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

which point the inelastic strain has attained a critical value ( p ε )crit . This process is illustrated schematically in Figure 3.4, where the reduction of stress occurs over an endzone distance R . Further analysis of the spatial and temporal distribution of energy dissipation suggested by the more than 5 meters of elliptical taper near the ends of the bands reported by Sternlof et al. (2005) is warranted and should contribute to a better understanding of the conditions needed for propagation. σ − σ σp σ − σ + = M∆/h R x σp σ − σ (ε ) crit p Figure 3.4. Schematic illustration of the hypothetical spatial distribution of stress near the edge (tip) of a CB. (a) As the tip is approached from the right (σ+ side), the stress increases to a maximum value σp , then drops below the remote background value of σ+ to approach the relaxed value of σ— as the total inelastic compactive strain (ε p ) reaches its critical value (ε p )crit at a distance R behind the tip. 6. Acknowledgements The authors thank Jim Rice for a suggestion concerning the model and Teng-fong Wong for discussion of his laboratory results. Principal financial support for this work was provided by the U. S. Department of Energy, Office of Basic Energy Science, Geosciences Research Program through grants to Northwestern University (John Rudnicki) and Stanford University (David Pollard and Atilla Aydin). Partial support during preparation of the initial manuscript while Rudnicki was a visitor at the Kavli Institute for Theoretical Physics was provided by the National Science Foundation under Grant No. PHY99-07949 (Preprint No. NSF-KITP-05-26). Additional support was provided by the Stanford Rock Fracture Project. 84 ε p
1. Abstract Chapter 4 Propagation of compaction bands in sandstone as anticracks: Field evidence, mechanical theory and numerical simulation Outcrop and petrographic observations of compaction bands exposed in the Aztec sandstone of southeastern Nevada suggest that the mechanics of their propagation and interaction can be approximated using anticrack theory. Our numerical simulations of anticrack band propagation using the boundary element method confirm this, while suggesting refinements to better account for the compacted-inclusion character of the bands. Using realistic, field-based ranges for all physical parameters, we find that, as with opening-mode cracks, the degree to which adjacent anticrack bands interact is inversely proportional to the magnitude of the remote differential stress acting upon them. This model observation suggests that the tendency toward anastomosis along the trend of a subparallel compaction band array—and thus the extent to which it would impede fluid flow in that direction—can be predicted from knowledge of the remote stress state in which it formed. Conversely, the orientations and relative magnitudes of all three principal paleo stresses can be estimated from directional variations in the degree of anastomosis revealed by a well-exposed (or imaged) compaction band array. 2. Introduction Compaction bands (CBs) are a phenomenon of localized compressive failure commonly observed in outcrops of porous sandstone. They represent one kinematic end- member of a family of structures known collectively as deformation bands (DBs), which also includes shear and dilation bands, as well as mixed-mode combinations (Antonellini et al., 1994; Aydin, 1978; DuBernard et al., 2002; Mollema and Antonellini, 1996; Rudnicki and Sternlof, 2005; Sternlof et al., 2005). As thin, tabular features of porosity- loss compaction and order-of-magnitude permeability reduction that are millimeters to centimeters thick and tens of meters or more in planar extent, compactive DBs act as baffles to subsurface fluid flow under saturated conditions (Pittman, 1981; Freeman, 1990; Antonellini and Aydin, 1994; Crawford, 1998; Gibson, 1998; Taylor and Pollard, 2000; Sigda and Wilson, 2003; Sternlof et al., 2004). Where present as pervasive arrays, 85
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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
Page 46 and 47: possible, and use these to better c
Page 48 and 49: 1.5(ρgz) (b) WEST Willow Tank Uppe
Page 50 and 51: 9. Acknowledgements My sincere than
Page 52 and 53: The term compaction band (CB) was c
Page 54 and 55: Pollard, 2002). The particular util
Page 56 and 57: Hue-based image analysis using MATL
Page 58 and 59: a direct genetic relationship (Hill
Page 60 and 61: Compaction band fin Depositional be
Page 62 and 63: suggests—that to first approximat
Page 64 and 65: Porosity Porosity 0.3 0.25 0.2 0.15
Page 66 and 67: pore-clogging clay—due presumably
Page 68 and 69: 500 µm Figure 2.9. Electron backsc
Page 70 and 71: (a) (b) σ 3 σ 1 x 3 x 1 x 1 (c) u
Page 72 and 73: 6. Elastic properties Despite a lon
Page 74 and 75: 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 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 126 and 127: 6.3. Approaching tip interactions A
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
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4. Application to the Aztec sandsto
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Permeability (mD) 10 4 10 3 10 2 10
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B‘ A‘ A c f m c m c f c f c f c
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equivalent of the Aztec sandstone,
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effective permeability represents a
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NV UT CA AZ Park Road Map Detail Pa
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Commonly from ~1 mm to ~1.5 cm in t
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Although systematic arrays of DBs p
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to 2 m, with both sets in a cross-h
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y identical blocks all subject to t
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contiguous areas. This type of char
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(0,b) n 3 (0,0) f 2 n 2 n 1 (a,0) (
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6.1. Parallel Effective permeabilit
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By contrast, band-parallel effectiv
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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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