Research Article Wellbore Stability in Oil and Gas...

Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 720271 9 pageshttpdxdoiorg1011552013720271

Research ArticleWellbore Stability in Oil and Gas Drilling withChemical-Mechanical Coupling

Chuanliang Yan12 Jingen Deng1 and Baohua Yu1

1 State Key Laboratory of Petroleum Resource and Prospecting China University of Petroleum Beijing 102249 China2Department of Petroleum Engineering China University of Petroleum Beijing 102249 China

Correspondence should be addressed to Chuanliang Yan yanchuanliang163com

Received 28 April 2013 Accepted 18 June 2013

Academic Editors K Kabiri A Vorontsov and Y-M Wu

Copyright copy 2013 Chuanliang Yan et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wellbore instability in oil and gas drilling is resulted from both mechanical and chemical factors Hydration is produced in shaleformation owing to the influence of the chemical property of drilling fluid A new experimental method to measure diffusioncoefficient of shale hydration is given and the calculation method of experimental results is introduced The diffusion coefficientof shale hydration is measured with the downhole temperature and pressure condition then the penetration migrate law of drillingfluid filtrate around the wellbore is calculated Furthermore the changing rules of shalemechanical properties affected by hydrationand water absorption are studied through experiments The relationships between shale mechanical parameters and the watercontent are established The wellbore stability model chemical-mechanical coupling is obtained based on the experimental resultsUnder the action of drilling fluid hydration makes the shale formation softened and produced the swelling strain after drillingThis will lead to the collapse pressure increases after drilling The study results provide a reference for studying hydration collapseperiod of shale

1 Introduction

Maintaining wellbore stability is an important issue in oil andgas industry [1ndash10] In the process of drilling the economiclosses caused by wellbore instability reaches more than onebillion dollar every year [11] and the lost time is accountingfor over 40 of all drilling related nonproductive time [12] Itis also reported that shale account for 75 of all formationsdrilled by the oil and gas industry and 90 of wellborestability problems occur in shale formations [13ndash18] Whena well is drilled the formation around the wellbore mustsustain the load that was previously taken by the removedformation As a result an increase in stress around thewellbore and stress concentration will be produced [19ndash23]If the strength of the formation is not strong enough thewellbore will be failure [24ndash28] Wellbore stability is not onlya pure rock mechanical problem but also the interactionof drilling fluid and shale is a more important influencefactor [29ndash35] There are various chemicals in the drillingfluid which physically and chemically interact with shale

formations One hand these interactions will result in theproduction of swelling stress [36ndash43] On the other hand italleviates the mechanical strength of the wellbore wall rock[44ndash46] Furthermore it results in wellbore instability

When studying the wellbore stability in shale chemicalfactor must be combined with mechanical factor Before the1990s the combinations are mainly on experimental studyChenevert studiedmechanical properties of shale after hydra-tion since 1970s [44] The results showed that the hydrationwould decrease the shale strength After 1990s the combi-nations came into a quantitative research stage Yew et al(1990) [29] and Huang et al (1995) [47] combined shalehydrated effect quantitatively into the mechanical modelbased on thermoelasticity theory Their method attributedthe rock mechanical properties change with total watercontent Take shale as a semipermeablemembrane Hale et al(1993) [48 49]Deng et al (2003) [50] andZhang et al (2009)[51] introduced equivalent pore pressure to study interactionof shale and water base drilling fluid Ghassemi et al (2009)[52] proposed a linear chemo-thermo-poroelasticity coupling

2 The Scientific World Journal

Stress and resistivity sensor

Transmitter

Measuring system

Computer acquisition

Confining pressure

load

Temperature controller

Safety system

Drilling fluid

circulating system

Temperature controller of drilling fluid

Axial load system

Electrical bridge

Figure 1 The experimental equipment sketch

model which considers the influence of chemical potentialand temperature Wang et al (2012) [53 54] built a fluid-solid-chemistry coupling model in which they consideredelectrochemical potential fluid flow caused by ion diffusion

The chemical effect of drilling fluid on shale can beultimately attributed to the variation of rock mechanicalproperties and stress around the wellbore Water migrationin shale is the basement of all wellbore stability modelswith chemical-mechanical coupling A new experimentalequipment to measure in situ water diffusion coefficient ofshale is developed in this paper And a sample model toevaluate time-dependent collapse pressure with chemical-mechanical coupling is presented

2 Experimental Research onthe Hydration of Shale

The free water and ion will penetrate into shale under thedriving force of chemical potential and pressure differencebetween the pore fluid and drilling fluid [55ndash58] Watercontent of shale changes by various mechanisms such asosmosis flow viscous flow and capillary flow Osmosis flowdriving force is due to chemicals and ions with differentcomposition in drilling fluid and pore fluid In order toevaluate the hydration of drilling fluid the coefficient ofwater absorption and diffusion and the swelling ratio mustbe determined first [36]

21 Experimental Research on the Water Absorption of Shale

211 Experimental Equipment Cherevent let one end face ofshale sample contact with drilling fluid and the other endface wrapped up by plastic film then he measured the watercontent increment in different location But his experiment

can only be conducted in room temperature and with zeroconfining pressure But during drilling process in deepformation it is in the condition of high temperature and highpressure Shale hydration is influenced by temperature andpressure seriously so his experimental result was inconsistentwith actual drilling In order to test the coefficient of waterdiffusion of shale we developed an in situ test equipmentof water diffusion coefficient which can fit the downholetemperature and pressure condition while drilling (Figure 1)

Technical parameters of this designed equipment are asthe following

(1) Temperature room temperature to 150∘C which canimitate the temperature condition of the formationwith 5000 meters depth

(2) Pressure confining pressure 0MPa to 70MPa axialpressure 0MPa to 200MPa

(3) Imitate the maximum differential pressure of drillingfluid with 10MPa

(4) Sample size 120601 25mm times 50mm

The experimental process are as follows

(1) Determine the original water content of the rocksamples first wrap the samples with separation sleeveand put into the core holder Put the drilling fluid intothe tank and check the test system to make sure it isin good condition

(2) Turn on the temperature controller warm the coresamples to the same temperature with downholeconditionThen load the confining pressure and axialpressure to proper value and start timing

(3) During the test data acquisition control system isused to keep the test values constant

The Scientific World Journal 3

(4) Cooling uninstall when the test time reaches thepredetermined value (50 hours in this research)remove the rock samples quickly and measure thewater content at different distance from the end face

