APPLIED GEOPHYSICS, Vol.11, No.1 (March 2014), P. 63-72, 14 Figures. DOI: 10.1007/s11770-014-0412-x
Numerical simulation of surface and downhole deformation induced by hydraulic fracturing* He Yi-Yuan1, Zhang Bao-Ping2, Duan Yu-Ting1, Xue Cheng-Jin2, Yan Xin1, He Chuan1, and Hu Tian-Yue1♦ Abstract: Tiltmeter mapping technology infers hydraulic fracture geometry by measuring fracture-induced rock deformation, which recorded by highly sensitive tiltmeters placed at the surface and in nearby observation wells. By referencing Okada’s linear elastic theory and Green’s function method, we simulate and analyze the surface and downhole deformation caused by hydraulic fracturing using the homogeneous elastic half-space model and layered elastic model. Simulation results suggest that there is not much difference in the surface deformation patterns between the two models, but there is a significant difference in the downhole deformation patterns when hydraulic fracturing penetrates a stratum. In such cases, it is not suitable to assume uniform elastic half-space when calculating the downhole deformation. This work may improve the accuracy and reliability of the inversion results of tiltmeter monitoring data. Keywords: Hydraulic fracturing, surface tilt field, downhole tilt field, layered model, numerical simulation
Introduction Monitoring the hydraulic fracturing process and understanding the fracture shape and orientation can improve hydraulic fracturing and guide oilfield development. During hydraulic fracturing, the induced deformation field radiates in all directions, causing ground and underground strata to tilt. Tiltmeter mapping technology is a very effective fracture monitoring technology, inferring the scale and orientation information of fractures from recorded tilt field data. The surface tilt field is more sensitive to changes in the
fractures dip, whereas borehole tilt is sensitive to the geometry of fractures. Therefore, by combining surface and downhole monitoring offers a comprehensive analysis of the orientation and scale of fractures. Surface tiltmeters are placed near the borehole to measure the induced deformation field at the surface, which depends to the fracture dip, azimuth, and depth of the fracture center. When the fracture depth is far greater than the created fracture dimension, the ground tilt field is slightly sensitive to the fracture scale; thus, downhole tiltmeter mapping is necessary. Downhole tiltmeters are distributed in offset observation wells nearby, measuring the deformation of underground strata (Figure 1). The
Manuscript received by the Editor November 1, 2013; revised manuscript received February 20, 2014. *This research is supported by the National Basic Research Program of China (No. 2013CB228602), the National Science and Technology Major Project of China (No. 2011ZX05014-006-006) and the National High Technology Research Program of China (No. 2013AA064202). 1. School of Earth and Space Sciences, Peking University, Beijing 100871, China. 2. Research Institute of Petroleum Engineering Technology, Sinopec, Beijing 100101, China. ♦Corresponding author: Hu Tian-Yue (Email:
[email protected]) © 2014 The Editorial Department of APPLIED GEOPHYSICS. All rights reserved.
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Surface and downhole deformation induced by hydraulic fracturing strata deformation caused by hydraulic fracturing is too small to be directly measured but, fortunately, the tilt field (the gradient of the deformation field) can be easily recorded by tiltmeters. With surface and downhole tilt data, fracture parameters, such as the orientation, length, and height can be inferred using geophysical inversion methods. Surface tiltmeters
Depth
Downhole tiltmeters in offset well
Fracture
of tiltmeter mapping, referencing Okada’s linear elastic theory (Okada, 1984; Okada, 1992) and the Green’s function approach (Wang et al., 2006). By simulating the surface and downhole tilt field induced by rectangular tensile fractures of different dip, azimuth, and scales for the uniform elastic half-space model and layered model, respectively, we studied the difference in the rock deformation patterns caused by different forms of fractures and the effect of the layer formation on the rock deformation pattern. This research comes to some results in accordance with Wright et al. (1998a, 1998b); this paper also points out in layered medium, when the fracture penetrates a rock layer, the downhole tilt pattern may be quite different from that in homogeneous medium. In such cases, it is improper to use Okada’s linear elastic theory to calculate strata deformation under the assumption of homogeneous semi-infinite space.
