Methods to estimate stresses and orientation

This article discusses estimation of stresses encountered during drilling that could cause fracturing or formation damage in the near wellbore area.

Estimates of least principal stress, S₃ from ballooning

Ballooning is a process that occurs when wells are drilled with equivalent static mud weights close to the leakoff pressure. It occurs because during drilling, the dynamic mud weight exceeds the leakoff pressure, leading to near-wellbore fracturing and seepage loss of small volumes of drilling fluid while the pumps are on. When the pumps are turned off, the pressure drops below the leakoff pressure, and the fluid is returned to the well as the fractures close. This process has been called “breathing” or “ballooning” because it looks like the well is expanding while circulating, and contracting once the pumps are turned off. This behavior can be identified on a pressure while drilling (PWD) log (Fig. 1.a). It can be differentiated from a small kick or gas influx (which often is used as an indication to increase mud weight owing to the perception that it reveals gas pressures higher than the equivalent static mud weight), as shown in Fig. 1.b. Increasing the mud weight in a ballooning well can lead to massive lost circulation.

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  Fig. 1 (a)Signature of normal connections (top) and moderate and severe ballooning (middle and bottom) on a PWD log. The difference between ballooning and a potential well-control incident can be detected in a plot of mud volume vs. time after pumps-off (b) (after Ward and Beique).

Ballooning is an important measure of least principal stress magnitude because it is essentially an inadvertent leakoff test conducted while drilling. The static mud weight is a lower bound on the magnitude of the least stress, and the dynamic mud weight is an upper bound. In some cases, a shut-in break can be detected, which is a very accurate measure of the least stress. The only problem is that it can be difficult to identify the depth at which the ballooning incident took place (although it is reasonable to assume that it occurred close to the bit). This is a particular problem when there is a very long openhole interval. Fortunately, it is often possible to find the location of the fractures created by the ballooning incident by a change in logging while drilling (LWD) resistivity recorded before and after the event.

Using wellbore failure to constrain the magnitude of S_Hmax

Once independent knowledge of S_v and S_Hmin is available, SHmax can be determined from the widths of wellbore breakouts in vertical boreholes. Because the stress concentration around the well and the rock strength are equal at the point of the maximum breakout width, it is possible to re-arrange Eq. 1 to solve for S_Hmax, as shown in Fig. 2. Solving for SHmax also requires a model for rock strength and knowledge of the pore pressure and mud weight. While the equations presented here are technically accurate only for elastic, brittle rock, utilizing the results to select the appropriate mud weight for drilling future wells requires only that the same model be applied to predict wellbore stability as was used to determine the stresses.

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  Fig. 2—Schematic diagram of a breakout and the Kirsch equations that are used to constrain stress magnitudes based on the widths of wellbore breakouts and the presence or absence of drilling induced tensile wall fractures. These equations apply to a vertical well when S_v is a principal stress (courtesy GeoMechanics Intl. Inc.).

Once breakouts have formed, they deepen but do not widen. Thus, the original width of the breakout is largely preserved, and calculations of stress magnitudes based on breakout width do not have to be adjusted for changes in the wellbore shape associated with subsequent failure (see Fig. 3).

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  Fig. 3—Theoretical computations performed using boundary element methods reveal that once a breakout has formed, additional failure will occur only at the back of the breakout (left image after Ref. 8, M.D. Zoback et al., “Wellbore Breakouts and In-Situ Stress,” J. Geophysical Research, Vol. 90, No. B7, 5523; © American Geophysical Union; reproduced/modified by permission of the American Geophysical Union). Thus, the breakout may deepen with time, but not widen. Laboratory experiments reveal that breakout formation is consistent with this prediction (right image after Haimson and Herrick).

As previously discussed, breakout width can be determined very accurately using acoustic or electrical image logs run after the well has been drilled. With the advent of resistivity, density, and porosity LWD tools that produce an image of the borehole wall behind the bit, it is now possible to determine breakout widths while drilling, which then makes it possible to determine S_Hmax in real time. On the other hand, in the absence of borehole image data, we can only place bounds on the width of presumed breakouts if they can be detected using the electrode pads of a dipmeter tool (pad width is typically about 30° in an 8.5-in. hole). Therefore, using mechanical calipers, it is possible only to place constraints on the magnitude of S_Hmax.

The presence of tensile fractures in a well also gives some indication of relative stress magnitudes. This is because, as previously discussed, tensile fractures can develop at the wellbore wall only if the far-field horizontal stresses are sufficiently different. For example, when the mud weight is equal to the pore pressure, a strike-slip equilibrium state of horizontal stress is required for tensile wall fractures to develop in a vertical well.

