Orientation and magnitude of in situ stress to 6.5 km depth in the Baltic Shield

Transcription

1 PERGAMON International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169±190 Orientation and magnitude of in situ stress to 6.5 km depth in the Baltic Shield B. Lund a, *, M.D. Zoback b a Department of Earth Sciences, Uppsala University, VillavaÈgen 16, Uppsala, Sweden b Department of Geophysics, Stanford University, Stanford, CA , USA Accepted 29 November 1998 Abstract Understanding the state of stress in the earth is important for a broad range of engineering and geological problems. To obtain the state of stress in boreholes where conditions are such that conventional stress measurement techniques are impossible, we have used recent developments in the analysis of compressive and tensile wellbore failure in an integrated stress measurement strategy, involving also direct measurement of the least principal stress. The analysis is carried out in the two deep boreholes in the Siljan Ring area of the Baltic Shield. The Gravberg-1 borehole reached 6779 m true vertical depth (TVD) in the Siljan region, central Sweden, and the Stenberg-1 borehole, drilled 10 km to the south of Gravberg-1, was completed at 6529 m TVD. Analysis of vertical, drilling-induced tensile fractures in the nondeviating part of the Gravberg-1 well indicated that one principal stress is vertical and thus could be calculated from density estimates. Borehole breakouts and tensile fractures indicated that the average direction of the maximum horizontal stress, S H, is N728W278 in Gravberg-1 and N538W298 in the Stenberg-1 well. The direction of S H is on average very stable in both wells. Lower bound limits on the magnitude of the minimum horizontal stress, S h, in the Gravberg-1 well were obtained from controlled and uncontrolled hydraulic fracturing and formation integrity tests. At 5 km depth in the Gravberg-1 borehole the minimum horizontal stress is approximately two-thirds of the vertical stress. We estimated the magnitude of the maximum horizontal stress in Gravberg-1 on the basis of drilling-induced tensile fractures identi ed in the borehole. S H was estimated by calculating the stress at the borehole wall necessary to cause tensile failure of the formation, incorporating our lower bound S h estimates, corrections for the cooling of the wellbore by drilling uids and di erential uid pressures. Our results indicate a strike-slip faulting regime in the Siljan area and that the state of stress is in frictional equilibrium with a coe cient of friction in the range 0.5 to 0.6. # 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction Direct knowledge of the magnitudes of in situ stresses is important at all scales from engineering applications, such as the stability of boreholes and mine shafts, to placing constraints on geological problems such as how plate-driving forces are transmitted through the lithosphere. While the methodology for determining the orientation and relative magnitude of crustal stresses is now well-established [1±3] and has been utilized at literally thousands of sites around the * Corresponding author. Tel.: ; fax: ; address: bl@geofys.uu.se (B. Lund). world, e.g. Zoback [4], there have been extremely few sites where in situ stress magnitude has been measured at depths greater than 2±3 km, see review in Brudy et al. [5]. This is in part due to the very few deep boreholes drilled but also because conventional stress magnitude measurement techniques, e.g. overcoring and hydraulic fracturing, are technically extremely di cult in deep boreholes. Recent developments [6±8] in the interpretation and analysis of drilling-induced compressive and tensile failures in wellbore image data have, however, made stress orientation and magnitude estimation considerably easier and also allows for a continuous stress pro le along the borehole. An application of these techniques and a notable exception to the absence of direct measurements of /99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S (98)

2 170 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169±190 Fig. 1. Map of Scandinavia with the Siljan region enclosed in the rectangle. Directions of maximum horizontal stress on the map are from the World Stress Map Project [4] using their terminology and de nitions, see legend. Inset is a geological map of the Siljan Ring impact structure with the location of the two deep wells marked with lled triangles. Geological map simpli ed after Hjelmqvist [14].

3 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169± stress magnitude at great depth are the data from the ultra-deep KTB scienti c research well in Germany. Zoback et al. [9] and Brudy et al. [5] report on an integrated program of in situ stress measurements to 8 km depth utilizing detailed observations of wellbore failure. An integrated stress measurement strategy (ISMS) was utilized at KTB to estimate the magnitude and orientation of all three principal stresses. The ISMS involves combining direct measurement of the least principal stress, made with hydraulic fracturing, and detailed analysis of extensive drilling-induced wellbore failure. This integrated methodology was rst utilized to determine stress magnitudes in the Cajon Pass borehole near the San Andreas fault in California [10]. It should be emphasized that the ISMS, using high resolution wellbore image tools, is a valuable method for stress pro ling also in shallower boreholes due to the relative ease of including the image tools in the regular logging program. We report here the application of an ISMS, similar to that utilized in the KTB borehole, in the Gravberg- 1 and Stenberg-1 deep boreholes in Sweden. In the search for deep abiogenic gas within the Siljan Deep Drilling Project, two wells were drilled into the Siljan Ring, a meteorite impact structure formed approximately 360 Ma ago [11±13] in central Sweden, see Fig. 1. The Siljan impact is situated in the Baltic Shield, the crust below Siljan is about 45 km thick [15] and heat ow is estimated to 60±65 mw/m 2 [16]. The Gravberg-1 well was drilled into the northern part of the impact structure whereas the Stenberg-1 well was drilled into the central region of the impact. Fig. 2. (A) N308E projection of the geometry of the Gravberg-1 well onto the N±S trending seismic section line 5 [18]. TD refers to the total drilled depth along each borehole. The well penetrated mostly granitic rocks but also several subhorizontal dolerite intrusions, three of which were identi ed as prominent seismic re ectors [19]. (B) Deviation of the Gravberg-1 well with depth. The lled circles represent the original hole, the open circles the rst side-track and the crosses the second side-track. Deviation increases rapidly below 4.5 km but never reaches more than 458 in the section of the well that is of interest in our study. The vertical bars to the left in the gure indicate the sections of the well where we have data from the BGT, the bars to the right indicate the FMS logs. (C) Deviation of the Stenberg-1 well with depth. Data from the original hole, which was abandoned at 4133 m, and the side-track have been merged. The vertical bar to the left indicates the section where we have BGT data.

