From Table 3 it can be seen that the longitudinal wavevelocity decreases gradually with the dip angleWhen the dipangle equals 0deg the longitudinal wave propagates parallel to

the bedding surface consuming the minimal energy and theshortest penetrating time thus having the greatest wavevelocity But for the samples with the dip angle of 90deg thepropagation direction of the longitudinal wave is perpen-dicular to the bedding planes so the longitudinal wave has topenetrate the bedding layers to spread which causes themaximum energy consumption and the longest travel timeand results in the minimum wave velocity in the process ofspreading So the wave velocity is a factor to reflect theanisotropy of the tight sandstone -e ratio of the wavevelocity of the direction in 0deg and 90deg is 1206 which issomewhat lower than that of the Longmaxi shale [11]-erefore the anisotropy of tight sandstone exists but islower than that of shale

Table 2 Triaxial compression testing results of samples with different strata angles

Confining pressure (MPa) Dipangle (deg)

Peak strength(MPa)

Elastic modulus(GPa)

Poissonrsquosratio

Peakstrain ()

Ruptureangle (deg)

Residual strength(MPa)

0

0 5457 508 016 155 83 mdash30 4184 339 031 148 88 mdash45 4622 438 034 165 82 mdash60 5653 474 035 164 825 mdash90 5268 445 019 152 90 mdash

15

0 18215 925 015 210 705 904630 15803 842 016 191 695 819845 14807 809 021 203 65 579860 15430 780 021 222 635 599790 15490 752 018 215 68 5710

30

0 25550 1112 019 239 715 984030 20599 1058 024 192 60 1019245 21804 988 030 238 625 1006060 23023 949 027 255 695 1126290 22086 822 024 248 62 9900

45

0 33319 1424 017 259 61 1420330 27211 1263 021 206 565 1541545 27582 1194 026 227 57 1298260 28280 1140 023 280 695 1374890 27760 1081 021 296 63 mdash

0

50

100

150

200

250

300

350

0 05 1 15 2 25 3 35 4

Axi

al st

ress

(MPa

)

Axial strain ()

0 MPa15 MPa

30 MPa45 MPa

(a)

Axi

al st

ress

(MPa

)

0

50

100

150

200

250

0 05 1 15 2 25 3 35 4Axial strain ()

0 MPa15 MPa

30 MPa45 MPa

(b)

Figure 3 Typical curves of stress-strain of tight sandstone samples with the same dip angle under different confining pressure (a) Angleα 0deg (b) Angle α 60deg

4 Advances in Materials Science and Engineering

332 Elastic Modulus Anisotropy Elastic modulus is a basicmechanical parameter which is also an important factor toshow the anisotropy of the tight sandstone Based on theuniaxialtriaxial compression tests in the laboratory all the

elastic moduli of the 20 tested samples are calculated -etriaxial compression tests are conducted under the confiningpressures of 15MPa 30MPa and 45MPa Table 4 shows theelastic modulus anisotropy values of the tight sandstonesamples under different confining pressures and dip anglesAs shown in Figure 6 when the confining pressure is 0MPa(which corresponds to the uniaxial compression test) withthe increase of dip angle the change of the elastic modulus isapproximately a U shapeWhen the dip angle is 0deg the elasticmodulus has a maximum value of 508GPa but when thedip angle equals 30deg the elastic modulus has a minimumvalue of 339GPa In addition when the confining pressureis respectively 15MPa 30MPa and 45MPa with the in-crease of the dip angle the elastic modulus decreasesgradually

For the condition with different confining pressure thecalculation method of the elastic modulus anisotropy [21] isas follows

RE Emax

Emin (2)

where RE is the anisotropy degree of elastic modulus Emax isthe maximum elastic modulus of the sample which

0

10

20

30

40

50

60

70

0 05 1 15 2 25

Axi

al st

ress

(MPa

)

Axial strain ()

0deg30deg45deg

60deg90deg

(a)

0deg30deg45deg

60deg90deg

0

50

100

150

200

250

300

0 05 1 15 2 25 3 35 4

Axi

al st

ress

(MPa

)

Axial strain ()

(b)

Figure 4 Typical curves of stress-strain of tight sandstone samples with different dip angle under the same confining pressure (a) Confiningpressure σ3 0MPa (b) Confining pressure σ3 45MPa

Table 3 Longitudinal wave velocity of tight sandstone samples with different dip angle

Dip angle (deg) Longitudinal wave velocity (ms) Average velocity (ms)

0 2331 2331 2272 2259 23162254 2354 2311 2419

30 2156 2176 2028 2261 21562155 2111 2092 2270

45 2068 2088 1973 1919 20302022 2072 2065 mdash

60 2036 2015 1981 1873 19912097 1937 1981 2008

90 1994 1944 1878 1906 19211966 1803 1959 mdash

1750

2000

2250

2500

2750

0 15 30 45 60 75 90 105

Vel

ocity

of l

ongi

tudi

nal w

ave

(m

s)

Dip angle αdeg

Velocity of longitudinal waveAverage velocity

Figure 5 Longitudinal wave velocity of tight sandstone sampleswith different dip angles

Advances in Materials Science and Engineering 5

corresponds to the dip angle of 0deg and Emin is the minimumelastic modulus

According to equation (2) the anisotropy degree of theelastic modulus was calculated as shown in Table 4 For thesamples under the confining pressure of 0MPa the elasticmodulus of the tight sandstone is of obvious anisotropy -eanisotropy degree of RE equals 164 For the samples underthe confining pressure of 15MPa 30MPa and 45MPa theanisotropy degree (RE) of the elastic modulus becomes lowerthan that under the confining pressure of 0MPa rangingbetween 125 and 136 -erefore the existence of confiningpressure has decreased the anisotropy of the tight sandstoneof Xujiahe Formation which causes the anisotropy of elasticmodulus to become much weaker As for the laboratory testof hydraulic fracturing of tight sandstone samples the hy-draulic fracturing calculation model and the numericalsimulation of the Xujiahe tight sandstone considering thatthe anisotropy degree of elastic modulus is much weakerwhen subjected to three-directional stress state the elasticmodulus in an isotropic plane and vertical plane isotropicelastic modulus can be taken as the average elastic modulusfor a rough estimation But for an accurate calculation it isstill suggested that the anisotropy influence of elasticmodulus cannot be neglected

333 Compressive Strength Anisotropy Figure 7 shows theanisotropy curves of triaxial compressive strength forsamples with different dip angles under different confiningpressures Under the same confining pressure for thesamples with the dip angles of 0deg and 90deg (the dip angle of 0deg

corresponds to the maximum strength) the compressivestrength of samples is relatively high For samples with thedip angles of 30deg and 45deg the compressive strength ofsamples is relatively low -e overall evolution of thecompression strength performs a U shape which is high atboth sides and low in the middle location Under thecondition of different confining pressures the calculationmethod for the anisotropy degree of the compressivestrength anisotropy of RP [21] is as follows

RP σmax

σmin (3)

where RP is the anisotropy degree of compressive strength σ(max) is the maximum compressive strength of sampleswhich corresponds to the dip angle of 0deg and σmin is theminimum compressive strength

According to equation (3) the anisotropy degree of thecompressive strength of the tight sandstone samples in thisstudy can be calculated as shown in Table 5 With an increasein the confining pressure the anisotropy degree of thecompressive strength decreases When the confining pressureis 0MPa the anisotropy degree of the compressive strengthRP is 151 when the confining pressure is 15MPa 30MPaand 45MPa the anisotropy degree of the compressivestrength RP ranges from 124 to 130 -erefore from theviewpoint of compressive strength it has an obvious an-isotropy -e confining pressure has a negligible influence onthe anisotropy degree for the tight sandstone in this study Inthe field reservoir of the tight sandstone of Xujiahe Forma-tion the influences of the anisotropy and the in situ stressstate should both be considered for gas production

Table 4 Anisotropy degree of elastic modulus

Confining pressure (MPa) Max elastic modulus (GPa) Min elastic modulus (GPa) Degree of anisotropy0 524 319 16415 941 750 12530 1115 822 13645 1447 1075 135

0

3

6

9

12

15

18

0 15 30 45 60 75 90 105

Elas

tic m

odul

us (G

Pa)

Dip angle αdeg

0 MPa30 MPa

15 MPa45 MPa

Figure 6 Elastic modulus anisotropy of the tight sandstonesamples with different dip angles when subjected to differentconfining pressure

0

100

200

300

400

0 15 30 45 60 75 90 105

Peak

stre

ngth

(MPa

)Dip angle (deg)

0 MPa30 MPa

15 MPa45 MPa

Figure 7 Triaxial compression strength anisotropy of samples withdifferent strata angles

6 Advances in Materials Science and Engineering

334 Anisotropy of Fracture Morphology Figure 8 showsfailure mode under the conditions of different confiningpressure and different dip angles -e failure modes of thesamples can be mainly divided into three types splittingfailure shear failure and shear-expansion failure

When the confining pressure is 0MPa the predominantfailure mode of all the samples is splitting failure but somedifferences exist among the samples with different dip anglesFor instance the sample with the dip angle of 0deg has a mainsplitting fracture and several secondary fractures and somesecondary fractures are inclined showing shear failure per-formance-is is a reflection that the matrix perpendicular tothe bedding direction has the greatest strength As for thesample with the dip angle of 90deg only one splitting fractureappears on the sample surface parallel to the axial loadingdirection -is indicates that the matrix along the beddingdirection has a low strength For the samples with the dipangles of 30deg 45deg and 60deg the failure fracture is straight in themiddle location and somewhat inclined at each end -isshows that the propagation direction of the failure fracturemay be influenced by the bedding plane So under theuniaxial compression test (confining pressure 0MPa) an-isotropy exists in the review point of failure morphology

