Research ArticleThe Experimental Investigation of Longmaxi Shale DynamicParameters under Water-Based Mud Soaking

Guangjian Dong ,1,2,3 Ping Chen ,1,2 Heyi Yuan ,4 and Yudi Lu1,2

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu,Sichuan 610500, China2School of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, China3Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, CanadaT2N 1N44Northwestern Sichuan Gas District, PetroChina Southwest Oil & Gasfield Company, Jiangyou 621709, China

Correspondence should be addressed to Ping Chen; chenping@swpu.edu.cn and Heyi Yuan; 306380283@qq.com

Received 9 October 2018; Revised 11 December 2018; Accepted 17 January 2019; Published 23 June 2019

Academic Editor: Reza Rezaee

Copyright © 2019 Guangjian Dong et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Shale damage investigation is important in shale gas development. This paper is concerned with the experimental identification ofultrasonic wave velocities and damage mechanic parameters of Longmaxi shale under water-based mud soaking and confiningpressure loading. The wave velocities increased with increasing confining pressure, while wave velocities decreased withincreasing soaking time. The anisotropy of Young’s modulus decreases when confining pressure increases. As soaking timeincreases, the anisotropy coefficient increases. As soaking time and confining pressure rise, the damage parameters also showcomplex changes. The results are beneficial for shale gas development.

1. Introduction

During the drilling and development of shale gas, basic wavevelocities and mechanical parameters play an important role[1–3]. The coupling effect of water-based mud (WBM) andconfining pressure on the wave velocity and mechanicalparameters of Longmaxi (LMX) shale is key to studyingshale. The static mechanical properties of LMX shale havebeen largely studied for the past few years [4–6]. However,no elastic wave velocity data at WBM soaking and confiningpressure loading are available in the literature for LMX shale.Indeed, elastic wave velocity measurements are well knownas being very sensitive to damage in rocks [7–10]. Themonitoring of elastic wave velocities in shale under mechan-ical loading is relatively common. Generally, most of thedynamic experimental studies reported in the literature onshale samples have been performed under hydrostaticloading conditions [9, 11, 12]. However, elastic wave velocitymeasurements on shale are reported by Yin [13] under

triaxial and polyaxial loading and by Podio et al. [14] underuniaxial loading. In addition, Dewhurst and Siggins [15]reported elastic wave velocity data on shale samples undertriaxial loading. Sarout and Guéguen [16, 17] studied theanisotropy of elastic wave velocities in deformed shale.

Nowadays, there are no studies on the coupling effect ofWBM and confining pressure on the four-rank-orderdamage of LMX shale. Lots of experiments were carriedout. The wave velocity data and anisotropy coefficients of thispaper are different with those in previous works. The param-eter (β1111, β1133, and β3333) analysis is different and deeperthan in the previous work [16–18]. The wave velocity test isan effective and well-tested method to interpret anisotropyand mechanical damage parameters [19–23]. Shale is fea-tured with the sensitivity of wave velocity, which is favorablefor studying the change rules of mechanical parameters ofLMX shale [24–27]. To interpret quantitatively the elasticwave velocity data in terms of microstructural propertiesof rock, a micromechanical model developed by Sarout

HindawiGeofluidsVolume 2019, Article ID 2128373, 12 pageshttps://doi.org/10.1155/2019/2128373

[16, 17], based on effective medium-theory concepts, is usedin the investigation of this paper. The application of thismodel to experimental data allows us to discuss the evolutionof damage parameters. The main outcomes of the experi-ments reported here are (1) the identification of dynamicelastic wave velocity measurements at various states ofWBM soaking and confining pressure loading and (2) theassessment of elastic anisotropic extent and damage undervarious WBM soaking and confining pressure loadings.

