1. INTRODUCTION

Drilling with a bottomhole pressure less than the formation pore pressure (Underbalanced Drilling, UBD) usually increase the risk of borehole instability due to yielding or failure of the rock adjacent to the borehole. However, if the borehole would overcome the initial failure risk, the risk of instability is reduced if wellbore pressure and pore pressure are equilibrated. But due to the extremely low permeability of shale, the pore fluid cannot flow freely [7-11]. Both drained and undrained fluid flow mechanisms and their impact on evolving strain are demanding to be clarified. Underbalanced drilled wells in shale usually bring up mechanical borehole collapse challenges [1-3, 10]. Fig.1 presents several hypothesis of near wellbore stress pattern for UBD candidates. The critical region is indicated by a blue shaded area where the shear and radial tensile failure are the resultant mechanisms to cause borehole

instability. Shear failure of the borehole wall will take place when the stress concentration around the borehole exceeds the compressive strength of the rock, whereas sufficient negative effective radial stress promotes radial tensile failure [7,10, 11,12]. Both of these failure mechanisms are associated with pore pressure consolidation, material dilation, redistributed borehole stresses and rock strength. The evaluation criterion of these failure mechanisms are complex and very often diagnosis does not agree with field operational practices. But, the accuracy of predictions of material failure state under undrained circumstances around the wellbore are essential in order to address wellbore instability problems. Using an adequate constitutive model for shale is vital in obtaining better predictions of the stress changes and rock deformation. However, an improved understanding of the behavior of shale during UBD will enable the main features to be included and facilitate more rational predictions. To fulfill such aims, a

ARMA 10-433

Evaluation of Consolidation and Material Yielding during Underbalanced Drilling Well in Shale - A Numerical Study

Islam, M.A. Deaprtment of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, NTNU, Trondheim, Norway

Skalle, P. Deaprtment of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, NTNU, Trondheim, Norway

Søreide, O.k. STATOIL, Trondheim, Norway.

Copyright 2010 ARMA, American Rock Mechanics Association

This paper was prepared for presentation at the 44th US Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium, held in Salt Lake City, UT June 27–30, 2010.

This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or

ABSTRACT

Establishment of pore pressure equilibrium in shale is a time dependent process which is governed by shale’s intrinsic properties. The extremely low permeability of shale is a key parameter involved in the consolidation process and restriction of fluid flow (undrained mechanism). Underbalanced drilling in shale usually increases the risk of borehole instability due to yielding or failure of the rock adjacent to the borehole. In addition, shale has both a ductile and brittle nature. Material plasticity is strongly influenced by the consolidation and material dilation process. The distribution of pore pressure is taking a crucial role in the consolidation process, and has to be clarified for undrained mechanism. Therefore, the aim of this work is to quantify pore pressure distribution and material yielding when the borehole reaches underbalanced conditions. The M-C elasto-plastic numerical material model was applied to accomplish the study goal. The simulation results indicated that with decreasing mud pressure increased yielding in the dilating region took place. Time delayed pore pressure distribution is influenced by material dilation. Pore pressure distribution behaved anomalously after yielding. Here the dilating angle seemed to be the critical parameter. The outcome of this study will help to understand the physics of material yielding and the impact of consolidation on time delayed borehole instability.  KEYWORDS: wellbore stability, UBD, shale, yielding, dilation, pore pressure distribution, finite element method.

Pp

σr

Rw

P

r/Rw

Pf

Pfo , t = 0

Pf , t = α

Consolidation effect, under UBD condition

Shear & radial tensile failure zone

Pp

σr

Rw

P

r/Rw

Pf

Pfo , t = 0

Pf , t = α

Consolidation effect, under UBD condition

Shear & radial tensile failure zone

numerical material model was developed with the ability to evaluate and quantify time delayed borehole failure risk under UBD operation in shale, by addressing: - Quantitative time delayed pore pressure

distribution with material dilation for undrained circumstances.

