1

1. INTRODUCTION

The Andes Cordillera in South America [1] extends considerable distances northward into Venezuela and southward into Argentina. The Sub-Andean basins are very important for hydrocarbon exploration, where billions bbl of recoverable oil have been discovered.

However, this tectonic region presents other challenges [2, 3] to the oil industry not normally encountered on oil field development. This area is characterized by high tectonic stresses complicated by geological factors, including: steeply dipping beds, folds, faults, volcanic intrusions, etc.

The horizontal stress magnitudes and orientation in such environment is the Geomechanical parameter that has the greatest uncertainty during the mechanical earth model (MEM) development [4,5].

The mechanical earth model is a numerical representation of the state of stress and rock mechanical properties for a specific Stratigraphic section in a field or basin. The model is linked to geologic structure through the local stratigraphy. In its basic form, the MEM consists of depth profiles:

of the elastic and/or elasto-plastic parameters, rock strength and the earth stresses referenced to the local Stratigraphic section. References 4 and 5 give a more detailed description of the mechanical earth model and its applications.

The implication of this for wellbore stability is that the greater the ratio of the maximum to minimum horizontal stresses the greater the probability of wellbore instability. Drilling wells in such tectonically active setting is technically and economically challenging, where well costs can be as high as $40 million [2], and taking up to a year or more to be drilled. Practical applications of the horizontal stress knowledge in this area, as part of the mechanical earth model construction, minimize the nonproductive time associated with wellbore instability [5, 6, 7, 8, 9, 10]. Other practical applications include sand management analysis [11, 12] and hydraulic fracturing optimizations [13].

This paper discusses horizontal stress estimation in tectonically active areas. We present techniques developed over the past 5 years, in more than 90 MEM creations, that have proven to be efficient for horizontal stress estimation in such complex areas.

ARMA/USRMS 06 - 985

Using breakouts for in situ stress estimation in tectonically active areas Frydman, M. and Ramirez, H.A. Schlumberger Geomechanics, Bogotá, Colombia

Copyright 2006, ARMA, American Rock Mechanics Association This paper was prepared for presentation at Golden Rocks 2006, The 41st U.S. Symposium on Rock Mechanics (USRMS): "50 Years of Rock Mechanics - Landmarks and Future Challenges.", held in Golden, Colorado, June 17-21, 2006.

This paper was selected for presentation by a USRMS Program Committee following review of information contained in an abstract submitted earlier by the author(s). Contents of the paper, as presented, have not been reviewed by ARMA/USRMS and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of USRMS, ARMA, their officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: Well drilling in a tectonically active setting is technically and economically challenging. Wellbore instability is responsible for many costly stuck pipe incidents. Building a mechanical earth model (MEM) during the well planning phase and revising it in real time has proven to be extremely valuable in delivering complex wells safely while minimizing unplanned well construction costs. The main uncertainties on the MEM creation are the horizontal stresses. Breakout direction has been used to estimate stress direction, while its width is used for the horizontal stress magnitudes. An investigation on breakouts (direction and magnitudes) for real cases on the Andes foothills was carried out. It is shown that the effects of faults, rock anisotropy and brittle failure, should be considered when using breakouts for in situ stress estimation. Maximum horizontal stress estimated through traditional elastic approach overestimate the magnitude of the stresses and the use of these simplified models for horizontal stresses estimation without knowledge of the implicit simplifications may lead to wrong conclusions. The present paper discusses how the horizontal stresses are related to the structural setting and tectonic regime.

2

2. STRESS DIRECTION ANALYSIS

Regional stress direction can be initially estimated from the World stress map [14]. Fig. 1 shows an example for the World stress map for the Camisea area where it can be noted a predominant tendency for the maximum horizontal stress (SH) in NE-SW direction.

Fig. 1. Direction of SH inferred from World Stress Map for the Ucayali basin.

Other option for an initial estimate for the stress direction is through the local and regional geology. This is however not ideal as it is often the case, in tectonically active regions, that stress direction may change over geological time. The Andersonian Faulting Model (Fig. 2) helps to identify a first estimate of the stress direction and relative magnitudes.

