Coupled THM Modelling of Wellbore Stability with Drilling ...

Research ArticleCoupled THM Modelling of Wellbore Stability with DrillingUnloading Fluid Flow and Thermal Effects Considered

Shanpo Jia 12 CaoxuanWen 3 Fucheng Deng 3

Chuanliang Yan 4 and Zhiqiang Xiao 3

1e State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Chengdu China2Institute of Unconventional Oil amp Gas Northeast Petroleum University Daqing China3Yangtze University Jingzhou China4China University of Petroleum Qingdao China

Correspondence should be addressed to Fucheng Deng dengfucheng128163com

Received 26 December 2018 Revised 18 February 2019 Accepted 11 March 2019 Published 9 April 2019

Academic Editor Francisco J Montans

Copyright copy 2019 Shanpo Jia et al This 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

Both overbalanced drilling and underbalanced drilling will lead to the change of pore pressure around wellbore Existing researchis generally based on hydraulic-mechanical (HM) coupling and assumes that pore pressure near the wellbore is initial formationpressure which has great limitations According to the coupled theory of mixtures for rockmedium a coupled thermal-hydraulic-mechanical (THM) model is proposed and derived which is coded with MATLAB language and ABAQUS software as the solverThen the wellbore stability is simulated with the proposed model by considering the drilling unloading fluid flow and thermaleffects between the borehole and the formationThe effect of field coupling on pore pressure stress redistribution and temperaturearound a wellbore has been analyzed in detail Through the study of wellbore stability in different conditions it is found that (1)for overbalanced drilling borehole with impermeable wall is more stable than that of ones with permeable wall and its stabilitycan be improved by reducing the permeable ability of the wellbore wall (2) for underbalanced drilling the stability condition ofpermeable wellbore is much higher than that of impermeable wellbore (3) the temperature has important influence on wellborestability due to the variation of pore pressure and thermal stress the wellbore stability can be improved with cooling drilling fluidfor deep well The present method can provide references for coupled thermal-hydraulic-mechanical-chemical (THMC) processanalysis for wellbore

1 Introduction

Boreholes as the access for the development of oil gasand geothermal energy as well as deep geological storageof CO2 experience instability phenomena such as sloughingand borehole wall fracturing during drilling process whicharise from removal of the original supporting rock and theinteraction between the drilling fluid and formation [1ndash3]Wellbore stability is an important factor considered in drillingengineering which seriously affects the quality of the welland even leads to drilling failure Wellbore instability alwayshas been a major problem in petroleum geomechanics andengineering

The causes of wellbore instability can be classified intoeithermechanical (ie failure of the rock around the borehole

because of high stresses low rock strength or inappropri-ate drilling practice) or chemical effects which arise fromdamaging interaction between the rock and the drillingfluid [4ndash6] In recent years wellbore stability analysis hasmainly focused on the chemical interaction between rockand drilling fluid It is generally believed that the wellboreinstability by hydration also is caused by the stress aroundwellbore exceeding a certain limit value due to the decreasingof rock strength [6ndash8] Therefore the accurate calculationof the stress state near wellbore is of great significance forjudging whether the wellbore is unstable or not With thedevelopment of analysis models for wellbore stability it wasfound that the formation fluid drilling fluid properties andtemperature have a great influence on the wellbore stability[9ndash11] Mechanical behavior pore pressure and heat flux all

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 5481098 20 pageshttpsdoiorg10115520195481098

2 Mathematical Problems in Engineering

influence wellbore stability while instances of instability area result of a combination of coupled effects Analysis involvesstudying the interactions among changes of related effectivestress temperature and pore pressure during drilling processIn the process of overbalanced drilling the pressure ofdrilling fluid column is greater than formation pressurewhich would cause dynamic and static water loss of drillingfluid into formationThe stress state near awellbore is affectedseriously due to drilling fluid into formation For air or foamdrilling (underbalanced) the drilling fluid column pressurecan be lower than formation pressure which may causeformation fluid flow into wellbore resulting in the change ofpore pressure and stress state near wellbore In geothermalenvironments drilling fluid circulation will lead to relativelygreater disturbance near the well resulting in higher thermalstress which will affect wellbore stability More and moreanalytical models on wellbore stability issues have focused oncouplingmechanisms but these studies generally assume thatthe pore pressure around wellbore is the initial pore pressure[12ndash14] When the formation is drilled the equilibriumstate is disturbed causing the stress redistribution aroundborehole The drilling is essentially an excavation unloadingprocess [15] For numerical analysis of wellbore stability moststudies have focused on HM coupling elastic behavior andoverbalanced drilling without considering the influence ofdrilling unloading process stress redistribution filter cakequality and permeability change of the borehole wall [16 17]which is not consistent with the real case

In this article thermal effect and drilling unloadingprocess will be introduced into wellbore stability analysis in anumerical modeling framework to make such analyses moregeneral According to the previous studies the THM coupledmathematical model of rock medium has been proposedand the strategy to solve this model is discussed Then thedrilling unloading fluid flow and thermal effect of wellboreare analyzed in overbalanced drilling and under balanceddrilling and the influence of drilling fluid and thermal effecton pore pressure and stress redistribution around boreholewith time are all discussed

2 Coupled THMModelling Framework forWellbore Stability

21 e Basic Idea of Excavation Unloading Before theformation is drilled the stress state of rock mass is mainlycontrolled by in-situ stress and the stress state in the forma-tion is in equilibrium During the drilling process the initialstress equilibrium in the formation is disturbed causing thestress redistribution around the surrounding rock until a newbalance is reached (as shown in Figure 1)The change of stressand displacement field in the formation caused by drillingis essentially an unloading process After the formation isdrilled the excavated rock in the hole is replaced by drillingfluid and the stress state near the wellbore is redistributedand the mechanical characteristics of the rock around thewellbore will inevitably be affected

For unloading process modelling external boundaryloading method and excavation unloading method are usu-ally used [6 7 15]The displacement obtained by the external

Initial stress equilibrium Drilling unloadingDrilling fluid

Hσ Hσ

hσhσ

Figure 1 Drilling unloading process

boundary loading method is actually a comprehensive resultof the initial stress field and the excavation boundary whichhas no obvious practical significance while the excavationunloading method truly reflects the displacement changescaused by excavation Correct modelling the unloading pro-cess is the key to analyze thewellbore stability in drilling engi-neering The element removing and reactivating techniqueis an ideal method to realize wellbore unloading processwhich is realized bymodifying the stiffness of element set Forelement removing process the element is not really removedbut instead the stiffness of the element is multiplied by a verysmall coefficient (usually 1times10minus6) The mass of the removedelement and other parameters are set to 0 thus the load andstrain of the element is equal to 0

Before the elements are removed the mechanical equilib-rium equation is defined as [15]

P = [K] U (1)

where [K] is stiffness matrix of element U is node displace-ment array and P is the load array

Introducing the parameter 120589119894 to control the elementremoving and reactivating the modified equilibrium equa-tion is given

P = [K] U (2)

where

[K] =[[[[[[[

1205891111989611 1205891211989612 sdot sdot sdot 120589111989911989611198991205892111989621 1205892211989622 sdot sdot sdot 12058921198991198962119899 sdot sdot sdot 12058911989911198961198991 12058911989921198961198992 sdot sdot sdot 120589119899119899119896119899119899

]]]]]]] (3)

22 ermal Transfer Model of Rock Assuming the porosityof a rock element is 119899 the proportion of solid skeleton is 1 minus119899 According to the principle of conservation of energy andFourierrsquos law [16 17] the energy conservation equation of thesolid skeleton is as follows

nabla [(1 minus 119899) 120582snabla119879] + (1 minus 119899) [119902s minus 3119870120573119897 (119879 minus 1198790) 120597120576v120597119905 ]= 120597 [(1 minus 119899) 120588s119888s (119879 minus 1198790)]120597119905

