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Monitoring of fracture propagation by quartz tiltmeters
Engineering Geology 79 (2005) 33 – 42 www.elsevier.com/locate/enggeo
Monitoring of fracture propagation by quartz tiltmeters Bassam Saleha,T, Pierre Antoine Blumb a
Dept. of Surveying and Geomatics Engineering, Faculty of Engineering, Al-Balqa’ Applied University, Al-Salt 19117, Jordan b Earth’s Physics, Institut de Physique du Globe de Paris, 4 Place Jussieu, 75252 Paris Cedex 5, France Received 24 June 2003; received in revised form 28 April 2004; accepted 1 October 2004 Available online 20 April 2005
Abstract The growth of a hydrofracture can be monitored by observation of the ensuing deformation of the earth’s surface. The field data are processed and analyzed to yield a characterization of the deformation source. Several methods are used for measuring the surface deformation. Geodetic techniques are used for monitoring slow deformation over large areas, where tiltmeters may be used to complement geodetic networks by providing continuous records. In this paper, two different case studies are presented in which tiltmeters are used for measuring surface deformation. The first case deals with measurements of surface tilts obtained during an induced hydraulic fracture experiment. The fracture characteristics are obtained by comparing the measured deformation with those provided by a mathematical model. Nonlinear inversion of surface tilts gave estimates of the fracture geometry: depth, length, and thickness. The second case deals with tilts measured during a naturally induced hydraulic fracture in a volcanic area. The analysis of field data enabled good understanding of the volcano behavior. D 2005 Elsevier B.V. All rights reserved. Keywords: Tiltmeter; Hydrofracture; Volcano; Deformation; Vertical displacement; Tilt; Inflation; Deflation
1. Introduction Recently a considerable research effort has been directed toward the formulation of practical guidelines for predicting the geometrical characteristics of hydraulic fractures. Substantial advances have been made through theoretical and laboratory studies of the various mechanisms thought to play a role in determining fracture geometry (Davis, 1983, 1986; Okada, 1985, 1992; McTigue, 1987; Zeller and PolT Corresponding author. E-mail address: [email protected] (B. Saleh). 0013-7952/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2004.10.009
lard, 1992; Rani and Singh, 1992; Cayol and Cornet, 1997; Bonaccorso and Davis, 1999). Different techniques are used in fracture mapping. The seismic method is used to locate the path of fluid penetration into the medium from the hypocentral distribution of microseismic emissions stimulated as a result of increased pore pressure (Cornet and Yin, 1992). A variety of borehole logging techniques have been developed that are potentially sensitive to fracture geometry in the immediate vicinity of the wellbore. These include seisviewer imagery (Dudley, 1993), temperature logs, gamma ray logs (Blanks, 1976), and the use of impression packers. Although these
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technologies provide a means of deducing aspects of fracture geometry, they are not sensitive to fracture aperture. Downhole television is used to obtain directly the width of the fracture (Lau and Auger, 1987). Geodetic techniques are used in volcanic areas to obtain the vertical and horizontal displacements due to an inflation or deflation induced by a magmatic source (Bonaccorso et al., 2003; Jousset et al., 2000; Matsushima and Takagi, 2000; Miura et al., 2000; Nishi et al., 1999; Beauducel, 1998; Dvorac and Dzurisin, 1997). GPS and total stations are used for measuring these displacements. Fracturing pressure records can be used to determine some aspects of fracture behavior (Lili, 1997; Nolte and Smith, 1981). The latter approach to fracture mapping has become known as the surface tiltmeter technique, it is found that the most practical way of obtaining a satisfactory description of the elastic field is through the deployment of an array of continuously recording tiltmeters (Fujita et al., 2002; Ukawa et al., 2000; Yamashina and Shimizu, 1999; McTigue and Segall, 1988; Evans et al., 1982). The surface tiltmeter technique is sensitive to the broad-scale geometry of fractures and not limited to near-wellbore fracture detection. It is particularly well-suited to the study of shallow fracture growth and shut-in consolidation characteristics (Evans et al., 1982). Mean width of the fracture also can be estimated from the amplitude of the surface deformation. This technique is limited by the depth of hydraulic fracture. The depth should not exceed 450 m (Evans, 1983). Different analytic models are used for the interpretation of tilt data. Mogi model (1958) is widely used in the literature for volcanic areas and represents the magma chamber as a spherical source of dilatation. Sun (1969) considered the case of a horizontal coinshaped crack in which the fluid pressure is uniform. Pollard and Holzhausen (1979) represented the fracture as a uniformly pressured fluid-filled crack of a dipping plain-strain. Savage (1980) among others is an important reference in the area of dislocation theory. Davis (1983) represented the fracture by an opening mode slit of arbitrary dip that is rectangular in both cross-sectional and plane views. Okada (1985, 1992) investigated 3D problems of surface deformation and internal deformation due to shear and tensile faults in a half-space. Cayol and Cornet (1997) developed a 3D boundary element method combining the direct and displacement continuity methods.