4 172 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169±190 Spudded on July 1, 1986, the Gravberg-1 well was drilled [17] in two drilling operations down to a true vertical depth of 6779 m, see Fig. 2. The well was sidetracked three times due to severe downhole conditions with the drill bit frequently becoming stuck. All four holes deviate to the north-northeast, see Fig. 2, up to as much as 458 from the vertical in the lower part of sidetrack 1. Only 8.5 m of core was recovered from the well. The well penetrated almost exclusively granites, varying in age from 1.7 to 1.9 Ga [20, 21] and without any foliation. Dolerite sills at depth were identi ed in the well [20, 21] and the region is cut by preimpact dolerite dikes [22, 23]. A number of fracture zones of varying thickness were drilled through, many of them in conjunction with the dolerite intrusions [24]. Four high amplitude re ectors were identi ed in re ection seismic investigations in the area, three of them were penetrated by the borehole and have been correlated with major dolerite intrusions [19], see Fig. 2. The state of stress in the Gravberg-1 well has been investigated earlier by several authors. Stephansson et al. [25] presented directions of the maximum horizontal stress, S H, to 4 km depth and estimates of the magnitude of the minimum horizontal stress, S h, based on data from the well [26]. They also estimated the magnitude of S H by extrapolating results from shallower boreholes [26]. Qian and Pedersen [27], corrected by Qian et al. [28], used a nonlinear inversion scheme to invert the borehole breakouts in Gravberg-1 for the direction of the horizontal stresses and the ratios S H /S V and S h /S V, assuming that S V is a principal stress. Zajac and Stock [29], with an unfortunate misspelling of Siljan both in the title and in the text of the paper, inverted the data published by Qian and Pedersen [27] with a genetic algorithm and a nongradient N-dimensional optimizer to nd the directions of the three principal stresses and the shape factor f =(s 2 s 3 )/(s 1 s 3 ). We will comment on the results of these investigations in the appropriate sections below. Spudded in July, 1991 and drilled to a true vertical depth of 6529 m [30], see Fig. 2, the Stenberg-1 borehole was the second well in the Siljan deep drilling project. The well was drilled in the central part of the Siljan impact structure, see inset Fig. 1, and as the Gravberg-1 well penetrated predominantly granitic rock intersected by dolerite sills and fracture zones [31]. The Stenberg-1 well was also sidetracked, when the original hole had to be abandoned at 4133 m, but the deviation problems were less severe than in the Gravberg-1 well, see Fig. 2. The Stenberg-1 well has been less extensively investigated than the Gravberg-1 well. There are, for example, no image logs of the borehole wall from the Stenberg-1 well, and we thus use the Stenberg-1 data only to obtain the orientation of the stress tensor, using caliper information on borehole geometry which was measured in the entire well below 800 m. No core was recovered in the Stenberg-1 well. In the sections below, we basically follow the ISMS as employed in the KTB boreholes [5], with some modi cation to the estimation of the thermally induced stress, and attempt to utilize the observations of borehole failure in the Gravberg-1 and Stenberg-1 boreholes to constrain stress orientations and magnitudes to great depth in the Siljan area. Although no speci c stress measurement program was planned for the two boreholes and downhole conditions, with large deviations and wellbore failure, were very di cult, there are su cient data to use the integrated approach discussed above to estimate the full stress tensor. The stress estimates will then be tested against the hypothesis that the state of stress in the crust is in equilibrium with the theoretical frictional strength as de ned by laboratory data and frictional faulting theory. 2. Observations of borehole failure I: in situ stress orientation The orientation of horizontal principal stresses is routinely measured in vertical wellbores utilizing stress-induced wellbore breakouts. These form at the azimuth of the least principal horizontal stress, the point around the wellbore where the compressive stress concentration is maximum, e.g. Bell and Gough [32], Zoback et al. [33] and many others. Both 4-arm caliper [32, 34] and ultrasonic borehole televiewer [35] can be used to identify breakouts and determine stress orientation. As shown by Zoback et al. [33], Plumb and Hickman [34] and Shamir and Zoback [36], borehole televiewers are better for determining stress orientation from wellbore breakouts due to their higher resolution. As pointed out by Mastin [37], breakouts in deviated boreholes cannot be used to assess stress directions directly as the point of most compressive stress concentration around the wellbore is a ected by the magnitudes of all three principal stresses and the orientation of the wellbore. Peska and Zoback [7] analyzed this problem more fully and demonstrated that under appropriate circumstances one could use the orientation of breakouts in deviated wellbores to assess both stress orientation and stress magnitude. As the Gravberg-1 and Stenberg-1 wellbores are deviated signi cantly below 5 km but we lack the data to do a complete analysis according to Peska and Zoback [7], data from the deviated part of the well has not been used in estimating stress orientation. Following the general criterion of Plumb and Hickman [34] for distinguishing stress-induced wellbore breakouts from other types of drilling-induced wellbore enlargements such as key-seats and washouts (see