(4)

Mathematical Problems in Engineering 3

where 120582s 119888s and 120588s are the thermal conductivity specificheat and density of the solid skeleton respectively 119902s isthe energy generated per unit volume of skeleton per unittime 119879 is the temperature 1198790 is the initial temperature 120573119897 islinear expansion coefficient119870 is the volumemodulus of rockmedium and 120576V is volume strain

The energy conservation equation of the fluid phase canbe established in a similar way Since the fluid flow velocityin the formation is small the kinetic energy of the fluid canbe ignored The energy equation considering convection andconduction is given as

nabla (119899120582fnabla119879) + 119899119902f = 120597 [119899120588f119888f (119879 minus 1198790)]120597119905+ 119899119888f (119879 minus 1198790) 120597120588f120597119905 + 120588f119888f (119907nabla) 119879

(5)

where 120582119891 119888119891 and 120588119891 are thermal conductivity specificheat and density of the fluid respectively 119902119891 is the energygenerated per unit volume of fluid per unit time 119907 is Darcyflow velocity and (119907nabla)119879 is convection item which indicatesthe change rate of temperature caused by the movement offluid particles

According to theory of mixtures [18] the total energyequation of the rockmedium is superimposed by the propor-tion of material component

nabla (120582nabla119879) + 119902 minus 3119870120573119897 (119879 minus 1198790) (1 minus 119899) 120597120576V120597119905 = 119888120597119879120597119905+ 120588f119888f (119907nabla) 119879 + (119879 minus 1198790)sdot [(120588f119888f minus 120588s119888s) 120597119899

120597119905 + (1 minus 119899) 119888s 120597120588s120597119905 + 119899119888f 120597120588f120597119905 ](6)

where 120582 = (1minus119899)120582s+119899120582f 119902 = (1minus119899)119902s+119899119902f 119888 = (1minus119899)120588s119888s+119899120588f119888f 23 Coupled Flow Model Combined with Darcyrsquos law theflow equation considering rock deformation is defined as[16 17]

119896120583f [

12059721199011205971199092 +

12059721199011205971199102 +

12059721199011205971199112 ] = 120572120597119901

120597119905 minus 120573120597119879120597119905 + 120572120597120576V120597119905 + 119876f (7)

where 120583f is fluid viscosity 119896 is permeability of rock 119901 ispore pressure 120572 = 119899120572f + (1 minus 119899)120572s is comprehensivecompressibility 120572s is the compressibility of solid skeleton120572f is the compressibility of fluid 120573 = 119899120573f + (1 minus 119899)120573s iscomprehensive thermal expansion coefficient 120573s = 3120573l isvolumetric thermal expansion coefficient of solid skeleton 120573fis volumetric thermal expansion coefficient of fluid 120572 is Biotcoefficient and 119876f is internal and external fluid sources

In the process of fluid flow the permeability is relatedto the change of porosity and the change of pore volumeis related to pore pressure and stress so the permeability is

minus10 minus05 00 05 100

10

20

30

40

Volume strainn0=01n0=03

n0=05n0=07

kk 0

Figure 2 The relationship curve between permeability and volumestrain (negative volume strain represents in the compression)

dynamic change with fluid flow [15] The relations betweenpermeability porosity and volumetric strain are given

119899 = 1 minus 1 minus 1198990120576v + 1 (8)

119896 = 1198960 [( 11198990) (1 + 120576v)23 minus (1 minus 11989901198990 ) (1 + 120576V)minus13]

3

(9)

where 1198960 and 1198990 are initial permeability and porosity respec-tively

The relationship between permeability and volume strainis shown in Figure 2 The smaller the porosity the moreobvious is the effect of deformation on permeability

24 Coupled Mechanical Model According to Biotrsquos consoli-dation theory the effective stress can be expressed as

d1205901015840119894119895 = d120590119894119895 + 120572120575119894119895d119901 (10)

where 1205901015840 is the effective stress 120590119894119895 is total stress and 120575119894119895 isKronecker symbol In this study tensile stress is positive andcompressive stress is negative

To describe the thermal expansion and plastic deforma-tion of a rockmedium the total stress can be expressed in theform of increment

d120590119894119895 = d1205901015840119894119895 minus 120572120575119894119895119901= 119863e

ijkl (d120576kl minus d120576pkl minus d120576T119896119897) minus 120572d119901120575119894119895(11)

where119863e is elastic stiffness matrix 120576 is total strain tensor 120576pis plastic stiffness tensor and 120576T is strain tensor caused by thechange of temperature


hσ

HσbR

aR0R

Elastic zone

Damaged zone

Hole

Undisturbed zone Elastic zone

Damaged zone

Figure 3 Excavation damaged zone

unstable

failure line

mσ

3

1

(a)

mσ

unstable

failure line

3

1

(b)

Figure 4 Two types of Mohr-Coulomb criterion (a) Shear failure (b) Tensile failure

Equation (11) can be rearranged as

d120590119894119895 = 119863epijkl (d120576119896119897 minus d120576T119896119897) minus 120572d119901120575119894119895 (12)

where 120576119894119895 = (119906119894119895 + 119906119895119894)2 d120576119894119895 = d119906119894119895 d120576T119894119895 = 120573119897d119879120575119894119895 119906119894 isdisplacement components of rock and 119863ep is elastic-plasticstiffness matrix

Drilling excavation causes stress redistribution aroundwellbore and the zone where the stress state changes isusually called the excavation disturbed zone (as shown inFigure 3)That drilling changes the original equilibrium stateof the formation would cause stress concentration aroundthe wellbore and may lead to wellbore instability Wellboreinstability is generally divided into two types one is collapsecaused by shear failure and another is the fracturing causedby tensile stress

Due to the simplicity and practicability of the Mohr-Coulomb criterion it is the most commonly used for eval-uating wellbore stability (as shown in Figure 4) The shear

Mohr-Coulomb criterion is generally written in terms ofstress invariants [19]

119865 = 120590m sin 120601 + 1205901198701015840 minus 119888 cos 120601 = 0 (13)

where 120590m 120590 119888 120601 denote the average stress equivalent stresscohesion and friction angle respectively 1198701015840 is a function ofthe Lode angle 120579 and friction angle 120601

1198701015840 = cos 120579 minus 1radic3 sin 120601 sin 120579 (14)

In (13) 120590m and 120590 are defined by

120590m = 12059010158401 + 12059010158402 + 120590101584033 120590 = radic1198692

(15)

where 12059010158401 12059010158402 12059010158403 are the three principal stresses and 1198692 is thesecond invariant of the deviatoric stress


tσ Average stress mσ

Equi

vale

nt st

ress

σ

tσTensile Mohr-coulomb yield surface ( )Shear Mohr-coulomb yield surface (c )Modified Mohr-coulomb yield surface (c m)

Figure 5 Modified Mohr-Coulomb criterion in the meridionalplane

The tensile Mohr-Coulomb criterion is defined in termsof stress invariants [15]

119865 = 2radic3120590 sin (120579 + 1200) + 120590m minus 120590t = 0 (16)

where 120590t is the tensile strengthConsidering both tensile strength and shear strength of a

formation the yield surface is a combination of two differentfailure criteria shear failure and tensile failure The modifiedMohr-Coulomb (MMC) function is defined as follows (asshown in Figure 5)

119865 = 120590m sin 120601 + radic(1205901198701015840)2 + 11989821198882cos2120601 minus 119888 cos 120601 = 0 (17)

where 0 le 119898 le 1 is a parameter reflecting the tensilestrength of formationWhen119898 = 0 indicating a higher tensilestrength the MMC yield criterion becomes the shear Mohr-Coulomb criterion 119898 = 1 denotes that there is no tensilestrength In addition the parameter119898 can smooth the vertexof the yield surface and avoid the numerical divergence andslow convergence