Calculation of the deformation field Fig.1 Schematic of tiltmeter mapping (Wright et al., 1998b).
According to Wright et al. (1998a), the induced deformation field at the surface is primarily a function of the fracture azimuth, the dip, the depth-to-fracture center, and the total fracture volume. Moreover, it is almost completely independent of the reservoir mechanical properties. For example, a north–southgrowing vertical hydraulic fracture of a given geometry yields the same surface deformation pattern whether the fracture is in low-modulus diatomite, extremely hard carbonate, or unconsolidated sandstone. The deformation pattern is simply north-south-trending trough surrounded by symmetrical ridges. However, Wright et al. (1998a) had not pointed out whether the reservoir mechanical properties would affect the downhole deformation pattern. Tiltmeter mapping technology has been applied in many oil fields across the world (Castillo et al., 1997; Mayerhofer et al., 2000a, 2000b; Tang et al., 2009). Inclinometers and supporting software provided by Pinnacle have been tested in multiple oil fields, and the technology is relatively mature; however, the application of tiltmeter mapping in unconventional oil and gas fields in China has just started. Therefore, it is still difficult to interpret the monitoring data. Currently, tiltmeter mapping mainly calculates the deformation field based on Okada’s linear elastic theory under the assumption of uniform elastic half-space, ignoring the effect of the mechanical properties of the reservoir rocks. In this study, we discuss the theoretical principles 64
In the homogeneous elastic half-space model, Okada’s linear elastic model (1984) could be used to predict the deformation field caused by hydraulic fracturing. Zhang et al. (2013) pointed out that rectangular model and elliptical models can be used, when calculating the downhole deformation field in a homogeneous semiinfinite medium; however, when calculating the surface deformation field, because of the limitations imposed by the boundary conditions, only the rectangular model can be used. The results of the two models obviously differ only when the observation well is extremely close to the fractured well; hence, in this paper, the rectangular approximation for hydraulic fracturing is used in the simulations (Figure 2). Z
Y
X
-C
W
į
L
Fig.2 Geometry of fracture model (Okada, 1992). (L: fracture length; W: fracture height; C: depth of fracture center; δ: fracture dip)
He et al. In the layered model, the partial differential equation governing the static deformation in an elastic medium is (O +P )( u) P u ( u u) f ,
(1)
where λ and μ are the two Lame constants, u is the displacement field, and f is the body force. At the interfaces of the layered model, the continuity conditions must be satisfied u | 0, e n * | 0.
(2)
The free surface is expressed as en·Γ = 0, where en is the unit normal vector of the interface and Γ is the stress tensor. The Hankel transform is applied to calculate the deformation field u (Wang et al., 2003)
u( z , r ,T )
¦³ m
e z ī( z , r ,T )
f
0
ªU m ( z , k )Z mk (r ,T ) º « » m « Vm ( z , k )R k (r ,T ) » kdk , « » m ¬ Wm ( z , k )Tk (r ,T ) ¼
ª Em ( z , k )Z mk (r ,T ) º f« » ¦m ³0 « Fm ( z, k )R km (r ,T )»kdk , « » m ¬ Gm ( z , k )Tk (r ,T ) ¼
(3)
(4)
where U m, V m, W m, E m, F m, G m, are the wavenumber spectra of the displacement and stress field, and Zkm, Rkm, Tkm are the corresponding surface vector harmonics. Furthermore, using the improved Thomson–Haskell propagator algorithm (Wang et al., 2006), Um, Vm, Wm, Em, Fm, and Gm can all be calculated. Notice that singular value problems appear in the process of source discretization when using this method to calculate the deformation field induced by horizontal fracturing. This study introduces the threshold α and when the fracture dip is greater than α, the discrete step size along the fracture width is dy = dzs/sin (θ), where dzs is the discrete step size of the fracture depth and θ is the fracture dip. When the fracture dip is less than α, then dy = dx, where dx is the discrete step size along the fracture length.
