Rock Mechanics for Natural Resources and Infrastructure
SBMR 2014 – ISRM Specialized Conference 09-13 September, Goiania, Brazil
© CBMR/ABMS and ISRM, 2014
SBMR 2014
New Approach For Estimating Cavings Volume To Avoid
Wellbore Instabilities
Renato Gutiérrez Escobar
Wellbore Stability Research Group, Bucaramanga, Colombia, [email protected]
Zuly Himelda Calderon Carrillo
Universidad Industrial de Santander, Bucaramanga, Colombia, [email protected]
Yair Andres Quintero Peña
ECOPETROL, Bucaramanga, Colombia, [email protected]
SUMMARY: Most of the problems caused during drilling wells, such as pipe sticking, poor
wellbore cleaning, sidetracks and even wellbore lost, are generated by some phenomena manifested
in wellbore wall, such as Break-out, Wash-out y Kea-seat, which give origin to some slides of the
wellbore wall known as cavings, the above problems and their effects contributes to increase the
non productive time.
Currently, the caving volumes are used as a warning signal of wellbore instabilities during real
time monitoring, since according to its morphological classification and produced volume represent
kind of wellbore damage and its critical nature respectively. Considering the above aspects, the
main aim of this research is to propose a new approach to estimate cavings volumes, in order to
identify the kind of wellbore failure and the corrective actions in real time. Besides it can simulate
the most critical aspect of the problem predicting the cavings volumes and the depth which they
come from in order to prevent and mitigate them, thus reducing the non productive time during
wellbore drilling.
In this new approach, a simulation of drilled wellbore is carried out using the Finite Elements
Method taking into account the failure criterion and the material constitutive model to each cell of
the simulation mesh, these considering the rock mechanical properties, mud weight and in situ
stress state, in order to quantify the cells volume that failed in the simulation and reproduce the
cavings volume of wellbore wall that would be produced during drilling.
An analytical approach is proposed in order to validate the results of the simulation. It consists
approximating the cavings volume to the volume of a triangular prism, and calculating it by using
geomechanics parameters such as in situ stresses, break-out angle and its width, mud weight and
pore pressure. All these geomechanics parameters were obtained from wellbore logs.
KEYWORDS: Cavings, Abaqus, Finite Element Methods, Breakouts, Wellbore Instabilities
1. INTRODUCTION
Simulation techniques have been needed by the
petroleum industry in order to solve many field
problems reducing uncertainties associated
geomechanical and surfaces processes. This
implies new technology developments to make
investments more feasible since they could
decrease economical risks to make drilling
process more safe.
During drilling operations, the non productive
time can make the petroleum wellbore
economically unfeasible due problems such as
pipe stucking which is caused by a high cavings
volume in the borehole wall. The problem is
identified only when cavings arrives to surface
during field operation. The principal aim of this
paper is to present a methodology that allows
predicting cavings volume generated during an
instability event by using geomechanics
simulation with the Abaqus software. This way
to predict wellbore instabilities makes it easier
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to reduce the non productive time while drilling
the wellbore.
Currently it does not exist a tool that allows to
predict cavings volume before finishing drilling
process, therefore the analytical approach and
Abaqus simulation offer a great opportunity to
improve drilling process decreasing the non
productive time.
2. MOHR COULOMB FAILURE
CRITERIUM
The Mohr Coulomb strength criterion describes
the rock failure at different confining pressure
while performing a few triaxial tests (Abaqus,
2011). This criterion is represented by plotting
the Mohr circle for the rock stress state in terms
of maximum and minimum principal stresses
(Fjaer, 2008). The failure envelope of Mohr
Coulomb is the best straight line touching these
Mohr circles, see Fig 1.