212 Coefficient of Water Diffusion According to conserva-tion of mass water diffusion equations can be establishedSupposing 119902 is mass flow rate of the water diffusion 119862

119878(119903 119905)

is the weight percentage of water at the time 119905 and distance119903 away from the well axis according to conservation of massrequirement the following equation can be presented

nabla119902 =120597119862119878

120597119905 (1)

Consider that119902 = 119863effnabla119862119878 (2)

where nabla is the gradient operator and 119863eff is the coefficient ofwater diffusion

According to the above equations water diffusion equa-tion can be established as follows

120597119862119878

120597119905minus1

119903

120597

120597119903(119903

120597119862119878

120597119903)119863eff = 0 (3)

And the boundary conditions are

119905 = 0 119903119908le 119903 le infin 119862

119878= 1198620

119905 gt 0 119903 = 119903119908 119862119878= 119862119889119891

119905 gt 0 119903 997888rarr infin 119862119878= 1198620

(4)

where 119903119908is the wellbore radius 119862

119889119891is the saturated water

content of shale 1198620is the original water content

Sign 119906 = 119903radic119863eff119905 119862119878(119903 119905) = 120601(119906) then the followingequations can obtain that

120597119862119878

120597119905=119889120601

119889119906sdot120597119906

120597119905=119889120601

119889119906(minus

1

2119906) 119905minus1

120597119862119878

120597119903=119889120601

119889119906sdot120597119906

120597119903=119889120601

119889119906

1

radic119863eff119905

1205972119862119878

1205971199032=

119889

119889119903(119889120601

119889119906

1

radic119863eff119905) =

1

119863eff119905

1205972120601

1205971199062

(5)

Insert (5) to (3) then (6) can be obtained

12060110158401015840

= minus(119906

2+1

119906) 1206011015840

(6)

Equations (7) and (8) can obtain by integrating (6) that

1206011015840

= minus119860119906minus1

119890minus119906

24

(7)

119862119878(119903 119905) = 120601 (119906) =

119860

2int+infin

11990624

119909minus1

119890minus119909

119889119909 + 119861 (8)

Combining (8) and (4) the following equations can obtainthat

119860 =2 (119862119889119891minus 1198620)

int+infin

1199032

1199084119863eff119905

119909minus1119890minus119909119889119909

119861 = 1198620

(9)

0

2

4

6

8

10

12

1 2 3 4 5Distance from end face (cm)

Wat

er ra

tio (

)

Figure 2 Experimental results of water diffusion in shale

Thus the water content of shale formation around thewellbore can be written as follows

119862119878

= 1198620+ (119862119889119891minus 1198620)

times[1+2

120587intinfin

0

119890minus119863eff sdot120577

2sdot1199051198690(120577119903)119873

0(120577119903119908)minus1198730(120577119903) 1198690(120577119903119908)

11986920

(120577119903119908) + 11987320

(120577119903119908)

sdot119889120577

120577]

(10)

where 1198690( ) and 119873

0( ) are the zero order of Besselrsquos functions

of group one and two respectivelyIn a short period of time after drilling and within a short

distance from the wellbore wall (10) can be simplified to

119862119878= 1198620+ (119862119889119891minus 1198620)radic

119903119908

119903erfc(

119903 minus 119903119908

2radic119863eff119905) (11)

The water diffusion character of shale is measured using thisdesigned experiment equipment All the shale core samplesused in this paper were collected from Bohai Bay Basinof China The drilling fluid which contacted the shale inthis experiment was KCL drilling fluid The experimentalconfining pressure was 20MPa and the differential pressureof the fluid was 6MPa Core samples were taken out after 50hours and then cut into pieces to measure the water contentof each piece Three samples were tested in this research Theexperimental results of core sample 1-1 are shown in Figure 2Substituting the experimental results into (11) the coefficientof water diffusion of shale can be obtained All the calculatedwater diffusion coefficients and claymineral contents of thesethree samples are shown in Table 1 Smectite is the mineralmost prone to hydration [59 60] and the water diffusioncoefficient is higher with more smectite

22 Chemical Effect of Drilling Fluid on Shale MechanicalProperties Themechanical properties of shale can be alteredseriously after contacting with drilling fluid Existing formsof water in shale mainly include water vapor solid waterbound water adsorption water (film water) capillary water


Table 1 Clay mineral contents and water diffusion coefficient of shale

Core no Clay mineral total contents () Clay mineral relative contents () 119863eff

Smectite Illite Kaolinite Chlorite (cm2h)1-1 2168 45 19 17 19 002381-2 2928 51 24 13 12 002471-3 2668 32 20 26 22 00184

Diffusion layerFree water

Bound water Absorption water

Still layer

Rock particle

Figure 3 Water existing states in shale [63]

and gravity water (free water) (Figure 3) Owing to the directcontact with drilling fluid around the wellbore the freewater of drilling fluid diffuses into shale under physicaland chemical driving force During the drilling process theabsorption water will increase and the diffusion layer ofrock particle will thicken which will cause volume increaseof shale and produce swelling stress In order to calculatethe swelling stress caused by hydration the relation betweenwater absorption and the swelling must be researched firstthrough experiments The experiment methods are similarto that used by Yew et al [29] The experimental results areshown in Figure 4

The experiment results show that the swelling strain inthe direction perpendicular to the deposition surface is largerthan that of the parallel direction which is resulted fromthe difference of drainage and stress conditions in differentdirections in sedimentation [61 62]The relationship of watercontent and swelling strain is as follows

120576V = minus3248(Δ119862119878)3

+ 235(Δ119862119878)2

+ 037Δ119862119878

120576ℎ= minus1508(Δ119862

119878)3

+ 109(Δ119862119878)2

+ 017Δ119862119878

(12)

where 120576V and 120576ℎ are the swelling strain in the direction perpen-dicular and parallel to the deposition surface respectivelyΔ119862119878is the water content incrementWhen contacting with drilling fluid water sensitivity

minerals of shale will absorb water and make a chemicalreaction Clay mineral in shale will react with the ions indrilling fluid [63 64]

K09Al29Si31O10(OH)2+ 119899H2O

997888rarr K09Al29Si31O10(OH)2119899H2O

(13)

The properties of shale particle will change by above chemicalreaction and then weaken the cohesive force between shaleparticles whichwill soften the shale andweaken the strength