- Material deformation and plasticity effect.

First, we present time delayed transient pore pressure behaviour under geostatic condition in shale based on the M-C elastio-plastic material model [5]. The objective here is to recognize the transient nature of the stresses and pore pressure around the wellbore in underbalanced borehole. Sensitivity analyses provided factors that influenced material yielding and dilations. It was shown how such effects have to be accounted for in modeling of time delayed borehole instability. In addition to this, one aim in present paper is to evaluate the displacement and plastic deformation of the borehole. Rock failure is in this model associated with the transition from elastic to plastic behavior. Experimental analysis of directional mechanical properties and characterization of published and performed Pierre-1 shale under undrained condition were used to develop a numerical model. Laboratory observations were accompanied with numerical outcome. 2. GEOMECHANICAL EFFECTS IN THE NEAR

WELLBORE REGION During drilling of a well, there is the possibility for evolution of different zones of transmissibility and stiffness around a well, see Fig. 2. Potential zones that may exist around a wellbore while drilling in underbalanced are illuestrated. These zones are mechanically induced and are not associated with chemical instability. Some or all of the zones may lead to material failure. The potential zones are [12]:

1. A disaggregated zone : This zone can occur when the material surrounding the wellbore is allowed to dilate to the point of liquefaction where rock particulates are physically separated.

At the limit, hydrodynamic forces can move this material out from that zone.

2. A dilatant zone : Dilatancy occurs when loose

packing contract or dense packing expands during shearing. The volumetric strain is increasing whereas elastic constants are decreasing. Changing load path for UBD wells, can lead to a dilated zone depending on the proximity of the material to failure in the near wellbore region.

3. A compacting zone : compaction increase, this

zone may surround the dilatants’ region.

4. Elastic : The rock deforms elastically. 5. Virgin properties: Rock that has not reached a

failure surface; with.

Analysis of material yielding and dilating at around the borehole is a central feature of this paper.

3. ANALYSIS OF MATERIAL YIELDING 3.1 M-C Elastic-Plastic Model: Undrained Borehole Wall A 2-D & 3-D numerical material models was developed by using the finite element method (FEM). This model was developed for analysis of material yielding and time delayed pore pressure trends under undrained borehole condition. The model works based on M-C elasto-plastic materials under geostatic stress conditions. The virtual borehole and the applied stresses are represented by a cubic block of hard rock (i.e., shale). It includes a borehole drilled through its center; see Fig 3a. For model simplicity, four nodes, plane strain quadrilateral bilinear

Fig.1. Borehole stresses in UBD condition.

elastic

compacting

dilatant

disaggregated

wellbore

Virgin/Intact

Fig.2. Schematic drawing of radially damaged/altered zones around a wellbore.

solid continuum infinite elements were used. To avoid boundary effects, this model was designed by using infinite element segments at the extension of the model. Due to symmetry consideration, only a quarter of the structure (90 degrees on the horizontal plane) was analyzed. An 8.5 inch (22 cm) diameter hole was modeled with plane strain conditions. The schematic projection of the borehole and borehole radial distance is shown in Fig. 3b where in-situ stresses are situated at the boundary and pore pressure (Pf) is employed at the entire projection of the model. Initially pore pressure remains same at every node points but it trend to decrease at the near borehole wall when drilled through. Transient pore pressure trend exists. It is therefore a vital issue to set the accurate BC for Pf under an undrained borehole mechanism. Without accurate BC of Pf, the system would be numerically shocked and behaved anomaly. BC for horizontal planes is shown in Fig. 3c which indicate that borehole displacement is allowed only in the x and y directions. BC of undrained borehole is illustrated in Fig. 3d which inferred that fluid flow is restricted from the borehole to the reservoir. The developed numerical model has not employed gravity (vertical borehole) and chemical instability effect (restricted fluid communication between borehole and formation). The simulated wellbore can be rotated at 0, 15, 30, 45, 60, 75 and 90 degrees from the vertical axis, in a plane perpendicular to σH to quantify the borehole inclination effect on the material failure state. The differential stress is maximum on this particular plane (1-3) and represents the worse case. This paper is limited to focus on vertical borehole analysis only. Input file: A standard keyword version input material model is developed by using Finite Element Method (FEM) for underbalanced drilling in Pieere-1 shale and simulated the model through ABAQUS/CAE. This model is characterized by transient pore pressure distribution; recycling of borehole stresses, and material yielding subject to undrained circumstances. Borehole traction was used to confirm undrained conditions between borehole and formation fluids. Mean average horizontal stresses were used to achieve model simply. Mechanical properties of Pieere-1 shale were used as input into the developed material model. Extensive triaxial and hollow cylinder laboratory test of Pieere-1 shale were performed the shale intrinsic properties were characterized. This model is able to update and perform sensitivity analysis which may address material yielding and transient pore pressure distributed around the borehole walls which are influenced by material dilation, poison’s ratio, material friction angle, UCS, etc.