2. Rock Sample and Methodology

2.1. Description and Preparation of Shale Specimen. The rocksamples are LMX formation shale from Sichuan Basin. Threekinds of samples (ϕ25 × 50mm) at angles of 0°, 45°, and 90°

to the bedding plane are prepared, as shown in Figure 1.X-ray diffraction (XRD) analysis of 9 samples determines

the characteristics of mineral components of LMX shale, asshown in Figure 2. In XRD analysis, the reported % compo-sition of mineralogy is based on weight. The average contentof clay minerals and quartz is 48.90% and 4.29%, respectively;the average content of dolomite is 4.29%. The scanning elec-tron microscope (SEM) images of LMX shale is as shown in

Figure 3. The results show that porous clay and inclusionsare clearly visible and silty or sandy inclusions are randomlydistributed in rock samples. The surface of rock samples isrelatively flat with a few pores. The pores between clayparticles are geometrical, and most of them are curvedor reticulated. The shape of the organic matter (OM) holeof LMX shale samples is oval, microcrack, bubble-shaped,irregular, or round.

2.2. Preparation of Water-Based Mud. During drilling forthe shale formation, WBM is most commonly used mud.The conventional process of preparing water-based mudfor the experiment is as follows [28]. (1) Pre-hydrated ben-tonite slurry with solid content of 4% is prepared; (2) 400 gbentonite and anhydrous sodium carbonate containing 5%bentonite are added to 10000ml hot water; (3) the mixtureis shaken for 3-4 h at low speed; (4) the mixture to be usedas the raw slurry is kept still for 24h at room temperature;and (5) 0.5% sulfonated methypheuo formaldehyde is mixedin the raw slurry to be used as the base slurry.

2.3. Experimental Device and Process. The experimentaldevices consist of a high-pressure chamber, core holder,

VP33 VP45 VP11 VSV1 VSH1VV45 VH45VS3a VS3b

0° 45° 90°

Longmaxi shale sample

Longmaxi shale sketch

Figure 1: Schematic showing the three-plug method for anisotropic measurements.

2 Geofluids

emission end (transmitting sensor), receiving end (receivingsensor), pressure-stabilizing servo system (confining pres-sure pump, pressure sensor, and control valve), and datacollection and analysis system, which can provide themaximum confining pressure up to 90MPa, as shown inFigure 4. The frequency of the solitary pulse in this experi-ment is 1MHz. The test device is limited to provision ofconfining pressure, so shear failure will not occur in the rocksample. After the acoustic wave velocity is set at the startingpoint, the confining pressure will be increased gradually.The wave velocity is measured at the confining pressures of0MPa, 20MPa, 40MPa, and 60MPa.

The basic experiment process is soaking samples, wavevelocity testing, and dried samples. Each of them receivesthe immersion experiment at no soaking (0 h), soaking for1 h, and soaking for 3 h in WBM, followed by wave velocitytesting. The temperature (27°C) during the experiment iscontrolled at an accuracy of ±0.5°C.

3. Experiment Results

3.1. Effect of Wave Velocity of LMX Shale. The wave velocityand shapes of samples measured after soaking in WBM areshown in Figures 5 and 6. VP11, VS11, VP45, VS45, VP33, andVS33 are wave velocities in different directions, as shown inFigure 1. The initial wave velocities at no confining pressure(0MPa) and no soaking (0 h) are VP11 = 3769 6m/s, VS11 =2494 7m/s, VP45 = 3380 4m/s, VS45 = 2372 0m/s, VP33 =3257 9m/s, and VS33 = 2351 0m/s, respectively.

In order to study the wave velocity of LMX with differentsoaking time and confining pressure, the result of this paperis compared with previous work (Chicopee shale) [21]. Asshown in Figures 6(a), 6(c), and 6(e), WBM has an obviouseffect on wave velocity of shale. The change rule of the wavevelocities at different directions for soaked sample is asconsistent as that for the rock samples (0 h), VP11 > VP45 >VP33. The change rule of Chicopee shale is the same as thechange rule of LMX shale, but the wave velocities of Chicopeeshale are larger than those of LMX shale. The investigation ofChicopee shale did not consider the effect of mud soaking. Asthe soaking time increases, the wave velocities of LMX shalein a given direction decrease. Wave velocities increase atthe greatest rate for 1 h soaking in WBM. However, whenthe soaking time increases to 3 h, wave velocity presents alower drop rate than at 1 h soaking. VP11 and VP45 are very

55.345.9 50.7

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1 2 3 4 5 6 7 8 90

20

40

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Min

eral

com

pone

nts o

f who

le ro

ck (%

)

Sample no.