The plastic potential function can be defined from theyield function as follows

119866 = 120590m sin 120593 + radic(1205901198701015840)2 + 11989821198882cos2120593 (18)

where 120593 is the dilatancy angle Similarly 1198701015840 is a function ofthe Lode angle 120579 and the dilatancy angle 120593 Associated flowoccurs if 120593 = 120601 while nonassociated flow occurs if 0 le 120593 lt 120601

According to the MMC criterion the quantitative evalu-ation indices for wellbore collapse and rupture are given as[14]

119891119887 = 119888 + 120590119899120591 = 2119888 cos 120601 + (12059010158401 + 12059010158403) minus (12059010158401 minus 12059010158403) sin2120601(12059010158401 minus 12059010158403) cos2120601119891119891 = 2 minus 12059010158403120590119905

(19)

where 120590119899 120591 are normal stress and shear stress on the shearsurface The wellbore would collapse for 119891119887 le 1 and fracturefor 119891119891 le 13 Solution Strategy

The decoupled solution method is applied for the solution ofthis THM coupling model The HM coupling module andthermal module in ABAQUS software is used to solve thestress field flow field and temperature field The decoupledsolution between two modules is performed in MATLABThen the THM coupling software for rock medium canbe developed using MATLAB language as the platform andABAQUS software as the solver in which different partssuch as thermal hydraulic and mechanical modules canbe called The software framework for THM is shown inFigure 6 The solution method has been verified through atypical example of one-dimensional thermal consolidation[20 21]The decoupled method is also efficient and easy to bedeveloped which can be applied to the analysis of thermal-hydraulic-mechanical-chemical (THMC) coupling for rock

The programming process is given as follows(1) The main program of MATLAB is compiled and thecalculation parameter setting and control precision of cycleiteration are defined(2) Different physical fields are analyzed by ABAQUSsolver in sequence write command file (lowast inp) for differentphysical field based on ABAUQS and USDFLD subroutinefile (lowast for) for parameter evolution such as permeabilitychange with strain based on FORTRAN Call ABAUQSsolver to solve different field modules by the command code(system) in MATLAB(3) Compile ABQMAIN subroutine for data conversionthe field variable node data file (lowast fil) is formed for otherphysical field modules to call as field variable values(4) The coupled parameters in the command file (lowastinp)of ABAQUS is modified and updated in MATLAB(5) Compile the coupled cycle processing subroutinein MATLAB call the updated command file (lowastinp) andABAQUS solver to calculateThen read the current result file(lowastdat) of ABAQUS and compare it with the previous resultfile until the convergence tolerance error is satisfied and thecyclic iteration is completed

4 Parametric Study

During drilling fluid flow in the formation and the tem-perature difference between formation and drilling fluid willcause changes of pore pressure and temperature around the


Updated coupled parameters

HM coupling module ermal module

Data conversion

Input initial parameters

Convergence

Judge the final time

Cycle iteration setting

No

Yes

End


Data conversion

ABAQUS

Figure 6 Flow chart of THM analysis

Table 1 Material parameters of rock media

ElasticmodulusMPa

Poissonrsquosratio

CohesionMPa

Frictionangle∘

TensilestrengthMPa

PorosityThermal

conductivityJ(msdot∘C)

Thermalexpansion∘Cminus1

Specific heatJ(kgsdot∘C)

2 000 02 8 30 12 02 308 15times10minus5 840

Table 2 Fluid parameters

BulkmodulusMPa

Dynamicviscosity(Pasdots)

ThermalconductivityJ(msdot∘C)


Specific heatJ(kgsdot∘C) Permeability

ms

5 000 0001 058 20times10minus4 4200 1times10minus12

wellbore which will inevitably affect wellbore stability Inthis section a conceptual numerical model is applied tostudy the wellbore stability influenced by flow conditions andtemperature

41 Modelling Approach A plane strain model was studiedbased on the proposed method (as shown in Figure 7) Theradius of the wellbore is 0108 m Due to the symmetry of themodel a 14 portion with the length and the width of 5 mwasestablished

The overburden strata stress 120590V horizontal maximumtotal stress 120590119867 the minimum total stress 120590ℎ and the for-mation pressure 119875119901 are 69MPa 75MPa 54MPa and 45Mparespectively The fluid column pressure of drilling fluid is50MPa for overbalanced drilling and 40 for underbalanceddrilling The properties of the rock and the fluid are listed in

vσ

Hσhσ

x

z

y

Figure 7 Calculation model

Tables 1 and 2 respectively The hydration effect by drillingfluid is not considered in this analysis


(a) (b)

Figure 8 The technique of element birth and death for drilling (a) Initial state (b) Drilling excavation

TemperaturePore pressure

Pressure surface load

Symmetry boundarySymmetry boundary

XY

Z

Vertical stress

Fixed displacement

Fixed displacementFixed displacement

Figure 9 Definition of wellbore boundary conditions

The numerical calculation process of wellbore stabilityincludes three steps which are defined as follows (1) Infirst step in-situ stress initial temperature and pore pressureare applied to the rock mass to simulate the undisturbedstate of formation (Figure 8(a)) (2) To simulate the drillingunloading the element removing technique is used to dealwith the excavated part of wellbore (Figure 8(b)) (3) Thedrilling fluid is injected and fluid temperature pore pressureand fluid pressure surface load are applied on the wall ofborehole (Figure 9)

42 Effect of Filtrate Cake Quality on Wellbore Stability Foroverbalanced drilling the drilling fluid column pressure isgreater than the formation pressure and the drilling fluidcan form a mud filtrate cake on the wellbore (as shown inFigure 10) The fluid flow depends greatly on the differentialpressure and filtrate cake quality which are the direct causesof fluid flow and pore pressure changes around wellboreTherefore the wellbore stability is influenced by filtrate cakequality

Two kinds of extreme conditions for filtrate cake qualitywere discussed One is impermeable wall or closed wellborewhich indicates that the filtrate cake is impermeable and thusthere is no fluid communication between the wellbore andthe formation Another scenario is permeable wall conditionwhich means drilling fluid and formation is connected Tostudy the influence of the filtrate cake quality on wellbore

FormationFiltrate cake

Drilling fluid

Figure 10 Diagram of mud filtrate cake

stability the temperature of drilling fluid is assumed the sameas that of the formation in this section

Compared with the initial stress state (Figure 11) theeffective radial stress near the wellbore decreased rapidlyafter drilling unloading and the stress continues to decreasegradually due to pore pressure change with time as shownin Figure 12 For a permeable wall condition the pressuresupport on the wellbore by drilling fluid will be reducedby seepage and the effective radial stress at the wellboredecreases gradually until to zero ultimately As for an imper-meable wall condition the hydraulic connection between thedrilling fluid and the formation water is eliminated by theclosure of good filtrate cake and then the liquid column


S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)

Figure 11 Initial effective stress and pore pressure of the formation (a) 1205901015840x (b) 1205901015840y (c) Initial pore pressure

of drilling fluid can provide an effective supporting for thewellbore The effective radial stress on the inner wall is -65MPa after 24 hours for impermeable wall whereas it is 0MPafor permeable wall

Figure 13 shows the effective hoop stress distributionnear wellbore region The maximum hoop stress is atthe location 05119903119908 from the wall after drilling unloadingFor a permeable wall the hoop stress decreases graduallywith time and shows a trend from compression to ten-sion after 24 hours For an impermeable wall the hoopstress is gradually reduced and stays in a compressive stressstate

Due to the impact of drilling unloading the pore pressurenear wellbore decreases rapidly after drilling excavation(Figure 14) For a permeablewall theminimumpore pressureis 28MPa at the location 04119903119908 from the wall Since thedrilling fluid in the wellbore is connected with formationfluid the pore pressure around wellbore increases to 50MPagradually after 24 hours For an impermeable wall the pore

pressure around wellbore goes to initial pore pressure 45MPagradually (Figure 11)