In order to evaluate wellbore stability after shale hydra-tion the mechanical properties of shale after hydration mustbe researched In order to ensure the uniformity of the coresamples used in the experiment the compressive acousticwave velocities of core samples were tested Only the sampleswhose velocity is close are chosen The core samples areshown in Figure 5The samples are immersed in KCL drillingfluid at the temperature of 55∘C MTS-816 rock test system(Figure 6) was adopted to test shale mechanical propertiesThe experiment results are showed in Table 2

The relationship of rock mechanical parameters withwater content increment is obtained by the experimentalresults

119864 = 55 times 103

119890minus45radicΔ119862

119878

V = 026 + 21Δ119862119878

(14)

UCS = 163 minus 149Δ119862119878 (15)

where 119864 is the Youngrsquos modulus V is the Poissonrsquos ratio UCSis the unconfined compressive strength

Assume that the variation of shale cohesion with watercontent increment is the same with the variation of UCS

120591 = 1205911015840

minus 149Δ119862119878 (16)

where 120591 is the cohesion 1205911015840 is the initial cohesion beforeimmersing which is tested as 52MPa

The shear failure of wellbore obeys Mohr-Coulombstrength criterion Mohr-Coulumb strength criterion can beexpressed by principal stress [23]

1205901= 1205903ctg2 (45∘ minus

120593

2) + 2120591 sdot ctg(45∘ minus

120593

2) (17)


Table 2 Experiment results of cores immersing in drilling fluid

Immersing time (h) 0 2 6 12 24 48 96 192Water content increment Δ119862

119878

() 0 082 203 270 328 446 511 568UCS (MPa) 1630 1356 1176 1224 948 828 852 660Poissonrsquos ratio 026 030 032 030 034 038 041 040Elastic modulus (MPa) 551837 405517 288129 217690 211145 175996 216525 159973

Vertical strainHorizontal strain

0 1 2 3 4 5 6ΔCS ()

0

1

2

3

4

Swel

ling

strai

n (

)

Figure 4 Experimental results of shale swelling

where 1205901and 120590

3are the maximum and minimum effective

principal stresses respectively120593 is the internal friction angleThere is 120590

3= 0 in the uniaxial compression experiment

Inserting (15) and (16) into (17) the variation of internalfriction angle with water content increment can be obtained

120593 = arctan(163 minus 149Δ119862

119878

104 minus 298Δ119862119878

) (18)

3 Wellbore Stability Model withChemical-Mechanical Coupling

Assuming that the shale is linear elastic material the consti-tutive equation in plane strain is shown as follows

120576119903=[120590119903minus V (120590

120579+ 120590119911)]

119864+ 120576ℎ

120576120579=[120590120579minus V (120590

119903+ 120590119911)]

119864+ 120576ℎ

120576119911=[120590119911minus V (120590

119903+ 120590120579)]

119864+ 120576V

(19)

where 120590119903 120590120579 and 120590

119911are radial tangential and vertical

stresses respectively 120576119903 120576120579 and 120576

119911are radial tangential and

vertical straines respectivelyThe formation is replaced by fluid column pressure after

drilling The original stress balance around the wellbore isbroken A new balance will be built The stress balanceequation is as follows [65]

119889120590119903

119889119903+120590119903minus 120590120579

119903= 0 (20)

where 120590119894119895is the total stress tensor and 119891

119894is the volume force

Figure 5 Standard samples of shale

Figure 6 MTS-816 rock test system

The strain components and displacement components ofthe formation should meet the following geometric equation[65]

120576119903=119889119906

119889119903

120576120579=119906

119903

(21)

where 120576119894119895is total strain tensor and 119906

119894is the displacement

componentInserting (19) and (20) to (21) the following obtains that

1199031198892120590119903

1198891199032+ (3 minus

119903

1198641

1198891198641

119889119903+

2V119903

V2 minus 1

119889V

119889119903)119889120590119903

119889119903

+ (4V + 1

V2 minus 1

119889V

119889119903minus

1

1198641

2V minus 1

V minus 1

1198891198641

119889119903)120590119903

=1198641(119897 + V)

V2 minus 1

119889120576V119889119903

+1198641120576V

V2 minus 1

119889V

119889119903

(22)


310 15 20 25

50 h100 h150 h

200 h250 h300 h

Distance to the borehole axis (cm)

6

9

12

Wat

er ra

tio (

)

Figure 7 Water content distribution around the wellbore

The boundary conditions for drilling are as follows [66]

120590119903= 119875119908 119903 = 119903

119908

120590119903= 119878 119903 = infin

(23)

where 119875119908is under the fluid column pressure and 119878 is the far

field horizontal in situ stressSolving (22) and (23) using finite-difference method

stress distribution around the wellbore and its change ruleswith drilling time are obtained Combined with Mohr-Coulumb failure criterion the time-dependent collapse pres-sure can be obtained

4 Time-Dependent Collapse Pressure

Based on the above model and experimental results thevariations of mechanical parameters of shale around thewellbore and time-dependent collapse pressure are analyzedThe calculation parameters are as follows well depth 119867 =1800m the initial water content 119862

0= 4 saturation water

content 119862119889119891

= 114 the water diffusion coefficient 119863eff =

00238 cm2h and thewellbore radius 119903119908= 108 cm the other

parameters are obtained by the experimental resultsFigure 7 shows the variation of water content in shale

formation around the wellbore with different open-hole timeThe water content at the wellbore wall reaches to saturatedstate quickly after the wellbore is opened in the same timethe water content would decrease with the increment ofdistance from the wellbore axis and the decreasing rate is thehighest near the wellbore wall Thus a hydrated area woulddevelop around the wellbore When the distance from thehole axis excesses 20 cm the water content of shale almost nolonger changes with the time increases and the water contentapproaches the initial water content in hydrated area thelonger the time the more the shale water content when thedistance is constant

The distribution character of UCS of shale around thewellbore is presented in Figure 8When a wellbore is openedthe UCSwould decrease as the time increasesWhen the timeis constant the UCS would increase as the distance from

50 h100 h150 h

200 h250 h300 h

Distance to the borehole axis (cm)10 12 14 16 18 20 22 24

4

8

12

16

20

UCS

(MPa

)

Figure 8 UCS distribution around the wellbore

Deff = 00184 cm2hDeff = 00238 cm2hDeff = 00247 cm2h

1200 50 100 150 200 250 300

Drilling time (h)

125

130

135

140

145

150C

ollap

se p

ress

ure (

gmiddotcm

3)

Figure 9 Time-dependent collapse pressure

the wellbore axis increases The increasing rate near thewellbore wall is the highest