Fig. 1. (a) Photography of the compact quartz tiltmeter. (b) Main parts of the compact tiltmeter.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
In this paper we present two case studies, in which the surface tiltmeter technique is used for fracture mapping. Sun’s model is used to calculate the geometric characteristics of the fracture in the first experiment because the induced hydraulic fracture is horizontal.
2. Description of the quartz tiltmeter Many types of tiltmeters were developed for deformation measurements during the last three decades (D’Oreye, 1998; Wyatt and Berger, 1980; Goulty, 1976). Due to the importance of measuring tilts using accurate devices of low drift and low cost, two tiltmeters of high resolution, in the range of 108 rad were developed by Blum and Saleh between 1981 and 1986 (Saleh and Blum, 1990; Saleh et al., 1991). The quartz tiltmeter with a mirror (Saleh and Blum, 1990) was used for the first experiment and the compact quartz tiltmeter (Saleh et al., 1991) was used for the second experiment (Fig. 1). It is a horizontal pendulum made of melted silica which can operate in
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vacuum, the rotation of the pendulum mass is transformable into voltage variation using a photoelectric detector. Both the range and the resolution depend on the pre-chosen natural period of the pendulum. The advantages of this instrument are: the low instrumental drift, which is estimated at 3 107 rad/year (Saleh and Blum, 1990); the low cost of manufacturing; and it can be installed on a horizontal or vertical surface. However, this instrument is not robust and the relative orientation is given with low precision compared with the modern bi-axial instruments. In our case study, the period of the instrument is fixed at 8 s, which gives a resolution of 107 rad.
3. Application to induced hydrofracture This experiment is carried out in the east of France (see Fig. 2) in order to connect two wells by an induced hydraulic fracture at 200 m depth. This technique is usually applied to increase the permeability of a petroleum reservoir or to make use of rocks at large
Fig. 2. Site location map of the induced hydrofracture experiment.
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depths for geothermal energy and other purposes. Sixteen tiltmeter stations were installed around the injection well to measure the surface deformation during the experiment. Each station is equipped by two quartz tiltmeters, one to measure the radial tilt and one to measure the tangential tilt. The resultant of the two components gives the tilt at each station. 3.1. Results and discussion The tilt signals were recorded continuously by XY recorders to follow the growth of the fracture in real time. Recording was started 1 h before the beginning of injection and continued 3 h after its end. Five stations did not work properly during the experiment due to problems with the acquisition system. The signals were digitized by taking one point each 2 min. Fig. 3 shows a typical example of tilt signals recorded by 5 stations during the experiment. Tilt variations were observed during the first 2 h of the experiment
Fig. 4. Surface deformation associated with a horizontal fracture.
due to injection interruptions. Then the rate of tilt became constant during 8 h of injection. The observed tilt at most stations is large in the radial direction and very small in the tangential direction. This indicates that the deformation takes the form of a dome and the fracture is horizontal (Davis, 1983; Evans, 1983) (see Figs. 4 and 5). The vectors shown in Fig. 5 represent the tilt resultants of the radial and tangential tilts observed at 11 stations. The tilt values are estimated
Fig. 3. Typical tilt signals recorded by different tiltmeter stations on Sep. 6th, 1982.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
37
5
6
7
16
11
4
2
Tranqueville
10
8
Forest path Injection well Reception well Tiltmeter station Tilt: downward direction
9
15
4x10-6 rad
0
50
100 m
Fig. 5. Tilt vectors observed at different tiltmeter stations on Sep. 6th, 1982.
with a relative error less than 5%. This error is due to uncertainties on the calibration factors of the instrument and on the drift estimation. The drift is approximately calculated at the injection interruptions. The effect of topography on tilt measurements is negligible because the ground surface is flat (Cayol and Cornet, 1998a). z Ground
The horizontal coin-shaped crack model (Sun, 1969) was used in the analysis of the experimental results. This model gives the vertical displacement of the surface at a distance r from the injection well in terms of the fracture depth h, radius a, volume V, maximum separation B, and the distance r as follows (Fig. 6): pffiffiffi h h h W ¼B k sin pffiffiffi cos 2 2 a k
Surface
where h
r
B a
B¼
3V pa2
pffiffiffi k¼
"
a
Fig. 6. Elliptical cross-section of the Sun (1969) penny shaped crack model.
h ¼ cot
1
r2 h2 þ 1 a2 a2
2
þ
r 2 þ h2 a2 : 2ah
2h a
2 #1=4
ð1Þ
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B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
The tilt at a distance r from the injection well is given by the first derivative with respect to r. An inversion method based on the least squares criteria was used to determine the geometric characteristics of the fracture. The error function E in terms of fracture depth h and radius a was defined as follows:
Eðh; aÞ ¼
i¼n X
ðtiltmeasured tiltcalculated Þ2
ð2Þ
i¼1
where n is the number of tiltmeter stations (n = 11 in our case study). E was computed for different values of h and a. The minimum value of E gave the best values of h and a. It is found that a = 77 m F 11 m, h = 225 m F 9 m, and B = 0.016 m F 0.004 m for an injection volume of 100 m3.
