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ARMA/USRMS 05-670 Poroelastic analysis of rock indentation failure by a dr

Zhang, Jincai CIRES, The University of Colorado, Boulder, CO 80309-0216, USA

Roegiers, J.-C. Mewbourne School of Petroleum and Geological Engineering, The University of Oklaho

Copyright 2005, ARMA, American Rock Mechanics Association This paper was prepared for presentation at Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS): Rock MechDevelopment in the Northern Regions, held in Anchorage, Alaska, June 25-29, 2005. This paper was selected for presentation by a USRMS Program Committee following review of information contained in an abstract submitted eaas presented, have not been reviewed by ARMA/USRMS and are subject to correction by the author(s). The material, as presented, does noARMA, their officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes withouPermission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must conand by whom the paper was presented.

ABSTRACT: A double porosity geomechanical model has been developed to analyze rock indenmodel, both the effects of solid deformation and fluid flow (matrix as well as fractures) are considin the case of naturally fractured porous media. It has been found that rock failures depend not onbut also on the formation characteristics. Numerical analyses show that the rock is more likely to a dual-porosity medium.

1. INTRODUCTION

Rock cutting by bit indentation is a basic process in borehole drilling and mechanical excavation. An accurate simulation of the rock cutting helps in planning efficient drilling operations and optimization of drill bit design. Many attempts have been made to understand the mechanisms of rock failure and chip formation under a drill bit. A number of researchers have performed indentation experiments and numerical modeling (e.g. Swenson and Jones, 1984; Huang et al., 1998). Rock indentation is normally represented by a circular flat-bottomed punch pressing against the surface of an elastic, semi-infinite body (Cook et al., 1984; Pierry and Charlier, 1994). Saouma and Kleinosky (1984) simulated the crack initiation and subsequent crack propagation with the finite element method. Alehossein and Hood (1996) used a distinct element code to model crack propagation under a spherical indentation. Liu et al. (2002) modeled the heterogeneous rock failure process induced by single and double indenters. All these authors treated rocks as either an elastic or an elastoplastic medium. However, for those cutting in naturally

fractured porous formatfailure needs to be furth

2. FAILURE CRITER

Many porous rock heterogeneous due discontinuities and naporous rock as a homoassociated single porproperly the rockmassinfluence and the modelconsidered using a concept. Naturally fratreated ideally as a duamedium. The fractured number of porous blockby a system of randomlythe fracture and matdifferent in both poroglobal flow occurs prpermeable, low-porosurrounding the matrixcontain the majority of tand act as the local sfracture system. In ad

ill bit

ma, Norman, OK 73019, USA

anics for Energy, Mineral and Infrastructure

rlier by the author(s). Contents of the paper, t necessarily reflect any position of USRMS, t the written consent of ARMA is prohibited. tain conspicuous acknowledgement of where

tation in porous media. In this ered, making it more applicable ly on the in-situ stress conditions, fail when assuming it behaves as

ions, the mechanism of rock er investigated.

IA IN POROUS MEDIUM

formations are inherently to the existence of

tural fractures. Thus, the geneous continuum with an osity may not simulate behavior. However, the ing of these fractures can be

dual-porosity continuum ctured formation is then l-porosity/dual-permeability rockmass is thought of as a s, separated from each other distributed fractures. Thus,

rix systems are distinctly sity and permeability. The imarily through the high-sity fracture system blocks. These last ones he reservoir storage volume ource or sink terms to the dition, these fractures are

interconnected and provide the main fluid flow path to the wells. For a separate and overlapping model, the finite element method was used to solve this coupled poromechanical formulation; a software package, i.e. RWAS (Reservoir and Wellbore Analysis Software) was developed and validated (Zhang, 2002).

As far as failure criteria are concerned, the numerical code considered all three mechanisms (i.e. tensile, compressive, or shear) and selected whichever was reached first. It is commonly accepted that the failure of the porous rock is controlled by Terzaghi’s effective stress concept (Zhang et al., 2003):

maijijij pδσσ −=′ (1)

where σ′ij is the effective stress tensor; σij is the total stress tensor; pma is the matrix pore pressure and δ is the Kronecker delta.

2.1. Mohr-Coulomb Failure In the principal space (σ′1,σ′2,σ′3), the Mohr-Coulomb failure criterion is given by:

31 σσσ ′+=′ qc (2)

where σ′1 , σ′3 are the maximum and minimum effective principal stresses, respectively; φ is the angle of internal friction; and )sin1()sin1( φφ −+=q ;

The effective shear failure stress can thus be defined as:

13 σσσσ ′−′+= qcmohr (3)

where σmohr is the effective shear failure stress.