Simulation of surface deformation The layered model used in this paper is based on the log data of the MWX-2 well at the Piceance basin of Colorado (Engler and Warpinski, 1997). Table 1 lists the
rock parameters near the fracturing depth. The center of hydraulic fracture is in the B-sand layer at a depth of 1391.5 m. The fracture is 15 m high and 160 m wide, and the fracture opening displacement is 10 mm (Engler and Warpinski, 1997). To compare the simulation results in layered medium with those in the homogeneous medium, we set the rock parameters of the homogeneous model as in the B-sand layer. Table.1 Rock parameters for layers near hydraulic fracture
Shale C-sand Shale Siltstone Shale B-sand Shale
Depth (m)
Young’s modulus (GPa)
Poisson ratio
1201–1311 1311–1337 1337–1362 1362–1373 1373–1382 1382–1401 1401–1508
20.68 36.20 20.68 24.13 13.79 31.51 16.55
0.22 0.18 0.22 0.13 0.28 0.20 0.25
Parameters cited from the GRI report paper (Engler and Warpinski, 1997)
Figure 3 shows the surface deformation fields induced by hydraulic fractures with different dips in the homogeneous medium, calculated by Okada’s method. Figure 4 shows the surface deformation fields induced by hydraulic fractures of different dips in the layered medium, using Green’s function and adopting the layered model in Table 1. The surface tiltmeters measure the tilt field, which is the gradient of the displacement field. Using the same fracture parameters, Figures 5 and 6 show the simulation results of the surface tilt fields induced by fractures of different dips. Figures 3 to 6 show that the surface deformation field and tilt field are sensitive to the fracture dip. Surface deformation pattern changes with fracture dip. It can be seen that a given fracture yields the same surface deformation pattern in the layered and in homogeneous medium. Only the layered formation has a small effect on the surface deformation. In Figures 5c and 6c, the surface tilt field owing to vertical fracturing is slightly different between homogeneous and layered media owing to the change of the distance between the two surface uplifts. However, it can be seen from Figures 3c and 4c that the total deformation pattern agrees. The above described simulation and analysis only consider fractures that are distributed in a single layer. Figure 7 shows the surface deformation induced by fractures that penetrate the formation and are present in more than one layer. Consider two fractures at 1391.5 m depth, one is a 60° inclined fracture and the other is vertical, the fracture azimuths are both 45°, the height 65
Surface and downhole deformation induced by hydraulic fracturing and width are 30 m and 160 m, and the fracture opening displacement is 10 mm. The surface deformation patterns in Figure 7 are the same with those in Figure 3. Therefore, when the fracture penetrates a certain layer, there will not be significant changes in the surface deformation pattern. x 10-6
x 10-6
6
x 10-6
3
4
2
0 2000 N-
S
(m
0
)
-2000 -2000
E W-
2 1 0 -1 2000
2000
0
1 Vertical displacement (m)
Vertical displacement (m)
Vertical displacement (m)
To analyze the influence of the fracture azimuth on the surface deformation pattern, we consider horizontal fractures, 60° inclined fractures, and vertical fractures of different azimuths and use the homogeneous model. The other fracture parameters remain the same as above.