Figure 15 shows the distribution of quantitative evalua-tion indices 119891119887 and 119891119891 near wellbore region respectively Itcan be found that the wellbore is easiest to collapse when 120579is equal to 90∘ or 270∘ and the wellbore is easiest to fracturewhen 120579 is equal to 0∘ or 180∘ (the direction of the maximumprincipal stress is horizontal)

For an impermeable wall drilling fluid and formationwater is separated by the filtrate cake The pore pressure nearwellbore changes obviously by drilling unloading After thatthe pore pressure near wellbore gradually tends to initialpore pressure In the condition of overbalanced drillingthe collapse resistance of the wellbore is improved with thesupporting effect by liquid column pressure on the boreholewall

For a permeable wall the drilling fluid is connected withthe formation fluid Due to the drilling liquid column asthe inner boundary of seepage field the supporting effect by


C

Drilling excavation 2 h

9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)

1 2 3 4 5 6 7 8 9 100Normalized radial distance rrw

(a)

Drilling excavation2 h

9 h24 h

B C

minus32minus30minus28minus26minus24minus22minus20minus18minus16minus14minus12minus10

minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)

Figure 12 Radial stress distribution along BC (negative represent compressive stress) (a) Permeable wall (b) Impermeable wall

0 1 2 3 4 5 6 7 8 9 10minus18minus16minus14minus12minus10

minus8minus6minus4minus2

02


9 h 24 h

Normalized radial distance rrw

Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)

Figure 13 The distribution of hoop stress along BC (a) Permeable wall (b) Impermeable wall

liquid column pressure on the formation is gradually reducedto zero while the effective load on far field boundary isthe difference between initial total stress and pore pressureThe pore pressure gradient is gradually decreased along thedirection of far field which can make a certain inhibitoryeffect on the wellbore deformation but the reduction ofwall support load promotes the wellbore deformation Inthe condition of overbalanced drilling the pore pressureof borehole wall gradually tends to the pressure of liquidcolumn which is higher than that of far field With thedecrease of effective stress the capacity of the wellbore toresist tension failure decreased

Due to the effect of pore fluid pressure gradient andreduction of wellbore supporting load both radial stress and

hoop stress of permeable wellbore are lower than those ofimpermeable wellbore Thus wellbore stability of imperme-able wall is higher than that of permeable wellbore so it isparticularly important to improve the filter cake quality ofdrilling fluid under the condition of overbalanced drilling

43 Effect of Fluid Flow on Wellbore Stability for Under-balanced Drilling In the process of underbalanced drillingformation fluid can flow into the borehole and the stressaround the wellbore will be redistributed with the seepageof formation fluid thus affecting the wellbore stability Twokinds of wellbore conditions were analyzed in this sectionone is impermeable wall of wellbore another scenario ispermeable condition


0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)

Figure 14 The distribution of pore pressure near borehole along BC (a) Permeable wall (b) Impermeable wall

The radial stress near wellbore decreased rapidly afterdrilling unloading as shown in Figure 16 After that theseepage effect makes the stress decrease continuously Fora permeable wall the supporting load of wellbore wall isdecreased by the seepage and the effective radial stress of rockaround wellbore decreased gradually and tends to 0 MPaFor an impermeable wall the pressure of liquid column islower than the initial pore pressure of formation and thedeformation of wellbore makes the stress state of rock intotension

Figure 17 shows the hoop stress distribution aroundwellbore The maximum hoop stress is at the location 04119903119908from the wall The hoop stress keeps in compressive stressstate with time

Figure 18 shows pore pressure distribution of near well-bore region For a permeable wall the pore pressure aroundwellbore tends to 40MPa after 24 hours For an impermeablewall the drilling fluid in wellbore cannot connect with the farpore pressure field and the pore pressure goes to initial porepressure gradually with time

For an impermeable wall in underbalanced drilling con-dition thewellbore shrinkage and a large change of pore pres-sure near the wellbore occurred The pore pressure aroundwellbore has the tendency to initial formation pressure andthe radial stress is in tension gradually which make wellborestability worse For a permeable wall the pore pressure nearwellbore wall tends to the pressure of liquid column whichis lower than the far formation pressure and the stabilityof wellbore increased Therefore the wellbore stability withpermeable wall is higher than that of impermeable wall inunderbalanced drilling condition (Figure 19)

44 Effect of Temperature onWellbore Stability To discuss theeffect of temperature on wellbore stability different coupledrelationships are illustrated through the following three cases

which are shown in Figure 20 Case 1 and case 2 are twotypes of incomplete coupling forms while case 3 is fullycoupled THM form For case 1 the coupling effect betweentemperature field and stress field is not considered but theinfluence of temperature field and stress field on seepagefield is considered For case 2 the coupling effect betweentemperature field and seepage field is not considered but theinfluence of seepage field and temperature field on stress fieldis considered Taking overbalanced drilling with good filtratecake quality as an example the importance of temperaturecoupling on wellbore stability is analyzed in which thetemperature of drilling fluid and formation are 120 degreesCelsius and 70 degrees Celsius respectively

Figures 21 and 22 show the comparison of temperaturedistribution after 24 hours under different cases Due to lowerthermal conductivity and higher specific heat of fluid thetemperature field is least affected in case 1 The temperaturefield ismost affected in case 2 for higher thermal conductivityof solid skeleton Because the theory of mixtures is applied inthis fully coupled THM model [18] the temperature field ofcase 3 has shown a moderate degree

Figure 23 shows the comparison of pore pressure after24 hours under different cases Due to the fact that thethermal-hydraulic coupling (TH) is not considered in case2 the pore pressure difference between wellbore wall andthe formation is the smallest For case 3 the THM couplingis fully considered so the pore pressure difference betweenwellbore and the formation is the largest For stress field(Figure 24) the radial and hoop stress are basically in acompressive state and the distributions around wellbore aresimilar for different cases The temperature on stress field isaffected most in case 3 and least in case 2 which is similar topore pressure

Figure 25 shows the distribution of collapse index andfracture index under different cases It can be found that the


0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22

Permeable wellbore) Closed wellbore

(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789

Permeable wellbore Closed wellbore

(b)

Figure 15 Distribution of quantitative evaluation indices near the wall in overbalanced condition (a) Collapse index 119891119887 (b) Fracture index119891119891


0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)

Figure 16 Radial stress distribution along BC for underbalanced drilling (a) Permeable wall (b) Impermeable wall

0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)

Figure 17 Hoop stress distribution along BC for underbalanced drilling (a) Permeable wall (b) Impermeable wall

distributions of failure indices under three cases are similarFor collapse failure the collapse index under case 2 is thesmallest and thewellbore ismost easy to collapse For fracturefailure the fracture index under case 2 is the smallest and thewellbore is most easy to break There are obvious differencesin stress pore pressure and temperature of wellbore by full-coupled model and partial-coupled models During drillingthe temperature difference between the drilling fluid and theformation will lead to temperature change near wellboreThe disturbed range of temperature is related to the thermaldiffusivity of the formation and the fluid inside which leadsto the great change of pore pressure and effective stress inthe near-wellbore zone and inevitably affects the wellborestability Therefore it is necessary to take full-coupled model

into account when dealing with the evaluation of wellborestability [22]

The influence of temperature fluctuation on wellborestability is studied by changing drilling fluid temperatureusing THM fully coupled model The results are shownin Figures 26 and 27 When the formation is heated bythe drilling fluid the larger the temperature difference thesmaller the collapse index and fracture index of wellborewhich indicates that the instability possibility of wellbore isgreater When the drilling fluid temperature is lower thanthe formation temperature the stress around wellbore tendsto decrease with the increase of temperature difference Thelarger the temperature difference is the smaller the instabilitypossibility of wellbore occurs


0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)

