Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

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CHAPTER 6. GENERATING ANISOTROPIC SEISMIC MODELS BASED ON GEOMECHANICAL SIMULATION 1.0 1784 5000 1784 1.0 1788 4000 1788 0.8 4500 0.8 3500 Normalized crack density 0.6 0.4 0.2 Velocity (m/s) 4000 3500 3000 Normalized crack density 0.6 0.4 0.2 Velocity (m/s) 3000 2500 0.0 2500 0.0 2000 −0.2 0 20 40 Pressure (MPa) 2000 0 20 40 Pressure (MPa) −0.2 0 20 40 Pressure (MPa) 1500 0 20 40 Pressure (MPa) 1.0 1909 4500 1909 1.0 1950 5500 1950 0.8 4000 0.8 5000 Normalized crack density 0.6 0.4 0.2 Velocity (m/s) 3500 3000 Normalized crack density 0.6 0.4 0.2 Velocity (m/s) 4500 4000 3500 3000 0.0 2500 0.0 2500 −0.2 0 20 40 Pressure (MPa) 2000 0 20 40 Pressure (MPa) −0.2 0 20 40 Pressure (MPa) 2000 0 20 40 Pressure (MPa) 1.0 2194 4000 2194 0.8 3500 Normalized crack density 0.6 0.4 0.2 Velocity (m/s) 3000 2500 0.0 2000 −0.2 0 20 40 Pressure (MPa) 1500 0 20 40 Pressure (MPa) Figure 6.2: Inverted scalar crack densities and back calculated velocities for the Clair samples: Left-hand panels show α as a function of pressure (red - α 11, blue - α 22, green - α 33). Right-hand panels show observed velocity data (symbols) and back calculated velocities (lines) corresponding to the calculated α (red - V P x, blue - V P y, green - V P z, black - V P 45, cyan - V Sxy, magenta - V Sxz, yellow - V Syz). 112
6.3. A MICRO-STRUCTURAL MODEL FOR NONLINEAR ELASTICITY and α mm is the trace of α (α mm = α 11 + α 22 + α 33 ). By rearranging equations 6.18 and 6.19 I can rewrite β in terms of α and the ratio B N /B T , such that β 1111 = 1 ( ) BN − 1 α mm . (6.20) 3 B T Substitution of this relationship into equations 6.11 and 6.12 yields the overall stiffness as a function of both the second and fourth order crack density tensors, by way of the ratio B N /B T , [ ] ⎫ C ii = (Sjk r + f 9 αm ) 2 − (Sjj r + α jj + f 3 αm )(Skk r + α kk + f 3 αm ) /D ⎬ [ ] C ij = (Sij r + f 9 αm )(Skk r + α kk + f 3 αm ) − (Sik r + f 9 αm )(Sjk r + f 9 αm ) /D ⎭ i ≠ j ≠ k ≤ 3 C ii = (S r ii + α jj + α kk + 4f 9 αm ) −1 i ≠ j ≠ k ≥ 4 (6.21) where D = (S r 11 + α 11 + f 3 αm )(S r 23 + f 9 αm ) 2 + (S r 22 + α 22 + f 3 αm )(S r 13 + f 9 αm ) 2 +(S r 33 + α 33 + f 3 αm )(S r 12 + f 9 αm ) 2 −2(S r 12 + f 9 αm )(S r 13 + f 9 αm )(S r 23 + f 9 αm ) −(S r 11 + α 11 + f 3 αm )(S r 22 + α 22 + f 3 αm )(S r 33 + α 33 + f 3 αm ) , (6.22) f = ( ) BN − 1 . (6.23) B T Having defined a set of equations for the overall stiffness with the fourth order crack density tensor written in terms of the second order crack density tensor and B N /B T ratio, the inversion for crack density and B N /B T can then be performed using an iterative Newton-Raphson approach with model update: The vector model misfit is evaluated δb l = C obs l where the matrix Jacobian is inverted to evaluate the vector model update α ii = α ii + δm i , i = 1, 3. (6.24) − C model l l = 11, 22, 33, 44, 55, 66, 12, 13, 23 , (6.25) J il = ∂Cmodel l (6.26) ∂α i δm i = J −1 il δb l . (6.27) The matrix Jacobian of derivatives with respect to the second order crack density tensor α ii is evaluated using the following set of equations below. The partial derivatives of the denominator term 113
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Microseismic Monitoring and Geomech
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Abstract Capture of CO 2 produced a
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Author’s Declaration I declare th
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Acknowledgments There are many thin
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Table of Contents Abstract Author
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TABLE OF CONTENTS 5.4 Results . . .