Pyrite

DolomiteOrthoclase

Quartz

CalciteAnorthoseClay minerals

(a)

71% 75% 74% 74% 73%

57%62%

73% 74%

7% 3% 3% 5% 6%

18% 12%

3% 3%

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ive c

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min

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%)

Sample no.ChloriteSmectiteIllite

(b)

Figure 2: Composition analysis of minerals in LMX shale ((a) mineral components of whole rock, (b) relative clay mineral content).

1 𝜇m

(a)

2 𝜇m

(b)

4 𝜇m

(c)

10 𝜇m

(d)

Figure 3: The SEM images of LMX shale.

3Geofluids

much close at 1 h soaking and 3h soaking; 1 h soaking is athreshold time.

With the confining pressure increasing, wave velocitiesincrease in all directions and were divided into stage 1 andstage 2, as shown in Figures 5, 6(b), 6(d), and 6(f). In stage1, the maximum increase rate in wave velocity occurs in thepressure range 0-20MPa. In stage 2, the increase rate in wavevelocity in the pressure range 20-60MPa is slower than instage 1. The experimental result shows that 20MPa confiningpressure is a special value of pressure conditions thataffect the wave velocity of LMX shale. The experimentalresults mentioned above that there is an inverse relationshipbetween hydration time and confining pressure in terms ofthe effect on wave velocity of shale; that is, the soaking timedecreases wave velocity at a given confining pressure, whileconfining pressure increases wave velocity for a given soakingtime. The conclusion above is different from the previousstudy [17, 19–21], mainly because this experiment takesinto account the soaking time in WBM and confiningpressure loading.

3.2. Effect of Anisotropy Coefficient of LMX Shale. Three-plugmethods have been used to study the mechanical propertiesby many authors [17, 19–21], as shown in Figure 7.

The degree of anisotropy can be represented by the ratioof elastic modulus in different directions:

ζ = EH

Eh=

C211 − C2

12C11C33 − C2

13, 1

where

C11 = ρV2P11, 2

C12 = C11 − 2ρV2S11, 3

C33 = ρV2P33, 4

C44 = ρV2S33, 5

C13 = −C44 + C11 + C44 − 2ρ2V2P45 C33 + C44 − 2ρV2

P451/2,

6

where Ev and Eh are the dynamic Young’s modulus; ρ is therock density; C11, C12, C33, C44, and C13 are stiffness con-stants; and VP11, VP33, VP45, VS11, and VS33 are the measuredultrasonic wave velocities.

The anisotropy coefficient for Young’s modulus can beobtained using Eq. (1). The anisotropy coefficient of theinitial elasticity modulus at 0MPa is 1.33 (soaked 0 h), 1.41(soaked 1h), and 1.46 (soaked 3h), respectively. The anisot-ropy of Young’s modulus decreases when confining pressureincreases. As hydration increases, anisotropy coefficientincreases, which indicates that Eh − Ev difference increasesas hydration time increases, as shown in Figure 8.

3.3. Effect of Damage Parameter of LMX Shale. The damageparameters α11, α33, β1111, β3333, and β1133 can be calculatedby Eq. (A8)-Eq. (A12) [19–21]. The damage parametersα11, α33, β1111, β3333, and β1133 were affected by the wavevelocities. The detailed process of the reference is shown

Transmittingsensor

Functiongenerator

Signal amplifier

Voltagedivider

Receiving sensor

Filter amplifier

Digital oscilloscope

Date acquisition system

Confining pressure pump

Confining pressure pump

Core holder

Shale plug

Valve

Pressure sensor

0°

45°

90°

Figure 4: Schematic diagram of wave velocity test device in a high-pressure environment.

4 Geofluids

0 20 40 60 80 100 120 140 160 180−2000

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plitu

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plitu

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v)

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(l)

Figure 5: The typical shapes of LMX shale without soaking.

5Geofluids

0 10 20 30 40 50 602500

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P11 (

m/s

)

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(a)

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(b)

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(c)

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(d)

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(e)

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/s)

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Stage 2

Stage 1

Confining pressure (MPa)

(f)

Figure 6: Wave velocities of LMX shale compared with Chicopee shale.