Figure 18 The distribution of pore pressure along BC for underbalanced drilling (a) Permeable wall (b) Impermeable wall

0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)

Figure 19 Distribution of quantitative evaluation indices near the wall in underbalanced drilling (a) Collapse index 119891119887 (b) Fracture index119891119891

T

H M

T

H M

T

H M

Case 1 Case 2 Case 3

Figure 20 Three cases of temperature coupling


TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X

(Avg 75)+1199e+02+1159e+02+1119e+02+1079e+02+1039e+02+9993e+01+9594e+01+9194e+01+8795e+01+8395e+01+7996e+01+7596e+01+7197e+01

(c)Figure 21 Temperature distribution after 24 hours under different cases (a) Case 1 (b) Case 2 (c) Case 3

65707580859095

100105110115120125


Tem

pera

ture

(∘C)

2 4 6 8 10 12 140Normalized radial distance rrw

Figure 22 Comparison of temperature distribution along BC

353637383940414243444546


Pore

pre

ssur

e (M

Pa)


Figure 23 Comparison of pore pressure distribution along BC





minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)

Figure 24 Comparison of radial stress and hoop stress distribution along BC (a) Radial stress (b) Hoop stress

0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236

case 1 case 2 case 3

(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)

Figure 25 Distribution of quantitative evaluation indices under different cases (a) Collapse index 119891119887 (b) Fracture index 119891119891

45 Discussion A well located in the Jidong oilfield ofChina is selected as an example to investigate the wellborestability in a mudstone formation According to laboratorytests field data logs and related geological data the cal-culation parameters at the depth of 4100m are defined asoverburden strata stress 916MPa the maximum horizontalstress 812MPa the minimum horizontal stress 687MPaand the formation pressure 425MPa the elastic modulus ofrock 202GPa Poissonrsquos ratio 016 cohesion 241MPa andthe internal friction angle 217∘ permeability of formation101mD and the porosity 9The thermal expansion of rock

media is 54times10minus5 specific heat 886 Jkg∙∘C and thermalconductivity 325 J(m∙∘C) In drilling stage the temperatureof drilling fluid is 10 degrees Celsius lower than that of theformation

The failure process of wellbore is simulated with thedrilling fluid density of 11 12 and 13 gcm3 respectivelyThedistribution of damaged zone caused by drilling unloadingis shown in Figures 28 and 29 In the drilling unloadingthe drilling time is short and thus the borehole stability ismainly controlled by the liquid column pressure of drillingfluid When the drilling fluid density is 11 the failure


0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)

Figure 26 Distribution of quantitative evaluation indices when the formation is heated by drilling fluid (a) Collapse index 119891119887 (b) Fractureindex 119891119891

0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)

Figure 27 Distribution of quantitative evaluation indices when the formation is cooled by drilling fluid (a) Collapse index 119891119887 (b) Fractureindex 119891119891

depth of wellbore is about 007m in the horizontal mini-mum principal stress (EF line) with a maximum equivalentplastic strain of 4574times10minus3 after drilling unloading Withthe increasing of drilling fluid density the failure depthdecreases gradually When the drilling fluid density is 13the failure depth of wellbore is about 002m When thedrilling fluid density is greater than 135 the rock massaround the wellbore is basically in an elastic state and has

reached a stable state which is consistent with that of fieldtesting

According to the failure depths in horizontal and verticaldirection the enlargement rate of wellbore can be defined as(Figure 3)

120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)

Figure 28 The failure distribution of wellbore with different drilling fluid density (a) Drilling fluid density of 11 gcm3 (b) Drilling fluiddensity of 12 gcm3 (c) Drilling fluid density of 13 gcm3

00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F

Density 11 Density 12 Density 13

E

Equi

vale

nt p

lasti

c str

ain

005 010 015 020000Distance from the wellbore wall (m)

(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)

Figure 29 The failure depth of wellbore along EF and BC (a) Along EF (b) Along BC


where 1198770 is the radius of the bit and 119877 = (119877a + 119877b)2 is theaverage radius of wellbore after drilling

The traditional analytical model for collapse pressureprediction is given as [12]

119875119888 = 3120590119867 minus 120590ℎ minus 2119888119870 + [120575120585 + 1205751198991198702 + 120572 (1 + 1198702) (1 minus 120575) 119875119901 + 119864120573119904 (119879 minus 1198790) [3 (1 minus 120583)]]1 minus 120575120585 + 120572120575 + 1198702 (1 minus 120575119899 minus 120572120575) (21)

where 119875119901 is the formation pressure of 119870 = 119888119905119892(45 minus 1206012)120585 = 120572(1 minus 2120583)2(1 minus 120583) and 120575 is the seepage ability coefficientof filtrate cake 120575 = 1 for a permeable wellbore wall and 120575 = 0for an impermeable wall

Although the influence of temperature and seepage abilitycan be considered in the analytical models (Eq (21)) itonly provide a static value that cannot consider the porepressure and effective stress change with time as a transientresponse In the traditional model the wellbore is thoughtinstability once shear failure occurs around wellbore Inpractical engineering the wellbore can be allowed certainlocal failure and the enlargement rate of wellbore can becontrolled within 15 if the rock debris can be carried fromthe bottom of the well in time [23] In this numerical modelthe initial enlargement rate of wellbore is 108 when thedrilling fluid density is 13 As for the drilling fluid density of12 and 11 the wellbore enlargement rate is 181 and 325respectively The actual density of drilling fluid used in thiswell is 13 there is only slight sloughing in the constructionprocess and the stability condition of borehole meets therequirements of drilling construction which is consistentwith the numerical results

According to field data the studied wellbore is stable inthe drilling stages but local instability of wellbore appearsafter 2 days The reason is that the open-hole section is toolong (500m) in mudstone formation and thus the immersiontime of wellbore is increased by drilling fluid Thus thehydration effect cannot be neglected for long time drillingThe hydration effect causes the decrease of rock strengthand the increase of collapse pressure The drilling fluiddensity of 13 at this early stage can support the wellbore tomake wellbore stable but the drilling fluid density must beincreased to 159 after 2 days for keeping the wellbore stablein engineering field Therefore the wellbore instability is adynamic process and the collapse pressure is also a dynamicvalue which cannot be predicted by the traditional analyticalmodel

According to the laboratory tests [24 25] the hydrationeffect causes the surrounding rock to be deteriorated Theinitial water content of this mudstone formation is 2 andthe saturated water content is 10 after long time immersionby drilling fluid The evolution of strength parameters isgiven

119888 = 1198880 minus 27 (119908 minus 1199080)120601 = 1206010 minus 25 (119908 minus 1199080) (22)

where 1198880 and 1206010 are the cohesion and friction angle at initialwater content1199080 respectively and119908 is current water content

The evolution of strength parameters of rock is codedby USDFLD (user subroutine to redefine field variables ata material point) subroutine The enlargement rate curvesof wellbore considering the effect hydration are shown inFigure 30 It can be found that the enlargement rate increaseswith the increase of drilling fluid immersion time and thecollapse pressure increases accordingly

Wellbore stability is affected by in-situ stress drillingfluid temperature change wellbore seepage hydration effectcreep etc According to the above analysis if the immersiontime of wellbore is too long the hydration and creep effectsof wellbore need to be considered which should be coupledwith three fields of THM model The complete couplingbetween hydration creep and THM needs to be furtherstudied theoretically and experimentally

5 Conclusions

Based on continuum mechanics and the theory of mixturesa THM coupling model of rock medium is established andthen it is coded with MATLAB language as platform andABAQUS software as the solver Considering the drillingunloading the numerical model for wellbore analysis isestablished The variation laws of temperature pore pressureand stress around wellbore under different physical fieldcoupling are compared The results show that the stresspore pressure and temperature around wellbore obtained byfull-coupling and partial-coupling are quite different whichprove that the fully coupled model is reasonable for wellborestability analysis