2.2. Tensile Failure Tensile failure will occur when the effective least principal stress equals to rock tensile strength, that is:

T=′3σ (4)

where σ′3 is the least effective principal stresses (note that σ′3 is negative).

3. NUMERICAL ANALYSES

There are two types of rock failures induced by a bit: indentation and dragging or shearing. The

present study concentrates on the rock indentation. Figure 1 represents the finite element mesh used to analyze the interaction between the bit and the rock. Plane stress conditions were assumed to be valid and two cases were examined: normal stress and tectonic stress regime. The input parameters are given in Table 1.

-1

-0.8

-0.6

-0.4

-0.2

0-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Distance from cutter center (r/10R)

Dis

tanc

e fro

m c

utte

r cen

ter (

r/10R

)

-1

-0.8

-0.6

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0-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1


Dis

tanc

e fro

m c

utte

r cen

ter (

r/10R

)

R

Sz

Sx Sx

Sy Fig. 1. Finite element mesh for drilling bit cutting problem.

3.1. Influence of rock media Three different rock media were studied in order to evaluate the dual-porosity effect (i.e. elastic, single-, and dual-porosity media). The in-situ stress configurations (normal stress regime) as well as bit loading are shown in Figure 2.

Figure 3 illustrates the comparisons of effective shear failure stresses for elastic, single- and dual-porosity solutions (negative values for stress denote failure). It can be seen that in the case of a dual-porosity medium, shear failure potential is much higher except at the wellbore wall.

Figure 4 represents shear failure in the case when the bit loading is 40 MPa. It is obvious that such type of failure is mainly concentrated on the downward side of the cutter. Figure 5 represents tensile failure in the normal stress regime for a cutter loading of 50 MPa, and shows that, here again failure occurs in the same orientation. Hence, in a normal stress regime, failures concentrate mainly at the bottom of the drill hole (refer to Figure 6).

Sx

Sz = 29 MPaSx = 25 MPaSy = 20 MPap0 = 10 MPa

Bit loading p = 40 MPa

Sx

Sz

Sz

Sy

p = 40 MPa, t = 100 sec.

-20-15-10-505

1015202530

1 1.5 2 2.5r/R

She

ar fa

ilure

stre

ss (M

Pa)

3

Single porosityElasticDual-porosity

r/R

failurestable

Fig. 3. Stress configration for the bit and rock interaction in normal stress regime.

Fig. 2. Stress configration for the bit and rock interaction in normal stress regime. In the figure, bit loading is a uniform pressure acted on the rock produced by the drill bit. The fluid pressure is 10 MPa.

Table 1. Input parameters for the numerical analyses

Parameter Unit Value Analyses

Elastic modulus (E) GN/m2 20.6 A, B, C

Poisson’s ratio (ν) - 0.189 A, B, C

Fracture stiffness (Kn , Ksh) MN/m2/m 482.1 C

Fluid bulk modulus (Kf) MN/m2 419.2 B, C

Grain bulk modulus (Ks) GN/m2 48.2 B, C

Matrix porosity (nma) - 0.02 B, C

Fracture porosity (nfr) - 0.002 C

Matrix mobility (kma /µ) m4/MN·s 10-19 B, C

Fracture mobility (kfr /µ) m4/MN·s 10-18 C

Fracture spacing (s) m 1.0 C

Compressive strength (σc) MN/m2 20 A, B, C

Internal friction angle (ϕ) ° 30 A, B, C

Tensile strength MN/m2 0 A, B, C

Note, A = elastic; B = single-porosity; C = Dual-porosity.

-0.3

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-0.1

0-0.3 -0.2 -0.1 0 0.1 0.2 0.3


Dis

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m c

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)

Shear failureFEM mesh

Dual-porosity ( p = 40 MPa, t = 100 Sec.)

Fig. 4. Rock shear failure area around the cutter in the normal stress regime for cutter loading of 40 MPa at t = 100 s.

-0.3

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0-0.3 -0.2 -0.1 0 0.1 0.2 0.3


Dis

tanc

e fro

m c

utte

r cen

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r/10R

)

Tensile failureFEM mesh


Fig. 5. Rock tensile failure area around the cutter in normal stress regime for cutter loading of 50 MPa at t = 100 s.

Sz = 20 MPaSx = 25 MPaSy = 29 MPa

Bit loading p = 40 MPaSz

Sz

SxSx

Sy

Spalling failure

σmax

σmin

σmax

σmin

Fig. 7. Stress configration for the bit and rock interaction in tectonic stress regime. The fluid pressure is 10 MPa.