N-
(m)
Maximum displacement: 5.90 × 10−6 m (a) horizontal fracture
0.5 0 -0.5 -1 2000
S
2000
0
(m
0
)
-2000 -2000
N-
)
(m W-E
Maximum displacement: 2.57 × 10−6 m (b) 60° inclined fracture
2000 S
0 (m )
0 -2000 -2000
E W-
)
(m
Maximum displacement: 7.11 × 10−7 m (c) vertical fracture
Fig.3 Surface deformation induced by hydraulic fracturing in homogeneous medium. x 10-6
x 10-6 4
4
2 0 2000 N-
1 Vertical displacement (m)
Vertical displacement (m)
6 Vertical displacement (m)
x 10-6
2
0
-2 2000 S
(m
2000
0 )
-2000 -2000
N-
0 m) E( W-
Maximum displacement: 5.62 × 10−6 m (a) horizontal fracture
S
)
-1 -2 -3 2000
2000
0
(m
0
0 -2000 -2000
N-
)
(m W-E
S
(m
2000
0 )
-2000 -2000
Maximum displacement: 2.18 × 10−6 m (b) 60° inclined fracture
0 (m) E W-
Maximum displacement: 2.68 × 10−6 m (c) vertical fracture
2000
2000
1000
1000
1000
0
S-N (m)
2000
S-N (m)
S-N (m)
Fig.4 Surface deformation induced by hydraulic fracturing in layered medium.
0
0
-1000
-1000
-1000
-2000
-2000
-2000
-2000 5 nR
0 W-E (m)
2000
(a) horizontal fracture.
-2000 5 nR
0 W-E (m)
2000
(b) 60° inclined fracture.
-2000 2 nR
0 W-E (m)
(c) vertical fracture.
Fig.5 Surface tilt induced by hydraulic fracturing in homogeneous medium.
66
2000
He et al. It can be seen from Figures 8 to 10 that for vertical fractures the changes in azimuths lead to changes in the surface deformation field, whereas there is not much
difference in the surface deformation field induced by horizontal fractures of different azimuths.
1000
1000
1000
0
S-N (m)
2000
S-N (m)
2000
S-N (m)
2000
0
0
-1000
-1000
-1000
-2000
-2000
-2000
-2000 10 nR
0 W-E (m)
2000
-2000 5 nR
(a) horizontal fracture
0 W-E (m)
-2000 1 nR
2000
(b) 60° inclined fracture
0 W-E (m)
2000
(c) vertical fracture
Fig.6 Surface tilt induced by hydraulic fracturing in layered medium.
x 10-6
x 10-6 2 Vertical displacement (m)
Vertical displacement (m)
5
0
0
-2
-4
-5 2000
2000 2000
2000 N-S 0 (m )
N-S
0
(m) W-E
-2000 -2000
Maximum displacement: 4.51 × 10 m (a) 60° inclined fracture
0 (m
)
-2000 -2000
0 (m) W-E
Maximum displacement: 3.67 × 10−6 m (b) vertical fracture
−6
Fig.7 Surface deformation induced by fractures penetrating B-sand layer. x 10-5
1.5
1
0.5
0 2000
Vertical displacement (m)
1.5 Vertical displacement (m)
Vertical displacement (m)
x 10-5
x 10-5
1.5
1
0.5
2000
0
S(
m) -2000 -2000
(a) α = 0°
0 (m) W-E
N-
0.5
0 2000
0 2000
N-
1
S(
2000
0
m)
-2000 -2000
(b) α = 45°
0 (m) W-E
N-
S(
2000
0
m)
-2000 -2000
0 (m) W-E
(c) α = 90°
Fig.8 Surface deformation induced by horizontal fractures of different azimuths.
67
Surface and downhole deformation induced by hydraulic fracturing The above analysis implies that it is not difficult to infer the fracture dip with tilt data recorded by surface tiltmeters around the fractured well; however, the fracture azimuth estimation and its accuracy depend
x 10-6
x 10-6
x 10-6
6
Vertical displacement (m)
4 2 0
4 2 0
2000
S( 0 m)
-2000 -2000
N-
0 (m) W-E
4 2 0 -2 2000
-2 2000
-2 2000
N-
Vertical displacement (m)
6
6 Vertical displacement (m)
on the fracture dip. For subvertical fractures, the azimuth estimation may be more accurate but for nearly horizontal fractures, estimation would be difficult.