The change of pore pressure near wellbore is large atthe moment of drilling unloading For overbalanced drillingwellbore stability with permeable wall is lower than that ofimpermeable wall Under the condition of underbalanceddrilling the wellbore shrinkage will occur in impermeablewall which makes the wellbore in tension state and reducesthe wellbore stability but the wellbore stability will beimproved by the connectivity of permeable wall Under thecondition of overbalanced drilling something should payattention to the filtrate cake by reducing the disturbance ofdrill string and improving the protected capacity of drillingfluid as much as possible For underbalanced drilling thedrilling fluid should be selected to delay the formation offiltrate cake

As for designing drilling fluid for deep wells and wellswith large temperature gradient the variation of pore pres-sure and thermal stress caused by temperature change shouldbe taken into account When the formation temperature islower than the drilling fluid the possibility of wellbore failureincreases with the increase of temperature difference If the


Density 11 nonhydration Density 12 nonhydration Density 13 nonhydration Density 11 hydration Density 12 hydration Density 13 hydration

0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)

Figure 30 The enlargement rate change with time

drilling fluid temperature is lower than that of the formationthe larger the temperature difference is the smaller theinstability possibility of wellbore occurs In deep well drillingif equipped with cooling drilling fluid equipment it canincrease wellbore stability but also conducive to the normaloperation of logging and downhole instruments

The method proposed in this study provides an effectiveway to analyze the THM coupling process for wellbore andlays a foundation for further study of the THMC couplingproblem on wellbore stability

Data Availability

The data used to support the findings of this study areincluded within the article

Disclosure

Caoxuan Wen is a co-first author

Conflicts of Interest

There is no conflict of interests regarding this paper

Acknowledgments

The authors gratefully acknowledge the support of the OpenResearch Fund of State Key Laboratory of the Oil and GasReservoir Geology and Exploitation (Grant No PLN1507)and theNationalNatural Science Foundation of China (GrantNo 51504040)

References

[1] M A Islam ldquoUnderbanced drilling in shale-perspective offactors influences mechanical borehole instabilityrdquo in Proceed-ings of the international Petroleum Technology Coference DohaQatar 2009

[2] B Wu X Zhang R G Jeffrey and B Wu ldquoA semi-analyticsolution of a wellbore in a non-isothermal low-permeabilityporous medium under non-hydrostatic stressesrdquo InternationalJournal of Solids and Structures vol 49 no 13 pp 1472ndash14842012

[3] S He Y Chen D Ma J Zhou and W Wang ldquoA review onwellbore stability with multi-field coupling analysisrdquo Journal ofSouthwest Petroleum University vol 39 no 2 pp 81ndash92 2017

[4] M A Islam P Skalle A B M O Faruk and B Pierre ldquoAnalyti-cal and numerical study of consolidation effect on time delayedborehole stability during underbalanced drilling in shalerdquo inProceedings of the Kuwait International Petroleum Conferenceand Exhibition KIPCE 2009 Meeting Energy Demand for LongTerm Economic Growth SPE 127554 Kuwait 2009

[5] H Cheng and M Dusseault ldquoDevelopment and applicationof a fully-coupled two-dimensional finite element approach todeformation and pressure diffusion around a boreholerdquo Journalof Canadian Petroleum Technology vol 32 no 10 pp 28ndash381993

[6] H Roshan and S S Rahman ldquoAnalysis of pore pressure andstress distribution around awellbore drilled in chemically activeelastoplastic formationsrdquo RockMechanics andRock Engineeringvol 44 no 5 pp 541ndash552 2011

[7] S Yin B F Towler M B Dusseault and L Rothenburg ldquoFullycoupledTHMCmodeling ofwellbore stabilitywith thermal andsolute convection consideredrdquo Transport in Porous Media vol84 no 3 pp 773ndash798 2010

[8] G ChenM 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

[9] M Frydman and S Fontoura ldquoWellbore stability consideringthermo-poroelastic effectsrdquo in Proceedings of the Rio Oil amp GasConference pp 16ndash19 Rio de Janeiro Brazil 2000

[10] Y Wang and M B Dusseault ldquoA coupled conductivendashconvec-tive thermo-poroelastic solution and implications for wellborestabilityrdquo Journal of Petroleum Science and Engineering vol 38no 3-4 pp 187ndash198 2003

[11] M Li G Liu and J Li ldquoThermal effect on wellbore stabilityduring drilling operation with long horizontal sectionrdquo JournalofNaturalGas Science andEngineering vol 23 pp 118ndash126 2015

[12] C Yan J Deng B Yu et al ldquoBorehole stability in high-temperature formationsrdquoRockMechanics andRock Engineeringvol 47 no 6 pp 2199ndash2209 2014

[13] H Shiming A Wenhua W Shuqi C Mian L Faqian and CJun ldquoEffect of percolation on wellbore stability of underbal-anced drillingrdquo Oil Drilling amp Production Technology vol 30no 4 pp 12ndash18 2008

[14] G Li ldquoThe impact of geological environment on wellholestabilityrdquo Journal of Southwest Petroleum University vol 34 no1 pp 103ndash107 2012

[15] S P Jia L W Zhang B S Wu et al ldquoA coupled hydro-mechanical creep damagemodel for clayey rock and its applica-tion to nuclear waste repositoryrdquo Tunnelling and UndergroundSpace Technology vol 74 pp 230ndash246 2018


[16] Z Zhai K Zaki S Marinello and A Abou-Sayed ldquoCoupledthermo-poro-mechanical effects on borehole stabilityrdquo in Pro-ceedings of the SPE Annual Technical Conference and Exhibition2009 ATCE 2009 SPE 123427 pp 216ndash224 New OrleansLouisiana USA October 2009

[17] M Gomar I Goodarznia and S R Shadizadeh ldquoA transientfully coupled thermo-poroelastic finite element analysis ofwellbore stabilityrdquo Arabian Journal of Geosciences vol 8 no 6pp 3855ndash3865 2014

[18] G Voyiadjis andM Abu-Farsakh ldquoCoupled theory of mixturesfor clayey soilsrdquo Computers amp Geosciences vol 20 no 3-4 pp195ndash222 1997

[19] J J Munoz and J J Munoz ldquoThermo-hydro-mechanical analy-sis of soft rock Application to a large scale heating test and largescale ventilation testrdquo in Dessertation Universitat PolitecnicaDe Catalunya 2007

[20] S Jia X Ran Y Wang T Xiao and X Tan ldquoFully cou-pled thermal-hydraulic-mechanical model and finite elementanalysis for deformation porous mediardquo Chinese Journal ofGeotechnical Engineering vol 31 no S2 pp 3547ndash3556 2012

[21] B Bai ldquoOne-dimensional thermal consolidation characteristicsof geotechnical media under non-isothermal conditionrdquo Engi-neering Mechanics vol 22 no 5 pp 186ndash191 2005

[22] X Li L Cui and J-C Roegiers ldquoThermoporoelastic modellingof wellbore stability in non-hydrostatic stress fieldrdquo Interna-tional Journal of Rock Mechanics and Mining Sciences vol 35no 4-5 p 584 1998

[23] X Weiliang W Yan H Guoli et al ldquoApplication of underbal-anced drilling technology in igneous rock formation gas wellrdquoDrilling amp Production Technology vol 33 no 6 pp 12ndash14 2010

[24] L Chao L Xiangjun D Zhuang and L Meng ldquoExperimentalresearch of shalewellbore stability in an east areardquo West-ChinaExploration Engineering vol 31 no 11 pp 26ndash28 2015

[25] Z Kuanliang C Jinxia and L Shuqin ldquoStudy on stabilitymechanism of brittle shale borehole deep in Nanpu- structureand its applicationrdquo Drilling amp Production Technology vol 39no 5 pp 1ndash4 2016

