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Determining stress orientation
The most reliable way to determine stress orientation is to identify features (either geological features or wellbore failures) the orientation of which is controlled by the orientations of the present-day in-situ stresses. Other methods that rely on observing the effect of stress on rock properties using oriented core have been found to be less reliable and subject to influence by factors other than in-situ stress.
Using wellbore failure
As previously discussed, wellbore breakouts occur in vertical wells at the azimuth of SHmin, and drilling-induced tensile failures occur 90° to breakouts at the azimuth of SHmax. Therefore, the orientations of these stress-induced wellbore failures uniquely define the orientations of the far-field horizontal stresses when using data from vertical wells. This is true for breakouts whether they are detected using 4-arm- or 6-arm-oriented caliper logs or using electrical or acoustic images, whether obtained by wireline or logging while drilling (LWD) tools. In fact, with the advent of density and porosity LWD imaging tools, it is now possible to identify and orient wellbore failures while drilling.
Because mechanical calipers are still the most widely used tool in detecting breakouts, and because of the large amount of available data, a considerable amount of work has been carried out using data from these devices to identify stress orientations and their variations with depth and location. The results, when careful filtering criteria are used, indicate that stress orientations vary slowly with both depth and location. The exceptions are in cases of active faulting, rapid drawdown of compartmentalized reservoirs, and where other local stress perturbations cause changes in the stress field. Figs. 1 and 2 illustrate that local stress orientations are quite consistent and that stresses generally do not change with depth. In addition, Fig. 2 illustrates the expected result that wellbore breakouts and drilling-induced tensile fractures provide similar stress orientation results.
Fig. 1—Stress orientations derived from carefully filtered caliper logs in the North Sea (modified, after Wiprut et al.).
Fig. 2—Stress orientations in one well, from breakouts (open circles) and from drilling-induced tensile wall fractures (solid circles), are typically the same at similar depths and consistent over large depth intervals. Local variations are caused by slip on small weak faults that intersect the well and are activated by a near-wellbore pore-pressure increase caused by infiltration owing to the mud overbalance during drilling.
Using seismic anisotropy
It has long been known that elastic-wave velocities are a function of stress. That is, velocity will increase with confining pressure, as shown in Fig. 3. It has also been demonstrated that this is owing to the presence of microcracks and pores that close in response to applied load. The amount of change of velocity with stress depends both on the number of cracks and on their compliances. As the load increases and the most compliant cracks close, the sensitivity of velocity to confining pressure decreases. Once all cracks are closed, velocities change very little with stress, and under sufficiently high confining stress, it is possible to measure the “intrinsic velocities” of a sample that are functions only of its mineralogy and morphology.
Because rocks are intrinsically anisotropic and can also be anisotropic due to structural fabric such as joints or bedding planes, it is important to differentiate between stress-induced and intrinsic or structural anisotropy. This is rarely possible, except in cases in which the geological structures can be identified and their effects quantified and removed from the data prior to analysis. It is also possible to identify stress-induced anisotropy when the characteristics of the anisotropy that is stress-induced differ from the characteristics of structural or intrinsic anisotropy.
Laboratory experiments have confirmed that, in many rocks, velocities are anisotropic (a function of direction) and are most sensitive to the stress applied in the direction of propagation or of particle motion. Thus, because in-situ stresses vary with direction in the Earth, in-situ velocities are likely to be anisotropic. In the case of compressional P-waves, the velocity depends on the direction of propagation because P-wave particle motion is parallel to propagation direction. Under uniaxial stress, the P-wave velocity in the direction of applied stress increases with stress much more than the velocity in the direction perpendicular to the applied stress, as shown in Fig. 3.b. In the case of shear S-waves, in which particle motion is perpendicular to propagation direction, velocities depend both on the propagation direction and on the polarization direction (i.e., the direction of particle motion). Because almost all rocks in situ have a finite porosity, this offers the opportunity to derive stress directions from in-situ seismic velocities.
Multicomponent seismic sources and receivers have been developed and deployed, and 3D multicomponent seismic surveys have been designed, to take advantage of this effect. However, while there is clear evidence that vertically and horizontally polarized shear waves have different velocities in shales, it is rare to find an appreciable amount of azimuthal anisotropy. One exception has been in cases in which anisotropy occurs owing to oriented sets of vertical fractures or joints. In such cases, however, it is not clear if the stress orientations are related in any way to the anisotropy because the joints may have been created in a quite different stress field than pertains at present.