The variation of collapse pressurewith drilling time underdifferent water diffusion coefficients is shown in Figure 9Theresults show that the collapse pressure increases rapidly in ashort time after the wellbore opening due to shale hydrationThen the increasing rate of collapse pressure would decreaseAt last the collapse pressure would increase linearly witha very low increasing rate After the wellbore is opened10 days the collapse pressure nearly no longer changesAccording to Figure 9 after the wellbore opening increasingthe drilling fluid density to 145 gcm3 gradually is morebeneficial for long-time wellbore stability when the water dif-fusion coefficient 119863eff = 00238 cm2h The higher the waterdiffusion coefficient is the larger the increasing range ofcollapse is On the other hand the possibility of wellboreinstability will be increasing with more smectite in shale


5 Conclusions

Water content at different distance from the end face of shalesample is measured using the designed equipment in thecondition of downhole temperature and pressure

The water content of shale at the wellbore wall reachesto saturated state quickly when the wellbore is opened thewater content of shale would decrease with the increment ofdistance from wellbore axis and the decreasing rate is thehighest near the wellbore wall

Due to the impact of shale hydration the strength ofthe circumferential formation around the well is graduallyreduced with the increase of drilling time and increases withthe increase of the distance away from the wellbore

Collapse pressure of shale increases sharply in a shorttime after drilling and then slows downThe collapse pressureis basically steady after several days of the open-hole timeThe initial stable wellbore may collapse with the increase ofthe open-hole time

Shale containing more smectite is more prone to reactwith drilling fluid The possibility of wellbore instability ofshale is higher with more smectite as the increasing range ofcollapse pressure is larger

Acknowledgments

This work is financially supported by Science Fund forCreative Research Groups of the National Natural ScienceFoundation of China (Grant no 51221003) National NaturalScience Foundation Project of China (Grant no 51134004and Grant no 51174219) and National Oil and Gas MajorProject of China (Grant no 2011ZX05009-005 and Grant no2011ZX05026-001-01)

References

[1] W B Bradley ldquoMathematical concept-stress cloud can predictborehole failurerdquo Oil amp Gas Journal vol 77 no 8 pp 92ndash1011979

[2] F J Santarelli E T Brown and V Maury ldquoAnalysis of Boreholestresses using pressure-dependent linear elasticityrdquo Interna-tional Journal of Rock Mechanics and Mining Sciences and vol23 no 6 pp 445ndash449 1986

[3] B S Aadnoy ldquoIntroduction to special issue on borehole stabil-ityrdquo Journal of Petroleum Science and Engineering vol 38 no3-4 pp 79ndash82 2003

[4] B S Aadnoslashy andM Belayneh ldquoElasto-plastic fracturingmodelfor wellbore stability using non-penetrating fluidsrdquo Journal ofPetroleum Science and Engineering vol 45 no 3-4 pp 179ndash1922004

[5] L Bailey J H Denis and G C Maitland ldquoDrilling fluids andwellbore stability current performance and future challengesrdquoinChemicals in theOil Industry PHOgden Ed Royale Societyof Chemistry London UK 1991

[6] J S Bell ldquoPractical methods for estimating in situ stresses forborehole stability applications in sedimentary basinsrdquo Journalof Petroleum Science and Engineering vol 38 no 3-4 pp 111ndash119 2003

[7] YWang andM BDusseault ldquoA coupled conductive-convectivethermo-poroelastic solution and implications for wellbore sta-bilityrdquo Journal of Petroleum Science and Engineering vol 38 no3-4 pp 187ndash198 2003

[8] M D Zoback C A Barton M Brudy et al ldquoDetermination ofstress orientation and magnitude in deep wellsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 40 no 7-8pp 1049ndash1076 2003

[9] A M Al-Ajmi and R W Zimmerman ldquoStability analysis ofvertical boreholes using the Mogi-Coulomb failure criterionrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 43 no 8 pp 1200ndash1211 2006

[10] T Al-Bazali J Zhang M E Chenevert and M M SharmaldquoFactors controlling the compressive strength and acousticproperties of shales when interacting with water-based fluidsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 45 no 5 pp 729ndash738 2008

[11] M E Zeynali ldquoMechanical and physico-chemical aspects ofwellbore stability during drilling operationsrdquo Journal ofPetroleum Science and Engineering vol 82-83 pp 120ndash1242012

[12] J Zhang J Lang and W Standifird ldquoStress porosity andfailure-dependent compressional and shear velocity ratio andits application to wellbore stabilityrdquo Journal of Petroleum Scienceand Engineering vol 69 no 3-4 pp 193ndash202 2009

[13] F K Mody and A H Hale ldquoBorehole-stability model tocouple the mechanics and chemistry of drilling-fluidshaleinteractionsrdquo Journal of PetroleumTechnology vol 45 no 11 pp1093ndash1101 1993

[14] GChenM E ChenevertMM Sharma andMYu ldquoA study ofwellbore stability in shales including poroelastic chemical andthermal effectsrdquo Journal of Petroleum Science and Engineeringvol 38 no 3-4 pp 167ndash176 2003

[15] L C Coelho A C Soares N F F Ebecken J L D Alves and LLandau ldquoThe impact of constitutive modeling of porous rockson 2-D wellbore stability analysisrdquo Journal of Petroleum Scienceand Engineering vol 46 no 1-2 pp 81ndash100 2005

[16] H C H Darley ldquoA laboratory investigation of borehole stabil-ityrdquo Journal of PetroleumTechnology vol 246 pp 821ndash826 1969

[17] R T Ewy and N G W Cook ldquoDeformation and fracturearound cylindrical openings in rock-I Observations and anal-ysis of deformationsrdquo International Journal of Rock Mechanicsand Mining Sciences and vol 27 no 5 pp 387ndash407 1990

[18] O A Helstrup Z Chen and S S Rahman ldquoTime-dependentwellbore instability and ballooning in naturally fractured for-mationsrdquo Journal of Petroleum Science and Engineering vol 43no 1-2 pp 113ndash128 2004

[19] J L Yuan J G Deng Q Tan B H Yu and X C Jin ldquoBoreholestability analysis of horizontal drilling in shale gas reservoirsrdquoRock Mechanics and Rock Engineering In press

[20] J C Roegiers ldquoWellmodeling an overviewrdquoOil andGas Scienceand Technology vol 57 no 5 pp 569ndash577 2002

[21] M D Zoback D Moos L Mastin and R N AndersonldquoWell bore breakouts and in situ stressrdquo Journal of GeophysicalResearch vol 90 no 7 pp 5523ndash5530 1985