Figure 1. Mohr-Coulomb Criterium
Next equation describes failure envelope for
Mohr-Coulomb envelope
(1)
The Mohr Coulomb criterion asumes that
failure does not depend on the intermediate
principal stress effect and failure will occur
when:
(2)
(3)
3. PROPOSED METHODOLOGY
In order to quantify the cavings volume, this
paper proposes two different methodologies to
determine it, analytically or by using Abaqus
simulation.
3.1. Analytical cavings volume
It proposes to determine cavings volume from
Kirsch equation (Zoback, 2007):
Solving for Breakout angle becomes:
From Breakout angle, it can determine
Breakout width thus (Garcia, 2006):
In order to quantify cavings volume, one
assumption is made: the cavings volume is best
represented by a triangular prism volume, see
Fig 2 and Fig 3.
FAILURE ENVELOPE
FAILURE ZONE
SAFE ZONE
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𝐿𝑂𝑁𝐺.𝑇𝑅𝐼𝐴𝑁𝐺. = 𝐶𝐴𝐿𝐼 − 𝐵𝑆
𝑊𝑏𝑜 = 𝜋 − 2𝜃𝑏
Figure 2. Approaching of the cavings area to triangle
area. Zoback, 2007.
Figure 3. Approaching of the prism volume to cavings
volume
Finally the analytical cavings volume is given
by:
3.2. Cavings volume using Abaqus simulation
To determine this volume, the software Abaqus
was used providing its inlet parameters of a
geomechanical model. It assumes that width
breakout is the only failure mechanism present
in the wellbore.
The paragraph below it describes the
simulation model used to quantify the cavings
volume.
3.2.1. Simulation Model
A petroleum wellbore was simulated with
diameter of 0,31 m in 3D (third dimension) of
one rock lithology to a 2622 m in depth. Only
11 m in depth was simulated to decrease
computational cost (Schutjens, 2010), see Fig 4,
thereafter it was multiplied by 10 to reach the
whole rock lithology thickness of 110 m,
assuming symmetry in properties behavior
(Eckert, 2011). It highlights for the wellbore a
finer mesh density in the near wellbore region
comparing to the coarser mesh density in the
outer section (far field region) (Chatterjee,
2003) where the state of stress should be given
by the homogeneous far field stresses (Mora,
2005), see Fig 5.
Figure 4: Sketch of the simulation model
Figure 5: Zoom of the wellbore
LENGTH TRI. = CALI – B.S.
LENGTH TRI. DEPTH
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3.2.2. Simulation Steps
This simulation was divided in three steps
(Mackay, 2011), in the first step it provided the
model with the inlet parameters, boundary
conditions and initial state of in-situ stress. The
second step includes the use of the Abaqus
geostatic function, which allows achieving the
equilibrium between the state of stress, applied
loads and boundary conditions. The third step is
denominated Static step, which include a mud
pressure in order to simulate the drilling process
iterating to determine the state of stress during
this process (Botelho, 2008).
3.2.3. Failure in Abaqus
In order to determine how many finite elements
fractured during the drilling process, it was
applied to simulation model an Abaqus failure
indicator, which established finite element
failure when it passes from elastic zone to
plastic zone depending on the stress and strain
conditions (Abaqus, 2011), see figure 6.
Figure 6: Abaqus Failure Indicator
4. EXAMPLE
In order to apply the proposed methodology a
real case was used with data from a Colombian
field. This geomechanical model took into
account parameters such as strength, rock
mechanical properties (cohesion, angle of
internal friction, young modulus, poisson ratio,
permeability and porosity), it also included pore
pressure, mud weight and in situ stress state.
With all these data and the use of the Mohr
Coulomb failure criterion the state of rock in
specific conditions was evaluated, in order to
determine if studied rock fractures and how
many cavings will form. Next assumption, was
that the only failure mechanism present in
wellbore was width breakout in order to
calculate the cavings volume both analytically
and by Abaqus simulation.
The data used in this paper is resumed in table
1.