Constraining the magnitude of S_Hmax in deviated wellbores

In deviated wellbores, it is possible to constrain not only the orientation but also the magnitude of S_Hmax. This is because, in deviated wells, the position of wellbore breakouts depends on stress magnitude as well as on stress orientation (Fig. 4). It is also possible at the same time to constrain the rock strength using breakout width.

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  Fig. 4—In an inclined well, stress magnitudes can be determined simply from knowledge of the orientation of wellbore breakouts. In this case, given the magnitudes of S_v and S_Hmin and the orientation of S_Hmax, it is possible to constrain the magnitude of the maximum stress. In addition, it is possible to constrain in-situ strength using the breakout width. For example, if the azimuth of S_Hmax is 130°, its magnitude is 5,770 to 5,840 psi, and the in-situ unconfined compressive strength is approximately 3,600 psi.

This sort of analysis can be carried out in multiple wells by use of combined analyses of tensile and compressive wellbore failures. If the wells have a sufficient number of different deviations and azimuths, a very accurate stress state can be determined using a Monte Carlo approach. Essentially, this is simply a more quantitative way of doing the same thing as creating a figure similar to Fig. 4 for each of the wells and overlaying the figures to identify the one stress state that comes closest to matching all of the observations. If the results for all wells are not consistent with a single stress state, then it is clear that the stress state must be different at the locations of the anomalous wells. This provides powerful evidence for reservoir compartmentalization or the influence of local sources of stress.

The constraints on in-situ stress dictated by the strength of pre-existing faults shown in Fig. 5 can be combined with observations of tensile and compressive wellbore failures to refine estimates of in-situ stress, as shown in Fig. 6. The frictional strength limits are as described above. Overlain on these limits are lines defining the stress states for one specific well that would cause tensile or compressive failure to occur. The near-vertical, fine lines to the left of the stress polygon represent stress states (values of S_Hmax and S_Hmin) that would create tensile fractures at the wall of this deviated well for tensile strengths of 0, 500, and 1,000 psi. If the rock has a given tensile strength and tensile cracks are found, it indicates that the stress state must lie to the left of the appropriate line. Because in most cases pre-existing flaws exist that can be opened by elevated mud weights, the effective tensile strength is often assumed to be zero. Therefore, for this example, it is apparent that if tensile failure is observed, the stress state must lie at the extreme lower left-hand corner of the strike-slip region or the extreme left side of the normal faulting region, a transitional strike-slip or normal faulting stress state for which S_Hmax can range from 14 to as high as 38 lbm/gal. SHmin is much better constrained to between approximately 13 and 15 lbm/gal.

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  Fig. 5—This figure shows construction of the polygon that limits the range of allowable stress magnitudes in the Earth’s crust at a fixed depth and corresponding magnitude of S_v). It is a plot of S_Hmax vs. S_Hmin as constrained by the strength of well-oriented, pre-existing faults. The limits are constrained by Eq. 2, with S₁ and S₃ defined by Andersonian faulting theory, as shown in Table 1 (courtesy GeoMechanics Intl. Inc.).

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  Fig. 6—Plots of lines corresponding to the stress magnitudes required in an inclined well for breakouts to form with the given width (in light gray), and for tensile failure to be initiated for a given tensile strength (fine dark lines), superimposed on the stress limits dictated by the strength of the crust if stresses are limited by the frictional strength of pre-existing faults. These lines correspond to equations of the form shown in Fig. 2.

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  Table 1-Definitions Of S₁ And S₃ For Andersonian Faulting Classifications

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On the other hand, if no tensile fractures are observed and lab or log data indicate that C_o is between 10,000 and 15,000 psi, the stress state can lie anywhere to the right of the vertical lines, and within the region between the near-horizontal, light gray curves plotted for those values of C_o. In other words, SHmin can range from 13 to as high as 30 lbm/gal, and S_Hmax is somewhat better constrained to a range from 26 to 33 lbm/gal. If SHmin had been measured using an extended leakoff test to be approximately 20 lbm/gal, then the range of possible S_Hmax values would be only slightly smaller (between 28 and 33 lbm/gal). In general, in near-vertical wells, the presence of tensile cracks severely limits the magnitude of SHminwithout constraining S_Hmax, whereas observations of breakouts provide weaker constraints on SHmin than on S_Hmax. Multiple observations of breakouts in strong and weak rocks can be overlain to restrict the allowable stress state to the region common to the stress states allowed by all of the observations.