Under triaxial compression testing condition (15MPaand 30MPa) the difference in failure morphology remainsexistent for the samples with different dip angles For ex-ample the sample with 0deg dip angle has a steep failuresurface but the failure surface of the sample with dip angle of90deg is much gentler When the dip angle ranges from 30deg to60deg the failure surface has an inclination angle between thecases of 0deg and 90deg but the failure surface is already not aplane surface but a curved one -at is to say due to theexistence of bedding angle it has caused the failure surface tobe a curved surface With respect to the condition of highconfining pressure (45MPa) the failure mode has becomeshear-dilatant state-ere is onemain failure surface but theaperture of this surface is very small and there are numeroussmall fissures around this surface -e middle location of thesample has expanded showing a drum shape Moreoverexcept the cases with dip angles of 0deg and 90deg the failuresurfaces of the samples are all curved surfaces under theconfining pressure of 45MPa

From the above study one can deduce that the existence ofconfining pressure has largely changed the failure modes forthe tight sandstone During the increase process of the con-fining pressure (0MPa⟶ 15MPa⟶ 30MPa⟶ 45MPa)the failure morphology also changes from splitting failure toshear failure and to dilatant failure Combining with the stress-strain curves the greater the confining pressure is the largerstrength and larger deformation both appear So in the processfor gas production in such tight sandstone reservoir the

influence of confining pressure cannot be ignored -e tightsandstone reservoir usually has a large burying depth the insitu stress state of the rock is under three-directional stress stateWhen considering the hydrofracturing for the reservoir theinfluence of stress state on the strength and fracturingmodes ofthe tight sandstone should also be thoroughly considered

On the other hand under the triaxial compression condi-tion the application of confining pressure has decreased theanisotropy degree from viewpoints of the strength and me-chanical parameters but the anisotropy performances of thefailure morphology still cannot be neglected For instance theinclination angle between the axial loading direction and thefailure surface is different when the samples have different dipangle and so is themorphology of the failure surface-e samplewith a dip angle of 0deg has a plane failure surface and there arecurved surfaces for the samples with dip angles of 30deg and 45degand numerous small fissures also appear around the failuresurface for the samples with dip angles of 60deg and 90deg -at is tosay even so the confining pressure is high due to the anisotropyof the tight sandstone the difference in failure morphologyremains existent How will such a character influence the crack-net propagation of the tight sandstone under hydrofractureremains unknown so further investigation is still needed

4 Application

41 Material Parameters of Approximate Isotropic MaterialModels From the above study we can find that the tightsandstone of Xujiahe Formation has a certain degree of an-isotropy but the anisotropy will be low when subjected toconfining pressure In addition by observing the samplemorphology and analyzing the mechanical testing results thetight sandstone in this study can be regarded as a type oftransversely isotropic material and the stress-strain relationship(flexibility matrix) of this material can be expressed as [21 22]

εx

εy

εz

cxy

cyz

czx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1E

minusυE

minusυprimeE

0 0 0

minusυE

1E

minusυprimeE

0 0 0

minus minusυprimeE

minusυprimeE

1Eprime

0 0 0

0 0 01G

0 0

0 0 0 01

Gprime0

0 0 0 0 01

Gprime

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

σx

σy

σz

σxy

σyz

σzx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Table 5 Triaxial compression strength anisotropy of tight sandstone samples

Confining pressure (MPa) Max strength (MPa) Min strength (MPa) Anisotropy degree of compressive strength0 6057 4005 15115 18892 14509 13030 26044 20124 12945 33503 27116 124

Advances in Materials Science and Engineering 7

where E and Eprime are elastic moduli of the isotropic plane andthe plane perpendicular to the isotropic plane respectivelyG and Gprime are shear moduli of the isotropic plane and theplane perpendicular to the isotropic plane respectively v

and vprime both are Poissonrsquos ratio and they represent lateralstrain reduction of each isotropic plane which is caused bytensile stress in the same plane and lateral strain reduction ofeach isotropic plane that is caused by tensile stress which isperpendicular to this plane

From the above study we find that the elastic moduluschanges with the dip angle -at is when the axial directionof the sample has a different dip angle its elastic modulusalso changes In reality we concern not only the elasticmodulus of the isotropic plane and its perpendicular planebut also want to know the modulus of the plane that has aninclination angle with the isotropic plane

-emodulus of one plane which has an inclination angleof α can be expressed as [23]

1Eα

sin4α

E+

1Gprime

minus2]E

1113874 1113875cos2αsin

2α +

cos4α

Eprime (5)

where E is the elastic modulus of the isotropic plane(corresponding to the sample with a dip angle of 90deg) and Eprimeand Gprime are the elastic modulus and shear modulus of theplane perpendicular to the isotropic plane (corresponding tothe sample with a dip angle of 0deg)

By a transformation for equation (5) one obtains

1Eα

1 + 2]

Eminus

2Gprime

+1Eprime

1113874 1113875sin α4

+1

Gprimeminus2]E

minus2Eprime

1113874 1113875sin α2

+1Eprime

(6)

0 MPa 15 MPa 30 MPa 45 MPa

(a)

0 MPa 15 MPa 30 MPa 45 MPa

(b)

0 MPa 15 MPa 30 MPa 45 MPa

(c)

0 MPa 15 MPa 30 MPa 45 MPa

(d)

0 MPa 15 MPa 30 MPa 45 MPa

(e)

Figure 8 Fracture morphology of tight sandstone samples under different confining pressure (a) Dip angle α 0deg (b) Dip angle α 30deg(c) Dip angle α 45deg (d) Dip angle α 60deg (e) Dip angle α 90deg

8 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

ones for dip angle are prepared for this test So 20 samplesare used for the measurement of the longitudinal wavevelocity before the mechanical tests as shown in Table 2 Allthe tests are conducted by using the device of NonmetallicUltrasonic Detector JL-IUA6(a) According to the longitu-dinal wave velocity test on the tight sandstone samples theanisotropy properties of tight sandstone can be revealed insome aspects -e experimental results of ultrasonic velocityfor samples are shown in Table 3 -e change regularities oflongitudinal wave velocity with different dip angles of all thesamples are shown in Figure 5

From Table 3 it can be seen that the longitudinal wavevelocity decreases gradually with the dip angleWhen the dipangle equals 0deg the longitudinal wave propagates parallel to

the bedding surface consuming the minimal energy and theshortest penetrating time thus having the greatest wavevelocity But for the samples with the dip angle of 90deg thepropagation direction of the longitudinal wave is perpen-dicular to the bedding planes so the longitudinal wave has topenetrate the bedding layers to spread which causes themaximum energy consumption and the longest travel timeand results in the minimum wave velocity in the process ofspreading So the wave velocity is a factor to reflect theanisotropy of the tight sandstone -e ratio of the wavevelocity of the direction in 0deg and 90deg is 1206 which issomewhat lower than that of the Longmaxi shale [11]-erefore the anisotropy of tight sandstone exists but islower than that of shale

Table 2 Triaxial compression testing results of samples with different strata angles

Confining pressure (MPa) Dipangle (deg)

Peak strength(MPa)

Elastic modulus(GPa)

Poissonrsquosratio

Peakstrain ()

Ruptureangle (deg)

Residual strength(MPa)

0

0 5457 508 016 155 83 mdash30 4184 339 031 148 88 mdash45 4622 438 034 165 82 mdash60 5653 474 035 164 825 mdash90 5268 445 019 152 90 mdash

15

0 18215 925 015 210 705 904630 15803 842 016 191 695 819845 14807 809 021 203 65 579860 15430 780 021 222 635 599790 15490 752 018 215 68 5710

30

0 25550 1112 019 239 715 984030 20599 1058 024 192 60 1019245 21804 988 030 238 625 1006060 23023 949 027 255 695 1126290 22086 822 024 248 62 9900

45

0 33319 1424 017 259 61 1420330 27211 1263 021 206 565 1541545 27582 1194 026 227 57 1298260 28280 1140 023 280 695 1374890 27760 1081 021 296 63 mdash

0

50

100

150

200

250

300

350

0 05 1 15 2 25 3 35 4

Axi

al st

ress

(MPa

)

Axial strain ()

0 MPa15 MPa

30 MPa45 MPa

(a)

Axi

al st

ress

(MPa

)

0

50

100

150

200

250

0 05 1 15 2 25 3 35 4Axial strain ()

0 MPa15 MPa

30 MPa45 MPa

(b)

Figure 3 Typical curves of stress-strain of tight sandstone samples with the same dip angle under different confining pressure (a) Angleα 0deg (b) Angle α 60deg

4 Advances in Materials Science and Engineering

332 Elastic Modulus Anisotropy Elastic modulus is a basicmechanical parameter which is also an important factor toshow the anisotropy of the tight sandstone Based on theuniaxialtriaxial compression tests in the laboratory all the

elastic moduli of the 20 tested samples are calculated -etriaxial compression tests are conducted under the confiningpressures of 15MPa 30MPa and 45MPa Table 4 shows theelastic modulus anisotropy values of the tight sandstonesamples under different confining pressures and dip anglesAs shown in Figure 6 when the confining pressure is 0MPa(which corresponds to the uniaxial compression test) withthe increase of dip angle the change of the elastic modulus isapproximately a U shapeWhen the dip angle is 0deg the elasticmodulus has a maximum value of 508GPa but when thedip angle equals 30deg the elastic modulus has a minimumvalue of 339GPa In addition when the confining pressureis respectively 15MPa 30MPa and 45MPa with the in-crease of the dip angle the elastic modulus decreasesgradually

For the condition with different confining pressure thecalculation method of the elastic modulus anisotropy [21] isas follows

RE Emax

Emin (2)

where RE is the anisotropy degree of elastic modulus Emax isthe maximum elastic modulus of the sample which

0

10

20

30

40

50

60

70

0 05 1 15 2 25

Axi

al st

ress

(MPa

)

Axial strain ()