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influence wellbore stability while instances of instability area result of a combination of coupled effects Analysis involvesstudying the interactions among changes of related effectivestress temperature and pore pressure during drilling processIn the process of overbalanced drilling the pressure ofdrilling fluid column is greater than formation pressurewhich would cause dynamic and static water loss of drillingfluid into formationThe stress state near awellbore is affectedseriously due to drilling fluid into formation For air or foamdrilling (underbalanced) the drilling fluid column pressurecan be lower than formation pressure which may causeformation fluid flow into wellbore resulting in the change ofpore pressure and stress state near wellbore In geothermalenvironments drilling fluid circulation will lead to relativelygreater disturbance near the well resulting in higher thermalstress which will affect wellbore stability More and moreanalytical models on wellbore stability issues have focused oncouplingmechanisms but these studies generally assume thatthe pore pressure around wellbore is the initial pore pressure[12ndash14] When the formation is drilled the equilibriumstate is disturbed causing the stress redistribution aroundborehole The drilling is essentially an excavation unloadingprocess [15] For numerical analysis of wellbore stability moststudies have focused on HM coupling elastic behavior andoverbalanced drilling without considering the influence ofdrilling unloading process stress redistribution filter cakequality and permeability change of the borehole wall [16 17]which is not consistent with the real case

In this article thermal effect and drilling unloadingprocess will be introduced into wellbore stability analysis in anumerical modeling framework to make such analyses moregeneral According to the previous studies the THM coupledmathematical model of rock medium has been proposedand the strategy to solve this model is discussed Then thedrilling unloading fluid flow and thermal effect of wellboreare analyzed in overbalanced drilling and under balanceddrilling and the influence of drilling fluid and thermal effecton pore pressure and stress redistribution around boreholewith time are all discussed

2 Coupled THMModelling Framework forWellbore Stability

21 e Basic Idea of Excavation Unloading Before theformation is drilled the stress state of rock mass is mainlycontrolled by in-situ stress and the stress state in the forma-tion is in equilibrium During the drilling process the initialstress equilibrium in the formation is disturbed causing thestress redistribution around the surrounding rock until a newbalance is reached (as shown in Figure 1)The change of stressand displacement field in the formation caused by drillingis essentially an unloading process After the formation isdrilled the excavated rock in the hole is replaced by drillingfluid and the stress state near the wellbore is redistributedand the mechanical characteristics of the rock around thewellbore will inevitably be affected

For unloading process modelling external boundaryloading method and excavation unloading method are usu-ally used [6 7 15]The displacement obtained by the external

Initial stress equilibrium Drilling unloadingDrilling fluid

Hσ Hσ

hσhσ

Figure 1 Drilling unloading process

boundary loading method is actually a comprehensive resultof the initial stress field and the excavation boundary whichhas no obvious practical significance while the excavationunloading method truly reflects the displacement changescaused by excavation Correct modelling the unloading pro-cess is the key to analyze thewellbore stability in drilling engi-neering The element removing and reactivating techniqueis an ideal method to realize wellbore unloading processwhich is realized bymodifying the stiffness of element set Forelement removing process the element is not really removedbut instead the stiffness of the element is multiplied by a verysmall coefficient (usually 1times10minus6) The mass of the removedelement and other parameters are set to 0 thus the load andstrain of the element is equal to 0

Before the elements are removed the mechanical equilib-rium equation is defined as [15]

P = [K] U (1)

where [K] is stiffness matrix of element U is node displace-ment array and P is the load array

Introducing the parameter 120589119894 to control the elementremoving and reactivating the modified equilibrium equa-tion is given

P = [K] U (2)

where

[K] =[[[[[[[

1205891111989611 1205891211989612 sdot sdot sdot 120589111989911989611198991205892111989621 1205892211989622 sdot sdot sdot 12058921198991198962119899 sdot sdot sdot 12058911989911198961198991 12058911989921198961198992 sdot sdot sdot 120589119899119899119896119899119899

]]]]]]] (3)

22 ermal Transfer Model of Rock Assuming the porosityof a rock element is 119899 the proportion of solid skeleton is 1 minus119899 According to the principle of conservation of energy andFourierrsquos law [16 17] the energy conservation equation of thesolid skeleton is as follows

nabla [(1 minus 119899) 120582snabla119879] + (1 minus 119899) [119902s minus 3119870120573119897 (119879 minus 1198790) 120597120576v120597119905 ]= 120597 [(1 minus 119899) 120588s119888s (119879 minus 1198790)]120597119905

(4)





(5)




120597119905 + (1 minus 119899) 119888s 120597120588s120597119905 + 119899119888f 120597120588f120597119905 ](6)


119896120583f [

12059721199011205971199092 +

12059721199011205971199102 +

12059721199011205971199112 ] = 120572120597119901

120597119905 minus 120573120597119879120597119905 + 120572120597120576V120597119905 + 119876f (7)




10

20

30

40


n0=05n0=07

kk 0



119899 = 1 minus 1 minus 1198990120576v + 1 (8)


3

(9)




d1205901015840119894119895 = d120590119894119895 + 120572120575119894119895d119901 (10)



d120590119894119895 = d1205901015840119894119895 minus 120572120575119894119895119901= 119863e




hσ

HσbR

aR0R

Elastic zone

Damaged zone

Hole


Damaged zone


unstable

failure line

mσ

3

1

(a)

mσ

unstable

failure line

3

1

(b)








119865 = 120590m sin 120601 + 1205901198701015840 minus 119888 cos 120601 = 0 (13)




120590m = 12059010158401 + 12059010158402 + 120590101584033 120590 = radic1198692

(15)




Equi

vale

nt st

ress

σ










119866 = 120590m sin 120593 + radic(1205901198701015840)2 + 11989821198882cos2120593 (18)




(19)




4 Parametric Study





Data conversion


Convergence



No

Yes

End


Data conversion

ABAQUS



ElasticmodulusMPa

Poissonrsquosratio

CohesionMPa

Frictionangle∘

TensilestrengthMPa

PorosityThermal




2 000 02 8 30 12 02 308 15times10minus5 840


BulkmodulusMPa





ms





vσ

Hσhσ

x

z

y




(a) (b)





XY

Z

Vertical stress

Fixed displacement







Drilling fluid





S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)










C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018












(5)




120597119905 + (1 minus 119899) 119888s 120597120588s120597119905 + 119899119888f 120597120588f120597119905 ](6)


119896120583f [

12059721199011205971199092 +

12059721199011205971199102 +

12059721199011205971199112 ] = 120572120597119901

120597119905 minus 120573120597119879120597119905 + 120572120597120576V120597119905 + 119876f (7)




10

20

30

40


n0=05n0=07

kk 0



119899 = 1 minus 1 minus 1198990120576v + 1 (8)


3

(9)




d1205901015840119894119895 = d120590119894119895 + 120572120575119894119895d119901 (10)



d120590119894119895 = d1205901015840119894119895 minus 120572120575119894119895119901= 119863e




hσ

HσbR

aR0R

Elastic zone

Damaged zone

Hole


Damaged zone


unstable

failure line

mσ

3

1

(a)

mσ

unstable

failure line

3

1

(b)








119865 = 120590m sin 120601 + 1205901198701015840 minus 119888 cos 120601 = 0 (13)




120590m = 12059010158401 + 12059010158402 + 120590101584033 120590 = radic1198692

(15)




Equi

vale

nt st

ress

σ










119866 = 120590m sin 120593 + radic(1205901198701015840)2 + 11989821198882cos2120593 (18)




(19)




4 Parametric Study





Data conversion


Convergence



No

Yes

End


Data conversion

ABAQUS



ElasticmodulusMPa

Poissonrsquosratio

CohesionMPa

Frictionangle∘

TensilestrengthMPa

PorosityThermal




2 000 02 8 30 12 02 308 15times10minus5 840


BulkmodulusMPa





ms





vσ

Hσhσ

x

z

y




(a) (b)