4. Application to naturally induced hydrofracture
200
This experiment is carried out at Piton de la Fournaise volcano on the Reunion Island in the Indian Ocean. This volcano occupies the southeast
corner of the island. It is considered as one of the biggest and most active volcanoes in the world, Piton de la Fournaise erupts with surprising regularity (more than 100 times since the start of the last century, the last two eruptions both being in January 2002). The eruptions of Piton de la Fournaise, like Mauna Loa in Hawaii, are the result of the extrusion of a small magma pocket located near to the volcano’s summit (Le´nat and Bache` lery, 1990; Bureau et al., 1998a,b; Cayol and Cornet, 1998b). This reservoir is probably located between 500 and 1300 m below the summit craters of the volcano. Eruptions since 1977 are interpreted to be fed by a larger crystallizing reservoir located below sea level (Le´nat et al., 1989; Sapin et al., 1996; Albare`de, 1993). The nature of the connection between the deeper reservoir and the shallow reservoir is unknown. The magma migrates towards the flanks of the volcano where fissures appear. The hollow magma chamber left behind once the eruption has finished causes subsidence, creating a pit, which may be several hundreds of meters wide. This process eventually creates a large caldera. Such a caldera has formed in la Reunion. It is known as l’Enclos Fouque´. In the center of the caldera, or enclosure (also known as Le Grand Brule´) lies a
Eruption Phase e 160
d
120
a
b
80
Tilt ( µrad)
Radial Tilt
c e
40
d
0
Tangential Tilt
4
8
Jan. 18th 1990
12
16
20
00
Time(hours)
Fig. 7. Tilt curves observed by the first tiltmeter station during Jan. 18th, 1990 eruption. (a) Seismic swarm under dolomieu crater. (b) Beginning of magmatic intrusion. (c) Beginning of tremor. (d) Lava arrival on Dolumieu surface. (e) Beginning of the eruptive fissure extension.
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4.1. Results and discussion Eruption Jan. 18th 1990
Fig. 7 shows the tilt curves recorded by the first tiltmeter station during the eruptive episode of Jan. 18th, 1990. The surface deformation follows three phases:
Tangential Tilt
(i) The inflation phase, which is observed before eruption (Fig. 8), the total measured tilt by the first station over 8 months is 68 106 rad, which is due to the migration of magma toward a small magma pocket located near to the volcano’s summit. (ii) The eruption phase, which is associated with a variable deformation (Fig. 7). The follwing episodes are observed: (a) A seismic swarm under Dolomieu crater; (b) The beginning of the magamatic intrusion; (c) A tremor which is due to the magmatic dike propagation; (d) The arrival of lava on the surface of Dolomieu crater; and (e) The beginning of the eruptive fissure extension in the northwest and southeast directions. (iii) The deflation phase, which is observed during and after eruption (Figs. 7 and 8).
280
320
360
400
440
Time (Julian Days) Fig. 8. Tilt curves observed before and after Jan. 18th, 1990 eruption.
large volcanic cone of 400m height. The summit of this structure is flat and comprises two large craters: Bory, to the west, which is very old, and Dolomieu to the east, which appears in 1766. Four tiltmeter stations were installed around the craters to study the behavior of the volcano before, during and after eruption. PITON DE LA FOURNAISE
1 2
2600
Dolomieu Crater Jan. 18th 1990
Bory Crater
Lava Flow Fissure 3
Projection 2550
va
Fl
ow
Mallard Crater La
2450
Ja
n.
2400
90
4 19
2350
500m
2300
200 0
0
Tilt: Downward Direction
Projection
19 50
2250
Lava Flow
2200
2150 2100
Fissure
100 µrad
Langlois Crater
19 00
240
th
200
18
Tilt 50 µrad
Radial Tilt
2050
Fig. 9. Tilt vectors for the period 23/11/1989–28/2/1990.