Fig. 6 Schematic diagram of rock shear or tensile failure around the cutter in the normal stress regime.

3.2. Tectonic stress regime The other case considered in this paper is rock cutting in a tectonic stress regime, as shown in Figure 7. Using the same input parameter as listed in Table 1. Figures 8 and 9 show rock shear and tensile failures due to the cutter loadings (p = 40 MPa) at t = 100 s. It is obvious that the maximum shear and tensile failures are concentrated along the two wings of the cutter and there is basically no failure occurring in the cutter downward direction. In this case, increasing bit loading can be a good choice for insuring ‘making hole’.

It can be seen that the state of stress has a significant impact on the rock fragmentation. When rock cutting is performed in a normal stress regime, the rock shear and tensile failures concentrate downwards (Figure 6). However, in a tectonic stress regime, the rock shear and tensile failures are located on two sides of the cutter (Figure 10).

-0.3

-0.2

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0-0.3 -0.2 -0.1 0 0.1 0.2 0.3


Dis

tanc

e fro

m c

utte

r cen

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r/10R

)

Shear failureFEM mesh


Fig. 8. Formation shear failure area around the cutter in tectonic stress regime for cutter loading 40 MPa at t = 100 s.

-0.3

-0.2

-0.1

0-0.3 -0.2 -0.1 0 0.1 0.2 0.3


Dis

tanc

e fro

m c

utte

r cen

ter (

r/10R

)

Tensile failureFEM mesh


Fig. 9. Formation tensile failure area around the cutter in tectonic stress regime for cutter loading 40 MPa at t = 100 s.

Spalling failure

σmaxσmax

σmin

σ

Fig. 10. Schematic diagram of formation failure around the cutter in tectonic stress regime.

4. CONCLUSIONS

Rock failures caused by a drill bit have been analyzed in different states of in-situ stress and in different rock media using a dual-porosity/dual permeability approach. This study shed some light on understanding the mechanisms governing cutting failure and simulating rock/bit interaction. It was found that rock failures depend not only on the in-situ stress, but also on formation characteristics, such as elastic, single porosity or double porosity media.

Comparing to elastic and single-porosity solutions, the dual-porosity solution has the highest probability of inducing shear failure, and produces the largest shear failure zone around the wellbore. The in-situ state of stress in the rock formation has a significant impact on rock cutting failures. When rock cutting is performed in a normal stress regime, the rock shear and tensile failures concentrate downwards of the drilling hole; i.e. helping in ‘making hole’. However, in a tectonic stress regime, the rock shear and tensile failures are located on

two sides of the cutter. These may be of importance for bit design.

REFERENCES 1. Swenson, D.V. and Jones, A.K., 1981. Analytical and

experimental investigations of rock cutting using polycrystalline diamond compact drag cutters. SPE 10150 presented at the 56th Ann. Fall Tech. Conf. of SPE of AIME, San Antonio, Texas.

2. Huang, H., Damjanac, B. and Detournay, E., Normal wedge indentation in rocks with lateral confinement, Rock Mech. Rock Engng., 31 (2), 1998, 81-94.

3. Cook, N.G.W., Hood, M. and Tsai, F., 1984. Observations of crack growth in hard rock loaded by an indenter. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 2(2), 97–107.

4. Alehossein H. and Hood M., 1996. State-of-the-art review of rock models for disc roller cutters. In: Aubertin, Hassani, Mitri, editor. Rock Mechanics, Balkema, Rotterdam, p.693–700.

5. Liu, H. Y. , Kou, S. Q., Lindqvist P. –A. and Tang, C. A., 2002. Numerical simulation of the rock fragmentation process induced by indenters. Int. J. Rock Mech. Min. Sci. 39(4), 491-505.

6. Saouma V. E. and Kleinosky M., 1984. Finite element simulation of rock cutting: a fracture mechanics approach. Proc. 25th US Symp. on Rock Mech., ASCE, p.792–799.

7. Pierry, J. and Charlier, R., 1994. Finite element modeling of shear band localization and application to rock cutting. SPE 28052 presented at SPE/ISRM Rock Mech. in Petrol. Conf., Delft, The Netherlands.

8. Zhang, J., Dual-porosity approach to wellbore stability in naturally fractured reservoirs, Ph.D. dissertation, U. of Oklahoma, 2002.

9. Zhang, J., Bai, M. and Roegiers, J. -C., 2003. Dual-porosity analyses of wellbore stability. Int. J. Rock Mech. Min. Sci., 41, 473-483.

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