5 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169± below), we devised a standard procedure to analyze the large amounts of 4-arm caliper data at our disposal. Four constraints were applied to the caliper data before it could be accepted as breakouts. This procedure is described in detail in Appendix A and the following is a summary:. The di erence between the long and the short diameter of the hole should be more than X cm, when the original drill bit diameter was Y cm.. The short diameter of the hole should be close to the original diameter, to avoid washout zones, or zones of failure of the entire wellbore, where the wellbore is enlarged around its entire perimeter.. The tool should not be allowed to rotate within a breakout more than a few degrees within a given breakout interval (typically Z m's).. Data should be disregarded from the sections where the breakout direction is parallel to the direction of deviation of the borehole. In a deviated borehole the drill string will erode the high-side of the borehole wall (key seating) which might cause an enlargement of the diameter which cannot be distinguished from a breakout. In addition to breakouts, drilling-induced tensile wall fractures were observed in wellbore image data in the Gravberg-1 well and these can be used to determine stress orientations in the well [5, 6, 8, 38, 39]. As discussed at length in Brudy and Zoback [8], these fractures are small scale tensile fractures induced by the stress concentration at the wellbore wall. They occur when the point of least compressive stress around the wellbore goes into tension and do not propagate away from the borehole because of the rapid increase of compressive stress with distance from the wellbore [8]. In vertical wells this is the azimuth of the maximum horizontal compressive stress if one principal stress is vertical (corresponding to the overburden). The stress regime is important for the formation of induced tensile fractures. In near vertical wells, they form almost exclusively in strike-slip stress regimes where there is an appreciable di erence in the magnitude of the maximum and minimum horizontal principal stresses [7, 39]. These fractures are only detectable through borehole imaging as they do not alter the shape of the wellbore as breakouts do. As showed by Brudy and Zoback [8] and demonstrated below, with appropriate knowledge of other factors which a ect the stress concentration around the wellbore (principally cooling of the wellbore by the drill uid and the density and pumping pressure of the uid in the borehole) the occurrence of these features can be used to estimate the magnitude of the maximum horizontal stress. When the wellbore axis does not coincide with one principal stress, the fractures form at an angle inclined to the wellbore axis in an en echelon pattern [6, 7]. In practice, it is often not straight forward to determine whether linear, axial marks found on wellbore images are drilling induced tensile fractures. We utilize here the following indicators [8].. The fractures appear in pairs on opposite sides of the wellbore.. If the borehole is parallel to one principal stress the fractures are parallel to the borehole axis.. If the borehole deviates from the principal stresses, the induced tensile cracks form at angles to the borehole axis in an en-echelon pattern. The fractures usually show small kinks and are not perfectly straight.. The tensile fractures occur at the azimuth of the direction of the maximum horizontal stress in nearvertical wells. If there are breakouts present, there is a 908 di erence between the azimuth of the breakouts and the tensile cracks. Using these criteria, abundant drilling induced tensile fractures were identi ed in the KTB pilot hole and the Soultz-sous-Foreà ts GPK1 borehole as well as in the KTB main borehole [8]. Fig. 3 is an example of an induced tensile fracture at 5 km depth in the Gravberg-1 well. This section of the well was logged twice with the 2-pad FMS tool and we were able to follow the fracture trace on both sides in the wellbore. On both trips with the FMS tool one pad travelled approximately to the south in the borehole, which is why there are three strips in Fig. 3, not four The Gravberg-1 well Wellbore breakout data in the Gravberg-1 well come from two di erent tools, the borehole geometry tool (BGT) and the formation microscanner (FMS), an electrical imaging device [40], both equipped with four-arm calipers and magnetic orientation sensors. The BGT has 2 cm wide arms and is able to follow the breakouts deeper than the FMS which has 7 cm wide pads at the end of the arms. The BGT was run in almost the entire well, see the vertical bars to the left in Fig. 2B, and thus supplied the bulk of the breakout data. The FMS was run in 8 short intervals in logging suite 3, between 1250 and 3932 m, and continuously in logging suite 6, between 4167 and 5683 m in the original hole, see the thick vertical bars to the right in Fig. 2B. All depths referred to are measured depths (MD) along the borehole and unless stated otherwise all depths below in the remaining of the paper will also be MD. We received the BGT data from Gravberg-1 after some initial processing had been done, this is the same

6 174 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169±190 Fig. 3. Example of a FMS image from 5 km depth in the Gravberg-1 borehole. The section was logged twice and the two images have been joined to produce this gure, which is oriented as indicated by the directions on top of the gure. The induced tensile fracture is the obvious vertical feature on the left and right pad strips. A number of natural fractures cutting through the borehole can also be seen. data set that Qian and Pedersen used as a base for their further data reduction [27], consisting of over 7 km of data sampled every 30 cm (1 ft). The data was further processed by us as discussed above. The FMS caliper data were processed entirely by us according to the above scheme. The resulting S H directions, including both BGT and FMS caliper data, is presented as crosses in Fig. 4A. Each cross represents an average S H direction in a 10 m interval and only intervals with more than 5 samples left after the processing have been included. The horizontal bar on the data point is the standard deviation within that interval calculated with circular statistics according to Mardia [41]. (A discussion of factors contributing to the uncertainty in the S H direction estimates can be found in Appendix A.) Note that the standard deviation is highest in the upper part of the well, where the breakouts are generally fewer and more scattered. The mean orientation of breakouts indicates a west-northwest direction of maximum horizontal compression that is discussed below.