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Tilt vectors are calculated for the period 23/11/ 1989–28/2/1990 and represented in Fig. 9. These vectors indicate a rotation movement of the part of the volcanic cone situated to the west of the eruptive fissure in their direction. The amplitude, as well as the direction of each tilt is given in Table 1. The tilts are estimated with an error less than 5% as mentioned in paragraph 3. The effect of topography on tilt measurements is not negligible. McTigue and Segall (1988) showed that a slope of 208 implies ground surface displacements that are at some points 40% smaller than those associated with a flat ground surface. For an average slope of the volcano of 308, the tilt values in Table 1 are 50% smaller than those measured on a flat terrain (Cayol and Cornet, 1998a). According to seismic data (Le´nat et al., 1989; Sapin et al., 1996), the main magma reservoir is situated below see level at 5 km depth from the summit, so the estimated tilt by Mogi Model is less than 108 rad for pressure variations. This tilt is very small and less than the resolution of the tiltmeter. We conclude that the observed deformation is related with volume variations of the small magma pocket located near the volcano’s summit and intrusion of a magamatic dike during the eruptive episode. Approximately 2 h before each eruptive episode, seismic swarms were recorded to the southwest of Dolomieu crater (Le´nat et al., 1989). Then seismicity decreased before starting again at the eruption onset. Cayol and Cornet (1998b) assumed that these seismic swarms correspond to the initiation (first episode) and the reopening (second episode) of a macroscopic dike and that the subsequent decrease of seismicity corresponds to the quasi-static propagation of this dike toward the ground surface. They also assumed that the dike starts from the top of the seismic swarm at a depth of approximately 1000 m above see level, directly below the southwestern rim of Dolomieu crater. According to this hypothesis, the Table 1 Amplitude and azimuth of resultant tilts for the period 23/11/1989– 28/2/1990 Station number
Amplitude of resultant tilt (10 6 rad)
Azimuth of resultant tilt (deg)
1 2 3 4
157 22 59 100
313 329 252 220
dike propagated upward for an hour at an average speed of 0.3 m/s. The initial length of the dike is 400 m. The length of the dike near the ground surface is 1000 m over which eruptive fissures span. The dip of this dike is approximately 458. The strike of the deep dike is N1658E. The displacements induced by this dike for 1983–1984 eruption were modeled by Cayol and Cornet (1998b) using a 3D mixed boundary element method. The results were compatible with the above assumptions. The effect of topography is taken into account in this method. The measured tilts can be combined with geodetic measurements to constrain the previous modeling and to enable good understanding of the volcano behavior.
5. Conclusion Through the previous experiments, it was able to monitor the propagation of a hydraulic fracture with the quartz tiltmeters. The tilt vectors observed during the first experiment showed that the fracture was horizontal. The inversion of the tiltmeter data in the first experiment enabled the determination of the radius, depth and width of the induced hydraulic fracture using Sun’s model (1969). The surface tilt associated with Piton de la Fournaise volcano eruption on Jan. 18th, 1990 was successfully followed by the quartz tiltmeters. The tilts provided by four stations are partial and should be combined with geodetic data to get the geometric characteristics of the deformation source. Finally, we conclude that the surface tiltmeter method of studying the development of shallow hydraulic fractures has the following merits compared with the borehole installations: 1. The measurement is entirely passive and neither interrupts nor is interrupted by the injection operation. 2. The technique is sensitive to broad-scale features of the fracture geometry rather than having a field of view restricted to the immediate vicinity of the wellbore. 3. The technique is sensitive to fracture width, and, hence, the closure behavior of the fracture following shut-in can be inferred. 4. The occurrence of changes in the plane of fracture growth during any phase can be detected.
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Evans K.F., 1983. On the development of shallow hydraulic fractures as viewed through the surface deformation field: Part 2. Case histories. J. Pet. Technol., 411 – 420. Evans K.F., Holzhausen G.R., Wood M.D., 1982. The geometry of a large-scale nitrogen gaz hydraulic fracture formed in Devonian shales: an example of fracture mapping using tiltmeters. Soc. Pet. Eng. J., 755 – 763. Fujita E., Ukawa M., Yamamoto E., Okada Y., 2002. Scenarios of dike intrusions at the beginning of the Miyakejima volcano activities. Bull. Earthq. Res. Inst. 77, 67 – 75. Goulty N.R., 1976. Strainmeters and tiltmeters in geophysics. Tectonophysics 34, 245 – 256. Jousset Ph., Mori H., Okada H., 2000. Possible magma intrusion revealed by temporal gravity, ground deformation and ground temperature observations at Mount Komagatake (Hokkaido) during the 1996–1998 crisis. Geophys. J. Int. 143, 557 – 574. Lau J.S.O., Auger L.F., 1987. Subsurface fracture surveys using a borehole television camera and acoustic televiewer. Can. Geotech. J. 24, 499 – 508. Le´nat J.F., Bache`lery P., 1990. Structure and dynamics of the central zone of Piton de la Fournaise volcano. Le volcanisme de la Re´union-Monographie. CRV, Clermont-Ferrand, pp. 257 – 296. Le´nat J.F., Bache`lery P., Bonneville P., Hirn A., 1989. The beginning of the 1985–1987 eruptive cycle at Piton de la Fournaise (LA Re´union); new insights in the magmatic and volcano-tectonic systems. J. Volcanol. Geotherm. Res. 36, 209 – 232. Lili, 1997. Etude experimental du comportement hydromecanique d’une fracture, PhD thesis, Paris 7 University. France. Matsushima T., Takagi A., 2000. GPS and EDM monitoring of Unzen volcano ground deformation. Planets Space 52, 1015 – 1018. McTigue D.F., 1987. Elastic stress and deformation near a finite spherical magma body: resolution of the point source paradox. J. Geophys. Res. 92 (12), 931 – 940. McTigue D.F., Segall P., 1988. Displacements and tilts from dip-slip faults and magma chambers beneath irregular surface topography. Geophys. Res. Lett. 15, 601 – 604. Miura S., Ueki S., Sato T., Tachibana K., Hamaguchi H., 2000. Crustal deformation associated with the 1998 seismo-volcanic crisis of Iwate volcano, Northeastern Japan, as observed by a dense GPS network. Earth Planets Space 52, 1003 – 1008. Mogi K., 1958. Relations between the eruptions of various volcanoes and the deformation of the ground surfaces around them. Bull. Earthq. Res. Inst. Univ. Tokyo 36, 99 – 134. Nishi K., Ono H., Mori H., 1999. Global positioning system measurements of ground deformation caused by magma intrusion and lava discharge: the 1990–1995 eruption at Unzendake volcano, Kyushu, Japan. J. Volcanol. Geotherm. Res. 89, 23 – 34. Nolte K.G., Smith M.B., 1981. Interpretation of fracturing Pressures. J. Pet. Technol., 1767 – 1773. Okada Y., 1985. Surface deformation due to a shear and tensile faults in a half-space. Bull. Seismol. Soc. Am. 75, 1135 – 1154. Okada Y., 1992. Internal deformation due to shear and tensile faults in a half-space. Bull. Seismol. Soc. Am. 82, 1018 – 1040. Pollard D.D., Holzhausen G., 1979. On the mechanical interaction between a fluid-filled fracture and the earth’s surface. Tectonophysics 53, 27 – 57.