0deg30deg45deg

60deg90deg

(a)

0deg30deg45deg

60deg90deg

0

50

100

150

200

250

300

0 05 1 15 2 25 3 35 4

Axi

al st

ress

(MPa

)

Axial strain ()

(b)

Figure 4 Typical curves of stress-strain of tight sandstone samples with different dip angle under the same confining pressure (a) Confiningpressure σ3 0MPa (b) Confining pressure σ3 45MPa

Table 3 Longitudinal wave velocity of tight sandstone samples with different dip angle

Dip angle (deg) Longitudinal wave velocity (ms) Average velocity (ms)

0 2331 2331 2272 2259 23162254 2354 2311 2419

30 2156 2176 2028 2261 21562155 2111 2092 2270

45 2068 2088 1973 1919 20302022 2072 2065 mdash

60 2036 2015 1981 1873 19912097 1937 1981 2008

90 1994 1944 1878 1906 19211966 1803 1959 mdash

1750

2000

2250

2500

2750

0 15 30 45 60 75 90 105

Vel

ocity

of l

ongi

tudi

nal w

ave

(m

s)

Dip angle αdeg

Velocity of longitudinal waveAverage velocity

Figure 5 Longitudinal wave velocity of tight sandstone sampleswith different dip angles

Advances in Materials Science and Engineering 5

corresponds to the dip angle of 0deg and Emin is the minimumelastic modulus

According to equation (2) the anisotropy degree of theelastic modulus was calculated as shown in Table 4 For thesamples under the confining pressure of 0MPa the elasticmodulus of the tight sandstone is of obvious anisotropy -eanisotropy degree of RE equals 164 For the samples underthe confining pressure of 15MPa 30MPa and 45MPa theanisotropy degree (RE) of the elastic modulus becomes lowerthan that under the confining pressure of 0MPa rangingbetween 125 and 136 -erefore the existence of confiningpressure has decreased the anisotropy of the tight sandstoneof Xujiahe Formation which causes the anisotropy of elasticmodulus to become much weaker As for the laboratory testof hydraulic fracturing of tight sandstone samples the hy-draulic fracturing calculation model and the numericalsimulation of the Xujiahe tight sandstone considering thatthe anisotropy degree of elastic modulus is much weakerwhen subjected to three-directional stress state the elasticmodulus in an isotropic plane and vertical plane isotropicelastic modulus can be taken as the average elastic modulusfor a rough estimation But for an accurate calculation it isstill suggested that the anisotropy influence of elasticmodulus cannot be neglected

333 Compressive Strength Anisotropy Figure 7 shows theanisotropy curves of triaxial compressive strength forsamples with different dip angles under different confiningpressures Under the same confining pressure for thesamples with the dip angles of 0deg and 90deg (the dip angle of 0deg

corresponds to the maximum strength) the compressivestrength of samples is relatively high For samples with thedip angles of 30deg and 45deg the compressive strength ofsamples is relatively low -e overall evolution of thecompression strength performs a U shape which is high atboth sides and low in the middle location Under thecondition of different confining pressures the calculationmethod for the anisotropy degree of the compressivestrength anisotropy of RP [21] is as follows

RP σmax

σmin (3)

where RP is the anisotropy degree of compressive strength σ(max) is the maximum compressive strength of sampleswhich corresponds to the dip angle of 0deg and σmin is theminimum compressive strength

According to equation (3) the anisotropy degree of thecompressive strength of the tight sandstone samples in thisstudy can be calculated as shown in Table 5 With an increasein the confining pressure the anisotropy degree of thecompressive strength decreases When the confining pressureis 0MPa the anisotropy degree of the compressive strengthRP is 151 when the confining pressure is 15MPa 30MPaand 45MPa the anisotropy degree of the compressivestrength RP ranges from 124 to 130 -erefore from theviewpoint of compressive strength it has an obvious an-isotropy -e confining pressure has a negligible influence onthe anisotropy degree for the tight sandstone in this study Inthe field reservoir of the tight sandstone of Xujiahe Forma-tion the influences of the anisotropy and the in situ stressstate should both be considered for gas production

Table 4 Anisotropy degree of elastic modulus

Confining pressure (MPa) Max elastic modulus (GPa) Min elastic modulus (GPa) Degree of anisotropy0 524 319 16415 941 750 12530 1115 822 13645 1447 1075 135

0

3

6

9

12

15

18

0 15 30 45 60 75 90 105

Elas

tic m

odul

us (G

Pa)

Dip angle αdeg

0 MPa30 MPa

15 MPa45 MPa

Figure 6 Elastic modulus anisotropy of the tight sandstonesamples with different dip angles when subjected to differentconfining pressure

0

100

200

300

400

0 15 30 45 60 75 90 105

Peak

stre

ngth

(MPa

)Dip angle (deg)

0 MPa30 MPa

15 MPa45 MPa

Figure 7 Triaxial compression strength anisotropy of samples withdifferent strata angles

6 Advances in Materials Science and Engineering

334 Anisotropy of Fracture Morphology Figure 8 showsfailure mode under the conditions of different confiningpressure and different dip angles -e failure modes of thesamples can be mainly divided into three types splittingfailure shear failure and shear-expansion failure

When the confining pressure is 0MPa the predominantfailure mode of all the samples is splitting failure but somedifferences exist among the samples with different dip anglesFor instance the sample with the dip angle of 0deg has a mainsplitting fracture and several secondary fractures and somesecondary fractures are inclined showing shear failure per-formance-is is a reflection that the matrix perpendicular tothe bedding direction has the greatest strength As for thesample with the dip angle of 90deg only one splitting fractureappears on the sample surface parallel to the axial loadingdirection -is indicates that the matrix along the beddingdirection has a low strength For the samples with the dipangles of 30deg 45deg and 60deg the failure fracture is straight in themiddle location and somewhat inclined at each end -isshows that the propagation direction of the failure fracturemay be influenced by the bedding plane So under theuniaxial compression test (confining pressure 0MPa) an-isotropy exists in the review point of failure morphology

Under triaxial compression testing condition (15MPaand 30MPa) the difference in failure morphology remainsexistent for the samples with different dip angles For ex-ample the sample with 0deg dip angle has a steep failuresurface but the failure surface of the sample with dip angle of90deg is much gentler When the dip angle ranges from 30deg to60deg the failure surface has an inclination angle between thecases of 0deg and 90deg but the failure surface is already not aplane surface but a curved one -at is to say due to theexistence of bedding angle it has caused the failure surface tobe a curved surface With respect to the condition of highconfining pressure (45MPa) the failure mode has becomeshear-dilatant state-ere is onemain failure surface but theaperture of this surface is very small and there are numeroussmall fissures around this surface -e middle location of thesample has expanded showing a drum shape Moreoverexcept the cases with dip angles of 0deg and 90deg the failuresurfaces of the samples are all curved surfaces under theconfining pressure of 45MPa

From the above study one can deduce that the existence ofconfining pressure has largely changed the failure modes forthe tight sandstone During the increase process of the con-fining pressure (0MPa⟶ 15MPa⟶ 30MPa⟶ 45MPa)the failure morphology also changes from splitting failure toshear failure and to dilatant failure Combining with the stress-strain curves the greater the confining pressure is the largerstrength and larger deformation both appear So in the processfor gas production in such tight sandstone reservoir the

influence of confining pressure cannot be ignored -e tightsandstone reservoir usually has a large burying depth the insitu stress state of the rock is under three-directional stress stateWhen considering the hydrofracturing for the reservoir theinfluence of stress state on the strength and fracturingmodes ofthe tight sandstone should also be thoroughly considered

On the other hand under the triaxial compression condi-tion the application of confining pressure has decreased theanisotropy degree from viewpoints of the strength and me-chanical parameters but the anisotropy performances of thefailure morphology still cannot be neglected For instance theinclination angle between the axial loading direction and thefailure surface is different when the samples have different dipangle and so is themorphology of the failure surface-e samplewith a dip angle of 0deg has a plane failure surface and there arecurved surfaces for the samples with dip angles of 30deg and 45degand numerous small fissures also appear around the failuresurface for the samples with dip angles of 60deg and 90deg -at is tosay even so the confining pressure is high due to the anisotropyof the tight sandstone the difference in failure morphologyremains existent How will such a character influence the crack-net propagation of the tight sandstone under hydrofractureremains unknown so further investigation is still needed

4 Application

41 Material Parameters of Approximate Isotropic MaterialModels From the above study we can find that the tightsandstone of Xujiahe Formation has a certain degree of an-isotropy but the anisotropy will be low when subjected toconfining pressure In addition by observing the samplemorphology and analyzing the mechanical testing results thetight sandstone in this study can be regarded as a type oftransversely isotropic material and the stress-strain relationship(flexibility matrix) of this material can be expressed as [21 22]

εx

εy

εz

cxy

cyz

czx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1E

minusυE

minusυprimeE

0 0 0

minusυE

1E

minusυprimeE

0 0 0

minus minusυprimeE

minusυprimeE

1Eprime

0 0 0

0 0 01G

0 0

0 0 0 01

Gprime0

0 0 0 0 01

Gprime

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

σx

σy

σz

σxy

σyz

σzx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Table 5 Triaxial compression strength anisotropy of tight sandstone samples

Confining pressure (MPa) Max strength (MPa) Min strength (MPa) Anisotropy degree of compressive strength0 6057 4005 15115 18892 14509 13030 26044 20124 12945 33503 27116 124

Advances in Materials Science and Engineering 7

where E and Eprime are elastic moduli of the isotropic plane andthe plane perpendicular to the isotropic plane respectivelyG and Gprime are shear moduli of the isotropic plane and theplane perpendicular to the isotropic plane respectively v

and vprime both are Poissonrsquos ratio and they represent lateralstrain reduction of each isotropic plane which is caused bytensile stress in the same plane and lateral strain reduction ofeach isotropic plane that is caused by tensile stress which isperpendicular to this plane