7 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169± Fig. 4. Directions of the maximum horizontal stress, S H. The crosses are stress orientations from borehole breakouts averaged over 10 m sections in the boreholes, the circles stress orientations from induced tensile fractures. Superimposed on the breakout data points are the standard deviations as a horizontal bar. (A) Direction of S H in the Gravberg-1 well. The average orientation over the borehole from 0 to 4850 m, where the deviation is less than 158, is N728W278. (B) Direction of S H in the Stenberg-1 well. The average orientation over the borehole from 0 to 5950 m, deviation less than 158, is N538W298.

8 176 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169±190 The data presented in Fig. 4A show a remarkable similarity to the pro le of maximum horizontal stress directions determined from wellbore breakouts encountered from 1.7 to 3.5 km depth in the Cajon Pass scienti c research well near the San Andreas fault [36] and in the KTB ultra-deep well in Germany [5]. There is a well-de ned average stress direction that does not change systematically with depth, but there are both long- and short-wavelength variations of stress orientation and several abrupt jumps in stress orientation that have been interpreted to be caused by slip on active faults [26, 36, 42]. This is discussed at greater length below. The formation microscanner tool run in the Gravberg-1 well was a 2-pad tool, i.e. only two of the four pads were equipped with electrodes to create a micro-resistivity image. The tool thus gives two strips of images of the borehole wall, 908 apart, and covers only about 20% of the borehole circumference in a wellbore with 21.6 cm diameter. From these images it is possible, but di cult, to reconstruct the trace of a natural fracture intersected by the borehole, and thus determine its strike and dip. Due to the deep breakouts in long sections of the well, the FMS pad travelling in the breakout very often had poor contact with the borehole wall and thus the image from the pad became blurred. This caused problems in determining whether or not a feature, e.g. a fracture, seen on one pad image was continuous around the borehole or not. Drilling induced fractures along the borehole axis should appear 908 away from the breakouts and at that azimuth the pad usually had good contact with the wall but without exclusive evidence from the second pad it was di cult to be sure that the fracture trace did not cut through the borehole. Some short intervals were logged twice with the FMS tool thus increasing the coverage of the borehole wall enabling us to more easily identify the drilling induced vertical fractures. Because of the low circumferential coverage of the borehole wall with the 2-pad FMS tool it was di cult (and often impossible) to meet all the criteria mentioned above for drilling induced tensile fractures. We have, however, been conservative in our identi cation scheme and only incorporated features which comply with most of the indicators listed above. The open circles in Fig. 4A are the S H directions inferred from drilling induced tensile fractures. We have not included any estimates of the uncertainty in these data points since the main uncertainty arises in the identi cation of the fracture. Errors in nding the fracture's orientation in the borehole amounts to less than 58. Most of the S H directions agree with the breakout directions obtained from the caliper data but there are a number of anomalous points where the S H directions are almost 908 away from the caliper data directions. It is not known if these represent actual anomalies of the stress eld or whether they simply represent misidenti cation of tensile fractures. It is interesting to note that in some cases these anomalous points occur where there are no breakouts. Zones with no breakouts were used as an indication of fracture zones in the Gravberg-1 well [24] and in the upper suite 3 the FMS tool was run mainly to investigate these zones of intense natural fracturing. Both the strength of the rock around the borehole and the stress eld itself might be quite di erent to the strength and stress eld around the well in sections of intact rock, thus producing the anomalous tensile fractures. On the other hand, in both the KTB borehole [8] and the Cajon Pass borehole [10] where numerous active faults intersect the wellbore and produce localized perturbations of the stress eld [36, 42] rotations of the stress eld are much smaller (typically 208±308) and 908 rotations are not observed. Thus, one suspects that a number of the anomalous points indicated as tensile fractures in Fig. 4A may simply be the result of misidenti cation of marks on the wellbore wall, perhaps incipient breakouts that never developed, as tensile fractures The Stenberg-1 well The breakout information in the Stenberg-1 well comes only from caliper data from a BGT. Data are available from 780 to 6600 m, see Fig. 2C. The caliper data were processed by us as described brie y above and in detail in Appendix A. The resulting S H directions are presented in Fig. 4B where the crosses again represents directions averaged over 10 m intervals and the horizontal bars on the data points show the standard deviation in each interval. In the Stenberg-1 well the standard deviations increase signi cantly as we go deeper into the well. The lack of data between 1 and 2.3 km and between 4.5 and 5.2 km is due to enlargements of the borehole in all directions. These were identi ed by both pair of caliper arms indicating enlargement of the borehole with respect to bit size and rotation of the BGT tool which occurs because there is no preferred direction for the arms to follow. It is interesting to compare the large sections of no data in Stenberg-1 to the situation in the Gravberg-1 well. It is likely that the rejected sections are due to wellbore failure all around the perimeter of the borehole. This indicates either that the di erential stress magnitude is greater in Stenberg-1 than in Gravberg-1, which is less likely, or that the rock in Stenberg-1 is weaker. Papasikas and Juhlin [31], using other well logs from Stenberg-1, argue that the Stenberg-1 well is signi cantly more fractured than the Gravberg-1 well. This agrees with the increased failure we observed in the Stenberg-1 well.

