structural geology, propagation mechanics and - Stanford School of ...

More documents

Recommendations

Info

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

1973; Mardon, 1988; Peck et al., 1985). Given that our observations come from the tips of CBs that did naturally cease to propagate, however, raises the possibility that damage halos were originally present, but were consumed by subsequent compaction. On the other hand, small pods of grains involved in what appears to be incipient collapse can be distinguished outside of established CBs and interpreted as Griffith-type flaws or proto- bands (Sternlof et al., 2005). 3.3 Anticrack-inclusion interpretation The elliptical tip-to-tip profiles and uniform uniaxial internal compaction observed for straight (planar) CBs corresponds to a pure closing-mode sense of relative boundary displacement, albeit one distributed across a thin, but finite band thickness rather than the knife-edge surface of displacement discontinuity that defines solution surfaces (Fletcher and Pollard, 1981; Mardon, 1988). This elliptical distribution of closing-mode (anti-mode I) displacement (Figure 4.9) defines the bands kinematically and mechanically as anticracks (Mollema and Antonellini, 1996; Sternlof et al., 2005). In fact, Sternlof et al. (2005) show that the local state of stress induced in a linear elastic material by the plastic compaction of a perfectly planar CB oriented symmetric to the maximum remote compressive stress is, for all intensive purposes, independent of the evolving material properties inside the band. Corroborating the anticrack interpretation is the fact that many of the characteristic CB patterns observed in Aztec outcrop—particularly the hook and eye configurations— are distinctly reminiscent of those described for opening-mode cracks (joints), many of which can be explained as resulting from mechanical interactions between propagating tips within the framework of linear elastic fracture mechanics (e.g. Cotterell and Rice, 1980; Cruikshank et al., 1991; Fleck, 1991; Olson and Pollard, 1989; Pollard and Aydin, 1988; Segall and Pollard, 1983; Sempere and Macdonald, 1986; Sumi et al., 1985; Swain and Hagan, 1978; Thomas and Pollard, 1993). This suggests by analogy that CB patterns may also largely express the mechanical interactions of brittle cracks or, in this case, anticracks. Complicating this virtual anticrack approximation of CBs, however, is their physical reality as highly eccentric, oblate ellipsoidal inclusions of compacted grains, whose internal material properties must exert nonzero tractions along their boundaries with the 96
(a) (b) (c) σ 3 σ 1 x 3 x 1 x 1 Figure 4.9. Schematic representations of the idealized compaction band model (from Sternlof et al., 2005). (a) Axisymmetric geometry of the eccentric ellipsoidal band aligned with the principal remote stresses. (b) Cross-sectional area of the band (solid ellipse) relative to the pre-compacted area originally occupied by the same detrital grains (dashed ellipse). As inelastic compaction progresses, the boundary around the grains involved contracts as indicated by the displacement arrows (u1). This inward displacement of the elliptical boundary corresponds to the uniform uniaxial plastic strain of an Eshelby inclusion, and the area between the dashed and solid ellipses corresponds to the volume loss associated with the compaction. (c) Two-dimensional anticrack representation of the model band as an elliptical distribution of closing-mode displacement discontinuity equivalent to the uniform Eshelby compaction strain. In this virtual treatment, two material lines (solid lines) interpenetrate by an amount equivalent to the volume loss associated with the compaction (dashed ellipse) as shown by the displacement arrows (u1). Actual interpenetration does not occur. Because of its extreme eccentricity, however, solutions for the state of stress induced around the model band using the Eshelby and anticrack approaches are substantially similar. 97 u 1 u 1 x 2 x 2 u 1 σ 2
Page 1 and 2:
STRUCTURAL GEOLOGY, PROPAGATION MEC
Page 4 and 5:
Abstract Low-porosity, low-permeabi
Page 6 and 7:
delivered with fortitude, humor, su
Page 8 and 9:
Chapter 3—Energy-release model of
Page 10 and 11:
List of Illustrations Figure A. Cov
Page 12 and 13:
Figure A. Cover photo that accompan
Page 14 and 15:
likely present in subsurface sandst
Page 16 and 17:
hooking-tip interactions—using th
Page 18 and 19:
and sandstone, my co-authors—Moha
Page 20 and 21:
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 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 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
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
Page 176 and 177:
(a) (b) (c) 0 meters 3 = 10-2 kb /k
Page 178 and 179:
Though grossly systematic, anastomo
Page 180 and 181:
168
Page 182 and 183:
100 meters 5 meters NV UT CA AZ Par
Page 184 and 185:
compaction band trend 500µm Figure
Page 186 and 187:
Cover Outcrop Band N 100 meters 20
Page 188 and 189:
(CBs) and the matrix rock in all si
Page 190 and 191:
The finite volume discretization fo
Page 192 and 193:
isotropic) can lead to numerical di
Page 194 and 195:
5. Simulations Three sets of 2-D si
Page 196 and 197:
Normalized ∆P ∆P ratio (n/p) 4.
Page 198 and 199:
P P P P I I P P Case 1 P P Case 2 I
Page 200 and 201:
Case 1 Case 1 Case 1 (a) (b) (c) In
Page 202 and 203:
5.2.2. Discussion The elliptical pa
Page 204 and 205:
5.3.1. Results With the regional gr
Page 206 and 207:
(a) (b) Leak 200 meters Regional gr
Page 208 and 209:
anticipated sustainable pumping rat
Page 210 and 211:
Finally, there is the issue of fore
Page 212 and 213:
200
Page 214 and 215:
Bakke, S., and Øren, P. E., 1997,
Page 216 and 217:
Carpenter, D. G., and Carpenter, J.
Page 218 and 219:
Eichhubl, P., Taylor, W. L., Pollar
Page 220 and 221:
Karimi-Fard, M., Durlofsky, L. J.,
Page 222 and 223:
-, 1987, Fracture from a straight c
Page 224 and 225:
Shipton, Z. K., and Cowie, P. A., 2
Page 226:
Wong, T. F., David, C., and Zhu, W.
show all

structural geology, propagation mechanics and - Stanford School of ...

Create successful ePaper yourself

Delete template?

Save as template?