Although this can be used to identify a general direction, it is best to use more local means to account for stress field variations. Several methods for identifying stress direction from wireline logs are available including borehole breakout orientation, natural and hydraulic fracture orientation, shear sonic anisotropy and 3 components VSP.

maxim

um

intermediate

minimum

Normal

minim

um

intermediate

maximum

Thrust

maximum

intermediate

minimum

Strike-slip or wrench

Fig. 2. The Andersonian Faulting Model

Fig. 3 and 4 below present examples of first estimate of stress direction based on geology.

Fig. 3. Stress direction based on local geology.

Fig. 4. Stress direction based on regional geology.

3

2.1. Stress direction from breakouts

Compressive and tensile failure of a wellbore is a direct result of the stress concentration around the wellbore that results from drilling a well into already stressed rock mass. Compressive wellbore failures or wellbore breakouts and induced fractures are useful to determination of stress orientation. (Fig. 5). The minimum horizontal stress (Sh) is in the direction of the breakouts while the maximum horizontal stress SH follows the direction of the drilling induced fractures.

Fig. 5. Direction of SH with respect with the induced fractures and breakouts.

Fig. 6 below presents an example of an UBI image where a stress related breakout is developed, suggesting SH direction at N20.3E.

Fig. 6. Breakout at an UBI image.

Breakout azimuth can be ambiguous, especially if other failure modes are occurring (i.e hole enlargement due to poor mud system, excessive reaming, reactive clays, or plane of weakness effect). To reduce this uncertainty, it is important to differentiate between stress induced and mechanical induced breakout [15]. When breakout occurs in the same azimuth as the wellbore, is likely due to mechanical action of the drilling process and not stress. Additionally, breakouts can occur due to the

plane of weakness effect, or shear stress associated to natural fractures and bedding planes.

Results of some methods are displayed on the Noi/Ene surface along with San Martin and Cashiriari wells (Fig. 7) in the Ucayali basin. It can be seen that for this field, the maximum horizontal stress direction is in good agreement with the regional stress direction (Fig. 1) and Geology.

Fig. 7 Summary of San Martin stress direction for three methods.

2.2. Stress direction for laminated formations

The plane of weakness effect is common in the Andean foothills where complex geology and high formation dips exists. Studies have shown [16, 17, 2] that wellbore stability is not only influenced by stress orientation, but also wellbore/formation angle, and borehole size. It also impacts wells where the relative borehole-formation intersection angle is high, such as high angle trajectories in low formation dip areas. Wells is such environments reports problems with a high production of tabular cavings and poor hole conditions leading to big washouts. This failure mechanism is more evident in laminated shale sections, with presence of cleavage or natural fractures. In such cases, a high volume of tabular cavings can be generated due to instability on pre-existing planes of weakness. Key characteristics of tabular cavings are, one or more parallel surfaces, surfaces tend to be relatively smooth and planar and failure initiates on high side of wellbore. The least favorable borehole orientation would be parallel to the bedding planes (for normal stress) and the most favorable borehole orientation would be perpendicular to the bedding planes.

For such failure mechanism, we may find breakouts in different directions not related only to the stress

4

field. Fig. 8 and 9 present identified breakouts in UBI images for a well. In this image, it was identified many breakouts and some induced fractures. Based on the image analysis, two families of breakouts were identified (Fig. 8 and 9). The first family and the existent induced fractures are consistent with the regional stress direction; however the second family is not. It was determined by the image analysis that the second family of breakouts is more related to the pre-existent planes of weakness.

To understand the differences between the two breakouts systems, a wellbore stability analysis, in drilling condition, was done [18]. In this computation, the effect of the pre-existent planes of weakness was taken into account (Fig. 10). The results of this analysis are presented in Fig. 11 In these graphics, the green color and above in the color scale are indicating that the material is failing, i.e., yield factor more than one. It can be noted that the two systems of breakouts are consistent with the stress effect and to the plane of weakness effect. Based on that, it was possible to conclude that there are two breakout directions. The first one is related to the in situ stresses and corresponds to N26E deg. The second is related to the material anisotropy effect and its value is N60W deg. The minimum horizontal stress direction is 26 deg and the maximum horizontal stress direction is 116 deg.