9 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169± Crustal stress orientation Because the traces of all drilling-induced tensile fractures found on the FMS images from the Gravberg-1 well are approximately parallel to the borehole axis and because the well is nearly vertical to 4.5 km depth, this implies that the overburden stress is also a principal stress at least to this depth, see e.g. Brudy and Zoback [6], Peska and Zoback [7]. To consider the orientation of crustal stress from the wellbore failure data summarized in Fig. 4A and B for the Gravberg-1 and Stenberg-1 wells, it is necessary to consider the orientation of the wellbores with respect to vertical. In inclined wellbores (or if principal stresses are inclined with respect to vertical and horizontal planes), it has long been known that the position around the wellbore at which a breakout forms depends not only on the direction of in situ stress, but also on the deviation and deviation direction of the borehole [7, 37] with respect to the stress eld as well as the magnitude of in situ stresses. As deviations from vertical of less than 15±208 do not have a signi cant e ect on the breakout orientation in most wells, we have decided to only use the apparent S H directions from those sections of the two wells where the deviation is 158 or less when calculating the average S H direction for each well. Utilizing the 158 limit enables us to include the data above 4850 m in the Gravberg-1 well and above 5950 m in the Stenberg-1 well. In the Gravberg-1 well the borehole breakout data supplies the bulk of the information for the determination of the direction of the horizontal stresses, both due to the fact that the combination of the BGT and FMS caliper data covers almost the entire well and because the induced tensile fractures are rather scarce. There are few S H direction estimates above 1 km, as seen in Fig. 4A, and they are scattered with high standard deviations. From approximately 1.5 km depth the S H estimates are more consistent. The mean orientation of S H averaged over the depth interval 0±4850 m, is N728W 278, using circular statistics [41] for the standard deviation. Although rather stable, the orientation of S H is not constant over depth, as seen in Fig. 4A. The shallow estimates indicate a more northerly stress direction, albeit with large errors. Deeper down there is a pronounced northerly rotation of the S H direction just above 4 km and then the orientation turns back westerly again below a troublesome zone with bad borehole conditions at 4 km. At approximately 5 km, the direction of S H changes very rapidly by 15 to 208. Juhlin [24], using well log and seismic data, suggests that there might be a fault intersecting the borehole just below 5 km, the fault having a dip greater than 608. The FMS data show that most high angle fractures at 5 km depth strike WNW, and the seismic data for the proposed fault does not contradict that direction. This stress perturbation is thus very likely explained by slip on an active fault. There is another rapid change, now towards the west, in the stress orientation at approximately 5.5 km. As discussed earlier, the breakout direction change with the deviation of the borehole and we would thus expect changes in the apparent S H directions in Fig. 4A with increasing deviation. Comparing Fig. 2, with the deviation data, and Fig. 4A there is, however, very little consistent change in the S H direction data to be seen. There is an overall shift in S H to the east of approximately 158 between 5 and 6 km which coincides with an increase in deviation by 258. The direction of S H then turns to the west again below 6 km. To test the signi cance of borehole azimuth and deviation on the breakout directions we simulated a stress eld using the average direction of S H that we obtained from the Gravberg-1 well above and for the magnitudes of S h and S H we used results from the later part of this paper, a strike-slip regime with S H /S V = 1.1 and S h / S V = 0.7. The results show a remarkably stable breakout direction of approximately N728W down to 5.8 km, with only a slight shift of a few degrees to the east between 5 and 5.8 km. Between 5.8 and 6.2 km there is a more pronounced shift to the east of about 5 degrees and then an even more obvious shift back to the west between 6.2 km and the end of our data of about 10 degrees. The amount of change in S H direction depends on the stress ratios assumed and should not be taken to literally, however, the direction of the shifts remain valid. The simulation thus show that there is a component of borehole deviation dependence on the S H directions in the lower section of Fig. 4A, but that much of the behaviour of the direction of S H has to be explained in other terms, such as slip on active faults. In the Stenberg-1 well, the directions span a depth from 780 to 6600 m, see Fig. 4B. As seen in Fig. 4B the data is overall more scarce than in the Gravberg-1 well and the data errors become increasingly larger with depth. The mean direction of S H in the Stenberg- 1 well, averaged over the interval 780 to 5950 m, was found to be N538W298. Due to frequent failure all around the wellbore, the Stenberg-1 data comes from three intervals in the well and the S H directions are relatively stable within the three intervals. There is a slight shift to the east below 2.8 km but then there are no more data until 3 km where the S H orientations equal that at 2.8 km. The orientation of S H between 3 and 4.5 km is stable and the interval has a slightly more northerly S H direction than the interval below 5 km. Because of the lack of data in between these intervals it is di cult to assess whether this is a slow trend or a rapid change at some depth. The uctuations in the deviation of the well, which are small above 6 km, are not obvious in the S H orientation data. The rapid