6 Geofluids

in the appendix. As shown in Figures 9 and 10, the initialdamage parameters (0MPa, no soaking) are α11 = 0 003(GPa-1), α33 = 0 042 (GPa-1), β1111 = 0 003 (GPa-1), β3333 =0 002 (GPa-1), and β1133 = 0 0002 (GPa-1), respectively. Asshown in Figures 9(a), 9(c), 10(a), and 10(c), the first directobservation to be reported here is that α33 is always largerthan α11, which indicates a higher amount of bedding-parallel cracks than bedding-orthogonal cracks. With thesoaking time increasing, α11 and α33 increase. As shown inFigures 9(e) and 9(e), as the soaking time increases, the mag-nitude of α11 − α33 increases, which is consistent with theincrease in anisotropy with soaking time as reported inFigure 8. It can be noted that α33 of the sample is greater thanα11. At low confining pressure, α33 may be ten times α11, andα11 is always maintained at a low value and decreases whenthe confining pressure goes up. With the increasing ofconfining pressure, both α11 and α33 decrease in WBM.

As the confining pressure rises, β1111, β1133, andβ3333show complex changes and can be divided into stage 1 andstage 2, as shown in Figures 9(b), 9(d), and 9(f). During stage1, between 0 and 20MPa, β1111, β1133, andβ3333 decrease withincreasing confining pressure at 0 h soaking. When shalesamples were soaked for 1 h and for 3 h, β1111, β1133, and

β3333 increase with the confining pressure increasing. Duringstage 2, between 20 and 60MPa, β1111, β1133, and β3333decreases with increasing confining pressure with lowdecreasing rate. These experimental results draw a conclu-sion that an increase in confining pressure leads to smallerand even closed fractured pores. The microscopic porestructure of shale is direction-dependent.

As the soaking time rises, β1111, β1133, andβ3333 also showcomplex changes, as shown in Figures 10(b), 10(d), and10(f). During 20-60MPa, when soaking lasts longer, β1111and β1133 increase (0-1 h) and then decrease (1-3 h), whileβ3333 increases. However, when the confining pressure is0MPa, with the soaking time increasing, β1111, β1133, andβ3333 decrease. The experimental result shows that 1 hsoaking is a special time condition for the damage ofLMX shale.

4. Discussion

The degree of shale damage shows a drastic change undersoaking time and confining pressure loading. A higher degreeof damage occurs in the vertical direction. The damagequantity α33 (horizontal direction) is much higher than α11(vertical direction), which means that most of the crack-likepores or microcracks in shale are subhorizontal, while thereare fewer of them in the vertical direction; this is why confin-ing pressure has less effect on α11. α11 increases more than α33does with soaking time at a given confining pressure. Themicrocrack further expands, propagates, converts, andconnects to be macrocrack that becomes wider and extendsto be fracture, which will develop until breaking. For0-20MPa, the pore direction, size, and structure of LMXshale are sensitive to confining pressure. For 20-60MPa con-fining pressure, the sensitivity of pore to confining pressure islower than that at 0-20MPa. LMX shale shows a complexchange in nonhorizontal and nonvertical directions.

The wave velocities and damage of LMX shale are sensi-tive to the soaking time. As the soaking time increases, thewave velocities in a given direction decrease. Wave velocitiesdrop at the greatest rate for 1 h soaking in WBM. However,when the soaking time increases to 3 h, wave velocitypresents a lower drop rate than 1h soaking. The anisotropycoefficient of the elasticity modulus increases with soakingtime increasing. When WBM enters the rock matrix, thedamage of shale matrix occurs in short time.

5. Conclusion

The ultrasonic wave velocities of LMX shale underWBM andconfining pressure were measured and analyzed. The shaledamage mechanic parameters were determined by means ofultrasonic velocity measurements. With the confining pres-sure increasing, wave velocities increase in all directions,while wave velocities decreased with increasing soaking time.The anisotropy of Young’s modulus decreases when the con-fining pressure increases. As soaking time increases, theanisotropy coefficient increases, while the damage parame-ters also show complex changes. In the future, the soakingtime and pressure conditions should be increased to study

0° 45°

90°

x

y

z

Bedding plane

Samples

Figure 7: The three-plug method schematic.