Using crossed-dipole sonic logs
Modified sonic logging techniques can also be used to determine stress orientations. This is because, in a wellbore, it is possible using oriented sources and receivers to generate modes that bend the borehole in one direction. These dipole modes propagate efficiently at low frequencies and have been used to measure S-wave velocity where standard sonic logs cannot (that is, where S-wave formation velocity is lower than the acoustic velocity of fluids in the well). When velocity is stress-sensitive, dipole velocity becomes a function of the orientations of the sources and receivers, owing both to the presence of a near-wellbore stress concentration and to differences in the far-field stresses. Two modes are produced: a slow shear wave and a fast shear wave. At low frequencies, these propagate at the orientations of the least and greatest stress, respectively, perpendicular to the well. By adding an orientation device to a dipole logging tool, it is possible both to derive the velocities of the fast and slow shear waves and also to determine their directions.
Crossed-dipole logs are recorded in such a way as to allow computation of the velocities and orientations of fast and slow dipole modes. One potential benefit of these analyses is that theoretical considerations and laboratory measurements indicate that it is possible to differentiate between stress-induced and intrinsic anisotropy based on plots of velocity vs. frequency of the dipole modes. However, it is rare that field data are of sufficient quality to make this possible. In fact, reliable stress orientations are generally only possible in sands, porous limestones, and shales where the well is nearly perpendicular to bedding, where intrinsic anisotropy is low and the rocks are fairly compliant. In addition, these measurements should only be attempted when wells are drilled within approximately 20° of a principal stress direction. Finally, analyses should be believed only when very restrictive quality-assurance conditions can be met (e.g., Fig. 4).
Fig. 4—Data and display from a Schlumberger crossed dipole log (xDSI™) showing results and quality control curves. A high-quality crossed-dipole analysis result has large maximum energy and low minimum energy (Track 1), a consistent orientation with a small uncertainty (Track 3), and large time- and velocitydomain anisotropy (Track 4). A low quality result has low maximum energy and very small anisotropy; a consistent orientation and low uncertainty are meaningless when this is the case.
Core-based analysis of stress orientation
Considerable effort has been devoted to developing and validating core-based stress analysis techniques. The one thing these have in common is the idea that post-coring deformation is dominated by expansion occurring because of removal of the core from in-situ stress conditions. The assumption is that the recovery-induced strains will have the same relative magnitudes and orientations as the original in-situ stresses. Therefore, by measuring the strains caused by removal or reloading, it is possible to constrain at least the directions of the principal stresses and their relative magnitudes.
There are basically three classes of techniques. These include:
- Measuring strain relaxation as a function of time after core removal,
- Measuring strain as a function of orientation while reloading under isotropic conditions (possibly including monitoring for noise caused by microscopic slip events), and
- Measuring velocities as a function of orientation under isotropic reloading.
To orient stresses based on these techniques, it is necessary to know the original orientation of the core, which adds to the complexity of coring operations. Also, because the orientations of the principal strains are unknown prior to testing, to determine them it is necessary to attach more than three strain gauges to the sample.
Strain relaxation measurements
In strain relaxation measurements, the core is recovered as quickly as possible, instrumented with strain gauges to monitor deformation as a function of time, and maintained in a constant (fixed) temperature/humidity environment. The principal strain axes are assumed to define the principal in-situ stress axes, and the relative strain magnitudes are assumed to correspond to the relative stress magnitudes. Thus, the vertical and horizontal relative stress magnitudes and the horizontal stress orientations can be derived from the principal strain orientations and magnitudes. Because most of the strain occurs during the first few minutes following removal from in-situ conditions, rapid recovery is essential to ensure accurate results.
Measuring strain while reloading
The second (reloading) technique relies on the assumption that samples are much “softer” at stresses that are below their original confining stress than they are at stresses above their original confining stress. This assumption can be extended to cases in which the original stress state was anisotropic, so that the stress at which the sample gets stiffer is different in different directions. By isotropically loading a rock and monitoring strain as a function of confining stress and orientation, it is possible to determine the magnitudes of the three principal stresses by identifying the point in plots of stress vs. strain at which each curve bends over, indicating that the sample has suddenly become less sensitive to applied stress. The in-situ stress orientations and Andersonian stress state can be derived using the relative stress magnitudes at which this occurs, after resolving them into principal stress coordinates. If the sample has been instrumented to observe acoustic emissions from microscopic slip events, these will sometimes increase once the in-situ stress has been exceeded.