10 178 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169±190 increase in hole deviation below 6 km is not very well re ected in the S H orientation data, simulations as in the Gravberg-1 case above show that changes in the S H direction due to borehole deviation should be slightly to the east and then westward. Just as in the Gravberg-1 borehole the variations in the direction of S H in Stenberg-1 needs to be explained by other means, such as slip on active faults. Our results indicate that the mean stress orientations at Gravberg-1 and Stenberg-1 are not within one standard deviation of one another despite the fact that the two wells are only 10 km apart. The direction of S H in the Gravberg-1 well is slightly more westerly than S H in the Stenberg-1 well. The two wells are drilled into di erent parts of the impact structure which might cause the di erence in stress orientation although considering the age of the impact, 360 Ma, regional stress perturbations should now be relaxed. The S H directions published by Stephansson et al. [25] to 4 km depth agree well with our results. The inversion of the Gravberg-1 breakout data by Qian and Pedersen [27] and Qian et al. [28] gave a stable estimate of the direction of S H N71.68W20.38, in perfect agreement with our result, except for the di erence in standard deviation. Zajac and Stock's [29] inversion nds the maximum principal stress, s 1, very well constrained in the direction N73.28W plunging 3.58, also in excellent agreement with our result. The fact that the di erent investigations of the direction of S H agree so well is not surprising considering the stability of the breakout directions, see Fig. 4A. Earlier investigations in the Siljan area prior to drilling the two deep wells were conducted in a pilot hole at StajsaÊ s, see inset map in Fig. 1, which was hydrofractured at 11 depths between 39 and 492 m to infer the stress state [43]. The results indicate an east±westerly direction of S H in the upper 200 m rotating to the north with depth to approximately N608W at 450 m depth, albeit with large uctuations. Considering the fractured nature of the upper 1 km of the crust in Siljan the agreement with the results from Gravberg-1 and Stenberg-1 is satisfactory. The mean stress direction at Gravberg-1 and Stenberg-1 agrees very well with earthquake focal mechanisms [44] for south and central Sweden. The earthquakes were predominantly of strike-slip type and the orientations of horizontal principal compression showed remarkable consistency in the direction N608W. The mean stress orientations in these wells are generally consistent with other stress orientation data in Central Fennoscandia (see Fig. 1). The data in the gure are taken from the world stress map (WSM) data base [4] and include data such as breakouts, earthquake focal mechanisms, over-coring and hydraulic fracturing stress measurements. The two data points on the map in the Siljan region are the estimates from Gravberg-1 and Stenberg-1 determined here. 3. Pore pressure, vertical stress and minimum horizontal stress The pore pressure, P 0, in the Gravberg-1 well has been estimated by drillstem tests [45]. Two successful tests performed at approximately 1.3 and 2 km showed hydrostatic conditions and a third drillstem test at 5.5±6.9 km indicated that the pore pressure was somewhat lower than hydrostatic, see the open squares in Fig. 5. The data from the deep drillstem test is, however, uncertain. Pore pressure measurements in the shallow pilot holes, down to 500 m, drilled in the Siljan area prior to drilling the deep wells all show approximately hydrostatic conditions [45]. When referring to the pore pressure later we will assume hydrostatic conditions throughout the borehole. For reference we have also included the drill uid pressure, P b, in the original hole in the Gravberg-1 well, thin full line in Fig. 5. Down to 3.9 km water was used as drill uid, deeper down in the well di erent density bentonite muds were used. The common assumption that one principal stress is approximately vertical in the upper crust seems to be borne out by the fact that the orientation of drillinginduced tensile fractures are essentially parallel to the near vertical wellbore (except for localized perturbations) to approximately 8 km depth in the KTB wellbore [5]. The similar observations to approximately 5 km in the Gravberg-1 well quoted above supports this hypothesis. Thus, we assume that at this site we can consider the stress eld to be characterized by three principal stresses, two of which are horizontal, S H and S h, and one of which is vertical and can be estimated by integration of rock density. The vertical stress in the Gravberg-1 well, see Fig. 5, was calculated from a density pro le obtained from a combination of borehole density logs and modelling of the gravity eld [46]. The next step in constraining the magnitude of the stress tensor is the determination of the least principal horizontal stress, S h. This is often measured with relative ease and reliability by hydraulic fracturing [47]. The magnitude of the least principal stress is obtained from both the pressure required to propagate the fracture away from the wellbore and the instantaneous shut in pressure [48, 49]. In very deep boreholes where high temperature, high pressure and signi cant wellbore failures preclude use of conventional open-hole hydraulic fracturing with in atable packers [50], sections of the wellbore must be hydraulically isolated in other ways.