0 10 20 30 40 50 601.20

1.25

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1.40

1.45

1.50

Ani

sotro

py co

effici

ent

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0 h1 h3 h

Stage 1

Stage 2

Figure 8: Shale anisotropy coefficient with confining pressure andWBM soaking.

7Geofluids

0 10 20 30 40 50 60–0.004

0.000

0.004

0.008

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0.016

0.020

𝛼11

(GPa

–1)

Confining pressure (MPa)

0 h1 h3 h

Stage 1

Stage 2

(a)

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–0.004

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𝛽11

11 (G

Pa–1

)

0 h1 h3 h

Confining pressure (MPa)

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Stage 2

(b)

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𝛼33

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–1)

0 h1 h3 h

Confining pressure (MPa)

Stage 1

Stage 2

(c)

0 10 20 30 40 50 60–0.001

0.000

0.001

0.002

0.003

0.004

0.005𝛽

3333

(GPa

–1)

0 h1 h3 h

Stage 1 Stage 2

Confining pressure (MPa)

(d)

0 10 20 30 40 50 60–0.12

–0.10

–0.08

–0.06

–0.04

–0.02

0.00

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0.04

𝛼11

– 𝛼

33 (G

Pa–1

)

0 h1 h3 h

Stage 1

Stage 2

Confining pressure (MPa)

(e)

0 10 20 30 40 50 60–0.002

–0.001

0.000

0.001

0.002

𝛽11

33 (G

Pa–1

)

0 h1 h3 h

Stage 1Stage 2

Confining pressure (MPa)

(f)

Figure 9: The relationship of damage parameters of shale and confining pressure.

8 Geofluids

0.0 0.5 1.0 1.5 2.0 2.5 3.0–0.004

0.000

0.004

0.008

0.012

0.016

0.020

Soaking time (h)

0 MPa20 MPa

40 MPa60 MPa

Stage 1

Stage 2

𝛼11

(GPa

–1)

(a)

0.0 0.5 1.0 1.5 2.0 2.5 3.0–0.008

–0.004

0.000

0.004

0.008

Soaking time (h)

Stage 2

Stage 1

𝛽11

11 (G

Pa–1

)

0 MPa20 MPa

40 MPa60 MPa

(b)

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40 MPa60 MPa

(c)

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0.000

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0.004

0.005

Stage 1

Soaking time (h)

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𝛽33

33 (G

Pa–1

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0 MPa20 MPa

40 MPa60 MPa

(d)

0.0 0.5 1.0 1.5 2.0 2.5 3.0–0.12

–0.10

–0.08

–0.06

–0.04

–0.02

0.00

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Stage 1

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𝛼11

– 𝛼

33 (G

Pa–1

)

0 MPa20 MPa

40 MPa60 MPa

(e)

0.0 0.5 1.0 1.5 2.0 2.5 3.0–0.002

–0.001

0.000

0.001

Stage 2Stage 1

Soaking time (h)

𝛽11

33 (G

Pa–1

)

0 MPa20 MPa

40 MPa60 MPa

(f)

Figure 10: The relationship of damage parameters of shale and soaking time.

9Geofluids

the coupled effect on the wave velocities and mechanicdamage.

Appendix

Shale can be simplified as a rock element with many sphericalpores [20–22]. For one pore in the shale element, the volumeof transversely isotropic media is V , and the elastic attribute

is CO = SO−1. When V∗ is inserted, the elastic attribute is

C∗ = S∗ −1, as shown in Figure 11. The equatorial plane ofthe pore is parallel to the shale bedding, which is assumedto coincide with the symmetry plane of the TI rock, and theeffect of bulk modulus K f of fluid in the pore uniformity islower than that of the bulk modulus KO of the solid phaseon the same.