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Rani S., Singh S.J., 1992. Static deformation of a uniform half-space due to a long dip-slip fault. Geophys. J. Int. 109, 469 – 476. Saleh B., Blum P.A., 1990. Study of temperature effect on behavior of structures. J. Surv. Eng., ASCE 116 (1), 1 – 12. Saleh B., Blum P.A., Delorme H., 1991. New silica compact tiltmeter for deformations measurement. J. Surv. Eng., ASCE 117 (1), 27 – 35. Sapin M., Hirn A., Le´pine J.C., Nercessian A., 1996. Stress, Failure and fluid flow deduced from earthquakes accompanying eruptions at Piton de la Fournaise volcano. J. Volcanol. Geotherm. Res. 70, 145 – 167. Savage J.C., 1980. Dislocation in seismology. In: Nabarro, F.R.N. (Ed.), Dislocation in Solids, vol. 3. North Holland Publishing Co., Amsterdam, The Netherlands, pp. 251 – 339. Sun R.J., 1969. Theoretical size of hydraulically induced horizontal fracture and corresponding surface uplift in an idealized medium. J. Geophys. Res. 74 (25), 5995 – 6009.
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Monitoring of fracture propagation by quartz tiltmeters Bassam Saleha,T, Pierre Antoine Blumb a
Dept. of Surveying and Geomatics Engineering, Faculty of Engineering, Al-Balqa’ Applied University, Al-Salt 19117, Jordan b Earth’s Physics, Institut de Physique du Globe de Paris, 4 Place Jussieu, 75252 Paris Cedex 5, France Received 24 June 2003; received in revised form 28 April 2004; accepted 1 October 2004 Available online 20 April 2005
Abstract The growth of a hydrofracture can be monitored by observation of the ensuing deformation of the earth’s surface. The field data are processed and analyzed to yield a characterization of the deformation source. Several methods are used for measuring the surface deformation. Geodetic techniques are used for monitoring slow deformation over large areas, where tiltmeters may be used to complement geodetic networks by providing continuous records. In this paper, two different case studies are presented in which tiltmeters are used for measuring surface deformation. The first case deals with measurements of surface tilts obtained during an induced hydraulic fracture experiment. The fracture characteristics are obtained by comparing the measured deformation with those provided by a mathematical model. Nonlinear inversion of surface tilts gave estimates of the fracture geometry: depth, length, and thickness. The second case deals with tilts measured during a naturally induced hydraulic fracture in a volcanic area. The analysis of field data enabled good understanding of the volcano behavior. D 2005 Elsevier B.V. All rights reserved. Keywords: Tiltmeter; Hydrofracture; Volcano; Deformation; Vertical displacement; Tilt; Inflation; Deflation
1. Introduction Recently a considerable research effort has been directed toward the formulation of practical guidelines for predicting the geometrical characteristics of hydraulic fractures. Substantial advances have been made through theoretical and laboratory studies of the various mechanisms thought to play a role in determining fracture geometry (Davis, 1983, 1986; Okada, 1985, 1992; McTigue, 1987; Zeller and PolT Corresponding author. E-mail address: [email protected] (B. Saleh). 0013-7952/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2004.10.009
lard, 1992; Rani and Singh, 1992; Cayol and Cornet, 1997; Bonaccorso and Davis, 1999). Different techniques are used in fracture mapping. The seismic method is used to locate the path of fluid penetration into the medium from the hypocentral distribution of microseismic emissions stimulated as a result of increased pore pressure (Cornet and Yin, 1992). A variety of borehole logging techniques have been developed that are potentially sensitive to fracture geometry in the immediate vicinity of the wellbore. These include seisviewer imagery (Dudley, 1993), temperature logs, gamma ray logs (Blanks, 1976), and the use of impression packers. Although these
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B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
technologies provide a means of deducing aspects of fracture geometry, they are not sensitive to fracture aperture. Downhole television is used to obtain directly the width of the fracture (Lau and Auger, 1987). Geodetic techniques are used in volcanic areas to obtain the vertical and horizontal displacements due to an inflation or deflation induced by a magmatic source (Bonaccorso et al., 2003; Jousset et al., 2000; Matsushima and Takagi, 2000; Miura et al., 2000; Nishi et al., 1999; Beauducel, 1998; Dvorac and Dzurisin, 1997). GPS and total stations are used for measuring these displacements. Fracturing pressure records can be used to determine some aspects of fracture behavior (Lili, 1997; Nolte and Smith, 1981). The latter approach to fracture mapping has become known as the surface tiltmeter technique, it is found that the most practical way of obtaining a satisfactory description of the elastic field is through the deployment of an array of continuously recording tiltmeters (Fujita et al., 2002; Ukawa et al., 2000; Yamashina and Shimizu, 1999; McTigue and Segall, 1988; Evans et al., 1982). The