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$Drilling-induced tensile wall-fractures - Stanford University$

6.3. Approaching tip interactions Aside from the effects of heterogeneous stress fields and/or mechanical anisoptropies related to sedimentary architecture (e.g. shear along fine-grained deflation-plane boundaries separating major, teardrop-shaped dune sequences), which this paper does not attempt to address, the primary source of mechanical interaction for a propagating CB is the close approach of an adjacent tip. Within the framework of our simple model, there are two primary variables that can affect the mechanical interaction of straight bands propagating toward each other along parallel trends symmetric to σ11 r : the spacing between them and the magnitude of the remote differential stress. In order to examine the interplay of these variables in determining the degree of interaction realized between bands, we performed a suite of simulations for σ d = 0, 0.25 and 0.5 at spacing intervals (s) of 2.5 cm, 25 cm and 2.5 m (Figure 4.21), starting with two 25-m-long bands identical to that used in the calibration section above. In all cases the model results match our qualitative expectations based on theoretical considerations—the tips at first curve slightly away from each other and then curve more strongly toward each other, while the interaction is distinctly more pronounced for σ d = 0 and s = 2.5 cm. The absolute magnitudes of path divergence from the established linear trend, however, can not be intuited, and the results reveal several interesting relationships. When the remote stress state is isotropic, interaction is quite pronounced, even at s = 2.5 m for which the final overlapped spacing drops by half to 1.25 m before parallel propagation is restored. At s = 25 cm and 2.5 cm, the overlapped band tips end up on intersecting trends, although the approach is distinctly more asymptotic for s = 25 cm. When σ d = 0.5, interaction is negligible except at s = 2.5 cm, when the final overlapped spacing drops by about one third to 1.6 cm. Even then, parallel propagation resumes before intersection occurs. Perhaps most interesting is that the results for σ d = 0.25 are all but indistinguishable from those of σ d = 0.5. Again, even at s = 2.5 cm, parallel propagation resumes prior to intersection. In fact, because the initial repulsive effect is more pronounced than for σ d = 0.5, the final overlapped spacing ends up the same at 1.6 cm. In sum, these results suggest that strongly anastomosing band patterns, particularly those involving very close encounters and the effective merging of bands, can only occur 114
when the ambient stress state is nearly isotropic and/or bands are spaced less than a meter apart. One other factor mentioned in the section on mechanical theory as a potential influence on the propagation paths of interacting CBs is the effective drag or “inertia” imposed by their pre-existing length. As a test of the general validity of this notion, we undertook a series of three simulations identical in every respect except for the initial lengths of the model bands: two 25-m bands (as above and in Figure 4.21), one 25 m band and one 5 m band, and two 5 m bands. In order to ensure adequate space and propagation reactivity to render variations in path distinguishable on a single plot, a spacing of 2 m and an isotropic remote stress state were chosen (Figure 4.22). When both bands are 25 m long, their mutual influence is substantially similar to that when spacing is 2.5 m. When one band is 5 m long, its impact on the continued propagation of the longer band is perceptibly diminished, both in terms of the initial repulsion and the subsequent attraction. The effect of the longer band on the shorter one, however, is even more noticeably enhanced. When both bands are 5 m long, their responses again mirror each other, but are completely different from either of the first two cases. In particular, they initially repel and attract each other somewhat less robustly than the pair of 25-m- long bands, but, at the point when parallel propagation resumes in both earlier examples, attraction between the shorter bands re-intensifies and they propagate toward intersection at a relatively high angle of approach (> 30°). The final path has a slight hitch in it that produces a mild, s-shaped curvature. This simple example demonstrates both that band length can influence the strength of tip interactions, and that the most general case involving different length bands interacting is likely to produce noticeably asymmetric patterns of hooking. Finally, we note that, although the simulations presented in Figures 4.21 and 4.22 generally predict the resumption of parallel propagation paths following initial overlap, the normalized magnitude of σθθ max rapidly drops toward one. This suggests that, for any reasonable critical threshold value, propagation would cease. Outcrop observations, however, demonstrate that long, sub-parallel overlaps between bands spaced even millimeters apart are common. 115
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STRUCTURAL GEOLOGY, PROPAGATION MEC
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Abstract Low-porosity, low-permeabi
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delivered with fortitude, humor, su
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Chapter 3—Energy-release model of
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List of Illustrations Figure A. Cov
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Figure A. Cover photo that accompan
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likely present in subsurface sandst
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hooking-tip interactions—using th
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and sandstone, my co-authors—Moha
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the hard data from which accurate p
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Although the Aztec sandstone experi
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Waterpocket Fault 36 o 26‘ N 0 1
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Cenozoic Mesozoic Paleozoic Quatern
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3.3. Deformation The Aztec also has
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There also are relatively high-angl
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(e) (f) (c) 500µm compaction band
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dihedral angle of 80° or more, and