Table 1: Wellbore properties
SIMULATION MODEL DATA
PROPERTIES MAGNITUD
Model Volume [m3] 1100
Wellbore Radio [m] 0.31
Mud Weight [MPa] 48
Young Modulus [MPa] 13793
Poisson Ratio 0.2678
Cohesion [MPa] 4.39
AIF 31.6
Porosity 0.26
[MPa] 16.886
[MPa] 11.819
[MPa] 18.448
Effective stresses were used; where the
maximum horizontal stress is acting in Y axis,
the minimum horizontal stress is acting in X
axis and the vertical stress is acting in Z axis
both analytically and by Abaqus simulation.
5. RESULTS ANALYSIS
5.1. Results of the simulation static step
In this step it simulates the drilling process
whose results obtained in Abaqus were
compared with those obtained analytically,
hence Fig 7 shows that greater magnitudes of
elastic strain are obtained in the minimum
horizontal stress direction (X axis), which is
correct according to width breakout
characteristics. Negative signs in the elastic
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strains magnitudes are caused by compressive
stresses, whereas positive signs are caused by
tension stresses.
Figure 7: Elastic strain in X axis
5.2. Calibration of the simulation model
This calibration was based on Kirsch equations
(Fjaer, 2008) to calculate the axial, tangential
and radial stresses analytically (Zoback, 2007)
and then they were compared to with those
stresses obtained by using of Abaqus
simulation.
Figures 9, 10 y 11 show the comparison
between analytical stresses and simulation
stresses. A very good match is shown.
Figure 9: Radial stress vs Wellbore radio
Figure 10: Tangencial stress vs Wellbore radio
Figure 11: Axial stress vs Wellbore radio
5.3. Validation of Abaqus simulation
This step it calculates the simulation cavings
volume that subsequently is compared to the
cavings volume estimated with the prism
triangular approach. Fig 12 illustrates the
PEMAG identifier (Plastic Strain Magnitude),
that Abaqus offers to determine the failure of
finite elements if its magnitude is different to
zero (Abaqus 2011). As shown in the figure
below, it is seen that width breakout
characteristics at the borehole, where indicates
that zones with different color to dark blue have
fractured. This assertion matches to the
wellbore behavior when it was drilled.
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Figure 12: Plastic Strain Magnitude identifier
6. COMPARISON OF RESULTS OBTAINED BOTH ANALYTICALLY AND BY ABAQUS SIMULATION
Table 2 shows the cavings volume magnitude
determined by using the prism triangular
approach (Analytical) and the determined by
Abaqus simulation, highlighting a good match
between them.
Table 2. Comparison of cavings volumes
Volumen de cavings Magnitude
Analytical [m3]
75.69
Abaqus [m3]
54.93
Achieving this match, it could predict the
cavings volume that would produce during
wellbore drilling decreasing the non productive
time caused by pipe stuck due an excessive
cavings volume.
CONCLUSIONS
An analytical approach was developed to
determnine cavings volume for width breakout
failure mechanism as the only failure
mechanism present in the whole wellbore.
The results showed a % error of 27 %, which
means an acceptable match between cavings
volumes determined both analytically and by
Abaqus simulation.
With this methodology it can predict cavings
volume generated during drilling process in a
near wellbore to zone where data comes from,
decreasing associated uncertainties and non
productive time.
LIST OF SYMBOLS
Shear Stress
Normal Stress
Cohesion
Angle of Internal Friction
Major Principal effective stress
Minor Principal effective stress
Uniaxial Compressive Strength Failure Plane Angle
Mud Weight
Pore Pressure
Maximum Horizontal Stress
Minimum Horizontal Stress
𝜃 Breakout Angle
𝑊 Breakout Width
Caliper Data
Bit size
Radial Stress
Tangencial Stress
Wellbore Radio
Vertical Stress
Axial Stress
Analysis Radio
Angel between
Poisson Ratio
ACKNOWLEDGEMENTS
I want to thank especially to wellbore stability
research group for their support, patience and
dedication.
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