Model Assumptions:

Elasto-plastic material. Fixed contact between the modeled rock, and

both the underlying and the overlying rock. Incompressible fluid (water based mud) Thermal and cooling effects are neglected. Impermeable borehole wall (undrained

mechanism). Week heterogeneous formation (Pieere-1 shale).

3.2 Simulation Steps Some basic steps listed below in a step-wise fashion describe the model generation and evaluation.

• Structured nodes, elements and sets of the model geometry.

• Defined material and fluid properties. • Defined initial in-situ stresses including pore

pressure and applied boundary condition (BC) according to Fig. 3b. At loading phase following the conditions are valid at borehole:

i) Pf =Pw ii) h = Pw iii) = 0

• Employed BC for removal of cuttings by borehole mud.

• Gradually decreased mud pressure to reach and pass UBD condition. Set the BC conditions for borehole pressure reduction and establish consolidation to quantify material yielding and transient Pf. Hardening effect is accounted for changing the dilating angle. Rate dependent borehole displacement need to be clarified both experimentally and numerically and calibrated. But such type of study is outside the scope of this paper.

• Calculate the induced force components (normal & shear) at every node surrounding the borehole wall see Fig. 3d. Shear force is accounted for at inclined nodes points. The model accounts for induced force components together with existing in-situ stresses.

• The following is evaluate: i) Material yielding & dilation in terms of

material plasticity. ii) Transient pore pressure distribution over

simulation steps. iii) Minimum mud weight to prevent

borehole collapse. iv) Time delayed MW window.

σH

r/Rw

Pf

Pfo , t = 0

Pw

σh

σV

σH

r/Rw

Pf

Pfo , t = 0

Pw

σh

σV

x

y

t*

Pwell , MPa

Pi =48.5

0

01

0 1

SimulationReducing mud weight

48.5 Mpa to 0

Initial conditionGenerate mud weight

0 to 48.5 Mpa

0.255 0.26

Pyield = 36.12

Pw,c = 35.9

t*

Pwell , MPa

Pi =48.5

0

01

0 1

SimulationReducing mud weight

48.5 Mpa to 0

Initial conditionGenerate mud weight

0 to 48.5 Mpa

0.255 0.26

Pyield = 36.12

Pw,c = 35.9

a)

Pw

σh

σv

σH

Pw

σh

σv

σH

b)

c)

d)

Pw

x

yn

m

X

Y Hhn ,,,

Fig. 3. Numerical model and its components: a) virtual borehole showing in-situ stress direction, b) geostatic pressure employed at model, c) borehole boundary conditions in the horizontal plane d) impermeable borehole wall (undrained) with induced force components at the nodes.

Fig. 4. Simulation flow chart to evaluate borehole collapse risk. First loading and then gradually reducing mud pressure to reach UBD conditions.