To derive principal stress orientations using velocity measurements, samples are instrumented with ultrasonic transmitters and receivers at a number of orientations, and the travel times of ultrasonic pulses are measured as a function of confining stress. As in the case of reloading, changes in velocity for each principal stress direction while confining pressure is below the original stress are larger than changes in velocity when confining pressure is above the original stress.
Pitfalls of core-based stress analysis techniques
All three techniques suffer from the same limitation, which is that nearly all rocks are intrinsically anisotropic. In other words, their elastic moduli (which control the amount of strain that is caused by a given applied stress) are a function of direction. Anisotropic rocks will have different amounts of strain in different directions, even if they are subjected to an isotropic stress state. If the intrinsic anisotropy is large enough, which it generally is in shales, laminated sands, and other finely bedded or foliated rocks, strains related to that anisotropy can mask strains caused by stress changes. Thus, while there are some situations in which these techniques work, there are many pitfalls, and the results should be used with caution.
Geological indicators of stress orientation
In the absence of better data, it is sometimes useful to look at earthquake focal mechanisms within the region or to map local geological structures to help provide a “first look” estimate of the relative magnitudes and orientations of the current stresses. In the case of earthquake focal mechanisms, it is important to utilize data from many earthquakes within a small region to derive a “composite focal mechanism,” to avoid the large uncertainties associated with individual analyses. In the case of geological structure, it is critically important to remember that many structures are inherited from older stress fields and that the only structures that do provide information are those that are currently active. Fig. 5 is an example, from South Eugene Island in the Gulf of Mexico, where the stress direction, confirmed by wellbore breakout analysis, is consistent with the orientation of a nearby large, active normal fault.
Fig. 5—Structure map in the South Eugene Island area of the Gulf of Mexico, showing large, active, WNW-ESE-trending normal faults. Given this fault orientation, the least stress is expected to be horizontal and oriented NE-SW. Stress orientations from breakouts confirm this (outward-facing arrows) (modified after Finkbeiner et al.).
Salt domes can significantly perturb the local stress field because extension predominates above active salt intrusions, whereas beside the salt compression acts radially away from its walls. This is because salt is virtually unable to sustain a significant stress difference, and thus all three stresses in salt bodies are nearly equal and close to the vertical stress. This not only increases the local horizontal stresses, but also causes a rotation in the principal stress axes to be perpendicular and parallel to the salt face. Salt domes rarely have vertical walls, and thus the vertical stress may no longer be a principal stress close to their flanks.
- Wiprut, D.J. and Zoback, M.D. 1998. High Horizontal Stress in the Visund Field, Norwegian North Sea: Consequences For Borehole Stability and Sand Production. Presented at the SPE/ISRM Rock Mechanics in Petroleum Engineering, Trondheim, Norway, 8-10 July. SPE-47244-MS. http://dx.doi.org/10.2118/47244-MS.
- Rai, C.S. and Hanson, K.E. 1988. Shear-wave velocity anisotropy in sedimentary rocks: a laboratory study. Geophysics 53 (6): 800–806. http://dx.doi.org/10.1190/1.1442515.
- Gregory, A.R. 1976. Fluid Saturation Effects on Dynamic Elastic Properties of Sedimentary Rocks. Geophysics 41 (5): 895-921. http://dx.doi.org/10.1190/1.1440671.
- Finkbeiner, T., Zoback, M., Flemings, P. et al. 2001. Stress, Pore Pressure, and Dynamically Constrained Hydrocarbon Columns in the South Eugene Island 330 Field, Northern Gulf of Mexico. Am. Assoc. Pet. Geol. Bull. 85 (6): 1007-1031. http://dx.doi.org/10.1306/8626CA55-173B-11D7-8645000102C1865D.
Noteworthy papers in OnePetro
Bruno, M.S. and Winterstein, D.F. 1992. Some Influences of Stratigraphy and Structure on Reservoir Stress Orientation, SPE Annual Technical Conference and Exhibition, 4-7 October. 24746-MS. http://dx.doi.org/10.2118/24746-MS.
Owen, L.B., T.W. and Peterson, R.E. 1988. Reliability of Anelastic Strain Recovery Estimates for Stress Orientation in the Travis Peak Formation, Harrison County, Texas, SPE Annual Technical Conference and Exhibition, 2-5 October. 18165-MS. http://dx.doi.org/10.2118/18165-MS.
Fersheed Mody, Ph.D., P.E.