From the above study we find that the elastic moduluschanges with the dip angle -at is when the axial directionof the sample has a different dip angle its elastic modulusalso changes In reality we concern not only the elasticmodulus of the isotropic plane and its perpendicular planebut also want to know the modulus of the plane that has aninclination angle with the isotropic plane

-emodulus of one plane which has an inclination angleof α can be expressed as [23]

1Eα

sin4α

E+

1Gprime

minus2]E

1113874 1113875cos2αsin

2α +

cos4α

Eprime (5)

where E is the elastic modulus of the isotropic plane(corresponding to the sample with a dip angle of 90deg) and Eprimeand Gprime are the elastic modulus and shear modulus of theplane perpendicular to the isotropic plane (corresponding tothe sample with a dip angle of 0deg)

By a transformation for equation (5) one obtains

1Eα

1 + 2]

Eminus

2Gprime

+1Eprime

1113874 1113875sin α4

+1

Gprimeminus2]E

minus2Eprime

1113874 1113875sin α2

+1Eprime

(6)

0 MPa 15 MPa 30 MPa 45 MPa

(a)

0 MPa 15 MPa 30 MPa 45 MPa

(b)

0 MPa 15 MPa 30 MPa 45 MPa

(c)

0 MPa 15 MPa 30 MPa 45 MPa

(d)

0 MPa 15 MPa 30 MPa 45 MPa

(e)

Figure 8 Fracture morphology of tight sandstone samples under different confining pressure (a) Dip angle α 0deg (b) Dip angle α 30deg(c) Dip angle α 45deg (d) Dip angle α 60deg (e) Dip angle α 90deg

8 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

332 Elastic Modulus Anisotropy Elastic modulus is a basicmechanical parameter which is also an important factor toshow the anisotropy of the tight sandstone Based on theuniaxialtriaxial compression tests in the laboratory all the

elastic moduli of the 20 tested samples are calculated -etriaxial compression tests are conducted under the confiningpressures of 15MPa 30MPa and 45MPa Table 4 shows theelastic modulus anisotropy values of the tight sandstonesamples under different confining pressures and dip anglesAs shown in Figure 6 when the confining pressure is 0MPa(which corresponds to the uniaxial compression test) withthe increase of dip angle the change of the elastic modulus isapproximately a U shapeWhen the dip angle is 0deg the elasticmodulus has a maximum value of 508GPa but when thedip angle equals 30deg the elastic modulus has a minimumvalue of 339GPa In addition when the confining pressureis respectively 15MPa 30MPa and 45MPa with the in-crease of the dip angle the elastic modulus decreasesgradually

For the condition with different confining pressure thecalculation method of the elastic modulus anisotropy [21] isas follows

RE Emax

Emin (2)

where RE is the anisotropy degree of elastic modulus Emax isthe maximum elastic modulus of the sample which

0

10

20

30

40

50

60

70

0 05 1 15 2 25

Axi

al st

ress

(MPa

)

Axial strain ()

0deg30deg45deg

60deg90deg

(a)

0deg30deg45deg

60deg90deg

0

50

100

150

200

250

300

0 05 1 15 2 25 3 35 4

Axi

al st

ress

(MPa

)

Axial strain ()

(b)

Figure 4 Typical curves of stress-strain of tight sandstone samples with different dip angle under the same confining pressure (a) Confiningpressure σ3 0MPa (b) Confining pressure σ3 45MPa

Table 3 Longitudinal wave velocity of tight sandstone samples with different dip angle

Dip angle (deg) Longitudinal wave velocity (ms) Average velocity (ms)

0 2331 2331 2272 2259 23162254 2354 2311 2419

30 2156 2176 2028 2261 21562155 2111 2092 2270

45 2068 2088 1973 1919 20302022 2072 2065 mdash

60 2036 2015 1981 1873 19912097 1937 1981 2008

90 1994 1944 1878 1906 19211966 1803 1959 mdash

1750

2000

2250

2500

2750

0 15 30 45 60 75 90 105

Vel

ocity

of l

ongi

tudi

nal w

ave

(m

s)

Dip angle αdeg

Velocity of longitudinal waveAverage velocity

Figure 5 Longitudinal wave velocity of tight sandstone sampleswith different dip angles

Advances in Materials Science and Engineering 5

corresponds to the dip angle of 0deg and Emin is the minimumelastic modulus

According to equation (2) the anisotropy degree of theelastic modulus was calculated as shown in Table 4 For thesamples under the confining pressure of 0MPa the elasticmodulus of the tight sandstone is of obvious anisotropy -eanisotropy degree of RE equals 164 For the samples underthe confining pressure of 15MPa 30MPa and 45MPa theanisotropy degree (RE) of the elastic modulus becomes lowerthan that under the confining pressure of 0MPa rangingbetween 125 and 136 -erefore the existence of confiningpressure has decreased the anisotropy of the tight sandstoneof Xujiahe Formation which causes the anisotropy of elasticmodulus to become much weaker As for the laboratory testof hydraulic fracturing of tight sandstone samples the hy-draulic fracturing calculation model and the numericalsimulation of the Xujiahe tight sandstone considering thatthe anisotropy degree of elastic modulus is much weakerwhen subjected to three-directional stress state the elasticmodulus in an isotropic plane and vertical plane isotropicelastic modulus can be taken as the average elastic modulusfor a rough estimation But for an accurate calculation it isstill suggested that the anisotropy influence of elasticmodulus cannot be neglected

333 Compressive Strength Anisotropy Figure 7 shows theanisotropy curves of triaxial compressive strength forsamples with different dip angles under different confiningpressures Under the same confining pressure for thesamples with the dip angles of 0deg and 90deg (the dip angle of 0deg

corresponds to the maximum strength) the compressivestrength of samples is relatively high For samples with thedip angles of 30deg and 45deg the compressive strength ofsamples is relatively low -e overall evolution of thecompression strength performs a U shape which is high atboth sides and low in the middle location Under thecondition of different confining pressures the calculationmethod for the anisotropy degree of the compressivestrength anisotropy of RP [21] is as follows

RP σmax

σmin (3)

where RP is the anisotropy degree of compressive strength σ(max) is the maximum compressive strength of sampleswhich corresponds to the dip angle of 0deg and σmin is theminimum compressive strength

According to equation (3) the anisotropy degree of thecompressive strength of the tight sandstone samples in thisstudy can be calculated as shown in Table 5 With an increasein the confining pressure the anisotropy degree of thecompressive strength decreases When the confining pressureis 0MPa the anisotropy degree of the compressive strengthRP is 151 when the confining pressure is 15MPa 30MPaand 45MPa the anisotropy degree of the compressivestrength RP ranges from 124 to 130 -erefore from theviewpoint of compressive strength it has an obvious an-isotropy -e confining pressure has a negligible influence onthe anisotropy degree for the tight sandstone in this study Inthe field reservoir of the tight sandstone of Xujiahe Forma-tion the influences of the anisotropy and the in situ stressstate should both be considered for gas production

Table 4 Anisotropy degree of elastic modulus

Confining pressure (MPa) Max elastic modulus (GPa) Min elastic modulus (GPa) Degree of anisotropy0 524 319 16415 941 750 12530 1115 822 13645 1447 1075 135

0

3

6

9

12

15

18

0 15 30 45 60 75 90 105

Elas

tic m

odul

us (G

Pa)

Dip angle αdeg

0 MPa30 MPa

15 MPa45 MPa

Figure 6 Elastic modulus anisotropy of the tight sandstonesamples with different dip angles when subjected to differentconfining pressure

0

100

200

300

400

0 15 30 45 60 75 90 105

Peak

stre

ngth

(MPa

)Dip angle (deg)

0 MPa30 MPa

15 MPa45 MPa

Figure 7 Triaxial compression strength anisotropy of samples withdifferent strata angles

6 Advances in Materials Science and Engineering

334 Anisotropy of Fracture Morphology Figure 8 showsfailure mode under the conditions of different confiningpressure and different dip angles -e failure modes of thesamples can be mainly divided into three types splittingfailure shear failure and shear-expansion failure

When the confining pressure is 0MPa the predominantfailure mode of all the samples is splitting failure but somedifferences exist among the samples with different dip anglesFor instance the sample with the dip angle of 0deg has a mainsplitting fracture and several secondary fractures and somesecondary fractures are inclined showing shear failure per-formance-is is a reflection that the matrix perpendicular tothe bedding direction has the greatest strength As for thesample with the dip angle of 90deg only one splitting fractureappears on the sample surface parallel to the axial loadingdirection -is indicates that the matrix along the beddingdirection has a low strength For the samples with the dipangles of 30deg 45deg and 60deg the failure fracture is straight in themiddle location and somewhat inclined at each end -isshows that the propagation direction of the failure fracturemay be influenced by the bedding plane So under theuniaxial compression test (confining pressure 0MPa) an-isotropy exists in the review point of failure morphology

Under triaxial compression testing condition (15MPaand 30MPa) the difference in failure morphology remainsexistent for the samples with different dip angles For ex-ample the sample with 0deg dip angle has a steep failuresurface but the failure surface of the sample with dip angle of90deg is much gentler When the dip angle ranges from 30deg to60deg the failure surface has an inclination angle between thecases of 0deg and 90deg but the failure surface is already not aplane surface but a curved one -at is to say due to theexistence of bedding angle it has caused the failure surface tobe a curved surface With respect to the condition of highconfining pressure (45MPa) the failure mode has becomeshear-dilatant state-ere is onemain failure surface but theaperture of this surface is very small and there are numeroussmall fissures around this surface -e middle location of thesample has expanded showing a drum shape Moreoverexcept the cases with dip angles of 0deg and 90deg the failuresurfaces of the samples are all curved surfaces under theconfining pressure of 45MPa