When using this sort of analysis, the important thing to keep in mind is that all you are doing is providing constraints on the stress state. For example, suppose that no breakouts had formed in the well described by Fig. 6 and the rock strength was somewhere between 10,000 and 15,000 psi. In that case, the stress state could definitely not lie above the line corresponding to C_o = 15,000 psi, and is most likely to lie below the line corresponding to C_o = 10,000 psi (i.e., anywhere within the low-stress region, which includes the entire normal faulting stress regime). Additional observations would be required to reduce the large uncertainty in this result.

Constraining the stress state in the visund field

As an example of an instance in which redundant data confirm the stress and strength values derived from combined analysis of wellbore failure and frictional constraints, consider Fig. 7 prepared on the basis of data from an inclined well in the Visund field, North Sea. The frictional faulting constraints were derived from Sv and Pp calculated as described above. Breakouts were identified in caliper data, and intermittent tensile fractures were also seen in both vertical and inclined sections of the well. Breakouts and tensile cracks in the vertical section provided information on the stress orientation. Based on log data, C_o ranged from 20 to 25 MPa. The light gray lines labeled 20 and 25 correspond to the stresses constrained by the breakout observations and the rock strength parameters.

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  Fig. 7—Taken from Wiprut and Zoback, this figure illustrates a case in which frictional constraints combined with observations of wellbore failure, calculated values of S_v and P_p, and measured rock strengths provided excellent constraints on the magnitudes of the horizontal stresses. A leakoff test analyzed separately from this analysis confirmed the predicted magnitude of S_Hmin.

Because tensile cracks are more likely to occur when circulation cools the well, it is necessary to account for that cooling in the stress constraints from their occurrence. That shifts the tensile failure line to the right. It is not necessary to include cooling in the breakout analysis, however, because the breakouts would be more likely to occur after the well temperature had equilibrated. The final constraint, based on frictional faulting theory, is that the stress state cannot lie outside the polygon.

Taken together, these observations constrain the stress state to lie in the small region bounded by the light gray lines on the top and bottom, the thin dark near-vertical line on the right, and the edge of the stress polygon on the left. This provides a very precise value for S_Hmin between 52.5 and 54.5 MPa, and it constrains S_Hmax to be between 73 and 76 MPa. A leakoff test provided redundant information on S_Hmin and confirmed its value predicted from the constraints imposed by observations of failure.

Nomenclature

Pp	= pore pressure, MPa, psi, lbm/gal
S1	= greatest principal stress, MPa, psi
S3	= least principal stress, MPa, psi
SHmin	= least horizontal stress, MPa, psi, lbm/gal
SHmax	= greatest horizontal stress, MPa, psi, lbm/gal
ΔP	= difference between the pressure of fluid in a well and the pore pressure
ΔT	= temperature difference between the fluid in a well and the adjacent rock
θ	= angle around the wellbore measured from the SHmax direction, degrees
μ	= coefficient of sliding friction on a pre-existing weak plane, where μ = tanΦ
σ	= Terzaghi effective stress, MPa, psi
σ1, σ2, σ3	= maximum, intermediate, and least effective stresses, MPa, psi
σrr	= effective normal stress acting in the radial direction, MPa, psi
σθθ;	= the effective hoop stress, MPa, psi

Noteworthy papers in OnePetro

Owen, L.B., Toronto, T.W., Terra Tek Inc. and Peterson, R.E. 1988. SPE Annual Technical Conference and Exhibition, 2-5 October. 18165-MS. http://dx.doi.org/10.2118/18165-MS.

Safdar K., Sajjad A., Hongxue H., and Nader K., 2011. Canadian Unconventional Resources Conference, 15-17 November. 149433-MS. http://dx.doi.org/10.2118/149433-MS

Fredrich, J.T.,Engler, B.P., Smith, J.A., Onyia, E.C., and Tolman, D.N. 2007. Pre-Drill Estimation of Sub-Salt Fracture Gradient: Analysis of the Spa Prospect to Validate Non-Linear Finite Element Stress Analyses. Presented at the SPE/IADC Drilling Conference, Amsterdam, The Netherlands, 20-22 February 2007. SPE-105763-MS. http://dx.doi.org/10.2118/105763-MS

External links

Stephansson, O., and Zang, A. 2012. ISRM Suggested Methods for Rock Stress Estimation—Part 5: Establishing a Model for the In Situ Stress at a Given Site. Rock Mechanics and Rock Engineering. November 2012, Volume 45, Issue 6, pp 955-96. http://dx.doi.org/10.1007/s00603-012-0270-x

See also

Stress strain relationships in rocks

Predicting rock properties

PEH:Geomechanics_Applied_to_Drilling_Engineering

Page champions

Fersheed Mody, Ph.D., P.E.