Additional stress sources from the fractured porethroughout the process of medium deformation. The far-field stress is σO, and in the absence of pore, the stressof the microscopic representative volume element (RVE)is εO, and the additional stress brought from the pore isΔε. For RVE, we have

εtotal = εO + Δε = SO + ΔS : σO, A1

where SO and ΔS refer to the flexibility tensors of backgroundmedium and fractured pore, respectively. S∗ is the flexibilitytensor of the elliptical pore, and the Eshelby tensor is denotedas S. The average displacement u of fractured pore isexpressed with flexibility tensor B and stress field σ.

ui = Bijσjknk, A2

where n is the unit vector at discontinuity in the verticaldirection as shown in Figure 12.

The flexibility tensor at discontinuity of infinite mediummay be expressed with normal component BN and tangentialcomponent BT

Bij = BNninj + BT δij − ninj A3

The pore-induced additional compliance tensor ΔS canbe expressed as

ΔSijkl =1V〠r

BrT4Ar δikn

rjn

rl + δiln

rjn

rk + δjkn

ri n

rl + δjln

ri n

rk

+1V〠r

BrN − Br

T Arnri nrjn

rkn

rl ,

A4

where δij is the tensor in Kronecker symbol, R is the countconstant, and Ar is the microfracture area r, in m2.

The second-order tensor and the four-order tensor α andβ are defined as

αij =1V〠r

BrTA

rnri nrj , A5

βijkl =1V〠r

BrN − Br

T Arnri nrjn

rkn

rl A6

Under macroscopic conditions, the additional compli-ance tensor is expressed as

ΔSijkl =14

δikαjl + δilαjk + δjkαil + δjlαik + βijkl A7

αij and βijkl parameters are directly related to frac-ture density and aspect ratio, where αij closely correlatesto void, while βijkl correlates to fluids in the void. αijand βijkl may be used as the evaluation parameters offracture change within shale and defined as damageparameters.

It can be drawn from the expressions that the condi-tions for obtaining the damage parameter are to first calcu-late the additional compliance tensor associated with thepresence of spheroidal pores (crack-like), which requiresthe calculation of the rock compliance tensor that can beobtained by laboratory experiment or logging data. How-ever, as shown in Eq. (A1), the compliance tensor of thewhole medium consists of two parts: compliance tensorSO of the background medium (ignoring the crack-likepores) and compliance tensor ΔS associated with thepresence of spheroidal pores (crack-like). The compliancetensor SO of the background medium is measured at highconfining pressure when all crack-like pores are assumedto be closed. When the confining pressure decreases, anychanges of the compliance tensor may be attributed to pore

Transversely isotropic solid

Spheroidal isotropic solid

C° = (S°)–1C⁎ = (S⁎)–1

Macroscopic RVE

Microscopic RVE

Volume = V – V⁎Volume = V⁎

Figure 11: The schematic diagram of the medium model with aspherical pore.

A′ n′

Clay platelets

Figure 12: Schematic diagram of shale equivalent model.

10 Geofluids

deformation. For extra compliance, therefore, the damageparameters α11, α33, β1111, β3333, and β1133 can be calculated.

α11 = −2ΔS11 +32ΔS66, A8

α33 = 2ΔS11 − 4ΔS13 + ΔS44 −32ΔS66, A9

β1111 = 3ΔS11−−32ΔS66, A10

β3333 = −2ΔS11 + 4ΔS13 + ΔS33 − ΔS44 +32ΔS66, A11

β1133 = ΔS13 A12

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

Ping Chen, Heyi Yuan, and Guangjian Dong designed thestudy. Heyi Yuan and Yudi Lu conducted the experimentsand analyzed the data.

Acknowledgments

This work is supported by the National Science and Tech-nology Major Project (Grant Nos. 2016ZX05022001 and2016ZX05028001), Major National Basic Research Devel-opment Program of China (973 Program) (Grant No.2013CB228003), the Science and Technology Support Pro-gram of Sichuan Province (Grant No. 2015SZ0003), the BasicResearch Subject of the State Key Laboratory of Oil & GasReservoir Geology and Exploitation (Southwest PetroleumUniversity) (Grant No. G3-1 and Grant No. G3), and ChinaScholarship Council (CSC) (No. 201808510213). We thankDr. Tao Huang who helped us to prepare the WBM. Weare immensely grateful to the anonymous reviewers andeditors for their constructive comments and suggestions toimprove this paper.

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12 Geofluids

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