11 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169± The magnitude of the minimum horizontal stress, S h, was estimated from a number of di erent measurements shown in Fig. 5. During drilling, 148 m 3 of drilling uid was lost at 6047 m and an additional 50 m 3 was lost later in a sidetrack at nearly the same depth. When the rst uid loss occurred there was a sudden increase in penetration rate and the lithology from that interval in the borehole showed increased microfracturing and decomposition minerals [26]. It is thus likely that the uid was lost in a zone of preexisting Fig. 5. Pore pressure, P 0, drill uid pressure, P b, minimum horizontal stress, S h, vertical stress, S V, and maximum horizontal stress, S H, in the Gravberg-1 well. For the pore pressure there are three data points from the well, open squares, we have then assumed hydrostatic pressure. The drill uid pressure was continuously measured during drilling, we have included only the data from the original hole. The minimum horizontal stress has been estimated from leak-o tests, pluses, which did not fracture the formation and hydrofracs, open circles. Two of the hydrofracs have large error bars, the third, at 6 km is more well de ned. The vertical stress was calculated from borehole density logs and surface gravity modelling. The maximum horizontal stress estimates from induced tensile fractures are shown as horizontal lines ranging from the lower bound of measured di erential pressure, DP, and a temperature di erence, DT, of108c to an upper limit where DP = DT = 0. We have only included S H estimates in the depth interval where S h is best constrained. The gure shows a strike-slip faulting regime.

12 180 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169±190 fractures. None of the uid was noted to have returned to the borehole and when the mud weight was reduced from 1.62 to 1.2 g/cm 3 drilling could continue without further loss of circulation [26]. This indicates that the mud was not lost by large scale injection into an open fracture zone but that the high mud pressure caused hydraulic fracture propagation into the formation. When the mud weight was reduced the hydraulic fracture closed and circulation could be reestablished. Since the fracture propagation pressure rapidly approaches S h as the fracture length increases beyond several meters [48, 49], the downhole mud pressure at which circulation was lost gives us an indication of the magnitude of S h. From the second uid loss, in side track 3, we have less data [24] but it seems to have occurred by the same mechanism as the rst. Depth control on the second uid loss was not very accurate, causing large error bars on the pressure in the well at the hydrofrac. These data points are indicated by the open circles in Fig. 5. After the completion of drilling, the well was stimulated in order to open the preexisting subvertical joints believed to exist in the rock, down to the target seismic re ector at approximately 7.5 km depth, see Fig. 2. Approximately 250 m 3 of heavy, nonuniform density, uids where displaced into the formation during the stimulation. There is operational evidence suggesting that the uid injection initiated below 6.3 km in the borehole [24, 51] and it has been suggested [26, 51] that the uids would have left the borehole close to total depth (TD) 6957 m. The mud weight at the stimulation was estimated by Juhlin and Moore [24]. We estimate S h from the mud pressure at the time the reopened fracture started to grow, due to the uncertainties in the estimates of mud weight and depth the error bars on the deepest data point in Fig. 5 are rather large. Despite the large uncertainties, the three data points shown in Fig. 5 indicate a value of S h that is approximately two-thirds that of the vertical stress. Additionally, there were 12 formation integrity tests performed in the well [45], seven below the casing shoe at 1250 m and an additional ve below the casing shoe at 4167 m. None of these tests fractured the formation and thus they only provide a lower bound on the magnitude of S h. These lower bound estimates of S h are indicated by pluses in Fig. 5. In general, they indicate minimum values of S h that are only slightly lower than those indicated by the observations of lost circulation and the hydrofrac experiment. Although only lower bounds of S h the formation integrity tests constrain the slope of our estimated S h and thus also constrain the estimation of the state of stress in Siljan below. Stephansson et al. [26], using the equations of Rummel [52], estimated the ratio S h /S V at 5 km depth to 0.68 which is in good agreement with our result. 4. Observations of borehole failure II: magnitude of the maximum horizontal stress Due to limitations in data availability and quality in the Gravberg-1 borehole our ISMS will only include data from drilling-induced tensile failure in the estimation of S H. Following the procedure in Brudy and Zoback [8] we calculate the principal stresses at the borehole wall necessary to cause tensile failure of the formation, which is assumed to occur when the minimum principal stress falls below the tensile strength of the rock. These stresses at the borehole wall include, as described in detail in [8], the tangential stresses, concentrated by drilling, the radial stress from the di erence between wellbore uid pressure and formation pore pressure, the pumping pressure and the thermal stress from the cooling of the wellbore by the drill uid, see equations in Appendix B and Appendix C. The equation for the hoop stress at tensile failure is: s yy ˆ s 11 s 22 2 s 11 s 22 cos 2y b 4ns 12 sin 2y b s Therm DPRT, where s ij are the e ective stresses; S ij P 0, where S ij are the absolute stresses and P 0 the pore pressure, y b is the azimuth in the borehole cross-section measured from the bottom side of the borehole, n is Poisson's ratio, s Therm the thermal stress, DP is the di erence between the borehole uid pressure, including the pumping pressure, and the pore pressure in the rock and T is the tensile strength of the intact rock. For a vertical borehole where the vertical stress is a principal stress and y b is measured from the direction of S H, Eq. (1) simpli es to: s yy ˆ 3S h S H s Therm 2P 0 DPRT Since almost all of the identi ed drilling-induced tensile fractures in Gravberg-1 occur in zones of natural fracturing, i.e. zones of higher permeability, we have included the pore pressure, as discussed above, in our estimates of S H. This is in contrast to the estimates from KTB, where tensile cracks were observed in intact, low porosity and low permeability rock and the pore pressure thus neglected [8]. The well head pressure, necessary to circulate the drill uid, never reached high levels [53], implying that after dynamic pressure losses in the drillpipe the resulting pressure increase at depth due to pumping can be ignored in comparison with the pressure from the drill uid column [8]. DP adds uncertainty to our estimates of S H since we do not know if the stress state is such that the tensile fractures would have formed even if there had been no di erential pressure. The thermal stress is discussed in detail in Appendix C, we will only note here that the thermal stress 1 2