A simple sketch was presented in Fig. 4 to show how the model predicts material yielding followed by gradual reduction of mud weight (MW). According to Fig. 4, the minimum MW to prevent borehole collapse is:

gD

tPwwell

*)0( 1

[1]

Here ρwell is the minimum MW to avoid borehole collapase. Pw,o is the initial mud pressure, t* is the simulation step time, g is gravity and D is depth of interest. 3.3 Sensitivity Analysis A sensitivity analysis was performed to examine how the model inputs parameters impact on material yielding on distribution of transient pore pressure, and on borehole displacement. Parameters of interest are:

Dilating angle. Elastic vs. elasto- plastic material. Material behavior for empty and undrained

borehole. Time delayed MW window.

Poisson’s ratio, material stiffness and rate dependent analysis is also vital for evaluation of material yielding. Dilating Angle This undrained material model is sensitive for material dilation because pore pressure distribution is strongly influenced by material dilation. Thus, it is essential to investigate the effect of material dilation on material yielding and pore pressure distribution around the borehole wall. Literature survey implied that pore

pressure would be reduced drastically with increasing material dilation [7-9]. The key reason is, under such situations material goes through a hardening phase and allows the material to expand, eventually increasing the pore volume resulting in decreased Pf. For a case sensitive analysis the model was tested for different dilating angles (0, 5, 20 and 30 degrees) to quantify material plasticity and transient Pf. Some results are shown in Figs. 5 & 6 (yielding for dilation angle 5 & 0 degrees) and Figs. 7 & 8 (Pf distribution for dilation angle 5 & 0 degrees). The necessary material properties and geostatic stresses used in this study are presented in Table 1 & 2. Table 1. Mechanical properties of Pierre-1 shale (undrained condition) when sample bedding is perpendicular to loading ( = 00).

θ Degr

UCS MPa

Degr

UCS MPa

E GPa

-

Degr

0 9.72 25 9.72 1.33 0.46 5 Material and fluid intrinsic properties:

Permeability: 14 D Fluid viscosity: 1 cP Void ratio: 0.33 Tensile strength: 0.62 Mpa

Table 2. Geostatic stresses under normal in-situ stress regimes. Data taken from [3].

In- situ Symbol Magnitude Unit

Vertical stress σV 52.5 MPa

Max. horizontal stress σH 50.5 MPa

Min. horizontal stress σh 46.5 MPa

Mean average horizontal stress

(σh+ σH)/2 48.5 Mpa

Pore pressure Pf 40 MPa

Initial mud pressure Pw 48.5 MPa

Simulated results show that the M-C, elasto-plastic numerical model is acceptably predicting mechanical failure stress state. The model enables to quantify material dilation and yielding effects at the near borehole wall region. The plastic zone spreads with decreasing mud weight after yielding (see Fig. 5 & 6). A quite large plastic area was obtained because the M-C elasto- plastic model is normally designed for large deformation and low MW. Initial mud pressure for this study was chosen to be 48.5 MPa while initial pore pressure was 40 MPa. For this study, MW was designed to decrease gradually during simulation to meet an UBD situation for evaluation of borehole failure risk. It was found that the material entered the yielding position when MW was reduced to 35.9 MPa (see Fig. 5a; for dilating angle of 5 degrees)

and to 35.89 MPa (see Fig. 6a for dilating angle of 0 degrees). It is seen that the dilating angle influences yielding to some extent but for distributed pore pressure the impact is extreme (discussed at a later stage). The consolidated pore pressure was established at 38.38 MPa (see Fig. 7a & 8a), which indicate that UBD may be possible to some extent and recommended mud pressure might be greater than 36.5 MPa at the present borehole collapse conditions. Outside of this yield region, the material remains elastic. Figs. 5 & 6 (b & c) and Figs. 7 & 8 (b & c) are showing an increase in the yielding region, which is the dilating region. At the end, the transient Pf is negative due to the boundary condition (untrained condition). The pore pressure should mathematically not go below zero [9]. The possible reasons for achieving negative transient Pf

is discussed at a later stage. In fact, negative Pf, is not a prime issue, it can be controlled by adjusting BC. If Pf boundary condition is applied as a drained (fluid communication between borehole and formation) at the ‘borehole’ nodes, the developed model will work under drained mechanisms. In this case, transient Pf would be equal as Pw at the yielding phase. A separate study will evaluate material yielding and Pf distribution under a drained situation.