2000
2000
S
(m
0
)
-2000 -2000
(a) α = 0°
N-
0 (m) W-E
S(
0
m)
0 -2000 -2000
(b) α = 45°
E W-
)
(m
(c) α = 90°
Fig.9 Surface deformation induced by 60° inclined fractures of different azimuths. x 10-6
x 10-6 2
1 0 -1
2 Vertical displacement (m)
Vertical displacement (m)
2 Vertical displacement (m)
x 10-6
1 0 -1 -2 2000
-2 2000 S(
0 m)
-2000 -2000
0 (m) W-E
0 -1 -2 2000
2000
2000 N-
1
N-S
(a) α = 0°
0 (m
)
0
-2000 -2000
(b) α = 45°
m)
( W-E
2000
N-
S(
0
m)
0
-2000 -2000
( W-E
m)
(c) α = 90°
Fig.10 Surface deformation induced by vertical fractures of different azimuths.
Simulation of downhole tilt In the observation well, downhole tiltmeters measure tilt data at different depths. The recorded signal is the absolute value of the tilt amount ∂ux/∂z. Wright et al. (1998b) found that when the observation well is not far from the fracture plane, the separation of tilt peaks can indicate the fracture height. The induced tilt is maximum at the depth of the fracture top, declines to zero tilt directly opposite the fracture center, and then reverses tilt direction and repeats the same pattern for the bottom half of the fracture, as is shown in Figure 11. Figure 11 shows the nearby downhole tilt induced by fractures of different geometric shapes in the homogeneous medium. 68
The azimuth and dip of the fractures are both 90˚ and the fracture opening displacement is 5 mm. Fracture I (Figure 11a) is 40 m high and its (wing) length is 10 m and the observation well is 15 m away from the fracture plane. Fracture II (Figure 11b) is 10 m high and its wing length is 40 m, and the observation well is 45 m away from the fracture plane. Figure 11 implies that it is and reliable to infer the fracture height from the separation of two tilt peaks, when the observation well is close enough to the fracture plane. When the monitoring distance is small enough, this is a direct and reliable procedure. Nevertheless, as the distance between the observation well and the fracture, named the monitoring distance d increases, the two peaks will spread further, as is shown in Figure
He et al. height. When d = 30 m, the separation of the tilt peaks is 44 m, which is slightly greater than the fracture height. For d = 60 m, the separation of the two peaks is 68 m. Therefore, with increasing monitoring distance, the height estimation becomes less reliable.
1300
1300
1320
1320
1340
1340
1360
1360
1380 40 m
1400 1420
1380
Depth (m)
Depth (m)
12. The latter shows the downhole tilt data induced by Fracture I recorded at different monitoring distances in the homogeneous medium. In Figure 12, the monitoring distances d for the three tilt curves are d = 15 m, 30 m, and 60 m, respectively. When d = 15 m, the separation of the tilt peaks is 40 m, which agrees with the fracture
Actual tilt magnitude
1440
Actual tilt magnitude
1460 1480
Absolute tilt magnitude
1420
Absolute tilt magnitude
1440
10 m
1400
1460 -20
-10
0
10 20 Tilt (uR)
30
40
1480 -20
50
(a) fracture I: height 40 m, wing length 10 m.
-10
0
10 Tilt (uR)
20
30
40
(b) fracture II: hight 10 m, wing length 40 m.
