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

undamaged host rock. That CBs cannot exactly be represented as traction-free surfaces of displacement discontinuity suggests that not all their interactions should be crack-like, as indeed some are not, notably their tendency to approach at low angle to within millimeters and then continue along parallel trends for meters. One can infer, for example, that the middle of a cm-thick CB, within which up to 50% of the available porosity has already been lost, represents a substantial physical barrier to the cross propagation of an adjacent, porosity-consuming band. Certainly, the complex material evolution occurring inside a propagating and curving band will affect the magnitude and distribution of displacement discontinuity (shear and compaction) realized across it. Nonetheless, the linear elastic anticrack approach to modeling CB mechanical interactions at the outcrop scale is substantially justified in that the physical inclusions which define them only accumulate as a direct consequence of the predominant closing-mode sense of displacement they accommodate. 4. Mechanical theory Sternlof et al. (2005) provide a thorough development and justification for the 2-D (plane strain) mechanical model of an isolated, static CB as an anticrack within an infinite, homogeneous, linear elastic, isotropic material subjected to uniform principal remote compressive stress loading (σ11 r ≥ σ22 r , σ12 r = 0). So long as the scale of observation exceeds a few millimeters, this constitutes a reasonable approximation of CBs in the porous, granular Aztec sandstone as visible in the sub-horizontal plane of outcrop exposure (Sternlof et al., 2005). In this section, we expand the anticrack model to consider the theoretical implications for propagation and interaction between multiple bands, with reference by analogy to classical elastic fracture mechanics (Irwin, 1960; Lawn and Wilshaw, 1975) as successfully applied to natural opening-mode fractures in rock and summarized by Olson and Pollard (1989) and Thomas and Pollard (1993). Throughout the rest of the paper, compression, compaction, and left-lateral senses of shear stress and displacement are taken as positive, as illustrated in Figure 4.10. For an isolated, perfectly linear (planar) anticrack oriented symmetric to σ11 r , the local state of stress induced in the near-tip region and expressed in the global (remote principal) coordinate system resembles the example distributions shown in Figure 4.11. High concentrations of compressive normal stress (σ11 and σ22) are readily apparent 98
σ22 r σ21 x 1 x 3 x 2 r σ12 D s r σ11 D n θ σ θθ Figure 4.10. Schematic diagram of the global 3-D cartesian (x1, x2, x3), and the 2-D local anticrack tip cartesian (x1, x2) and polar (r,θ) coordinate systems. All components of stress (σij) and displacement discontinuity (Dn, Ds) are shown as positive. 99 D s D n x 1 c r σ rθ x 2 c σ rr
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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
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 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 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
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
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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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