From the above study one can deduce that the existence ofconfining pressure has largely changed the failure modes forthe tight sandstone During the increase process of the con-fining pressure (0MPa⟶ 15MPa⟶ 30MPa⟶ 45MPa)the failure morphology also changes from splitting failure toshear failure and to dilatant failure Combining with the stress-strain curves the greater the confining pressure is the largerstrength and larger deformation both appear So in the processfor gas production in such tight sandstone reservoir the

influence of confining pressure cannot be ignored -e tightsandstone reservoir usually has a large burying depth the insitu stress state of the rock is under three-directional stress stateWhen considering the hydrofracturing for the reservoir theinfluence of stress state on the strength and fracturingmodes ofthe tight sandstone should also be thoroughly considered

On the other hand under the triaxial compression condi-tion the application of confining pressure has decreased theanisotropy degree from viewpoints of the strength and me-chanical parameters but the anisotropy performances of thefailure morphology still cannot be neglected For instance theinclination angle between the axial loading direction and thefailure surface is different when the samples have different dipangle and so is themorphology of the failure surface-e samplewith a dip angle of 0deg has a plane failure surface and there arecurved surfaces for the samples with dip angles of 30deg and 45degand numerous small fissures also appear around the failuresurface for the samples with dip angles of 60deg and 90deg -at is tosay even so the confining pressure is high due to the anisotropyof the tight sandstone the difference in failure morphologyremains existent How will such a character influence the crack-net propagation of the tight sandstone under hydrofractureremains unknown so further investigation is still needed

4 Application

41 Material Parameters of Approximate Isotropic MaterialModels From the above study we can find that the tightsandstone of Xujiahe Formation has a certain degree of an-isotropy but the anisotropy will be low when subjected toconfining pressure In addition by observing the samplemorphology and analyzing the mechanical testing results thetight sandstone in this study can be regarded as a type oftransversely isotropic material and the stress-strain relationship(flexibility matrix) of this material can be expressed as [21 22]

εx

εy

εz

cxy

cyz

czx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1E

minusυE

minusυprimeE

0 0 0

minusυE

1E

minusυprimeE

0 0 0

minus minusυprimeE

minusυprimeE

1Eprime

0 0 0

0 0 01G

0 0

0 0 0 01

Gprime0

0 0 0 0 01

Gprime

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

σx

σy

σz

σxy

σyz

σzx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Table 5 Triaxial compression strength anisotropy of tight sandstone samples

Confining pressure (MPa) Max strength (MPa) Min strength (MPa) Anisotropy degree of compressive strength0 6057 4005 15115 18892 14509 13030 26044 20124 12945 33503 27116 124

Advances in Materials Science and Engineering 7

where E and Eprime are elastic moduli of the isotropic plane andthe plane perpendicular to the isotropic plane respectivelyG and Gprime are shear moduli of the isotropic plane and theplane perpendicular to the isotropic plane respectively v

and vprime both are Poissonrsquos ratio and they represent lateralstrain reduction of each isotropic plane which is caused bytensile stress in the same plane and lateral strain reduction ofeach isotropic plane that is caused by tensile stress which isperpendicular to this plane

From the above study we find that the elastic moduluschanges with the dip angle -at is when the axial directionof the sample has a different dip angle its elastic modulusalso changes In reality we concern not only the elasticmodulus of the isotropic plane and its perpendicular planebut also want to know the modulus of the plane that has aninclination angle with the isotropic plane

-emodulus of one plane which has an inclination angleof α can be expressed as [23]

1Eα

sin4α

E+

1Gprime

minus2]E

1113874 1113875cos2αsin

2α +

cos4α

Eprime (5)

where E is the elastic modulus of the isotropic plane(corresponding to the sample with a dip angle of 90deg) and Eprimeand Gprime are the elastic modulus and shear modulus of theplane perpendicular to the isotropic plane (corresponding tothe sample with a dip angle of 0deg)

By a transformation for equation (5) one obtains

1Eα

1 + 2]

Eminus

2Gprime

+1Eprime

1113874 1113875sin α4

+1

Gprimeminus2]E

minus2Eprime

1113874 1113875sin α2

+1Eprime

(6)

0 MPa 15 MPa 30 MPa 45 MPa

(a)

0 MPa 15 MPa 30 MPa 45 MPa

(b)

0 MPa 15 MPa 30 MPa 45 MPa

(c)

0 MPa 15 MPa 30 MPa 45 MPa

(d)

0 MPa 15 MPa 30 MPa 45 MPa

(e)

Figure 8 Fracture morphology of tight sandstone samples under different confining pressure (a) Dip angle α 0deg (b) Dip angle α 30deg(c) Dip angle α 45deg (d) Dip angle α 60deg (e) Dip angle α 90deg

8 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

corresponds to the dip angle of 0deg and Emin is the minimumelastic modulus

According to equation (2) the anisotropy degree of theelastic modulus was calculated as shown in Table 4 For thesamples under the confining pressure of 0MPa the elasticmodulus of the tight sandstone is of obvious anisotropy -eanisotropy degree of RE equals 164 For the samples underthe confining pressure of 15MPa 30MPa and 45MPa theanisotropy degree (RE) of the elastic modulus becomes lowerthan that under the confining pressure of 0MPa rangingbetween 125 and 136 -erefore the existence of confiningpressure has decreased the anisotropy of the tight sandstoneof Xujiahe Formation which causes the anisotropy of elasticmodulus to become much weaker As for the laboratory testof hydraulic fracturing of tight sandstone samples the hy-draulic fracturing calculation model and the numericalsimulation of the Xujiahe tight sandstone considering thatthe anisotropy degree of elastic modulus is much weakerwhen subjected to three-directional stress state the elasticmodulus in an isotropic plane and vertical plane isotropicelastic modulus can be taken as the average elastic modulusfor a rough estimation But for an accurate calculation it isstill suggested that the anisotropy influence of elasticmodulus cannot be neglected

333 Compressive Strength Anisotropy Figure 7 shows theanisotropy curves of triaxial compressive strength forsamples with different dip angles under different confiningpressures Under the same confining pressure for thesamples with the dip angles of 0deg and 90deg (the dip angle of 0deg

corresponds to the maximum strength) the compressivestrength of samples is relatively high For samples with thedip angles of 30deg and 45deg the compressive strength ofsamples is relatively low -e overall evolution of thecompression strength performs a U shape which is high atboth sides and low in the middle location Under thecondition of different confining pressures the calculationmethod for the anisotropy degree of the compressivestrength anisotropy of RP [21] is as follows

RP σmax

σmin (3)

where RP is the anisotropy degree of compressive strength σ(max) is the maximum compressive strength of sampleswhich corresponds to the dip angle of 0deg and σmin is theminimum compressive strength

According to equation (3) the anisotropy degree of thecompressive strength of the tight sandstone samples in thisstudy can be calculated as shown in Table 5 With an increasein the confining pressure the anisotropy degree of thecompressive strength decreases When the confining pressureis 0MPa the anisotropy degree of the compressive strengthRP is 151 when the confining pressure is 15MPa 30MPaand 45MPa the anisotropy degree of the compressivestrength RP ranges from 124 to 130 -erefore from theviewpoint of compressive strength it has an obvious an-isotropy -e confining pressure has a negligible influence onthe anisotropy degree for the tight sandstone in this study Inthe field reservoir of the tight sandstone of Xujiahe Forma-tion the influences of the anisotropy and the in situ stressstate should both be considered for gas production

Table 4 Anisotropy degree of elastic modulus

Confining pressure (MPa) Max elastic modulus (GPa) Min elastic modulus (GPa) Degree of anisotropy0 524 319 16415 941 750 12530 1115 822 13645 1447 1075 135

0

3

6

9

12

15

18

0 15 30 45 60 75 90 105

Elas

tic m

odul

us (G

Pa)

Dip angle αdeg

0 MPa30 MPa

15 MPa45 MPa

Figure 6 Elastic modulus anisotropy of the tight sandstonesamples with different dip angles when subjected to differentconfining pressure

0

100

200

300

400

0 15 30 45 60 75 90 105

Peak

stre

ngth

(MPa

)Dip angle (deg)

0 MPa30 MPa

15 MPa45 MPa

Figure 7 Triaxial compression strength anisotropy of samples withdifferent strata angles

6 Advances in Materials Science and Engineering

334 Anisotropy of Fracture Morphology Figure 8 showsfailure mode under the conditions of different confiningpressure and different dip angles -e failure modes of thesamples can be mainly divided into three types splittingfailure shear failure and shear-expansion failure

When the confining pressure is 0MPa the predominantfailure mode of all the samples is splitting failure but somedifferences exist among the samples with different dip anglesFor instance the sample with the dip angle of 0deg has a mainsplitting fracture and several secondary fractures and somesecondary fractures are inclined showing shear failure per-formance-is is a reflection that the matrix perpendicular tothe bedding direction has the greatest strength As for thesample with the dip angle of 90deg only one splitting fractureappears on the sample surface parallel to the axial loadingdirection -is indicates that the matrix along the beddingdirection has a low strength For the samples with the dipangles of 30deg 45deg and 60deg the failure fracture is straight in themiddle location and somewhat inclined at each end -isshows that the propagation direction of the failure fracturemay be influenced by the bedding plane So under theuniaxial compression test (confining pressure 0MPa) an-isotropy exists in the review point of failure morphology