surface tiltmeter technique is sensitive to the broad-scale geometry of fractures and not limited to near-wellbore fracture detection. It is particularly well-suited to the study of shallow fracture growth and shut-in consolidation characteristics (Evans et al., 1982). Mean width of the fracture also can be estimated from the amplitude of the surface deformation. This technique is limited by the depth of hydraulic fracture. The depth should not exceed 450 m (Evans, 1983). Different analytic models are used for the interpretation of tilt data. Mogi model (1958) is widely used in the literature for volcanic areas and represents the magma chamber as a spherical source of dilatation. Sun (1969) considered the case of a horizontal coinshaped crack in which the fluid pressure is uniform. Pollard and Holzhausen (1979) represented the fracture as a uniformly pressured fluid-filled crack of a dipping plain-strain. Savage (1980) among others is an important reference in the area of dislocation theory. Davis (1983) represented the fracture by an opening mode slit of arbitrary dip that is rectangular in both cross-sectional and plane views. Okada (1985, 1992) investigated 3D problems of surface deformation and internal deformation due to shear and tensile faults in a half-space. Cayol and Cornet (1997) developed a 3D boundary element method combining the direct and displacement continuity methods.
Fig. 1. (a) Photography of the compact quartz tiltmeter. (b) Main parts of the compact tiltmeter.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
In this paper we present two case studies, in which the surface tiltmeter technique is used for fracture mapping. Sun’s model is used to calculate the geometric characteristics of the fracture in the first experiment because the induced hydraulic fracture is horizontal.
2. Description of the quartz tiltmeter Many types of tiltmeters were developed for deformation measurements during the last three decades (D’Oreye, 1998; Wyatt and Berger, 1980; Goulty, 1976). Due to the importance of measuring tilts using accurate devices of low drift and low cost, two tiltmeters of high resolution, in the range of 108 rad were developed by Blum and Saleh between 1981 and 1986 (Saleh and Blum, 1990; Saleh et al., 1991). The quartz tiltmeter with a mirror (Saleh and Blum, 1990) was used for the first experiment and the compact quartz tiltmeter (Saleh et al., 1991) was used for the second experiment (Fig. 1). It is a horizontal pendulum made of melted silica which can operate in
35
vacuum, the rotation of the pendulum mass is transformable into voltage variation using a photoelectric detector. Both the range and the resolution depend on the pre-chosen natural period of the pendulum. The advantages of this instrument are: the low instrumental drift, which is estimated at 3 107 rad/year (Saleh and Blum, 1990); the low cost of manufacturing; and it can be installed on a horizontal or vertical surface. However, this instrument is not robust and the relative orientation is given with low precision compared with the modern bi-axial instruments. In our case study, the period of the instrument is fixed at 8 s, which gives a resolution of 107 rad.
3. Application to induced hydrofracture This experiment is carried out in the east of France (see Fig. 2) in order to connect two wells by an induced hydraulic fracture at 200 m depth. This technique is usually applied to increase the permeability of a petroleum reservoir or to make use of rocks at large
Fig. 2. Site location map of the induced hydrofracture experiment.
36
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
depths for geothermal energy and other purposes. Sixteen tiltmeter stations were installed around the injection well to measure the surface deformation during the experiment. Each station is equipped by two quartz tiltmeters, one to measure the radial tilt and one to measure the tangential tilt. The resultant of the two components gives the tilt at each station. 3.1. Results and discussion The tilt signals were recorded continuously by XY recorders to follow the growth of the fracture in real time. Recording was started 1 h before the beginning of injection and continued 3 h after its end. Five stations did not work properly during the experiment due to problems with the acquisition system. The signals were digitized by taking one point each 2 min. Fig. 3 shows a typical example of tilt signals recorded by 5 stations during the experiment. Tilt variations were observed during the first 2 h of the experiment
Fig. 4. Surface deformation associated with a horizontal fracture.
due to injection interruptions. Then the rate of tilt became constant during 8 h of injection. The observed tilt at most stations is large in the radial direction and very small in the tangential direction. This indicates that the deformation takes the form of a dome and the fracture is horizontal (Davis, 1983; Evans, 1983) (see Figs. 4 and 5). The vectors shown in Fig. 5 represent the tilt resultants of the radial and tangential tilts observed at 11 stations. The tilt values are estimated
Fig. 3. Typical tilt signals recorded by different tiltmeter stations on Sep. 6th, 1982.