It is important to stress that the second breakout is not only related to the stress field direction, and its use through inversion methods to determine the current stress field will lead to wrong conclusions

Fig. 8. Breakout family compatible with the regional stress direction

Fig. 9. Breakout family not compatible with the regional stress direction

Fig. 10. Wellbore stability analysis taking into account the pre-existent planes of weakness.

Fig. 11. Results of a wellbore stability analysis taking into account the pre-existent planes of weakness.

2.3. Effects of faults on Stress direction

Stress direction is related to the geological setting and the contemporary stress regime. Active faults and folding can introduce local variations the stress direction. Special attention must be taken to the fact that the stress regime, under which a fault or folds were formed, is not necessarily the same stress regime acting on the current conditions.

Figure 12 shows an example of the stress direction measured in the nearby of a regional right lateral wrench fault in Llanos Basin, Colombia. Stress

5

direction constrained only from the geological setting, may indicate the SH azimuth around the E-W direction (approximately 30 degrees apart from the main fault trend). Borehole measurements with oriented calipers indicated SH direction N40W, with similar orientations at both sides of the wrench. This indicates that the contemporary stress regime is far apart from the most probable stress orientation that initiated the fault. A rotation of around 60 degrees has occurred over the geological time, due to the interaction of the tectonic forces, responsible of the Andean orogeny located at the east of the Llanos Basin.

MATANEGRA FAULT

CAÑO LIMON FAULT

250 0 250 500 m

MATANEGRA FAULT

CAÑO LIMON FAULT

250 0 250 500 m250 0 250 500 m

Nor

th

Major Right LateralWrench Faults

Constrains fromgeology (wrench fault)

Borehole measurements(Breakouts)

Fig. 12. Stress orientation in a wrench fault in Llanos Basin.

The possibility of stress rotations occurring in the geological time highlight the importance of acquiring direct stress orientation measurements, in order or ensure the correct inputs for oil industry applications, like: planning directional drilling, fracture design, oriented perforating, etc.

Results of large-scale numerical simulations indicate that stress rotations can occur in the nearby of active faults, rotating the maximum stress to a position normal to the active inverse faults [19, 20]. In this case, principal stresses will not lie in a horizontal plane as most probably occur in relaxed basins under lithostatic load. Large-scale simulation models present an important drawback, due to limitations of modeling the displacement rates at which are subjected the geological settings under continuous tectonic driving forces.

Figure 13 shows two structural contour maps of a intra-Andean geological setting, in Middle Magdalena Valley, Colombia. The area shown is dominated by a principal faulting tendency in SW-NE. These primary dominant faults have associated normal faults towards W-E direction, produced by a

complex transpressional system acting in the region. Table 1 shows the stress direction from breakout orientation [15] in the four vertical wells shown in Figure 13.

Top Layer 1, Shallower

CSBE0408RCSBE0408RCSBE0408RCSBE0408R

CSBE0173RCSBE0173RCSBE0173RCSBE0173R

CSBE0387RCSBE0387RCSBE0387RCSBE0387R

CSBE0164RCSBE0164RCSBE0164RCSBE0164R

Well #4

Well #1

Well #3

Well #2

CSBE0408RCSBE0408RCSBE0408RCSBE0408R

CSBE0173RCSBE0173RCSBE0173RCSBE0173R

CSBE0387RCSBE0387RCSBE0387RCSBE0387R

CSBE0164RCSBE0164RCSBE0164RCSBE0164R

Well #4

Well #1

Well #3

Well #2

Top Layer 2, Deeper

CSBE0408RCSBE0408RCSBE0408RCSBE0408R

CSBE0173RCSBE0173RCSBE0173RCSBE0173R

CSBE0387RCSBE0387RCSBE0387RCSBE0387R

CSBE0164RCSBE0164RCSBE0164RCSBE0164R

Well #4

Well #1

Well #3

Well #2

Fig. 13. Structural maps over an area of MVV showing SH direction determined from borehole breakouts.

Well #1 Well #2 Well #3 Well #4

SH azimuth (mean value): 98.5° 96.5° 109.3° 94°

Standard deviation: 15.7° 10.0° 13.3° 5.0°

Category: C D C D

Table 1. SH direction from borehole breakouts.

The category shown corresponds to the quality classification proposed for the World Stress Map [21], varying from A: Best to E: Worst.