[22] C A Barton M D Zoback and K L Burns ldquoIn-situ stressorientation and magnitude at the Fenton Geothermal siteNewMexico determined fromwellbore breakoutsrdquoGeophysicalResearch Letters vol 15 no 5 pp 467ndash470 1988

[23] E Fjaeligr R M Holt P Horsrud et al Petroleum Related RockMechanics Elsevier 2nd edition 2008


[24] R Narayanasamy D Barr and A Milne ldquoWellbore instabilitypredictions within the cretaceous mudstones clair field west ofshetlandsrdquo in Offshore Europe Aberdeen 2009

[25] E T Brown J W Bray and F J Santarelli ldquoInfluence of stress-dependent elastic moduli on stresses and strains aroundaxisymmetric boreholesrdquoRockMechanics andRock Engineeringvol 22 no 3 pp 189ndash203 1989

[26] P A Nawrocki M B Dusseault and R K Bratli ldquoAssessmentof some semi-analytical models for non-linear modeling ofborehole stressesrdquo International Journal of Rock Mechanical ampMining Science vol 35 no 4-5 pp 522ndash531 2002

[27] V M Maury and J M Sauzay Borehole Instability CaseHistories Rock Mechanics Approach and Results SPE 1987


[29] C H Yew M E Chenevert E Martin et al ldquoWellbore stressdistribution produced by moisture adsorptionrdquo SPE DrillingEngineering vol 5 no 4 pp 311ndash316 1990

[30] E van Oort ldquoOn the physical and chemical stability of shalesrdquoJournal of Petroleum Science and Engineering vol 38 no 3-4pp 213ndash235 2003

[31] ZQiu J Xu K Lu L YuWHuang andZWang ldquoMultivariatecooperation principle for well-bore stabilizationrdquo Acta PetroleiSinica vol 28 no 2 pp 117ndash119 2007

[32] M Yu M E Chenevert and M M Sharma ldquoChemical-mechanical wellbore instabilitymodel for shales accounting forsolute diffusionrdquo Journal of Petroleum Science and Engineeringvol 38 no 3-4 pp 131ndash143 2003

[33] A Ghassemi and A Diek ldquoLinear chemo-poroelasticity forswelling shales theory and applicationrdquo Journal of PetroleumScience and Engineering vol 38 no 3-4 pp 199ndash212 2003

[34] B S Aadnoy ldquoA complete elastic model for fluid-induced andin-situ generated stresses with the presence of a boreholerdquoEnergy Sources vol 9 no 4 pp 239ndash259 1987

[35] L Cui Y Abousleiman A H-D Cheng and J-C RoegiersldquoTime-dependent failure analysis of inclined boreholes in fluid-saturated formationsrdquo Journal of Energy Resources Technologyvol 121 no 1 pp 31ndash39 1999

[36] M E Chenevert and V Pernot ldquoControl of shale swellingpressures using inhibitive water-base mudsrdquo in Proceedings ofthe 67th SPE Annual Technical Conference and Exhibition pp27ndash30 SPE New Orleans La USA 1998

[37] P T Chee and G R Brian Effects of Swelling and HydrationStress in Shale on Wellbore Stability SPE 1997

[38] P T Chee and G R Brian ldquoIntegrated rock mechanics anddrilling fluid design approach to manage shale instabilityrdquo inSPEISRM Rock Mechanics in Petroleum Engineering 1998

[39] J P Simpson H L Dearing and D P Salisbury ldquoDownholesimulation cell shows unexpected effects on shale hydration onborehole wallrdquo SPE Drilling Engineering vol 4 no 1 pp 24ndash301989

[40] A H Hale F K Mody and D P Salisbury ldquoExperimentalinvestigation of the influence of chemical potential on wellborestabilityrdquo in Drilling Conference pp 377ndash389 February 1992

[41] F K Mody and A H Hale ldquoBorehole stability model to couplethe mechanics and chemistry of drilling fluid shale interactionrdquoin Proceedings of the SPEIADC Drilling Conference pp 473ndash490 February 1993

[42] E Oort A H Hale and F K Mody ldquoManipulation of coupledosmotic flows for stabilisation of shales exposed to water-baseddrilling fluidsrdquo in Proceedings of the SPE Annual TechnicalConference and Exhibition pp 497ndash509 October 1995

[43] C P TanMAmanullah F KMody andUA Tare ldquoNovel highmembrane efficiency water-based drilling fluids for alleviatingproblems in troublesome shale formationsrdquo in Proceedingsof the IADCSPE Asia Pacific Drilling Technology pp 63ndash72November 2002

[44] M E Chenevert ldquoShale Alteration by Water AdsorptionrdquoJournal of Petroleum Technology vol 22 no 9 pp 1141ndash11481970

[45] G Z Chen A study of wellbore stability in shales includingporoelastic chemical and thermal effects [PhD dissertation]The University of Texas at Austin 2001

[46] Y H Lu M Chen Y Jin X Q Teng W Wu and X Q LiuldquoExperimental study of strength properties of deep mudstoneunder drilling fluid soakingrdquoChinese Journal of RockMechanicsand Engineering vol 31 no 7 pp 1399ndash1405 2012

[47] R Z Huang M Chen and J G Deng ldquoStudy on shale stabilityof wellbore by mechanics coupling with chemistry methodrdquoDrilling Fluid amp Completion Fluid vol 12 no 3 pp 15ndash21 1995

[48] A H Hale and F K Mody ldquoBorehole-stability model tocouple the mechanics and chemistry of drilling-fluidshaleinteractionsrdquo Journal of PetroleumTechnology vol 45 no 11 pp1093ndash1101 1993

[49] A H Hale F K Mody and D P Salisbury ldquoInfluence ofchemical potential on wellbore stabilityrdquo SPE Drilling andCompletion vol 8 no 3 pp 207ndash216 1993

[50] J Deng D Guo J Zhou and S Liu ldquoMechanics-chemistrycoupling calculationmodel of borehole stress in shale formationand its numerical solving methodrdquo Chinese Journal of RockMechanics and Engineering vol 22 no 1 pp 2250ndash2253 2003

[51] L W Zhang D H Qiu and Y F Cheng ldquoResearch on thewellbore stability model coupled mechanics and chemistryrdquoJournal of Shandong University Engineering Science vol 39 no3 pp 111ndash114 2009

[52] A Ghassemi Q Tao and A Diek ldquoInfluence of coupledchemo-poro-thermoelastic processes on pore pressure andstress distributions around a wellbore in swelling shalerdquo Journalof Petroleum Science and Engineering vol 67 no 1-2 pp 57ndash642009