Fig.11 Downhole tilt in homogeneous medium. 1300 d = 15 m d = 30 m d = 60 m
1320 X: 0.4437 Y: 1358 X: 3.063 Y: 1370
1340
Depth (m)
1360
X: 23.34 Y: 1372
1380 1400 1420
X: 23.34 Y: 1412
X: 3.063 X: 0.4437 Y: 1414 Y: 1426
1440 1460 1480
0
5
10
Tilt (uR)
15
20
25
Fig.12 Downhole tilt data at different monitoring distances in homogeneous medium. (Fracture I: height 40 m, wing length 10 m)
The above simulation results for the homogeneous medium agree with the conclusion of Wright et al. (1998b). However, Wright et al. did not explicitly point out whether the downhole tilt field is affected by the mechanical properties of the rock and whether the same fracture in the layered and homogeneous medium would cause the same downhole deformation pattern. To model the downhole tilt induced by hydraulic fracturing in layered media, we use Green’s function. Using the layered model listed in Table 1, we studied the downhole tilt induced by Fracture III and Fracture IV. The fracture centers are at 1391.5 m deep, the
fracture wing lengths are 80 m and the fractures are 15 m high, the fracture opening displacements are 10 mm, and the monitoring distances are 15 m. Fracture III is vertical and Fracture IV is an 60° inclined fracture, both fractures are in the B-sand layer. Figure 13 shows the simulation results. The vertical and inclined fractures that do not penetrate the middle layer lead to similar downhole tilt patterns in the layered and homogeneous model. The tilt peaks generally indicate the fracture top and bottom depths. However, at depths near the layer interface, the tilt pattern is slightly different, as shown with the red circle in Figure 13. 69
Surface and downhole deformation induced by hydraulic fracturing Because Fractures III and IV do not penetrate the middle layer, to study the downhole tilt pattern induced by fractures that penetrate the specific layer, we consider the following two fractures. A vertical fracture (Fracture V) and a 60° inclined fracture (Figure IV), both at a 1300
1300
Homogeneous medium Layered medium
1320
1340
1340
1360
1360
1380
1380
Depth (m)
Depth (m)
1320
depth of 1391.5 m depth. In addition, both are 30 m high and have wing lengths of 80 m, the fracture opening displacements are 10 mm, and the distance between the observation well and fracture centers is 60 m. In addition, both fractures penetrate the B-sand layer.
1400
1400
1420
1420
1440
1440
1460
1460
1480 -200
0 Tilt (uR)
1480 -400
200
Homogeneous medium Layered medium
-200
0
200
Tilt (uR)
(a) fracture III: vertical fracture
(b) fracture IV: inclined fracture
Fig.13 Downhole tilt induced by fractures III and IV. The star symbols indicate the sampling points in the calculation of downhole tilt.
According to the simulation results shown in Figure 14, at depths near the layer interfaces, there is significant difference in the downhole tilt pattern between the layered and the homogeneous medium. Moreover, the 1300
1300
Homogeneous medium Layered medium
1320 1340
1340
1360
1360
1380 1400
1380 1400
1420
1420
1440
1440
1460
1460
1480
-20
0 Tilt (uR)
Homogeneous medium Layered medium
1320
Depth (m)
Depth (m)
downhole tilt data in the layered medium have more than two extreme values, as shown in Figure 14 with the red circles. There are signal extremes near the depths of the layer interfaces except for the extremes near the depths
20
(a) fracture V: vertical fracture
1480 -20
0
20 Tilt (uR)
(b) fracture VI: inclined fracture
Fig.14 Downhole tilt induced by fractures V and VI. The star symbols indicate the sampling points in the calculation of downhole tilt.
70
40
He et al. of the fracture top and bottom. In such cases, it is be unreliable to determine the fracture height relying on the distance between the strongest tilt signals. From the above discussion, we infer that the conclusion of Wright et al. (1998b) for estimating the fracture height from the separation of the tilt peaks is only applicable to the homogeneous medium and not to the layered medium. In the layered medium, if the fracture is distributed in only one layer and does not penetrate interfaces, this conclusion is generally applicable as well. However, if the fracture penetrates the layer interfaces, the downhole tilt pattern can be complex. There may appear more than two tilt signal extremes and near the depths of the layer interfaces, the tilt pattern may be significantly different from that in the homogeneous medium. Therefore, when calculating the downhole tilt field and inversing the fracture height, it is necessary to consider the effect of the strata layering.