Regardless of the geological context, and the regular quality stress direction indicators, the results indicate no important variations on the maximum horizontal stress direction from one location to another.

6

Wells #1 to #3 are located close to minor normal faults dipping to the east. For these wells, maximum horizontal stress appears almost perpendicular to these minor faults. In this area, where the maximum horizontal is the intermediate stress (Sv> SH> Sh), the stress direction shows that regional stress tendency (SH towards E-W) prevail over the local geological setting, which indicate the minor horizontal stress is perpendicular to the fault (Andersonian fault model). Well #3 crosses a minor fault, and no stress rotation in the vicinity of the fault area was observed.

For Well #4, two apparent sets of breakouts appear, as shown in the rose plots in Figure 14.Well #4 was drilled crossing a major normal fault. The maximum horizontal stress direction above the fault (hanging block) appeared oriented parallel to the fault’s azimuth (N50W), and below the fault (laying block), it is close to the regional direction (S86E) observed in the other wells. These results are evidences of a stress rotation from the regional stress in the deepest rocks below the fault (E-W tendency), to a total stress relaxation on the major normal fault accordingly to the Andersonian fault model.

SHSHSHSHSHSHSHSH

450 – 2500’ depth, Hanging Block

Well #4

SH azimuth, mean: 43.2°

Standard deviation: 5.1°

Category: D

SHSHSHSHSHSHSHSH

2500 – 5370’, Laying block

Well #4

SH azimuth, mean: 94°

Standard deviation: 5.0°

Category: D Fig. 14. Stress direction rotation in a major normal fault.

3. LEAST PRINCIPAL STRESS

An estimative of the magnitude of the least principal stress (S3) can be obtained from hydraulic fracturing. One of the classical articles in rock mechanics was published by Hubbert and Willis in 1957 [22] where it was shown that hydraulic fractures always propagate perpendicular to the orientation of the least principal stress. Leak-off test, mini-frac and hydraulic fracturing are

examples of field pressurization of wellbore that can be used for such estimate. These data points are used as a calibration point for continuous stress profile.

In all cases, the recorded pressure versus time curve is used to interpret the test results. For the mini-frac and hydraulic fracturing, techniques to estimate the least principal stress is well documented [23, 24]. However, these tests only give an estimate at the reservoir section.

The leak-off test is a field pressurization of the wellbore and is usually performed by the oil industry after the casing string is cemented. The recorded pressure versus time curve is used to evaluate the casing shoe integrity, and gives a good indication of an upper bound for the drilling mud weight to drill safely the next well phase. Figure 15 [25] presents schematic pressure–time history for an extended-leakoff test (XLOT)

Fig. 15. Illustration of some terms associated with an XLOT [25].

Following this nomenclature, and as described by Raaen et al [26], leak-off pressure (LOP) is the pressure where the pumping curve starts to deviate from the initial linear trend. The formation breakdown pressure (FBP) is the maximum pressure during the test. The fracture propagation pressure (FPP) is a more or less stable pumping pressure after formation breakdown. The instantaneous shut-in pressure (ISIP) is the pressure immediately after pumping has stopped, while the FCP denotes the fracture closure pressure and is equal to the least principal stress. The term leak-off test (LOT) is used for a test stopped between the LOP and the FBP, while the term extended leak-off test (XLOT) is used for tests where pumping is continued well

7

beyond the FBP. An extended leak-off test normally includes at least one repeat cycle.

Some references [27, 28] suggest that the leak-off pressure (LOP) is a good approximation for the fracture closure pressure (FCP). The authors disagree with this simplification. The pressure versus time curve during this test is result of a complex interaction between the type of fluid, pumping rate and rock type. Those factors affect the leak-off test, giving large variation on the results and making difficult its interpretation. Frydman and Fontoura [29] using numerical simulations, studied the effects of the pumping rate in a leak-off test. Fig. 16 shows results of this simulation where the leak-off pressure (LOP) and formation breakdown pressure (FBP) are not constant for the different pumping rate used.

Fig. 16. Pressure versus time curves for different values of injection rate. [29].