[53] QWang Y Zhou Y Tang andZ Jiang ldquoAnalysis of effect factorin shale wellbore stabilityrdquo Chinese Journal of Rock Mechanicsand Engineering vol 31 no 1 pp 171ndash179 2012

[54] Q Wang Y C Zhou G Wang H W Jiang and Y S LiuldquoA fluid-solid-chemistry coupling model for shale wellborestabilityrdquo Petroleum Exploration and Development vol 39 no4 pp 475ndash480 2012

[55] M E Chenevert and A K Sharma ldquoPermeability and effectivepore pressure of shalesrdquo SPE Drilling amp Completion vol 8 no1 pp 28ndash34 1993

[56] V X Nguyen Y N Abousleiman and S K Hoang ldquoAnalysesof wellbore instability in drilling through chemically activefractured-rock formationsrdquo SPE Journal vol 14 no 2 pp 283ndash301 2009

[57] E van Oort ldquoPhysico-chemical stabilization of shalesrdquo inProceedings of the SPE International Symposium on OilfieldChemistry pp 523ndash538 February 1997


[59] E Oort A H Hale F KMody and S Roy ldquoCritical parametersin modelling the chemical aspects of borehole stability inshales and in designing improved water-based shale drilling


fluidsrdquo in Proceedings of the SPE Annual Technical Conferenceamp Exhibition pp 171ndash186 September 1994

[60] M Chen Y Jin andGQ ZhangPetroleumEngineering RelatedRock Mechanics Science Press Beijing China 2008

[61] C E Weaver Clays Muds and Shales Elsevier 1989[62] S H Ong Borehole Stability [PhD dissertation] The U Of

Oklahoma 1994[63] X J Zhu ldquoWater-weakening properties of soften rocksrdquo Tech-

nology of Mineral Science vol 3-4 pp 46ndash50 1996[64] C-H Yang H-J Mao X-C Wang X-H Li and J-W Chen

ldquoStudy on variation of microstructure and mechanical proper-ties of water-weakening slatesrdquo Rock and Soil Mechanics vol 27no 12 pp 2090ndash2098 2006

[65] Z L Xu Elastic Mechanics Higher Education Press BeijingChina 1998

[66] J G Deng ldquoCalculation method of mud density to controlborehole closure raterdquo Chinese Journal of Rock Mechanics andEngineering vol 16 no 6 pp 522ndash528 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Stress and resistivity sensor

Transmitter

Measuring system

Computer acquisition

Confining pressure

load

Temperature controller

Safety system

Drilling fluid

circulating system

Temperature controller of drilling fluid

Axial load system

Electrical bridge

Figure 1 The experimental equipment sketch

model which considers the influence of chemical potentialand temperature Wang et al (2012) [53 54] built a fluid-solid-chemistry coupling model in which they consideredelectrochemical potential fluid flow caused by ion diffusion

The chemical effect of drilling fluid on shale can beultimately attributed to the variation of rock mechanicalproperties and stress around the wellbore Water migrationin shale is the basement of all wellbore stability modelswith chemical-mechanical coupling A new experimentalequipment to measure in situ water diffusion coefficient ofshale is developed in this paper And a sample model toevaluate time-dependent collapse pressure with chemical-mechanical coupling is presented

2 Experimental Research onthe Hydration of Shale

The free water and ion will penetrate into shale under thedriving force of chemical potential and pressure differencebetween the pore fluid and drilling fluid [55ndash58] Watercontent of shale changes by various mechanisms such asosmosis flow viscous flow and capillary flow Osmosis flowdriving force is due to chemicals and ions with differentcomposition in drilling fluid and pore fluid In order toevaluate the hydration of drilling fluid the coefficient ofwater absorption and diffusion and the swelling ratio mustbe determined first [36]

21 Experimental Research on the Water Absorption of Shale

211 Experimental Equipment Cherevent let one end face ofshale sample contact with drilling fluid and the other endface wrapped up by plastic film then he measured the watercontent increment in different location But his experiment

can only be conducted in room temperature and with zeroconfining pressure But during drilling process in deepformation it is in the condition of high temperature and highpressure Shale hydration is influenced by temperature andpressure seriously so his experimental result was inconsistentwith actual drilling In order to test the coefficient of waterdiffusion of shale we developed an in situ test equipmentof water diffusion coefficient which can fit the downholetemperature and pressure condition while drilling (Figure 1)

Technical parameters of this designed equipment are asthe following

(1) Temperature room temperature to 150∘C which canimitate the temperature condition of the formationwith 5000 meters depth

(2) Pressure confining pressure 0MPa to 70MPa axialpressure 0MPa to 200MPa

(3) Imitate the maximum differential pressure of drillingfluid with 10MPa

(4) Sample size 120601 25mm times 50mm

The experimental process are as follows

(1) Determine the original water content of the rocksamples first wrap the samples with separation sleeveand put into the core holder Put the drilling fluid intothe tank and check the test system to make sure it isin good condition

(2) Turn on the temperature controller warm the coresamples to the same temperature with downholeconditionThen load the confining pressure and axialpressure to proper value and start timing

(3) During the test data acquisition control system isused to keep the test values constant




119878(119903 119905)


nabla119902 =120597119862119878

120597119905 (1)




120597119862119878

120597119905minus1

119903

120597

120597119903(119903

120597119862119878

120597119903)119863eff = 0 (3)


119905 = 0 119903119908le 119903 le infin 119862

119878= 1198620

119905 gt 0 119903 = 119903119908 119862119878= 119862119889119891

119905 gt 0 119903 997888rarr infin 119862119878= 1198620

(4)





120597119862119878

120597119905=119889120601

119889119906sdot120597119906

120597119905=119889120601

119889119906(minus

1

2119906) 119905minus1

120597119862119878

120597119903=119889120601

119889119906sdot120597119906

120597119903=119889120601

119889119906

1


1205972119862119878

1205971199032=

119889

119889119903(119889120601

119889119906

1

radic119863eff119905) =

1

119863eff119905

1205972120601

1205971199062

(5)


12060110158401015840

= minus(119906

2+1

119906) 1206011015840

(6)


1206011015840


119890minus119906

24

(7)

119862119878(119903 119905) = 120601 (119906) =

119860

2int+infin

11990624

119909minus1

119890minus119909

119889119909 + 119861 (8)