Under triaxial compression testing condition (15MPaand 30MPa) the difference in failure morphology remainsexistent for the samples with different dip angles For ex-ample the sample with 0deg dip angle has a steep failuresurface but the failure surface of the sample with dip angle of90deg is much gentler When the dip angle ranges from 30deg to60deg the failure surface has an inclination angle between thecases of 0deg and 90deg but the failure surface is already not aplane surface but a curved one -at is to say due to theexistence of bedding angle it has caused the failure surface tobe a curved surface With respect to the condition of highconfining pressure (45MPa) the failure mode has becomeshear-dilatant state-ere is onemain failure surface but theaperture of this surface is very small and there are numeroussmall fissures around this surface -e middle location of thesample has expanded showing a drum shape Moreoverexcept the cases with dip angles of 0deg and 90deg the failuresurfaces of the samples are all curved surfaces under theconfining pressure of 45MPa

From the above study one can deduce that the existence ofconfining pressure has largely changed the failure modes forthe tight sandstone During the increase process of the con-fining pressure (0MPa⟶ 15MPa⟶ 30MPa⟶ 45MPa)the failure morphology also changes from splitting failure toshear failure and to dilatant failure Combining with the stress-strain curves the greater the confining pressure is the largerstrength and larger deformation both appear So in the processfor gas production in such tight sandstone reservoir the

influence of confining pressure cannot be ignored -e tightsandstone reservoir usually has a large burying depth the insitu stress state of the rock is under three-directional stress stateWhen considering the hydrofracturing for the reservoir theinfluence of stress state on the strength and fracturingmodes ofthe tight sandstone should also be thoroughly considered

On the other hand under the triaxial compression condi-tion the application of confining pressure has decreased theanisotropy degree from viewpoints of the strength and me-chanical parameters but the anisotropy performances of thefailure morphology still cannot be neglected For instance theinclination angle between the axial loading direction and thefailure surface is different when the samples have different dipangle and so is themorphology of the failure surface-e samplewith a dip angle of 0deg has a plane failure surface and there arecurved surfaces for the samples with dip angles of 30deg and 45degand numerous small fissures also appear around the failuresurface for the samples with dip angles of 60deg and 90deg -at is tosay even so the confining pressure is high due to the anisotropyof the tight sandstone the difference in failure morphologyremains existent How will such a character influence the crack-net propagation of the tight sandstone under hydrofractureremains unknown so further investigation is still needed

4 Application

41 Material Parameters of Approximate Isotropic MaterialModels From the above study we can find that the tightsandstone of Xujiahe Formation has a certain degree of an-isotropy but the anisotropy will be low when subjected toconfining pressure In addition by observing the samplemorphology and analyzing the mechanical testing results thetight sandstone in this study can be regarded as a type oftransversely isotropic material and the stress-strain relationship(flexibility matrix) of this material can be expressed as [21 22]

εx

εy

εz

cxy

cyz

czx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1E

minusυE

minusυprimeE

0 0 0

minusυE

1E

minusυprimeE

0 0 0

minus minusυprimeE

minusυprimeE

1Eprime

0 0 0

0 0 01G

0 0

0 0 0 01

Gprime0

0 0 0 0 01

Gprime

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

σx

σy

σz

σxy

σyz

σzx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Table 5 Triaxial compression strength anisotropy of tight sandstone samples

Confining pressure (MPa) Max strength (MPa) Min strength (MPa) Anisotropy degree of compressive strength0 6057 4005 15115 18892 14509 13030 26044 20124 12945 33503 27116 124

Advances in Materials Science and Engineering 7

where E and Eprime are elastic moduli of the isotropic plane andthe plane perpendicular to the isotropic plane respectivelyG and Gprime are shear moduli of the isotropic plane and theplane perpendicular to the isotropic plane respectively v

and vprime both are Poissonrsquos ratio and they represent lateralstrain reduction of each isotropic plane which is caused bytensile stress in the same plane and lateral strain reduction ofeach isotropic plane that is caused by tensile stress which isperpendicular to this plane

From the above study we find that the elastic moduluschanges with the dip angle -at is when the axial directionof the sample has a different dip angle its elastic modulusalso changes In reality we concern not only the elasticmodulus of the isotropic plane and its perpendicular planebut also want to know the modulus of the plane that has aninclination angle with the isotropic plane

-emodulus of one plane which has an inclination angleof α can be expressed as [23]

1Eα

sin4α

E+

1Gprime

minus2]E

1113874 1113875cos2αsin

2α +

cos4α

Eprime (5)

where E is the elastic modulus of the isotropic plane(corresponding to the sample with a dip angle of 90deg) and Eprimeand Gprime are the elastic modulus and shear modulus of theplane perpendicular to the isotropic plane (corresponding tothe sample with a dip angle of 0deg)

By a transformation for equation (5) one obtains

1Eα

1 + 2]

Eminus

2Gprime

+1Eprime

1113874 1113875sin α4

+1

Gprimeminus2]E

minus2Eprime

1113874 1113875sin α2

+1Eprime

(6)

0 MPa 15 MPa 30 MPa 45 MPa

(a)

0 MPa 15 MPa 30 MPa 45 MPa

(b)

0 MPa 15 MPa 30 MPa 45 MPa

(c)

0 MPa 15 MPa 30 MPa 45 MPa

(d)

0 MPa 15 MPa 30 MPa 45 MPa

(e)

Figure 8 Fracture morphology of tight sandstone samples under different confining pressure (a) Dip angle α 0deg (b) Dip angle α 30deg(c) Dip angle α 45deg (d) Dip angle α 60deg (e) Dip angle α 90deg

8 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

334 Anisotropy of Fracture Morphology Figure 8 showsfailure mode under the conditions of different confiningpressure and different dip angles -e failure modes of thesamples can be mainly divided into three types splittingfailure shear failure and shear-expansion failure

When the confining pressure is 0MPa the predominantfailure mode of all the samples is splitting failure but somedifferences exist among the samples with different dip anglesFor instance the sample with the dip angle of 0deg has a mainsplitting fracture and several secondary fractures and somesecondary fractures are inclined showing shear failure per-formance-is is a reflection that the matrix perpendicular tothe bedding direction has the greatest strength As for thesample with the dip angle of 90deg only one splitting fractureappears on the sample surface parallel to the axial loadingdirection -is indicates that the matrix along the beddingdirection has a low strength For the samples with the dipangles of 30deg 45deg and 60deg the failure fracture is straight in themiddle location and somewhat inclined at each end -isshows that the propagation direction of the failure fracturemay be influenced by the bedding plane So under theuniaxial compression test (confining pressure 0MPa) an-isotropy exists in the review point of failure morphology

Under triaxial compression testing condition (15MPaand 30MPa) the difference in failure morphology remainsexistent for the samples with different dip angles For ex-ample the sample with 0deg dip angle has a steep failuresurface but the failure surface of the sample with dip angle of90deg is much gentler When the dip angle ranges from 30deg to60deg the failure surface has an inclination angle between thecases of 0deg and 90deg but the failure surface is already not aplane surface but a curved one -at is to say due to theexistence of bedding angle it has caused the failure surface tobe a curved surface With respect to the condition of highconfining pressure (45MPa) the failure mode has becomeshear-dilatant state-ere is onemain failure surface but theaperture of this surface is very small and there are numeroussmall fissures around this surface -e middle location of thesample has expanded showing a drum shape Moreoverexcept the cases with dip angles of 0deg and 90deg the failuresurfaces of the samples are all curved surfaces under theconfining pressure of 45MPa

From the above study one can deduce that the existence ofconfining pressure has largely changed the failure modes forthe tight sandstone During the increase process of the con-fining pressure (0MPa⟶ 15MPa⟶ 30MPa⟶ 45MPa)the failure morphology also changes from splitting failure toshear failure and to dilatant failure Combining with the stress-strain curves the greater the confining pressure is the largerstrength and larger deformation both appear So in the processfor gas production in such tight sandstone reservoir the

influence of confining pressure cannot be ignored -e tightsandstone reservoir usually has a large burying depth the insitu stress state of the rock is under three-directional stress stateWhen considering the hydrofracturing for the reservoir theinfluence of stress state on the strength and fracturingmodes ofthe tight sandstone should also be thoroughly considered

On the other hand under the triaxial compression condi-tion the application of confining pressure has decreased theanisotropy degree from viewpoints of the strength and me-chanical parameters but the anisotropy performances of thefailure morphology still cannot be neglected For instance theinclination angle between the axial loading direction and thefailure surface is different when the samples have different dipangle and so is themorphology of the failure surface-e samplewith a dip angle of 0deg has a plane failure surface and there arecurved surfaces for the samples with dip angles of 30deg and 45degand numerous small fissures also appear around the failuresurface for the samples with dip angles of 60deg and 90deg -at is tosay even so the confining pressure is high due to the anisotropyof the tight sandstone the difference in failure morphologyremains existent How will such a character influence the crack-net propagation of the tight sandstone under hydrofractureremains unknown so further investigation is still needed

4 Application

41 Material Parameters of Approximate Isotropic MaterialModels From the above study we can find that the tightsandstone of Xujiahe Formation has a certain degree of an-isotropy but the anisotropy will be low when subjected toconfining pressure In addition by observing the samplemorphology and analyzing the mechanical testing results thetight sandstone in this study can be regarded as a type oftransversely isotropic material and the stress-strain relationship(flexibility matrix) of this material can be expressed as [21 22]

εx

εy

εz

cxy

cyz

czx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1E

minusυE

minusυprimeE

0 0 0

minusυE

1E

minusυprimeE

0 0 0

minus minusυprimeE

minusυprimeE

1Eprime

0 0 0

0 0 01G

0 0

0 0 0 01

Gprime0

0 0 0 0 01

Gprime

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

σx

σy

σz

σxy

σyz

σzx

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Table 5 Triaxial compression strength anisotropy of tight sandstone samples

Confining pressure (MPa) Max strength (MPa) Min strength (MPa) Anisotropy degree of compressive strength0 6057 4005 15115 18892 14509 13030 26044 20124 12945 33503 27116 124