Field examples of extended leak-off testes confirm that the assumption of LOP equal to the S3 is not always a valid simplification. Fig. 17 presents an example of an XLOT in Marañon basin in Peru. During the build-up phase (Fig. 18), it was estimated the LOP for both cycles around 6970 psi. From both cycles in the flow-back phase (Fig. 19), the ISIP is around 6800 psi and closure pressure around 6000 psi. For this specific test, the assumption that LOP is equal to the FCP will overestimate by 16%. A similar conclusion was reached by Raaen et al [26].

However, there are examples where is valid the assumption that the leak-off pressure (LOP) is a good approximation for the fracture closure pressure (FCP). For these cases, the authors believe that an induced fracture was created during the casing running process (excessive speeds) or during the cementing process. The LOP is in fact

measuring the induced fracture reopening, and can be used as an upper bound for fracture closure pressure (FCP).

Fig. 17. Exended leak-off pressure (XLOT) in Marañon basin in Peru [6].

5400

5600

5800

6000

6200

6400

6600

6800

7000

7200

83 84 85 86 87 88 89 90 91 92

Treatment Time (min)

-100

0

100

200

300

400

BHPOffset (psi) BHPOffset Deri. (psi/min)

Closure:6980.68

Sh_UB

LB

a) First cycle

4800

5000

5200

5400

5600

5800

6000

6200

6400

6600

6800

7000

7200

105 106 107 108 109 110 111 112 113 114

Treatment Time (min)

0

100

200

300

400

BHPOffset (psi) BHPOffset Deri. (psi/min)

Closure:6964.37

Sh_UB

LB

b) Second cycle

Fig. 18. Interpretation of an extended leak-off pressure (XLOT) in Marañon basin, build up phase [6].

8

5.30E+03

5.40E+03

5.50E+03

5.60E+03

5.70E+03

5.80E+03

5.90E+03

6.00E+03

6.10E+03

6.20E+03

6.30E+03

6.40E+03

6.50E+03

6.60E+03

6.70E+03

6.80E+03

6.90E+03

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

G Function

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

BHPOffset(psi) GdP/dG(psi)

ISIP : 6801.47

Pc : 5972.09

a) First cycle

5.60E+03

5.70E+03

5.80E+03

5.90E+03

6.00E+03

6.10E+03

6.20E+03

6.30E+03

6.40E+03

6.50E+03

6.60E+03

6.70E+03

6.80E+03

6.90E+03

7.00E+03

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

G Function

0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

1.60E+03

1.80E+03

2.00E+03

2.20E+03

2.40E+03

BHPOffset(psi) GdP/dG(psi)

ISIP : 6804.65

Pc : 6070.28

b) Second cycle

Fig. 19. Closure pressure interpretation of an Extended leak-off pressure (XLOT) in Marañon basin [6].

4. MINIMUM HORIZONTAL STRESS

The least principal stress (S3) corresponds to the minimum horizontal stress (Sh) for normal and strike-slip faulting areas (Fig. 2). For the Thrust fault areas, the vertical stress (Sv), or overburden, is the least principal stress.

Overburden (vertical stress) is computed by integrating formation density [5, 28]. This means that in the case of having the closure pressure equal to the computed overburden, the minimum horizontal stress may be equal or greater than the vertical stress.

Field examples show cases where both Sh and Sv are very close. One option to verify their relationship is through image logs, where vertical induced fractures will develop in zones where Sh is less than Sv, and consequently the least principal stress.

5. MAXIMUM HORIZONTAL STRESS

Direct measurement of maximum horizontal stress (SH) is not possible. However, it can be inferred through modeling using constraints from wellbore failure as indicated by images. Shear failure (wellbore breakout due to low mud weight) and tensile failure (hydraulic fracture due to high mud weight) are used to estimate SH.

Several authors [23, 28] promote the use of the breakout width (Fig. 20) to estimate maximum horizontal stress magnitude.

Fig. 20. Illustration of the breakout width.

