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

hooking-tip interactions—using the BEM code. The degree of success attained suggests that the linear elastic anticrack mechanical model provides a valid first approximation for conceptualizing and simulating CB propagation. Perhaps the most interesting and potentially useful result of this paper is the model observation that anticrack CBs respond to high compressive normal stress (σ2 ≈ σ1) oriented parallel to their trend with propagation-path instability. This is opposite to the instability effect observed for opening-mode cracks (Olson and Pollard, 1989; Thomas and Pollard, 1993), and could be used to help forecast the degree of anastomosis in subsurface CB arrays as a function of stress history. By the same token, the configuration of an exhumed CB array could be used to constrain the ambient principal paleostress state (orientation and magnitude) in which it formed. For this paper, I performed all the fieldwork, modeling, writing and figure drafting, with guidance and editing provided by second-author David Pollard. For the modeling, I used the BEM code written by third-author Gaurav Chopra (Chapter 2). Submission of a final manuscript based on Chapter 4 to Journal of Structural Geology is anticipated. Chapter 5 represents another outgrowth of my collaborative efforts, in this case with Tapan Mukerji and Youngseuk Keehm of the Stanford Rock Physics and Borehole Geophysics (SRB) Group. I had gone to Mukerji for help in using MATLAB® to perform automated image-analysis measurements of porosity from my thin-sections, the results of which contributed to every other chapter in this thesis. For the purposes of the fluid-flow modeling presented in Chapter 7, I had also contemplated collecting permeability measurements, but was dissuaded by the difficulty of obtaining reliable results from thin CBs at reasonable expense. Through Mukerji, however, I learned of the computational permeability estimation algorithm that had been developed in the SRB, principally by Keehm, and could be used to generate virtual permeability measurements from my existing thin sections. I recognized the opportunity to perform a practical test of this new tool within the context of the analog reservoir research concept. Specifically, we applied the method to my prize thin section and compared the estimation results to available permeability measurement data for both CBs and host rock from the Aztec and Navajo sandstones. Correspondence was excellent, suggesting that, for a subsurface equivalent of the CB-rich Aztec from which only scarce, potentially unconsolidated 4
samples were available, representative flow properties can be gleaned from even a single thin section. In addition to conceiving of the project, I conducted all the fieldwork and microscopy involved, and produced all the figures and text (except for the Methods section, which I edited, and Figure 5). Keehm and Mukerji performed the permeability estimations. David Pollard provided editing and valuable guidance. This manuscript has yet to be placed for publication. Chapter 6 began as a project undertaken in 1999 by Jeffrey Chapin, a visiting researcher working with David Pollard. Chapin abandoned the work while in draft form and switched disciplines from geology to mechanical engineering. I inherited the project and brought it to fruition. Initially I performed a thorough editing and culling job on the rough draft, including moderate rewriting, and submitted it to American Association of Petroleum Geologists Bulletin in September 2002 as second author after Chapin, with co- authors Louis Durlofsky and Pollard. That version of the manuscript was rejected. In assuming first authorship at Pollard’s behest, I then performed a complete rewrite, including a strategic reconceptualization, additional culling and the redrafting of all figures. This reformulated version of the paper, which presents an analytical and numerical framework for understanding how characteristic patterns of deformation bands exposed in the Aztec sandstone would transform bulk effective permeability, was published in the September 2004 issue of American Association of Petroleum Geologists Bulletin (v. 88, n. 9). Chapter 7 grew out of reviewer feedback that came with shepherding Chapter 6 through to publication, and my desire to assume more complete ownership of the earlier work by expanding the effort. Comments by the reviewers, both cogent and off-target, suggested that, in order convincingly to assess the potential flow effects of compaction bands, I needed to consider a realistic band pattern at a scale of clear relevance to aquifer and reservoir modeling, rather than appealing to arguments based on up-scaling techniques as in Chapter 6. I saw the opportunity to achieve this goal in low-altitude aerial photographs taken of the Valley of Fire for another purpose. Viewed at full resolution, the patterns of CBs cropping out in positive relief are clearly visible, which enabled me to construct a detailed and representative map of cm-thick CBs over an area of 150,000 m 2 . Using this map in conjunction with realistic flow properties for the bands 5
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 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
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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
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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,
Page 216 and 217:
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
Page 224 and 225:
Shipton, Z. K., and Cowie, P. A., 2
Page 226:
Wong, T. F., David, C., and Zhu, W.
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