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
37
5
6
7
16
11
4
2
Tranqueville
10
8
Forest path Injection well Reception well Tiltmeter station Tilt: downward direction
9
15
4x10-6 rad
0
50
100 m
Fig. 5. Tilt vectors observed at different tiltmeter stations on Sep. 6th, 1982.
with a relative error less than 5%. This error is due to uncertainties on the calibration factors of the instrument and on the drift estimation. The drift is approximately calculated at the injection interruptions. The effect of topography on tilt measurements is negligible because the ground surface is flat (Cayol and Cornet, 1998a). z Ground
The horizontal coin-shaped crack model (Sun, 1969) was used in the analysis of the experimental results. This model gives the vertical displacement of the surface at a distance r from the injection well in terms of the fracture depth h, radius a, volume V, maximum separation B, and the distance r as follows (Fig. 6): pffiffiffi h h h W ¼B k sin pffiffiffi cos 2 2 a k
Surface
where h
r
B a
B¼
3V pa2
pffiffiffi k¼
"
a
Fig. 6. Elliptical cross-section of the Sun (1969) penny shaped crack model.
h ¼ cot
1
r2 h2 þ 1 a2 a2
2
þ
r 2 þ h2 a2 : 2ah
2h a
2 #1=4
ð1Þ
38
B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
The tilt at a distance r from the injection well is given by the first derivative with respect to r. An inversion method based on the least squares criteria was used to determine the geometric characteristics of the fracture. The error function E in terms of fracture depth h and radius a was defined as follows:
Eðh; aÞ ¼
i¼n X
ðtiltmeasured tiltcalculated Þ2
ð2Þ
i¼1
where n is the number of tiltmeter stations (n = 11 in our case study). E was computed for different values of h and a. The minimum value of E gave the best values of h and a. It is found that a = 77 m F 11 m, h = 225 m F 9 m, and B = 0.016 m F 0.004 m for an injection volume of 100 m3.
4. Application to naturally induced hydrofracture
200
This experiment is carried out at Piton de la Fournaise volcano on the Reunion Island in the Indian Ocean. This volcano occupies the southeast
corner of the island. It is considered as one of the biggest and most active volcanoes in the world, Piton de la Fournaise erupts with surprising regularity (more than 100 times since the start of the last century, the last two eruptions both being in January 2002). The eruptions of Piton de la Fournaise, like Mauna Loa in Hawaii, are the result of the extrusion of a small magma pocket located near to the volcano’s summit (Le´nat and Bache` lery, 1990; Bureau et al., 1998a,b; Cayol and Cornet, 1998b). This reservoir is probably located between 500 and 1300 m below the summit craters of the volcano. Eruptions since 1977 are interpreted to be fed by a larger crystallizing reservoir located below sea level (Le´nat et al., 1989; Sapin et al., 1996; Albare`de, 1993). The nature of the connection between the deeper reservoir and the shallow reservoir is unknown. The magma migrates towards the flanks of the volcano where fissures appear. The hollow magma chamber left behind once the eruption has finished causes subsidence, creating a pit, which may be several hundreds of meters wide. This process eventually creates a large caldera. Such a caldera has formed in la Reunion. It is known as l’Enclos Fouque´. In the center of the caldera, or enclosure (also known as Le Grand Brule´) lies a
Eruption Phase e 160
d
120
a
b
80
Tilt ( µrad)
Radial Tilt
c e
40
d
0
Tangential Tilt
4
8
Jan. 18th 1990
12
16
20
00
Time(hours)
Fig. 7. Tilt curves observed by the first tiltmeter station during Jan. 18th, 1990 eruption. (a) Seismic swarm under dolomieu crater. (b) Beginning of magmatic intrusion. (c) Beginning of tremor. (d) Lava arrival on Dolumieu surface. (e) Beginning of the eruptive fissure extension.
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39
4.1. Results and discussion Eruption Jan. 18th 1990
Fig. 7 shows the tilt curves recorded by the first tiltmeter station during the eruptive episode of Jan. 18th, 1990. The surface deformation follows three phases:
Tangential Tilt
(i) The inflation phase, which is observed before eruption (Fig. 8), the total measured tilt by the first station over 8 months is 68 106 rad, which is due to the migration of magma toward a small magma pocket located near to the volcano’s summit. (ii) The eruption phase, which is associated with a variable deformation (Fig. 7). The follwing episodes are observed: (a) A seismic swarm under Dolomieu crater; (b) The beginning of the magamatic intrusion; (c) A tremor which is due to the magmatic dike propagation; (d) The arrival of lava on the surface of Dolomieu crater; and (e) The beginning of the eruptive fissure extension in the northwest and southeast directions. (iii) The deflation phase, which is observed during and after eruption (Figs. 7 and 8).