Advances in Materials Science and Engineering 7

where E and Eprime are elastic moduli of the isotropic plane andthe plane perpendicular to the isotropic plane respectivelyG and Gprime are shear moduli of the isotropic plane and theplane perpendicular to the isotropic plane respectively v

and vprime both are Poissonrsquos ratio and they represent lateralstrain reduction of each isotropic plane which is caused bytensile stress in the same plane and lateral strain reduction ofeach isotropic plane that is caused by tensile stress which isperpendicular to this plane

From the above study we find that the elastic moduluschanges with the dip angle -at is when the axial directionof the sample has a different dip angle its elastic modulusalso changes In reality we concern not only the elasticmodulus of the isotropic plane and its perpendicular planebut also want to know the modulus of the plane that has aninclination angle with the isotropic plane

-emodulus of one plane which has an inclination angleof α can be expressed as [23]

1Eα

sin4α

E+

1Gprime

minus2]E

1113874 1113875cos2αsin

2α +

cos4α

Eprime (5)

where E is the elastic modulus of the isotropic plane(corresponding to the sample with a dip angle of 90deg) and Eprimeand Gprime are the elastic modulus and shear modulus of theplane perpendicular to the isotropic plane (corresponding tothe sample with a dip angle of 0deg)

By a transformation for equation (5) one obtains

1Eα

1 + 2]

Eminus

2Gprime

+1Eprime

1113874 1113875sin α4

+1

Gprimeminus2]E

minus2Eprime

1113874 1113875sin α2

+1Eprime

(6)

0 MPa 15 MPa 30 MPa 45 MPa

(a)

0 MPa 15 MPa 30 MPa 45 MPa

(b)

0 MPa 15 MPa 30 MPa 45 MPa

(c)

0 MPa 15 MPa 30 MPa 45 MPa

(d)

0 MPa 15 MPa 30 MPa 45 MPa

(e)

Figure 8 Fracture morphology of tight sandstone samples under different confining pressure (a) Dip angle α 0deg (b) Dip angle α 30deg(c) Dip angle α 45deg (d) Dip angle α 60deg (e) Dip angle α 90deg

8 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

where E and Eprime are elastic moduli of the isotropic plane andthe plane perpendicular to the isotropic plane respectivelyG and Gprime are shear moduli of the isotropic plane and theplane perpendicular to the isotropic plane respectively v

and vprime both are Poissonrsquos ratio and they represent lateralstrain reduction of each isotropic plane which is caused bytensile stress in the same plane and lateral strain reduction ofeach isotropic plane that is caused by tensile stress which isperpendicular to this plane

From the above study we find that the elastic moduluschanges with the dip angle -at is when the axial directionof the sample has a different dip angle its elastic modulusalso changes In reality we concern not only the elasticmodulus of the isotropic plane and its perpendicular planebut also want to know the modulus of the plane that has aninclination angle with the isotropic plane

-emodulus of one plane which has an inclination angleof α can be expressed as [23]

1Eα

sin4α

E+

1Gprime

minus2]E

1113874 1113875cos2αsin

2α +

cos4α

Eprime (5)

where E is the elastic modulus of the isotropic plane(corresponding to the sample with a dip angle of 90deg) and Eprimeand Gprime are the elastic modulus and shear modulus of theplane perpendicular to the isotropic plane (corresponding tothe sample with a dip angle of 0deg)

By a transformation for equation (5) one obtains

1Eα

1 + 2]

Eminus

2Gprime

+1Eprime

1113874 1113875sin α4

+1

Gprimeminus2]E

minus2Eprime

1113874 1113875sin α2

+1Eprime

(6)

0 MPa 15 MPa 30 MPa 45 MPa

(a)

0 MPa 15 MPa 30 MPa 45 MPa

(b)

0 MPa 15 MPa 30 MPa 45 MPa

(c)

0 MPa 15 MPa 30 MPa 45 MPa

(d)

0 MPa 15 MPa 30 MPa 45 MPa

(e)

Figure 8 Fracture morphology of tight sandstone samples under different confining pressure (a) Dip angle α 0deg (b) Dip angle α 30deg(c) Dip angle α 45deg (d) Dip angle α 60deg (e) Dip angle α 90deg

8 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

In this study the mechanical parameters of the isotropicplane and its perpendicular plane are obtained for conductinguniaxial and triaxial compression tests Based on equation (6)the relationship between the reciprocal of elastic modulus of

plane with any angle to the isotropic plane (1Eα) and sin2

α can

be drawn Figure 9 gives the relationship of 1Eα and sin2

α ofXujiahe tight sandstone in this study when subjected to differentconfining pressures Fitting curves are also drawn in Figure 9

According to the fitting curves in Figure 9 and equation(6) the five independent material parameters of tightsandstone can be calculated under different confiningpressure -e calculating results are shown in Table 6

From the above study we can find that the differencebetween the elastic moduli of the isotropic plane and itsperpendicular plane is within 142ndash329 -e differencebetween Poissonrsquos ratios of the isotropic plane and its per-pendicular plane is about 166ndash213-e difference betweenthe shear moduli ranges between 69 and 229 Such an-isotropy degrees of the tight sandstone are not obvious enoughwhen compared to other rockmasses such as shale [23] So forsome rough and simplified estimation we also regarded thetight sandstone as a type of isotropic material -en the in-dependent mechanical parameters can be reduced to threeequivalent ones A suggested method for the calculation of theequivalent three mechanical parameters is as follows

Es E + Eprime( 1113857

2

]s ] + ]prime( 1113857

2

Gs G + Gprime( 1113857

2

(7)

where Es Vs and Gs are the three estimated equivalentmechanical parameters

If we want to simplify the Xujiahe tight sandstone into anisotropic rock mass (just for some rough estimations) thethree estimated equivalent mechanical parameters can becalculated by using equation (7) -e calculated results areshown in Table 7

42 e Values of c and φ From the CoulombndashNavier cri-terion [22] when a rock undergoes shear fracture along aplane it is related to not only the shear stress but also thenormal stress loaded on this plane -e fracture usuallydevelops along the most unfavorable plane on which theshear stress has a maximum value On this plane when theshear stress exceeds the shear strength envelope shearfailure occurs -is criterion is expressed as [22]

|τ| c + fσ

τ σ1 minus σ3

2sin 2θ

σ σ1 + σ3

2+σ1 minus σ3

2cos 2θ

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where τ and σ are the shear stress and normal stress of shearfracture surface c is the inherent cohesion strength of rocksf is internal friction coefficient of rocks θ is the angle be-tween the normal direction of the shear plane andmaximumprincipal stress

After simplifying equations (8) and (9) we can obtain

c σ1 minus σ3

2(sin 2θ minus f cos 2θ) minus

f σ1 + σ3( 1113857

2 (9)

To find a differential value of c for equation (9) one canobtain the maximum shear stress and can obtain

tan 2θ minus 1f

(10)

From equation (10) it can be seen that 90deglt 2θlt 180degand that

sin 2θ 1 + f2

1113872 1113873minus 12

cos 2θ minus f 1 + f2

1113872 1113873minus 12

⎫⎪⎬

⎪⎭ (11)

-e CoulombndashNavier criterion can be obtained bysubstituting equation (11) into equation (9)

2c σ1 1 + f2

1113872 111387312

minus f1113876 1113877 minus σ3 1 + f2

1113872 111387312

+ f1113876 1113877 (12)

-e relationship between the axial stress σ1 and theconfining pressure σ3 is plotted and the cohesion strength cand internal friction angle φ of the CoulombndashNavier cri-terion are calculated according to the following equation

c b1 minus sinϕ2 cosϕ

κ sinminus 1m minus 1m + 1

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

(13)

wherem and b are the slope and intercept of the relationshipcurve of axial stress σ1 and confining pressure σ3 -e re-lationship curves of axial stress σ1 and confining pressure σ3of different samples with different dip angles are shown inFigure 10 By fitting the curve linearly the slope m and theintercept b of the fitted straight line can be obtained and thecohesion c and internal friction angle φ of the Cou-lombndashNavier criterion can also be calculated by substitutingthe values ofm and b into equation (13) -e detailed resultsare shown in Table 8

Because cohesion strength c and internal friction angle φof the samples with different dip angles change a little in thenumerical simulation of hydraulic fracturing model of thetight sandstone reservoir of the Xujiahe Formation wesuggest that the cohesion strength and internal friction anglecan be replaced by the average values of cohesion strengthand internal friction angle

43 Stimulating Pressure Referring to the horizontal well ofthe Jianghan oilfield reservoir [24] an indoor three-axishydraulic fracturing physical simulation system was applied

Advances in Materials Science and Engineering 9

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

y45 = ndash0014x2 + 00376x + 01088R2 = 09893

y15 = ndash001x2 + 00313x + 00708R2 = 09902

y30 = 00239x2 + 00059x + 00907R2 = 0975

004

006

008

010

012

014

016

018

0 01 02 03 04 05 06 07 08 09 1

1E α

sin2α

15 MPa30 MPa45 MPa

Figure 9 Fitting curves of the reciprocal of elastic modulus (1Eα) versus sin α2

under different confining pressures

Table 6 -e five independent parameters of the tight sandstone samples

Confining pressure (MPa) E (GPa) Eprime (GPa) v vprime Gprime (GPa)0 508 445 016 019 17415 9191 7553 015 0182 329630 11025 8299 019 0236 409545 14124 10858 017 0214 4710Note G is an independent parameter that can be calculated using GE2(1 + v)

Table 7 -e three independent parameters of the tight sandstone samples

Confining pressure (MPa) Es (GPa) vs Gs (GPa)

0 4765 0175 180515 8372 0166 324630 9662 0213 372645 12491 0192 4591

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Axi

al st

ress

(MPa

)

Confining pressure (MPa)

0deg30deg45deg

60deg90deg

Figure 10 Relationship of confining pressure and axial stress of tight sandstone with different dip angle

10 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

to simulate the fracturing process in the open-hole stage-emodel parameters for this reservoir are shown in Table 9