To illustrate the theory behind that method, let us consider a vertical wellbore drilled through an elastic material, subjected to an in situ stress field (Sv, SH and Sh), a virgin pore-pressure (Pp), and an internal wellbore pressure (Pw). The elastic solution of Terzaghi effective stresses acting at the borehole wall [30] is:

( ) ( ) ( )

)(´

)(2cos´´2´´´

pwr

pwhHhH

PP

PPSSSS

−=

−−+−+=

σ

θσ θ (1)

The relationship between the breakout width (θb) and the angle θ is give by:

( )2

bθπθ

−= (2)

Considering the Mohr –Coulomb failure criteria, and the mode of failure [31] where the hoop stress is the principal stress (S1) and the radial the least principal stress (S3) at the borehole wall, we can derive:

( ) ( )( )

( )( )

( )b

bhpw

H

SUCSPP

Sθπ

θπφ

φ

−−

−+−+

−

++−

=cos21

cos21´sin1sin1

1

´ (3)

Where UCS is the unconfined compressive strength of the rock and φ is the friction angle.

s H

s H

θ /2 b

θ

S h s h

9

This method is simple and because that popular. It requires previous knowledge of the rock properties, pore pressure and minimum horizontal stress. In order to estimate the error on the method described above, it was applied in a field case where good knowledge of the rock properties were available through triaxial tests, and the minimum horizontal stress estimated by an hydraulic fracture operation. Table 2 below presents the used parameters.

Parameters Value

TVD 15032.2 ft

Overburden (Sv) 15514 psi°

Minimum Horizontal Stress (Sh) 10579 psi

Pore pressure (Pp) 5095.9 psi

Wellbore pressure (Pw) 7816.7 psi

Unconfined compressive strength (UCS) 18000 psi

Friction angle (φ) 42.8 deg

Poisson’s ratio (ν) 0.166

Young’s modulus (YME) 9.68e6 psi Table 2. Parameters used on the borehole breakout example.

Fig. 21 presents the identified breakout at 15032.2 ft. This image log shows a breakout width around 60 deg. Using Eq. 3, the maximum horizontal stress can be estimated at 22561 psi (1.5 psi/ft). A more detailed analysis is presented in section 7, where a maximum horizontal stress of 19177 psi (1.276 psi/ft) is much more consistent with other observations. The SH estimated using only the breakout information overestimated SH by 18%.

Fig. 21. Breakout example.

In order to understand this difference, the maximum horizontal stress estimated through traditional elastic approach is compared against a poroelastoplastic approach [32, 33]. The behavior of the vertical wellbore drilled through a saturated porous medium subjected to an anisotropic stress

field is analyzed (Fig. 21). The material properties and stresses for this example are described in Table 2. For the maximum horizontal stress, it was used 19177 psi (1.276 psi/ft).

In this graphic (Fig. 21), the pink color is indicating that the material is failing, i.e., yield factor more than one. Using this model, the breakout width (θb) is 41 degrees. Applying this θb in Eq. 3, the equivalent elastic solution is obtained with SH equal 20128.8 psi (1.34 psi/ft), showing 5% error with respect with the more consistent plastic solution.

Fig. 21. Yield factor – Poroelastoplastic model.

For this example, the breakout width approach overestimates SH by 18%. Reason why, this approach must be used with extreme caution as the breakout creation cannot be described by the simple analytical experiment described above. During drilling, the downhole pressure is not constant (especially during trips); there is a strong mechanical impact between the drill pipe and the borehole wall; the planes of weakness (section 2.1) affect the breakout geometry; and there is an important temperature difference between the drilling fluid and the formation fluid. Furthermore, the rock after failure cannot be properly described by the elastic equation, and there are others modes of failure not represented by the Eq. 3.

The authors suggest using the failure initiation as a lower bound for SH, and the breakout width (Eq. 3) as an upper bound.

6. CONSTRUCTING THE STRESS PROFILE

The in-situ stress state of the rock is a complex interaction between the rock properties, pore pressure, tectonic stress and vertical load.

10

Variations in the horizontal stress magnitudes can be induced by variations in the pore pressure, temperature and deformations. The two equations below [34, 35] relate the effective horizontal stress increments with these variations:

hHVH

HhVh

dE

dE

dTE

dpdSdS

dE

dE

dTE

dpdSdS

εν

νε

νν

α

ν

ν

ν

ν

εν

νε

νν

α

ν

ν

ν

ν

22´

22´

11111

11111

−+

−+

−+

−−

−=

−+

−+

−+

−−

−= (4)

Where: E Static Young’s Modulus ν Static Poisson’s Ratio α Biot’s Coefficient T Temperature Sv Vertical Stress p Pore Pressure Sh

´ Effective minimum horizontal stress SH

´ Effective maximum horizontal stress εh Strain in the direction of the minimum

horizontal stress direction εH Strain in the direction of the maximum

horizontal stress direction

Leak-off test, mini-frac and hydraulic fracturing are data points used as a calibration for a more complete stress profile. There are other constrains that can be used to help to built horizontal stress profile, like: breakouts and drilling induced fractures identified from images logs; and drilling events (caving, losses, etc) from close by wells.