After initiation of yielding, the dilation angle becomes a major factor for Pf distribution and the situation is extreme when material reaches at massive plastifying area. For example, Fig. 8 (c) is showing that Pf did not reach negative magnitudes compared to Fig. 7(c). This fact together with the observation that when material dilating angle goes to zero, in spite of undrained borehole, Pf distribution does not become negative. However, the magnitude of this distributed Pf was very small compared to the initial Pf which is not a vital issue since we are interested in seeing transient Pf effects at the material yielding phase. In that regards, it is seen that:

With dilating angle of 5 degrees the transient pore pressure at yield point was 38.83 MPa and at the end of the simulation process it has turned negative (Fig. 7). Up to yielding, Pf reduced 1.17 MPa.

With dilating angle of 0 degrees the Pf at yield point was 39.83 MPa and at the end it was not negative (Fig. 8). Up to yielding, Pf reduced 0.17 MPa.

Several reasons may be account for to explain the localized negative Pf. From a theoretical points of view, negative transient Pf implies that the stress model is

tensile instead of compressive (bullet 1 above). But from a practical point of view, pore fluid cannot be felt tensile mode. As water movement in shale is best described by a total aqueous potential difference between shale and wellbore water, which is restricted due to plasticization and undrained borehole. At this position the rock is in a plastifying state and loss its strength. The plastic deformation generates a volume increase, due to insufficient mud support and material dilation, consequently a sharp reduction of Pf will occur. Thus, at the simulation end point, the imposed BC may be responsible of the transient Pf anomaly.

The negative Pf distribution may also result in oscillation. It can happen when the required time increment to complete simulation is less than the minimum time presented through Eq. 2.

required mint t (2)

To avoid oscillation, it is necessary to confirm the Eq.3 condition in the developed model:

required mint t (3)

However, based on the above discussion it is seen that negative transient Pf was not found when model ran with dilating angle equal to zero. Oscillation effects may therefore not be involved to cause anomaly of Pf. It is crucial for borehole the selection of boundary conditions (drained or undrained) to evaluate time delayed failure.

Plastified zones lead to softening around the borehole, but may serve as a support to the rock behind. A borehole failure criterion can be specified by a critical amount of plastic strain, or by a critical extent of a plastic zone. From material behavior response, it is seen that elastic brittle material did not bear any load after failure initiation, while elasto-plastic material can still sustained load after failure initiation [6]. This study can quantify plastic initiation conditions and assess failure associated components. Plastic strain and borehole displacement is evaluated and presented in Fig. 9. This study confirms that borehole deformation is exponentially reduced with increasing normalized borehole distance (r/Rw).

Eastic vs. Elasto-Plastic Material

Elastic and plastic material behaviour under in-situ stress field have been reported by Islam et al [2] and Gil and Roegiers [6] and simulated results are presented in Fig. 10. From these works it is seen that elasto-plastic rocks are able to store more energy when deformed. This will