280
320
360
400
440
Time (Julian Days) Fig. 8. Tilt curves observed before and after Jan. 18th, 1990 eruption.
large volcanic cone of 400m height. The summit of this structure is flat and comprises two large craters: Bory, to the west, which is very old, and Dolomieu to the east, which appears in 1766. Four tiltmeter stations were installed around the craters to study the behavior of the volcano before, during and after eruption. PITON DE LA FOURNAISE
1 2
2600
Dolomieu Crater Jan. 18th 1990
Bory Crater
Lava Flow Fissure 3
Projection 2550
va
Fl
ow
Mallard Crater La
2450
Ja
n.
2400
90
4 19
2350
500m
2300
200 0
0
Tilt: Downward Direction
Projection
19 50
2250
Lava Flow
2200
2150 2100
Fissure
100 µrad
Langlois Crater
19 00
240
th
200
18
Tilt 50 µrad
Radial Tilt
2050
Fig. 9. Tilt vectors for the period 23/11/1989–28/2/1990.
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B. Saleh, P. Antoine Blum / Engineering Geology 79 (2005) 33–42
Tilt vectors are calculated for the period 23/11/ 1989–28/2/1990 and represented in Fig. 9. These vectors indicate a rotation movement of the part of the volcanic cone situated to the west of the eruptive fissure in their direction. The amplitude, as well as the direction of each tilt is given in Table 1. The tilts are estimated with an error less than 5% as mentioned in paragraph 3. The effect of topography on tilt measurements is not negligible. McTigue and Segall (1988) showed that a slope of 208 implies ground surface displacements that are at some points 40% smaller than those associated with a flat ground surface. For an average slope of the volcano of 308, the tilt values in Table 1 are 50% smaller than those measured on a flat terrain (Cayol and Cornet, 1998a). According to seismic data (Le´nat et al., 1989; Sapin et al., 1996), the main magma reservoir is situated below see level at 5 km depth from the summit, so the estimated tilt by Mogi Model is less than 108 rad for pressure variations. This tilt is very small and less than the resolution of the tiltmeter. We conclude that the observed deformation is related with volume variations of the small magma pocket located near the volcano’s summit and intrusion of a magamatic dike during the eruptive episode. Approximately 2 h before each eruptive episode, seismic swarms were recorded to the southwest of Dolomieu crater (Le´nat et al., 1989). Then seismicity decreased before starting again at the eruption onset. Cayol and Cornet (1998b) assumed that these seismic swarms correspond to the initiation (first episode) and the reopening (second episode) of a macroscopic dike and that the subsequent decrease of seismicity corresponds to the quasi-static propagation of this dike toward the ground surface. They also assumed that the dike starts from the top of the seismic swarm at a depth of approximately 1000 m above see level, directly below the southwestern rim of Dolomieu crater. According to this hypothesis, the Table 1 Amplitude and azimuth of resultant tilts for the period 23/11/1989– 28/2/1990 Station number
Amplitude of resultant tilt (10 6 rad)
Azimuth of resultant tilt (deg)
1 2 3 4
157 22 59 100
313 329 252 220
dike propagated upward for an hour at an average speed of 0.3 m/s. The initial length of the dike is 400 m. The length of the dike near the ground surface is 1000 m over which eruptive fissures span. The dip of this dike is approximately 458. The strike of the deep dike is N1658E. The displacements induced by this dike for 1983–1984 eruption were modeled by Cayol and Cornet (1998b) using a 3D mixed boundary element method. The results were compatible with the above assumptions. The effect of topography is taken into account in this method. The measured tilts can be combined with geodetic measurements to constrain the previous modeling and to enable good understanding of the volcano behavior.
5. Conclusion Through the previous experiments, it was able to monitor the propagation of a hydraulic fracture with the quartz tiltmeters. The tilt vectors observed during the first experiment showed that the fracture was horizontal. The inversion of the tiltmeter data in the first experiment enabled the determination of the radius, depth and width of the induced hydraulic fracture using Sun’s model (1969). The surface tilt associated with Piton de la Fournaise volcano eruption on Jan. 18th, 1990 was successfully followed by the quartz tiltmeters. The tilts provided by four stations are partial and should be combined with geodetic data to get the geometric characteristics of the deformation source. Finally, we conclude that the surface tiltmeter method of studying the development of shallow hydraulic fractures has the following merits compared with the borehole installations: 1. The measurement is entirely passive and neither interrupts nor is interrupted by the injection operation. 2. The technique is sensitive to broad-scale features of the fracture geometry rather than having a field of view restricted to the immediate vicinity of the wellbore. 3. The technique is sensitive to fracture width, and, hence, the closure behavior of the fracture following shut-in can be inferred. 4. The occurrence of changes in the plane of fracture growth during any phase can be detected.
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