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5. Compaction band orientations Ori
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n = 20 M n = 20 P n = 22 B n = 20 R
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were encountered, giving the dihedr
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Eichhubl et al., 2004) did not lend
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P (a) (c) S P S Figure 1.10. Stereo
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possible, and use these to better c
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1.5(ρgz) (b) WEST Willow Tank Uppe
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9. Acknowledgements My sincere than
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The term compaction band (CB) was c
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Pollard, 2002). The particular util
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Hue-based image analysis using MATL
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a direct genetic relationship (Hill
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Compaction band fin Depositional be
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suggests—that to first approximat
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Porosity Porosity 0.3 0.25 0.2 0.15
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pore-clogging clay—due presumably
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500 µm Figure 2.9. Electron backsc
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(a) (b) σ 3 σ 1 x 3 x 1 x 1 (c) u
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6. Elastic properties Despite a lon
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Comparison of the two approaches es
Page 76 and 77: term in (6a) and (6c) begins to dom
Page 78 and 79: MPa MPa 80 70 60 50 40 30 20 10 0 0
Page 80 and 81: 2002) and use a BEM approach (Crouc
Page 82 and 83: MPa 10 4 10 3 10 2 10 1 10 −5 10
Page 84 and 85: concentration of quartz plasticity
Page 86 and 87: conducted on well-cemented sandston
Page 88 and 89: ~ 62 m compaction band trend 500µm
Page 90 and 91: Sternlof et al. (2005) have suggest
Page 92 and 93: 2005). It consists of a long (infin
Page 94 and 95: ⎡ ∆ ⎤ ⎧ p 1 ∆ ⎛ M ⎞
Page 96 and 97: which point the inelastic strain ha
Page 98 and 99: they can exert significant effects
Page 100 and 101: interact is inversely proportional
Page 102 and 103: (a) (b) (c) (d) Figure 4.3. Typical
Page 104 and 105: Viewed individually, CB traces tend
Page 106 and 107: (a) (b) (c) (d) (e) (f) Figure 4.7.
Page 108 and 109: 1973; Mardon, 1988; Peck et al., 19
Page 110 and 111: undamaged host rock. That CBs canno
Page 112 and 113: 0.5 0.4 0.3 0.2 0.1 0.5 0.4 0.3 0.2
Page 114 and 115: Normalized stress magnitude 3 2.5 2
Page 116 and 117: helps to explain why the oblique ap
Page 118 and 119: and ts = G·ds + H·dn (2) where tn
Page 120 and 121: plastic compaction, as suggested by
Page 122 and 123: To determine the sensitivity of pro
Page 124 and 125: segments will self-correct to provi
Page 128 and 129: 0.2 0.15 0.1 0.05 0 −0.05 −0.1
Page 130 and 131: 0.2 0.15 0.1 0.05 0 −0.05 −0.1
Page 132 and 133: the hooking patterns commonly obser
Page 134 and 135: (a) (b) (c) σ1 compaction band max
Page 136 and 137: σ 3 σ 2 σ 1 Figure 4.24. Schemat
Page 138 and 139: NV UT CA AZ Park Road Map Detail Pa
Page 140 and 141: compaction band Figure 5.2. Typical
Page 142 and 143: 3. Computational method The methodo
Page 144 and 145: compaction band A 5 mm A‘ compact
Page 146 and 147: 4. Application to the Aztec sandsto
Page 148 and 149: Permeability (mD) 10 4 10 3 10 2 10
Page 150 and 151: B‘ A‘ A c f m c m c f c f c f c
Page 152 and 153: equivalent of the Aztec sandstone,
Page 154 and 155: effective permeability represents a
Page 156 and 157: NV UT CA AZ Park Road Map Detail Pa
Page 158 and 159: Commonly from ~1 mm to ~1.5 cm in t
Page 160 and 161: Although systematic arrays of DBs p
Page 162 and 163: to 2 m, with both sets in a cross-h
Page 164 and 165: y identical blocks all subject to t
Page 166 and 167: contiguous areas. This type of char
Page 168 and 169: (0,b) n 3 (0,0) f 2 n 2 n 1 (a,0) (
Page 170 and 171: 6.1. Parallel Effective permeabilit
Page 172 and 173: By contrast, band-parallel effectiv
Page 174 and 175: Relative Effective Permeability 1.0
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(a) (b) (c) 0 meters 3 = 10-2 kb /k
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Though grossly systematic, anastomo
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168
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100 meters 5 meters NV UT CA AZ Par
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compaction band trend 500µm Figure
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Cover Outcrop Band N 100 meters 20
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(CBs) and the matrix rock in all si
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The finite volume discretization fo
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isotropic) can lead to numerical di
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5. Simulations Three sets of 2-D si
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Normalized ∆P ∆P ratio (n/p) 4.
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P P P P I I P P Case 1 P P Case 2 I
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Case 1 Case 1 Case 1 (a) (b) (c) In
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5.2.2. Discussion The elliptical pa
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5.3.1. Results With the regional gr
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(a) (b) Leak 200 meters Regional gr
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anticipated sustainable pumping rat
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Finally, there is the issue of fore
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200
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Bakke, S., and Øren, P. E., 1997,
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Carpenter, D. G., and Carpenter, J.
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Eichhubl, P., Taylor, W. L., Pollar
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Karimi-Fard, M., Durlofsky, L. J.,
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-, 1987, Fracture from a straight c
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Shipton, Z. K., and Cowie, P. A., 2
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Wong, T. F., David, C., and Zhu, W.
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