ensure more stable borehole under the same loading conditions than a normal elastic rock. Elastic rock imposed maximum stress while for elasto-plastic rock the stress load was reduced at the borehole wall [see Fig. 10]. Recently, Islam et. al., [4] performed an elastic model comparative study between M-C and Mogi-Coulomb (see Fig. 11) to evaluate borehole collapse risk. For vertical wells, the Mogi-Coulomb model predicted minimum mud pressure to prevent borehole collapse to 39.25 MPa while for elasto-plastic material it was 36.5 MPa. The mean relative difference of CP between elastic and elasto- plastic model (in absolute value) was about 7 %. In this particular case the M-C elasto-plastic material model would require 7 % lower mud weight than in an elastic material to prevent borehole collapse. Empty Borehole Similarily, numerical analysis has to be performed for vertical boreholes applying empty borehole pressure. Material dilation and borehole displacement was clarified. Simulated results are shown in Fig. 12 and in Appendix A. It is seen that material yielding is large due to missing mud support at the borehole wall. Similarly, Pf distribution was found like for the 2-D model as discussed above. A large dilated zone and borehole deformation were found. However, such a model is unable to detect the material failure point. A discrete particle model is therefore recommended to identify the material failure initiation point. This model is directly applied for the tunnel design. Time Delayed MW window Transient pore pressure distribution improved the stability for UBD wells [5]. A comparative study of time delayed MW is presented in Fig 13. It is found that the initial risk for UBD wells is a vital subject to borehole collapse. Afterwards the stability is gradually improved. For this particular case study the borehole was open for 27 hours to evaluate the time delayed MW window. The MW window was improved by about 4.15 %. From the above discussion it may be mentioned that the developed M-C elasto-plastic model enables us to quantify plasticity effects for UBD candidates. But more in-depth studies within the specific interest section is needed.

a)

b) c)

Fig. 5. Material yielding in the dilating region with decreasing well pressure keeping dilating angle at 5 degrees, a) Started yielding, when Pw = 35.9 MPa, b) Spreading plasticity area when Pw = 18.43 MPa, c) Empty borehole, Pw = 0 MPa. Model input data from Table 1 & 2.

a)

b)

Fig. 6. Material yielding in the dilating region with decreasing well pressure keeping dilating angle at 0 degree, a) Started yielding, when Pw = 35.9 MPa, b) Empty borehole, Pw = 0 MPa. Model input data from Table 1 & 2.

a)

b)

c)

Fig. 7. Pore pressure trend with dilating angle of 5 degree under undrained borehole condition, a) Pore pressure variation at material yielding position, b) Spreading plasticity area and dramatically reduced pore pressure. c) Pore pressure goes to negative at Pw = 0. Model input data were taken from Table 1.

a)

b)

c)

Fig. 8. Pore pressure trend with dilating angle 5 degree under undrained borehole condition; a) Pore pressure variation at material yielding position, b) Spreading plasticity area and dramatically reduced pore pressure, c) Pore pressure magnitudes low but not negative at Pw = 0. Model input data were taken from Table 1.

Fig. 9. Borehole displacement for UBD wells. Plastic strain is exponentially decreasing with increasing true radial distance from the borehole wall. Data were taken from simulated 2-D model.

Fig. 10. Numerical result of induced stresses at borehole wall under normal in-situ stress state conditions. Elastic and elastoplastic (ep) material behaviour were quantified [2]. Material behavior under the three different in-situ stress magnitudes where evaluated. Similar in- situ stress data sets were used in case 3 (elastic 3 and ep3) and in current study. Table A-1 is presenting data sets for Fig. 10.

0 10 20 30 40 50 60 70 80 9039

40

41

42

43

44

Inclination [Degree]

Colla

pse

Pre

ssure

[M

Pa]

azimuth 04590

Fig. 11. Collapse Pressure prediction for elastic material through a Mogi-Coulomb model [4].

a)

b)

Fig. 12. Yielding and pore pressure trend when borehole missing mud support. a) Material yielding zones b) Transient pore pressure distribution. Model input data were taken from the Table 1.

0 20 40 60 80 1001.6

1.65

1.7

1.75

Angle [Degree]

Min

imu

m M

ud

Weig

ht

[s.g

]

After 27 HoursWithout Time Effect

Fig. 13. Time delayed MW window [5].