119860 =2 (119862119889119891minus 1198620)

int+infin

1199032

1199084119863eff119905

119909minus1119890minus119909119889119909

119861 = 1198620

(9)

0

2

4

6

8

10

12


Wat

er ra

tio (

)



119862119878

= 1198620+ (119862119889119891minus 1198620)

times[1+2

120587intinfin

0

119890minus119863eff sdot120577

2sdot1199051198690(120577119903)119873

0(120577119903119908)minus1198730(120577119903) 1198690(120577119903119908)

11986920

(120577119903119908) + 11987320

(120577119903119908)

sdot119889120577

120577]

(10)

where 1198690( ) and 119873




119862119878= 1198620+ (119862119889119891minus 1198620)radic

119903119908

119903erfc(

119903 minus 119903119908

2radic119863eff119905) (11)









Still layer

Rock particle




120576V = minus3248(Δ119862119878)3

+ 235(Δ119862119878)2

+ 037Δ119862119878

120576ℎ= minus1508(Δ119862

119878)3

+ 109(Δ119862119878)2

+ 017Δ119862119878

(12)



K09Al29Si31O10(OH)2+ 119899H2O

997888rarr K09Al29Si31O10(OH)2119899H2O

(13)




119864 = 55 times 103


119878

V = 026 + 21Δ119862119878

(14)

UCS = 163 minus 149Δ119862119878 (15)



120591 = 1205911015840

minus 149Δ119862119878 (16)



1205901= 1205903ctg2 (45∘ minus

120593

2) + 2120591 sdot ctg(45∘ minus

120593

2) (17)




119878



0 1 2 3 4 5 6ΔCS ()

0

1

2

3

4

Swel

ling

strai

n (

)


where 1205901and 120590





120593 = arctan(163 minus 149Δ119862

119878

104 minus 298Δ119862119878

) (18)



120576119903=[120590119903minus V (120590

120579+ 120590119911)]

119864+ 120576ℎ

120576120579=[120590120579minus V (120590

119903+ 120590119911)]

119864+ 120576ℎ

120576119911=[120590119911minus V (120590

119903+ 120590120579)]

119864+ 120576V

(19)

where 120590119903 120590120579 and 120590






119889120590119903

119889119903+120590119903minus 120590120579

119903= 0 (20)






120576119903=119889119906

119889119903

120576120579=119906

119903

(21)




1199031198892120590119903

1198891199032+ (3 minus

119903

1198641

1198891198641

119889119903+

2V119903

V2 minus 1

119889V

119889119903)119889120590119903

119889119903

+ (4V + 1

V2 minus 1

119889V

119889119903minus

1

1198641

2V minus 1

V minus 1

1198891198641

119889119903)120590119903

=1198641(119897 + V)

V2 minus 1

119889120576V119889119903

+1198641120576V

V2 minus 1

119889V

119889119903

(22)


310 15 20 25

50 h100 h150 h

200 h250 h300 h


6

9

12

Wat

er ra

tio (

)



120590119903= 119875119908 119903 = 119903

119908

120590119903= 119878 119903 = infin

(23)







content 119862119889119891






50 h100 h150 h

200 h250 h300 h


4

8

12

16

20

UCS

(MPa

)



1200 50 100 150 200 250 300

Drilling time (h)

125

130

135

140

145

150C

ollap

se p

ress

ure (

gmiddotcm

3)





5 Conclusions






Acknowledgments


References








































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119878(119903 119905)


nabla119902 =120597119862119878

120597119905 (1)




120597119862119878

120597119905minus1

119903

120597

120597119903(119903

120597119862119878

120597119903)119863eff = 0 (3)


119905 = 0 119903119908le 119903 le infin 119862

119878= 1198620

119905 gt 0 119903 = 119903119908 119862119878= 119862119889119891

119905 gt 0 119903 997888rarr infin 119862119878= 1198620

(4)





120597119862119878

120597119905=119889120601

119889119906sdot120597119906

120597119905=119889120601

119889119906(minus

1

2119906) 119905minus1

120597119862119878

120597119903=119889120601

119889119906sdot120597119906

120597119903=119889120601

119889119906

1


1205972119862119878

1205971199032=

119889

119889119903(119889120601

119889119906

1

radic119863eff119905) =

1

119863eff119905

1205972120601

1205971199062

(5)


12060110158401015840

= minus(119906

2+1

119906) 1206011015840

(6)


1206011015840


119890minus119906

24

(7)

119862119878(119903 119905) = 120601 (119906) =

119860

2int+infin

11990624

119909minus1

119890minus119909

119889119909 + 119861 (8)


119860 =2 (119862119889119891minus 1198620)

int+infin

1199032

1199084119863eff119905

119909minus1119890minus119909119889119909

119861 = 1198620

(9)

0

2

4

6

8

10

12


Wat

er ra

tio (

)



119862119878

= 1198620+ (119862119889119891minus 1198620)

times[1+2

120587intinfin

0

119890minus119863eff sdot120577

2sdot1199051198690(120577119903)119873

0(120577119903119908)minus1198730(120577119903) 1198690(120577119903119908)

11986920

(120577119903119908) + 11987320

(120577119903119908)

sdot119889120577

120577]

(10)

where 1198690( ) and 119873




119862119878= 1198620+ (119862119889119891minus 1198620)radic

119903119908

119903erfc(

119903 minus 119903119908

2radic119863eff119905) (11)









Still layer

Rock particle




120576V = minus3248(Δ119862119878)3

+ 235(Δ119862119878)2

+ 037Δ119862119878

120576ℎ= minus1508(Δ119862

119878)3

+ 109(Δ119862119878)2

+ 017Δ119862119878

(12)



K09Al29Si31O10(OH)2+ 119899H2O

997888rarr K09Al29Si31O10(OH)2119899H2O

(13)




119864 = 55 times 103


119878

V = 026 + 21Δ119862119878

(14)

UCS = 163 minus 149Δ119862119878 (15)



120591 = 1205911015840

minus 149Δ119862119878 (16)



1205901= 1205903ctg2 (45∘ minus

120593

2) + 2120591 sdot ctg(45∘ minus

120593

2) (17)




119878



0 1 2 3 4 5 6ΔCS ()

0

1

2

3

4

Swel

ling

strai

n (

)


where 1205901and 120590





120593 = arctan(163 minus 149Δ119862

119878

104 minus 298Δ119862119878

) (18)



120576119903=[120590119903minus V (120590

120579+ 120590119911)]

119864+ 120576ℎ

120576120579=[120590120579minus V (120590

119903+ 120590119911)]