similar to that in a homogeneous medium, except for the slight difference near the depths of the layer interfaces. Nonetheless, if the fracture penetrates the layer interfaces, the downhole tilt pattern will become complex with more than two tilt signal extremes and it will be more difficult to infer the fracture height; furthermore, near the depth of the layer interfaces, the tilt pattern may be significantly different from that in the homogeneous medium. Above all, when calculating the surface deformation or tilt field caused by hydraulic fracturing, the strata can be simplified and treated as a homogeneous medium using Okada’s linear elastic theory. However, when calculating the downhole tilt field, it is more reliable to use the layered model.
Conclusions
Castillo, D., Hunter, S., Harben, P., and Wright, C., 1997, Deep hydraulic fracture imaging: recent advances in tiltmeter technologies: International Journal of Rock Mechanics and Mining Sciences, 34(3), 47.e1 – 47.e9. Engler, B. P., and Warpinski, N. R., 1997, Hydraulic fracture imaging using inclinometers at M-site: finiteelement analysis of the B-sandstone experiments, Gas Research Institute Topical Report, GRI-97/0361. Mayerhofer, J. M., Demetrius, S., Griffin, L., Bezant, R. B., Nevans, J., and Doublet, L., 2000a, Tiltmeter hydraulic fracture mapping in the North Robertson Field, West Texas: SPE Permian Basin Oil and Gas Recovery Conference, Texas, SPE paper 59715. Mayerhofer, J. M., Walker, R. N., Urbancic, T., and Rutledge, J. T., 2000b, East Texas hydraulic fracture imaging project: measuring hydraulic fracture growth of conventional sandfracs and waterfracs: SPE Annual Technical Conference and Exhibition, Texas, SPE paper 63034. Okada, Y., 1984, Surface deformation due to shear and tensile faults in a half-space: Bulletin of the Seismological Society of America, 75(4), 1135 – 1154. Okada, Y., 1992, Internal deformation due to shear and tensile faults in a half-space: Bulletin of the Seismological Society of America, 82(2), 1018 – 1040. Tang, M. R., Zhang K. S., and Fan, F. L., 2009, The application of surface tiltmeters in fracture testing in Changing oilfield: Oil Drilling & Production Technology, 31(3), 107 – 110. Wang, R. J., Lorenzo Martin, F., and Roth, F., 2003, Computation of deformation induced by earthquakes in a multi-layered elastic crust-FORTRAN programs
During hydraulic fracturing, the created fractures lead to ground and underground deformation. The surface deformation field primarily depends on the fracture orientation and shape, and it is only slightly affected by the mechanical properties of the reservoir rocks. Therefore, the surface tilt field can be calculated assuming a homogeneous semi-infinite space and using simple theoretical models. The surface deformation is sensitive to the fracture dip. Nevertheless, for estimating the fracture azimuth, its accuracy depends on the fracture dip. For subvertical fractures, the azimuth estimation may be more accurate, whereas the estimation would be difficult for near-horizontal fractures. In a homogeneous medium, the downhole tilt field is sensitive to the fracture geometry when the observation well is close to the fracture plane and the fracture height can be inferred by the separation of the tilt peaks. However, when the distance between the observation well and the fracture increases, the two peaks will spread further and the estimation of the fracture height will be less reliable. If we can find out how the separation of the tilt peaks changes with monitoring distance, the downhole tilt data recorded from observation wells far away from the fracturing well can also be used in the height inversion. In a horizontal multilayered medium, if the fracture is entirely in only one layer and does not penetrate any interface, then the downhole tilt pattern is
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He Yi-Yuan, she received her B.Sc. from Peking University in 2011 and is currently a PhD student at the Department of Geophysics in Peking University. Her research work focuses on hydraulic fracturing monitoring methods in unconventional reservoirs and forward simulation of seismic waves in fractured media.