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

True Radial Distance [m]

Str

ain

Equivalent Plastic Strain

Magnitude Plastic Strain

0 10 20 30 40 50 60 70 80 9010

20

30

40

50

60

70

80

90

Borehole Inclination, degree

S

tres

s at

Bo

reh

ole

wal

l, M

Pa

Maximum stress at borehole

elastic3

ep3

elastic2

ep2

elastic1

ep1

4. CONCLUSIONS We propose a reasonable accurate way to compute “transient pore pressure behaviour and time delayed material failure” for UBD wells in shale. It enables the computation of material yielding, borehole deformation, transient pore pressure trend, borehole stress distribution, borehole collapse pressure etc. These attributes can be used at various steps of the borehole design workflow. We believe our approach exhibits a significant improvement to borehole collapse assessment for UBD wells in shale. It may help to obtain a proper diagnosis of material failure and thus a reduction of instability during UBD wells and also confident for designing Over balanced wells. The recommended MW differs when it is obtained by analytical (elastic) or by numerical models (elasto-plastic). The difference is caused by time dependent transient Pf effects on elasto-plastic rock which can sustain load even after failure initiation. The mean relative difference of borehole collapse pressure improvement was (in absolute value) 7% by applying the elasto-plastic material compared to the elastic material. Time delayed pore pressure increased the borehole stability for UBD wells if the borehole would overcome the initial failure risk. Elasto-plastic rocks are able to store more energy during deformation. The borehole wall of elasto-plastic rocks experience lower stress compared to elastic rocks. This will ensure more stable borehole for elasto-plastic rocks under the same loading conditions compared to a normal elastic rock. The dilating angle is a critical parameter to address in conjunction with time delayed Pf distribution under undrained borehole mechanisms. With increasing dilating angle it is indicated that the near borehole stress model is super critical for evaluation of transient Pf. Transient Pf is reduced drastically with increasing material dilation specifically when the material starts to plastify after yielding. Since several real–life situations were evaluated, the potential applicability of the results obtained here is apparent; adaption of such technique in drilling of hard rock and the results of these simulations could be used as a cross check for more particular situations in the field. Findings of this study can be useful for further research within the same area.

5. ACKNOWLEDGEMENT The authors want to thank IPT, NTNU for supporting and giving permission to write this paper. We would like to express our appreciation to Prof. Thomas Benz and PhD candidate David Unteregger, , both of Department of Geotechnical Engineering, Erling Fjær, SINTEF Petroleum Research and Bård Bostom, STATOIL for their contribution to the development of the numerical model and for discussion of critical issues in this work. We are thankful to STATOIL for providing funds towards the experimental investigation of borehole stability. Also, the extensive laboratory work carried out and partly funded by SINTEF Petroleum Research. This is appreciated and acknowledged.

6. NOMENCLATURES AND ABBREVIATION

Symbol Meaning Unit σV Vertical stress MPa σh Min. horizontal stress MPa σH Max. horizontal stress MPa σθ Tangential or hoop stress MPa σz Axial stress MPa σr Radial stress MPa σ Shear stress MPa Pf Pore pressure MPa Pfh Hydrostatic pressure MPa Pw Wellbore pressure MPa f Fluid viscosity D Poisson,s ratios - C0 Uniaxial compressive strength MPa c Cohesion MPa

To Tensile strength MPa Orientation of failure angle Degrees m Slope of induced force Degrees Material friction angle Degrees Dilating angle Degrees E Young modulus GPa T Tensile strength MPa

Abbreviation:

UCS : Uniaxial Compressive Strength CP : Collapse Pressure M-C : Mohr -Coulomb

MW : Mud Weight

UBD : Underbalanced Drilling OBD : Overbalanced Drilling OP : Over Pressure BC : Boundary Condition

Unit conversion: 1 nD = 10-21 m2/s 1 cP = 10-3 Pas

7. REFERENCES [1]. Søreide, O.K., Bostom. B., and Horsrud., P., 2009 “

Borehole stability simulations of an HPHT field using anisotropic shale modelling”, In Proceedings of the ARMA , Conference, Asheville, North Carolina, June 28 th – July 1, 2009.