According to the model parameters in Table 9 equation(14) can be used to calculate the bursting pressure P [24]

P 3σh minus σH minus σt minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859pp

1 minus β 1 minus 2υs( 1113857 1 minus υs( 1113857 minus φ1113858 1113859 (14)

where σH is the maximum horizontal in situ stress σV is thevertical in situ stress σh is the minimum horizontal in situstress σt is the tensile strength vs is Poissonrsquos ratio ofreservoir β is the effective stress coefficient ϕ is the porositydegree of the reservoir PP is the pore pressure of thereservoir

Regardless of the filtration effect with putting the in situstresses and other parameters into equation (14) it is cal-culated that the value of fracture pressure is 2267MPa -ebursting pressure is 2202MPa from the result of the hy-draulic fracturing test -e field-testing value has only adifference of 065MPa from the theoretical value in thisstudy So we think it is still reasonable to treat the Xujiahetight sandstone reservoir as an isotropic rock formationHowever if the tight sandstone has higher anisotropyperformance we should still regard it as anisotropy materialto avoid deviation

5 Conclusions

In this study a series of uniaxial and triaxial compressiontests have been conducted for tight sandstone of XujiaheFormation with different dip angles to the bedding plane-e influences of the dip angle and confining pressure arethoroughly investigated -e main conclusions and sug-gestions are proposed as follows

(1) Based on the evaluation criteria of the rock brittle-ness index by using mineral composition the brittleindex I of Xujiahe tight sandstone is 076 So thetight sandstone in this study is much brittle which isa high-fracturing reservoir

(2) -e ultrasonic wave velocity of the longitudinal wavedemonstrates the anisotropy characteristics of thetight sandstone that is the wave velocity has amaximum value when perpendicularly penetrating

the bedding plane and it decreases with an increasein the dip angle α

(3) Under the same confining pressure conditions withthe increasing of the dip angle α the elastic modulusdecreases and the anisotropy degree (RE) of elasticmodulus locates in the range of 125ndash136 showingan obvious but not strong anisotropy character

(4) Under the same confining pressure the compressivestrength shows a ldquoUrdquo shape evolution pattern whichis higher on each side and lower in themiddle regionand the degree of anisotropy RP is ranging from 124to 130 also showing a low anisotropy

(5) -e failure modes of the tight sandstone are mainlysplitting fracture for the uniaxial compression testbut differ in the fracture morphology meanwhile forthe triaxial compression test the failure mode of thetight sandstone is mainly of shear failure and shear-dilatancy damage At the same declining angleconditions with the increase in confining pressurethe angle between principal stress and shear planegradually decreases -e failure fracture is also dif-ferent when the sample has different dip angles

(6) -e Xujiahe tight sandstone has low anisotropy fromthe viewpoint of mechanical parameters thus it canbe also regarded as an isotropic material-emethodto calculate the equivalent mechanical parameters isproposed -e bursting pressure of the tight sand-stone formation is calculated and it differs a littlewith the field data-us it conforms the feasibility ofregarding the low anisotropy rock formation as anisotropic one

Data Availability

-e data used to support the findings of this study areavailable within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research was supported by the China ScholarshipCouncil project the National Natural Science Foundation ofChina (Grant nos 52074046 41674022 51834003U1704243 and 51709113) Guizhou Provincial GeologicalExploration Fund (Grant no 208-9912-JBN-UTS0) theNational Science and Technology Major Project of China

Table 9 Model parameters

σH(MPa)

σV(MPa)

σh(MPa)

σt(MPa)

ES(GPa)

vS

(MPa)GS

(GPa)

1312 1303 1115 251 837 017 327

Table 8 Parameters of CoulombndashNavier criterion of tight sandstone with different dip angles

α (deg) m B (MPa) φ (deg) c (MPa) -eory q (deg) Test q (deg)0 606 6997 458 1421 679 67730 493 5868 415 1321 658 62045 506 5821 421 1294 660 61560 503 6775 420 1510 660 67590 494 6540 416 1471 658 643Average 520 6400 426 1404 663 646

Advances in Materials Science and Engineering 11

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering

(Grant nos 2016ZX05060-004 and 2017ZX05036-003)Guangdong Science and Technology Department (Grant no2015B020238014) and Guangzhou Science Technology andInnovation Commission (Grant no 201604016021)

References

[1] C Zou R Zhu K Liu et al ldquoTight gas sandstone reservoirs inChina characteristics and recognition criteriardquo Journal ofPetroleum Science and Engineering vol 88-89 pp 82ndash912012

[2] X Ma A Jia J Tan and D He ldquoTight sand gas developmenttechnology and practices in Chinardquo Petroleum Explorationand Development vol 39 no 5 pp 611ndash618 2012

[3] X Yin andQ Liu ldquoAnisotropic rock physics modeling of tightsandstone and applicationsrdquo Journal of China University ofPetroleum vol 40 no 2 pp 52ndash58 2016

[4] L-T Song Z-H Liu C-C Zhou et al ldquoAnalysis of elasticanisotropy of tight sandstone and the influential factorsrdquoApplied Geophysics vol 14 no 1 pp 10ndash20 2017

[5] X Li X Lei and Q Li ldquoInfluence of bedding structure onstress-induced elastic wave anisotropy in tight sandstonesrdquoJournal of Rock Mechanics and Geotechnical Engineeringvol 13 no 1 pp 1ndash18 2020

[6] F Bashtani B Maini and A Kantzas ldquoSingle-phase and two-phase flow properties of mesaverde tight sandstone formationrandom-network modeling approachrdquo Advances in WaterResources vol 94 pp 174ndash184 2016

[7] G Liu M Sun Z Zhao X Wang and S Wu ldquoCharacteristicsand accumulation mechanism of tight sandstone gas reser-voirs in the upper paleozoic northern ordos basin ChinardquoPetroleum Science vol 10 no 4 pp 442ndash449 2013

[8] D Xiao S Lu J Yang L Zhang and B Li ldquoClassifyingmultiscale pores and investigating their relationship withporosity and permeability in tight sandstone gas reservoirsrdquoEnergy amp Fuels vol 31 no 9 pp 9188ndash9200 2017

[9] X-R Huang J-P Huang Z-C Li Q-Y Yang Q-X SunandW Cui ldquoBrittleness index and seismic rock physics modelfor anisotropic tight-oil sandstone reservoirsrdquo Applied Geo-physics vol 12 no 1 pp 11ndash22 2015

[10] S Heng X Liu X Li X Zhang and C Yang ldquoExperimentaland numerical study on the non-planar propagation of hy-draulic fractures in shalerdquo Journal of Petroleum Science andEngineering vol 179 pp 410ndash426 2019

[11] S Heng Y Guo C Yang J J K Daemen and Z Li ldquoEx-perimental and theoretical study of the anisotropic propertiesof shalerdquo International Journal of Rock Mechanics and MiningSciences vol 74 pp 58ndash68 2015

[12] G Zhang L Wang Y Wu Y Li and S Yu ldquoFailuremechanism of bedded salt formations surrounding salt cav-erns for underground gas storagerdquo Bulletin of EngineeringGeology and the Environment vol 76 no 4 pp 1609ndash16252017

[13] W Liu Z Zhang J Chen et al ldquoPhysical simulation ofconstruction and control of two butted-well horizontal cavernenergy storage using large molded rock salt specimensrdquoEnergy vol 185 pp 682ndash694 2019

[14] W Liu D Jiang J Chen J J K Daemen K Tang and F WuldquoComprehensive feasibility study of two-well-horizontalcaverns for natural gas storage in thinly-bedded salt rocks inChinardquo Energy vol 143 pp 1006ndash1019 2018

[15] L Louis P Baud and T-f Wong ldquoMicrostructural inho-mogeneity and mechanical anisotropy associated with

bedding in Rothbach sandstonerdquo Pure and Applied Geo-physics vol 166 no 5-7 pp 1063ndash1087 2009

[16] T Y Chen X T Feng X W Zhang W D Cao and C J FuldquoExperimental study on mechanical and anisotropic prop-erties of black shalerdquo Chinese Journal of Rock Mechanics andEngineering vol 33 no 9 pp 1772ndash1779 2014

[17] Y Ma Z Pan N Zhong et al ldquoExperimental study of an-isotropic gas permeability and its relationship with fracturestructure of Longmaxi shales Sichuan Basin Chinardquo Fuelvol 180 pp 106ndash115 2016

[18] R Feng S Chen and S Bryant ldquoInvestigation of anisotropicdeformation and stress-dependent directional permeability ofcoalbed methane reservoirsrdquo Rock Mechanics and Rock En-gineering vol 53 no 2 pp 625ndash639 2020

[19] ISRM ldquoSuggested methods for determining tensile strength ofrock materialsrdquo International Journal of Rock Mechanics andMining Sciences vol 15 no 3 pp 99ndash103 1978

[20] Y Wang and C H Li ldquoInvestigation of the P- and S-wavevelocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxialdeformationrdquo Journal of Petroleum Science and Engineeringvol 158 pp 253ndash267 2017

[21] J Singh T Ramamurthy and R G Venkatappa ldquoStrengthanisotropies in rocksrdquo Indian Geotechnical Journal vol 19no 2 pp 147ndash166 1989

[22] M F Cai M C He and D Y Liu Rock Mechanics andEngineering Science Press Beijing China 2009

[23] S Heng C H Yang B P Zhang Y T Guo L Wang andY LWei ldquoExperimental research on anisotropic properties ofshalerdquo Rock and Soil Mechanics vol 36 no 3 pp 609ndash6162015

[24] Y L Wei ldquoPhD Study on the laws of hydro-fractured crackspropagation of tight sandstone gas reservoirs in JiannanAreardquo PhD thesis Chongqing University Chongqing China2016

12 Advances in Materials Science and Engineering