XY

Z

Vertical stress

Fixed displacement







Drilling fluid





S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)










C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









hσ

HσbR

aR0R

Elastic zone

Damaged zone

Hole


Damaged zone


unstable

failure line

mσ

3

1

(a)

mσ

unstable

failure line

3

1

(b)








119865 = 120590m sin 120601 + 1205901198701015840 minus 119888 cos 120601 = 0 (13)




120590m = 12059010158401 + 12059010158402 + 120590101584033 120590 = radic1198692

(15)




Equi

vale

nt st

ress

σ










119866 = 120590m sin 120593 + radic(1205901198701015840)2 + 11989821198882cos2120593 (18)




(19)




4 Parametric Study





Data conversion


Convergence



No

Yes

End


Data conversion

ABAQUS



ElasticmodulusMPa

Poissonrsquosratio

CohesionMPa

Frictionangle∘

TensilestrengthMPa

PorosityThermal




2 000 02 8 30 12 02 308 15times10minus5 840


BulkmodulusMPa





ms





vσ

Hσhσ

x

z

y




(a) (b)





XY

Z

Vertical stress

Fixed displacement







Drilling fluid





S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)










C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018










Equi

vale

nt st

ress

σ










119866 = 120590m sin 120593 + radic(1205901198701015840)2 + 11989821198882cos2120593 (18)




(19)




4 Parametric Study





Data conversion


Convergence



No

Yes

End


Data conversion

ABAQUS



ElasticmodulusMPa

Poissonrsquosratio

CohesionMPa

Frictionangle∘

TensilestrengthMPa

PorosityThermal




2 000 02 8 30 12 02 308 15times10minus5 840


BulkmodulusMPa





ms





vσ

Hσhσ

x

z

y




(a) (b)





XY

Z

Vertical stress

Fixed displacement







Drilling fluid





S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)










C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018











Data conversion


Convergence



No

Yes

End


Data conversion

ABAQUS



ElasticmodulusMPa

Poissonrsquosratio

CohesionMPa

Frictionangle∘

TensilestrengthMPa

PorosityThermal




2 000 02 8 30 12 02 308 15times10minus5 840


BulkmodulusMPa





ms





vσ

Hσhσ

x

z

y




(a) (b)





XY

Z

Vertical stress

Fixed displacement







Drilling fluid





S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)










C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b)





XY

Z

Vertical stress

Fixed displacement







Drilling fluid





S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)










C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









S S11(Avg 75)

-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07-3000e+07

Y

X

(a)

S S22(Avg 75)

-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06-9000e+06

Y

X

(b)

Y

X

POR(Avg 75)

+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07+4500e+07

(c)










C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









C


9 h 24 h

B

minus30

minus27

minus24

minus21

minus18

minus15

minus12

minus9

minus6

minus3

0Ra

dial

stre

ss (M

Pa)


(a)


9 h24 h

B C


minus8minus6minus4

Radi

al st

ress

(MPa

)


(b)




02


9 h 24 h


Hoo

p str

ess (

MPa

)

(a)

0 1 2 3 4 5 6 7 8 9 10minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0


9 h 24 h

Hoo

p str

ess (

MPa

)


(b)







0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









0 5 10 15 20 25 30 3526283032343638404244464850


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)

Pore

pre

ssur

e (M

Pa)

0 5 10 15 20 25 30 35

242628303234363840424446


9 h 24 h


(b)












0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









0

30

60

90

120

150

180

210

240

270

300

330

06

08

10

12

14

16

18

20

22

06

08

10

12

14

16

18

20

22


(a)

0

30

60

90

120

150

180

210

240

270

300

330

0123456789

0123456789


(b)



0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









0 1 2 3 4 5 6 7 8 9 10minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

Radi

al st

ress

(MPa

)



9 h 24 h

(a)

Radi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus32

minus28

minus24

minus20

minus16

minus12

minus8

minus4

0

4



9 h 24 h

(b)


0 1 2 3 4 5 6 7 8 9 10minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

Hoo

p str

ess (

MPa

)



9 h 24 h

(a)

Hoo

p str

ess (

MPa

)

0 1 2 3 4 5 6 7 8 9 10

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8


9 h 24 h


(b)






0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









0 5 10 15 20 25 30 35

2628303234363840424446


9 h 24 h

Pore

pre

ssur

e (M

Pa)


(a)


9 h 24 h

Pore

pre

ssur

e (M

Pa)


0 5 10 15 20 25 30 352022242628303234363840424446

(b)


0

30

6090

120

150

180

210

240270

300

330

06

08

10

12

14

16

06

08

10

12

14

16


(a)

0

30

6090

120

150

180

210

240270

300

330

0

1

2

3

4

5

6

1

2

3

4

5

6


(b)


T

H M

T

H M

T

H M




TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









TEMP(Avg 75)

+1200e+02+1161e+02+1122e+02+1084e+02+1045e+02+1006e+02+9672e+01+9284e+01+8896e+01+8508e+01+8120e+01+7732e+01+7344e+01

Y

X

(a)

TEMP(Avg 75)

+1197e+02+1157e+02+1117e+02+1077e+02+1037e+02+9972e+01+9573e+01+9174e+01+8775e+01+8376e+01+7977e+01+7578e+01+7179e+01

Y

X

(b)

TEMP

Y

X



65707580859095

100105110115120125


Tem

pera

ture

(∘C)



353637383940414243444546


Pore

pre

ssur

e (M

Pa)







minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018












minus8minus6

Radi

al st

ress

(MPa

)

(a)


minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

Hoo

p str

ess (

MPa

)


(b)


0812162024283236

0

30

6090

120

150

180

210

240270

300

330

0812162024283236


(a)

2468

10121416

0

30

6090

120

150

180

210

240270

300

330

2468

10121416


(b)






0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









0

30

6090

120

150

180

210

240270

300

330

06081012141618

06081012141618

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

1234567

1234567

T-T0=35 T-T0=20 T-T0=10

∘C∘C∘C

(b)


0

30

6090

120

150

180

210

240270

300

330

0510152025303540

0510152025303540

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(a)

0

30

6090

120

150

180

210

240270

300

330

2468

10121416

2468

10121416

T-T0=-50 T-T0=-35 T-T0=-20

∘C∘C∘C

(b)





120596r = 119877 minus 11987701198770 times 100 (20)


PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018









PEEQ(Avg 75)

+4574e-03+4192e-03+3811e-03+3430e-03+3049e-03+2668e-03+2287e-03+1906e-03+1525e-03+1143e-03+7623e-04+3811e-04+0000e+00

X

Y

(a)

PEEQ(Avg 75)

+2906e-03+2664e-03+2422e-03+2179e-03+1937e-03+1695e-03+1453e-03+1211e-03+9686e-04+7265e-04+4843e-04+2422e-04+0000e+00

X

Y

(b)

PEEQ(Avg 75)

+1567e-03+1436e-03+1305e-03+1175e-03+1044e-03+9138e-04+7833e-04+6527e-04+5222e-04+3916e-04+2611e-04+1305e-04+0000e+00

X

Y

(c)


00

10x10minus3

20x10minus3

30x10minus3

40x10minus3

50x10minus3

F


E

Equi

vale

nt p

lasti

c str

ain


(a)

00

50x10minus5

10x10minus4

15x10minus4

20x10minus4

25x10minus4


CB

Equi

vale

nt p

lasti

c str

ain


(b)














5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018




















5 Conclusions






0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018










0

10

20

30

40

50

60

70

80

90

100

Well

bore

enla

rgem

ent r

ate (

)

2 4 6 8 10 12 140Time (day)




Data Availability


Disclosure




Acknowledgments


References


































Journal of












Journal of







Volume 2018






Volume 2018


























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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