119864+ 120576ℎ

120576119911=[120590119911minus V (120590

119903+ 120590120579)]

119864+ 120576V

(19)

where 120590119903 120590120579 and 120590






119889120590119903

119889119903+120590119903minus 120590120579

119903= 0 (20)






120576119903=119889119906

119889119903

120576120579=119906

119903

(21)




1199031198892120590119903

1198891199032+ (3 minus

119903

1198641

1198891198641

119889119903+

2V119903

V2 minus 1

119889V

119889119903)119889120590119903

119889119903

+ (4V + 1

V2 minus 1

119889V

119889119903minus

1

1198641

2V minus 1

V minus 1

1198891198641

119889119903)120590119903

=1198641(119897 + V)

V2 minus 1

119889120576V119889119903

+1198641120576V

V2 minus 1

119889V

119889119903

(22)


310 15 20 25

50 h100 h150 h

200 h250 h300 h


6

9

12

Wat

er ra

tio (

)



120590119903= 119875119908 119903 = 119903

119908

120590119903= 119878 119903 = infin

(23)







content 119862119889119891






50 h100 h150 h

200 h250 h300 h


4

8

12

16

20

UCS

(MPa

)



1200 50 100 150 200 250 300

Drilling time (h)

125

130

135

140

145

150C

ollap

se p

ress

ure (

gmiddotcm

3)





5 Conclusions






Acknowledgments


References








































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Still layer

Rock particle




120576V = minus3248(Δ119862119878)3

+ 235(Δ119862119878)2

+ 037Δ119862119878

120576ℎ= minus1508(Δ119862

119878)3

+ 109(Δ119862119878)2

+ 017Δ119862119878

(12)



K09Al29Si31O10(OH)2+ 119899H2O

997888rarr K09Al29Si31O10(OH)2119899H2O

(13)




119864 = 55 times 103


119878

V = 026 + 21Δ119862119878

(14)

UCS = 163 minus 149Δ119862119878 (15)



120591 = 1205911015840

minus 149Δ119862119878 (16)



1205901= 1205903ctg2 (45∘ minus

120593

2) + 2120591 sdot ctg(45∘ minus

120593

2) (17)




119878



0 1 2 3 4 5 6ΔCS ()

0

1

2

3

4

Swel

ling

strai

n (

)


where 1205901and 120590





120593 = arctan(163 minus 149Δ119862

119878

104 minus 298Δ119862119878

) (18)



120576119903=[120590119903minus V (120590

120579+ 120590119911)]

119864+ 120576ℎ

120576120579=[120590120579minus V (120590

119903+ 120590119911)]

119864+ 120576ℎ

120576119911=[120590119911minus V (120590

119903+ 120590120579)]

119864+ 120576V

(19)

where 120590119903 120590120579 and 120590






119889120590119903

119889119903+120590119903minus 120590120579

119903= 0 (20)






120576119903=119889119906

119889119903

120576120579=119906

119903

(21)




1199031198892120590119903

1198891199032+ (3 minus

119903

1198641

1198891198641

119889119903+

2V119903

V2 minus 1

119889V

119889119903)119889120590119903

119889119903

+ (4V + 1

V2 minus 1

119889V

119889119903minus

1

1198641

2V minus 1

V minus 1

1198891198641

119889119903)120590119903

=1198641(119897 + V)

V2 minus 1

119889120576V119889119903

+1198641120576V

V2 minus 1

119889V

119889119903

(22)


310 15 20 25

50 h100 h150 h

200 h250 h300 h


6

9

12

Wat

er ra

tio (

)



120590119903= 119875119908 119903 = 119903

119908

120590119903= 119878 119903 = infin

(23)







content 119862119889119891






50 h100 h150 h

200 h250 h300 h


4

8

12

16

20

UCS

(MPa

)



1200 50 100 150 200 250 300

Drilling time (h)

125

130

135

140

145

150C

ollap

se p

ress

ure (

gmiddotcm

3)





5 Conclusions






Acknowledgments


References








































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119878



0 1 2 3 4 5 6ΔCS ()

0

1

2

3

4

Swel

ling

strai

n (

)


where 1205901and 120590





120593 = arctan(163 minus 149Δ119862

119878

104 minus 298Δ119862119878

) (18)



120576119903=[120590119903minus V (120590

120579+ 120590119911)]

119864+ 120576ℎ

120576120579=[120590120579minus V (120590

119903+ 120590119911)]

119864+ 120576ℎ

120576119911=[120590119911minus V (120590

119903+ 120590120579)]

119864+ 120576V

(19)

where 120590119903 120590120579 and 120590






119889120590119903

119889119903+120590119903minus 120590120579

119903= 0 (20)






120576119903=119889119906

119889119903

120576120579=119906

119903

(21)




1199031198892120590119903

1198891199032+ (3 minus

119903

1198641

1198891198641

119889119903+

2V119903

V2 minus 1

119889V

119889119903)119889120590119903

119889119903

+ (4V + 1

V2 minus 1

119889V

119889119903minus

1

1198641

2V minus 1

V minus 1

1198891198641

119889119903)120590119903

=1198641(119897 + V)

V2 minus 1

119889120576V119889119903

+1198641120576V

V2 minus 1

119889V

119889119903

(22)


310 15 20 25

50 h100 h150 h

200 h250 h300 h


6

9

12

Wat

er ra

tio (

)



120590119903= 119875119908 119903 = 119903

119908

120590119903= 119878 119903 = infin

(23)







content 119862119889119891






50 h100 h150 h

200 h250 h300 h


4

8

12

16

20

UCS

(MPa

)



1200 50 100 150 200 250 300

Drilling time (h)

125

130

135

140

145

150C

ollap

se p

ress

ure (

gmiddotcm

3)





5 Conclusions






Acknowledgments


References








































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










310 15 20 25

50 h100 h150 h

200 h250 h300 h


6

9

12

Wat

er ra

tio (

)



120590119903= 119875119908 119903 = 119903

119908

120590119903= 119878 119903 = infin

(23)







content 119862119889119891






50 h100 h150 h

200 h250 h300 h


4

8

12

16

20

UCS

(MPa

)



1200 50 100 150 200 250 300

Drilling time (h)

125

130

135

140

145

150C

ollap

se p

ress

ure (

gmiddotcm

3)





5 Conclusions






Acknowledgments


References








































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 Conclusions






Acknowledgments


References








































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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Research Article Wellbore Stability in Oil and Gas...

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