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

Sternlof et al. (2005) have suggested a linear elastic anticrack model for CB propagation. An anticrack is the compressive, closing-mode counterpart of the more familiar tensile, opening mode crack but with the sign of the stresses and crack-surface displacements reversed. Although the model formally predicts interpenetration of the crack surfaces, for CBs this interpenetration is interpreted physically as the inelastic compaction accompanying porosity loss. In this model, a CB propagates because of the compressive stress concentration at the edge of the band. Currently, little is known about the magnitude of the stress concentration required to induce propagation in either the field or laboratory. Vajdova and Wong (2003) and Tembe et al. (2006) also used the anticrack model to interpret their experiments on notched specimens of Berea and Bentheim sandstone. From the nominal stress vs. displacement curves, Vajdova and Wong (2003) 2 estimated a lower bound on the “compaction energy” for Bentheim of 16 kJ/m . Tembe 2 et al. (2006) estimated 43 kJ/m for Berea, but because the band propagated at an angle of 55° from the plane ahead of the notch, it is likely to be a shear band. The stress at the edge of an anticrack is singular, as it is for a tensile crack. Consequently, the quantity relevant to the propagation of the band is the coefficient of the stress singularity, the stress intensity factor K , or, equivalently, the energy release rate E, related to K by E = (1 −ν ) K 2G 2 , (1) where G is the shear modulus and ν is Poisson’s ratio. At present the only estimates of critical values of K or E appear to be those by Vajdova and Wong (2003) and Tembe et al. (2006) of compaction energies. In addition, it is unclear how these critical values relate to the parameters of the band, in particular, the inelastic compactive strain accommodated. This article presents a very simple energy release model of CB propagation as a framework for identifying the relevant controlling parameters. 3. Formulation The model is based on an example calculation of Rice (1968) illustrating the use of the J-integral and is shown in Figure 3.2. Physically, it represents an idealized geometry based on outcrop observations from the Aztec sandstone (Figure 3.3 and Sternlof et al., 78
h strain energy = W - h strain energy = W + Figure 3.2. Model of a semi-infinite CB of maximum thickness ξh embedded in an infinite layer of thickness h. Boundaries of the layer are displaced toward each other by a total amount ∆. Propagation of the band a unit distance reduces the energy of a vertical slice far ahead of the tip (W + ) to that of a slice far behind the band tip (W - ). CB Tip Figure 3.3. Typical configuration of three parallel CBs in the Aztec sandstone, forming the basis for the model in Figure 3.2: left photo corresponds to vertical slice with elastic strain energy W - , right photo corresponds to vertical slice with energy W + , middle photo corresponds to transitional zone associated with the elliptical taper of the central band’s tip. In the photos, the hypothetical boundaries of the model layer surrounding the central band (Figure 3.2) fall between it and its two bounding neighbors, which are spaced 1. 2m apart. Thus, h in this case equals 06 . m. 79
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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
Page 40 and 41: were encountered, giving the dihedr
Page 42 and 43: Eichhubl et al., 2004) did not lend
Page 44 and 45: 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 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 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
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compaction band Figure 5.2. Typical
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3. Computational method The methodo
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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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