[2]. Islam, M.A., Skalle, P and Tantserev E. 2009

“Underbalanced Drilling in Shales- Perspective of Mechanical Borehole Instability” In proceedings of the IPTC 09/SPE drilling conference, Quater, December 7-9.

[3]. Islam, M.A., Skalle. P., 2009 “Prediction And

Evaluation Of Boreholes Shear Failures Risk In Shale Under In-Situ Stress State - A Sensitivity Analysis”” In proceedings of the international conference of mechanical engineer, 09 (ICME ) held in Dhaka December 25 -27, 2009. ICME, RT-40

[4]. Islam, M.A., Skalle. P., and Al- Ajmi, A.M., 2010.

“Stability Analysis in Shale through Deviated Boreholes using the Mohr and Mogi - Coulomb Failure Criteria” This paper was prepared for presentation at the 44th US Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium, held in Salt Lake City, UT June 27–30, 2010.

[5]. Islam, M.A., Skalle. P. and Faruk A.B.M 2009. “Analytical and Numerical Study of Consolidation Effect on Time Delayed Borehole Stability During Underbalanced Drilling in Shale” In proceedings of the KIPCE 09/SPE drilling conference, Kuwait,14 -16 December 2009. SPE 127554.

[6]. Gil, I., and Roegiers, J.C., 2002. “Borehole Design:

Stability Considerations” presented at the SPE/ISRM Rock Mechanics Conference held inving Texas, 20-23 October 2002.

[7]. Adachi, T, Oka F. 1995. “An elasto-plastic constitutive

model for soft rock with strain softening. International Journal for Numerical and Analytical Methods in Geomechanics 1995;19:233-47.

[8]. Biot, M.A. 1975 “General Theory of Three Dimentional

Consolidation “, J.Appl.Phys.., 12(1941) 155-164. [9]. Chen, X., Tan C.P, Habereld C.M., 1998 “Effects of

induced pore press- on stability of wellbores drilled in shales”. SPE/ISRM EUROCK'98: Rock Mechanics in Petroleum Engineering, Trondheim, Norway, vol. 1. 1998. p. 453-60.

[10]. Fjær, E., Holt. R.M., Horsrud. P., and Raaen., A.M.,

2008 “Petroleum related rock mechanics” 2nd addition.

[11]. Gazaniol, D, Thierry F, Boisson MJF, Piau J-M 1995

“Wellbore fail- mechanisms in shales: prediction and

prevention. Journal of Petroleum Technology 1995;47 (7):589-95.9,2009. IPTC/SPE 13475.

[12]. McLennan, J., Ahmed. S. 2002. “ Some Advances in

Near Wellbore Geomechanics”. Presented at the SPE/ISRM Rock Mechanics Conference held inving Texas, 20-23 October 2002.

Table A1: Stress field’s data used in simulation model: data from Gulfask field, North Sea.

Case name Stress Criteria, MPa Others parameters Case-1, 1200 m VhH σσσ

302524 Pp=18 MPa, C0= 5 MPa , To=1 MPa, =0.2 , = 300, , = 900

Case-II, Intermediate depth ( 1800m) hVH σσσ 4641.535

Pp=30 MPa, C0=10 MPa , To=2 MPa, =0.25, = 300, = 900,

Case-III, Ultra deep (2500m) hHV σσσ 52.550.546.5

Pp=40 MPa ,C0=10 MPa , To=2 MPa, =0.3 , = 300, = 900

8. Appendix A

Elastic rock: E = 10 MPa, = 0.46 Elasto- Plastic rock: E = 1.33, MPa, = 0.46 σyield0 = 20 Mpa, with p=0, σyieldf = 28 Mpa, with p=0.004

Fig. A-1. Pore pressure distribution with empty borehole mud support.