13 B. Lund, M.D. Zoback / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 169± depends on the temperature di erence between the undisturbed formation temperature and the temperature in the borehole wall shortly after drilling and circulation of colder drill uids. Since the thermal expansion coe cient, a, of the rock is temperature dependent the thermal stress also depends on the absolute temperature in the well at the time of failure of the formation. The temperature dependence of a is substantial and is responsible for most of the increase of s Therm with depth, see Appendix C. As with DP above, the thermal stress will add uncertainty to the S H estimates since we do not know if the tensile fractures would have formed even if there had been no cooling. In the Gravberg-1 well temperatures were recorded in each section of the well shortly after drilling the section and we use these temperatures as a measure of the amount of cooling experienced by the wellbore. 11 months after completing the borehole temperatures were once again measured [16] to obtain the equilibrium, or undisturbed formation, temperature. As discussed further in Appendix C, the maximum temperature di erence measured in the well was no more than 78C. The actual cooling during drilling could however been somewhat larger [8], so to obtain a conservative lower bound we use 108C as our maximum temperature di erence in the calculation of S H. No tests of the tensile strength were carried out on the Siljan granites but for the purpose of estimating S H from induced tensile fractures we consider the tensile strength to be zero. This is motivated by the hypothesis that drilling induced tensile fractures initiate most easily at preexisting aws in the borehole wall where no tensile strength has to be overcome [8]. Using zero tensile strength also ensures a lower bound estimate of S H. When calculating the magnitude of S H we have interpolated between the lower bound estimates of S h established above. Noting, however, that the S h magnitude is well constrained only in the lower section of the well we chose only to estimate S H below 4 km, see Fig. 5. Fortunately, the drilling-induced tensile fractures on the FMS images are also more easily identi able in this section. The lower bound nature of the S h magnitudes imply that the calculated S H magnitudes should also be interpreted as lower bounds. However, to explicitly show the uncertainties in S H magnitudes that DP and the thermal stress imposes we have calculated error bars on the S H estimates, see Fig. 5, using a DP range from zero to the actual measured DP and a temperature di erence range from zero to 108C. The lower bound is then the magnitudes associated with the measured DP and a 108C temperature di erence and the upper bound has zero pressure and temperature di erences. Uncertainties in other parameters used in the calculations further contributes to the overall error in the S H estimates, as do the low coverage of the borehole wall by the FMS tool which made it very di cult to properly assess the induced tensile fractures. The S H estimates in Fig. 5 indicates a strike-slip faulting regime in the Siljan region, con rming observations of more than 100 earthquakes with strike-slip fault plane solutions in south and central Sweden [44]. The lower bound nature of our S h and S H estimates also rules out the possibility of a normal faulting regime. The ratio of our lower bound S H estimates to the vertical stress is approximately 1.1 at 5 km depth, as seen in Fig. 5, decreasing slightly over the depth interval with data. The S h /S V ratio is approximately 0.68 at 5 km. Qian and Pedersen [27], later corrected in Qian et al. [28], in their linearized inversion scheme using the breakouts from Gravberg-1 and assuming one principal stress to be vertical, estimated the S H /S V ratio to and the S h /S V ratio to , for the entire depth of the well. In a nonlinear search for the uncertainty in the parameters they could, however, only put an upper bound of 1.05 on the S H /S V ratio, the lower bound being unconstrained by the data. Similarly their nonlinear S h /S V ratio has an upper bound of 0.98 and a lower bound of 0.0. Their optimal results thus agree surprisingly well with ours, considering their large uncertainties. The best tting stress tensor of Zajac and Stock [29] shows a reverse faulting regime with the maximum principal stress, s 1, in the direction N73.28W plunging 3.58, s 2 also almost horizontal, N16.78E plunging 2.58 and s 3 almost vertical plunging in the direction N108.38W. The relative size of s 2, de ned by Zajac and Stock [29] as f =(s 2 s 3 )/(s 1 s 3 ), was estimated to f = 0.40, for reference our shape factor is f = However, their 95% con dence level shows that the directions of s 2 and s 3 are almost unconstrained about an arbitrary rotation around s 1 and f is unconstrained between 0 and approximately 0.7. Although not absolutely de nite from the gures Zajac and Stock [29] presents it seems that their 95% con dence limit does not encompass the result of our analysis of the Siljan state of stress. The data we have presented above from the Gravberg-1 well indicates that a reverse faulting regime at depths below 1 km is unlikely. The Gravberg-1 well deviates from vertical in approximately the same direction as S h and the deviation is approximately 458 at the most. This, in combination with the nding that the breakout directions show very little consistent change with increasing deviation but a lot of changes that have other causes, as discussed thoroughly in the section on the crustal stress orientation above, causes problems for the two inversion approaches referred to above. The inversions are both based on only breakout data, where the deepest data point is not deeper than 6.05 km. Simulation of the formation of breakouts in the borehole down to 6 km show that there are a large number of stress states;