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

6. Elastic properties Despite a long history of diagenesis and deformation, analysis of the Aztec sandstone reveals a material arguably similar in terms of depositional structure and cementation to what it was during CB formation—a weakly cemented, cross-bedded, porous quartz sandstone. That autochthonous clay derived from the degradation of sparse feldspar has replaced thin hematite grain coatings as the primary cement is unlikely to have significantly altered the bulk material properties of the Aztec’s close-packed quartz-grain skeleton. We therefore infer that the elastic properties of the paleo Aztec resemble those of the present day. Published values for apparent Young’s modulus in sandstones based on laboratory testing range from 10 GPa to 46 GPa (mean of 22 GPa), while apparent Poisson’s ratio ranges from 0.1 to 0.4 (mean of 0.24) (Bieniawski, 1984). We have calculated values of apparent Young’s modulus for samples collected near Silica Dome from the results of triaxial compression tests conducted at Sandia National Laboratories. The results were 16.5 GPa and 21.0 GPa at confining pressures of 10 MPa and 50 MPa, respectively. Given the assumed lithostatic paleostress of 30 MPa, we therefore posit a Young’s modulus of 20 GPa and a Poisson’s ratio of 0.2 for the Aztec sandstone at Silica Dome during the period of CB formation. The CBs themselves, however, are a different matter. Preferential clay cementation of the bands subsequent to their formation has rendered them significantly more resistant and, presumably, stiffer than the friable host rock. Indeed, induration of the bands can occasionally resemble that of quartzite, suggesting that local pressure-solution healing of damaged grains may have occurred. Even if the current elastic properties of CBs could reliably be measured in the lab—a difficult challenge given their thin, tabular dimensions—we suggest that the results would not represent the bands as they formed. Additionally, the texture of the bands presents a paradox in that reduced porosity argues for increased shear stiffness, while intense micro-fracturing and effective grain-size reduction argues for increased shear compliance. It is reasonable to assume, however, that bulk modulus within CBs, which measures resistance to volume change, would increase as the result of both porosity loss and effective grain-size reduction. In the analyses that follow, we therefore consider a range of elastic properties for the model CB 60
y fixing the ratio of band to sandstone bulk moduli at 1.5. The interrelation of the essential elastic parameters—Young’s modulus (E), shear modulus (G), bulk modulus (K) and Poisson’s ratio (ν)—is given by E = 2G(1+ν) = 3K(1-2ν). 7. Mechanical analysis A logical minimum requirement for in-plane propagation of the model CB is that compressive stress just ahead of the tip—whether the component normal to the band trace, the mean value, or some other measure—exceeds the remote value. If the compacted material inside the band becomes elastically stiffer than the surroundings, the compressive stress at the tip will decrease. If the inside is softer, the compressive stress will increase. The other critical independent factor is the magnitude of the inelastic strain represented by the compaction, which would act to increase the magnitude of the near-tip compressive stress. In this section, we first use an embedded-layer model to develop these ideas in a quantitatively intuitive way, examining the relative influence of elastic moduli versus inelastic strain on the state of stress exactly at the tip of an infinitely thin band. We then turn to a full analytical solution of the Eshelby problem to examine the state of stress induced around a band matching the parameters of the field-based conceptual model. Finally, we compare the results obtained with the Eshelby solution to those derived from a two-dimensional (plane strain) BEM approximation of the model band as an anticrack, using a distribution of closing-mode displacement discontinuity elements to represent the 10% homogeneous uniaxial strain of the inclusion. 7.1. Embedded layer model Expressions for the stress and strain fields in and around an Eshelby inclusion are given by Rudnicki (1999) in terms of the remote values, the elastic constants of the inclusion and surrounding material, and an array of factors depending on the geometry of the inclusion and the Poisson’s ratio of the surroundings. He specifically treats the limiting case of interest here, where the aspect ratio of the inclusion goes to zero and its geometry approaches that of an embedded layer. The same result can be obtained more directly from the conditions given by Cocco and Rice (2002) for a planar fault zone. 61
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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
Page 22 and 23: Although the Aztec sandstone experi
Page 24 and 25: Waterpocket Fault 36 o 26‘ N 0 1
Page 26 and 27: Cenozoic Mesozoic Paleozoic Quatern
Page 28 and 29: 3.3. Deformation The Aztec also has
Page 30 and 31: There also are relatively high-angl
Page 32 and 33: (e) (f) (c) 500µm compaction band
Page 34 and 35: dihedral angle of 80° or more, and
Page 36 and 37: 5. Compaction band orientations Ori
Page 38 and 39: 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 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 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
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To determine the sensitivity of pro
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segments will self-correct to provi
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6.3. Approaching tip interactions A
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0.2 0.15 0.1 0.05 0 −0.05 −0.1
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0.2 0.15 0.1 0.05 0 −0.05 −0.1
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the hooking patterns commonly obser
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(a) (b) (c) σ1 compaction band max
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σ 3 σ 2 σ 1 Figure 4.24. Schemat
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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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