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

Relative Effective Permeability 1.00 0.10 Volume Fraction Deformation Bands (%) o kmax (15 ) kmax (30 o) kmax (60 o) k-isotropic (90 o) kmin (60 o) kmin (30 o) o kmin (15 ) 0.01 0 10 20 30 40 50 60 70 80 90 100 Figure 6.11. Principal effective permeability values (maximum and minimum) for evenly spaced cross-hatch DB patterns with a DB/sandstone matrix permeability ratio of 10 -2 . Relative permeability is plotted as a function of DB volume fraction for acute intersection angles of 15 o , 30 o , 60 o and 90 o . The range of DB volume fraction observed in the Aztec sandstone is highlighted in gray. Inset figure (lower left) illustrates the 2-D permeability ellipse for an evenly spaced cross-hatch set of DBs intersecting at an acute angle θ. 162
where kmax and kmin are the maximum and minimum principal effective permeability values, kp is the permeability parallel to the bands when θ=0°, kn is the permeability normal to the bands when θ =0°, and k+ is the isotropic permeability when half of the bands are set orthogonal to the other half (θ =90°). Since the analytical solution for k+ only holds for low percentages of DBs, we use k+ as calculated by our numerical method in the equations above to find the maximum and minimum effective permeability values as functions of wb/W, θ and kb/km. Figure 6.11 shows the results for kb/km=10 -2 over the entire range of wb/W for intersection angles of θ =15°, 30°, 60°and 90°. Both principal effective permeability values decrease as wb/W increases, with the reduction in kmin being most pronounced. The degree of this permeability anisotropy also decreases as θ increases, with an isotropic permeability drop attained at θ =90°. For kb/km=10 -3 , the anisotropy introduced is even more pronounced, approaching 2 orders of magnitude as θ approaches 0° and the pattern becomes essentially parallel. For the generally high intersection angles (~80) and low volume percents (~10%) exhibited for cross-hatch DB patterns in the Aztec, relatively isotropic permeability reductions ranging from about 0.7 to1.5 orders of magnitude would be expected. 6.3. Anastomosing No analytical solutions exist for the systematic, but irregular anastomosing pattern, so the purely numerical method was used to calculate effective permeability tensors for a finely discretized version of a real, 12 x 15 m DB outcrop pattern mapped in the Aztec on a low altitude balloon photograph (Figure 6.12). Not surprisingly, the maximum effective permeability is oriented roughly parallel to the mean trend of the bands, while minimum permeability is directed roughly perpendicular. We also compared the effective permeability of this real anastomosing pattern to an idealized parallel pattern using the same average spacing and wb/W ratio of 15%. As expected, effective band-parallel * p permeability (k ) was somewhat lower for the anastomosing pattern—0.79 versus 0.85 at kb/km=10 -2 —due presumably to band connectivity and associated compartmentalization * along trend. On the other hand, effective band-normal permeability ( k ) was significantly higher for the anastomosing pattern—0.26 versus 0.06 at kb/km=10 -2 —due presumably to 163 n
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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
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Compaction band fin Depositional be
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suggests—that to first approximat
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Porosity Porosity 0.3 0.25 0.2 0.15
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pore-clogging clay—due presumably
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500 µm Figure 2.9. Electron backsc
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(a) (b) σ 3 σ 1 x 3 x 1 x 1 (c) u
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6. Elastic properties Despite a lon
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Comparison of the two approaches es
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term in (6a) and (6c) begins to dom
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MPa MPa 80 70 60 50 40 30 20 10 0 0
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2002) and use a BEM approach (Crouc
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MPa 10 4 10 3 10 2 10 1 10 −5 10
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concentration of quartz plasticity
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conducted on well-cemented sandston
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~ 62 m compaction band trend 500µm
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Sternlof et al. (2005) have suggest
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2005). It consists of a long (infin
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⎡ ∆ ⎤ ⎧ p 1 ∆ ⎛ M ⎞
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which point the inelastic strain ha
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they can exert significant effects
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interact is inversely proportional
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(a) (b) (c) (d) Figure 4.3. Typical
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Viewed individually, CB traces tend
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(a) (b) (c) (d) (e) (f) Figure 4.7.
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1973; Mardon, 1988; Peck et al., 19
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undamaged host rock. That CBs canno
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0.5 0.4 0.3 0.2 0.1 0.5 0.4 0.3 0.2
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Normalized stress magnitude 3 2.5 2
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helps to explain why the oblique ap
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and ts = G·ds + H·dn (2) where tn
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plastic compaction, as suggested by
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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 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
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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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