To determine the horizontal stress profile through Geomechanical modeling, the process outlined in the Figure 22 is applied.

Fig. 22. Process for determining stress profile.

This is achieved by comparison of wellbore stability predictions using the MEM parameters, and instability evidences observed.

There are strong assumptions on Eq. 4, like: Elastic behavior during geologic time, constant stress direction for the tectonic deformation history, flat geometry, etc. However, when well calibrated it is able reproduce many features observed, like: the reduced Sh in sands when compared with shales; the bigger stress contrast in stiff rocks; breakouts in shales; and induced fractures in sandstones/limestones.

Fig. 23 presents results of this process. In this example, the synthetic image obtained from the calibrated Mechanical Earth Model is compared against actual UBI showing excellent agreement.

7. CONCLUSION

Most of the many wellbore stability simulators currently being used in practice by the industry are based on simple assumptions. This paper discusses horizontal stress estimation in tectonically active areas. We present techniques developed over the past 5 years, in more than 90 mechanical earth model (MEM) creations, that have proven to be efficient for horizontal stress estimation in such complex areas.

Compressive and tensile failure of a wellbore is a direct result of the stress concentration around the wellbore that results from drilling a well into already stressed rock mass. Compressive wellbore failures or wellbore breakouts and induced fractures are useful to determination of stress orientation. However, is important to include special analysis for the plane of weakness failure, where there are breakouts in different directions that are not related only to the stress field.

Stress direction is related to the geological setting and the contemporary stress regime. Active faults and folding can introduce local variations the stress direction. It was presented an example were an identified fault divides two different stress directions, one above and a different below the fault through a sharp rotation. However, this cannot be taken as a general rule, since there are many cases where no stress rotation is identified.

An estimative of the magnitude of the least principal stress can be obtained from hydraulic fracturing. The leak-off test is a field pressurization

No

Identify constrains for the stress profile construction

Compute key Mechanical Properties and stresses (UCS, φ , ν , E, S v )

Estimate ε H and ε h

Compute S H , S h and wellbore stability profile

Compare with observations

Obtain Mach?

Identify constrains for the stress profile construction

Compute key Mechanical Properties and stresses (UCS, φ , ν , E, S v )

Estimate ε H and ε h

Compute S H , S h and wellbore stability profile

Compare with observations

Obtain Mach? No

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of the wellbore and is usually performed by the oil industry after the casing string is cemented. The recorded pressure versus time curve during this test, when well conducted, is valuable information for least principal stress estimation. However, it is a common sense to assume the leak-off pressure as the least principal stress. Field examples of extended leak-off testes shows that this assumption is not always a valid simplification, and overestimates the least principal stress. The authors suggest using the leak-off pressure as an upper bound for the least principal stress.

Breakout width elastic approach to estimate the maximum horizontal stress magnitude is pessimistic and overestimates maximum horizontal stress magnitude. Reason why, this approach must be used with extreme caution as the breakout creation cannot be described by the simple analytical experiment. During drilling, the downhole pressure is not constant (especially during trips); there is a strong mechanical impact between the drill pipe and the borehole wall; the planes of weakness affect the breakout geometry; and there is an important temperature difference between the drilling fluid and the formation fluid. Furthermore, the rock after failure cannot be properly described by the elastic equation, and there are others modes of failure not represented by this approach. The authors suggest using the failure initiation as a lower bound for maximum horizontal stress magnitude, and the breakout width method as an upper bound.

The results presented demonstrated that stress direction and maximum horizontal stress magnitude can be misinterpreted by assuming simplified approaches. Those wrong assumptions can negatively impact the stability predictions for wellbore drilling, fracturing design and/or completions/sand control operations.

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Fig. 23. Calibrated Mechanical Earth Model – Comparison of the synthetic image with actual UBI.