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Preface ‘Research is not an end i
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6. D. Angus, J-M. Kendall, J.P. Ver
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1 Introduction A technology push ap
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1.2. CCS OVERVIEW Figure 1.2: CCS s
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1.3. THESIS OVERVIEW for CO 2 to be
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1.3. THESIS OVERVIEW as microseismi
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2 The Weyburn CO 2 injection projec
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2.2. WEYBURN GEOLOGICAL SETTING Fig
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2.2. WEYBURN GEOLOGICAL SETTING N F
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2.4. EVENT TIMING AND LOCATIONS 500
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2.4. EVENT TIMING AND LOCATIONS 500
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2.4. EVENT TIMING AND LOCATIONS Nor
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2.4. EVENT TIMING AND LOCATIONS Fig
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2.5. DISCUSSION 500 1000 1100 North
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2.6. SUMMARY 2.6 Summary • CO 2 s
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3 Inverting shear-wave splitting me
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3.2. INVERSION METHOD the additiona
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3.2. INVERSION METHOD 1. P-wave inc
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3.2. INVERSION METHOD 180 160 140 C
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3.2. INVERSION METHOD 2800 2800 260
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3.2. INVERSION METHOD Loop over γ,
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20 10 5 5 1 20 30 40 80 100 60 40 1
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3.4. SWS MEASUREMENTS AT WEYBURN th
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3.4. SWS MEASUREMENTS AT WEYBURN ei
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3.4. SWS MEASUREMENTS AT WEYBURN ξ
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3.4. SWS MEASUREMENTS AT WEYBURN da
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4 2 2 3.4. SWS MEASUREMENTS AT WEYB
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1 1 1 1 1 1 1 1 1 1 3.5. DISCUSSION
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3.6. SUMMARY 3.6 Summary • I have
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4 A comparison of microseismic moni
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4.2. EVENT LOCATIONS 2400 Velocity
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4.2. EVENT LOCATIONS 200 150 Northi
Page 79 and 80: 4.3. EVENT MAGNITUDES Pressure (MPa
Page 81 and 82: 4.3. EVENT MAGNITUDES 160 140 120 N
Page 83 and 84: 4.4. SHEAR WAVE SPLITTING 50 −3 E
Page 85 and 86: 4.5. INITIAL S-WAVE POLARISATION In
Page 87 and 88: 4.5. INITIAL S-WAVE POLARISATION 6
Page 89 and 90: 4.5. INITIAL S-WAVE POLARISATION of
Page 91 and 92: 4.6. INTERPRETATION OF SHEAR WAVE S
Page 93 and 94: 1 1 5 5 30 4.6. INTERPRETATION OF S
Page 95 and 96: 80 4.6. INTERPRETATION OF SHEAR WAV
Page 97 and 98: 2 3 3.5 4 5 2 1.8 1.4 4 4.6. INTERP
Page 99 and 100: 4.7. DISCUSSION 4.7 Discussion The
Page 101 and 102: pressure, P fl σ ′ ij = σ ij
Page 103 and 104: 5.2. EFFECTIVE STRESS AND STRESS PA
Page 105 and 106: 5.3. NUMERICAL MODELLING 5.3.1 Flui
Page 107 and 108: 5.3. NUMERICAL MODELLING MORE FLUID
Page 109 and 110: 5.3. NUMERICAL MODELLING (a) (b) Fi
Page 111 and 112: 5.4. RESULTS 0 500 1000 Depth (m) 1
Page 113 and 114: 5.4. RESULTS 1 0.9 0.8 Soft Med Sti
Page 115 and 116: 5.4. RESULTS Overburden Extension i
Page 117 and 118: 5.4. RESULTS 1z:100x:100y 1z:100x:5
Page 119 and 120: 5.5. SURFACE UPLIFT 1 0.9 0.8 Soft
Page 121 and 122: 5.5. SURFACE UPLIFT Figure 5.17: Ma
Page 123 and 124: 6 Generating anisotropic seismic mo
Page 125 and 126: 6.2. STRESS-SENSITIVE ROCK PHYSICS
Page 127 and 128: 6.3. A MICRO-STRUCTURAL MODEL FOR N
Page 129: 6.3. A MICRO-STRUCTURAL MODEL FOR N
Page 145 and 146: 6.4. CALIBRATION WITH LITERATURE DA
Page 147 and 148: 6.4. CALIBRATION WITH LITERATURE DA
Page 149 and 150: 6.5. COMPARISON OF ROCK PHYSICS MOD
Page 151 and 152: 6.5. COMPARISON OF ROCK PHYSICS MOD
Page 153 and 154: 7 Forward modelling of seismic prop
Page 155 and 156: 7.2. SEISMODEL c⃝ WORKFLOW time s
Page 157 and 158: 7.3. RESULTS FROM SIMPLE GEOMECHANI
Page 163 and 164: 7.4. SUMMARY 7.4 Summary • I have
Page 165 and 166: 8 Linking geomechanical modelling a
Page 167 and 168: 8.2. MODEL DESCRIPTION Layer Thickn
Page 169 and 170: 8.2. MODEL DESCRIPTION Unit E (GPa)
Page 171 and 172: 8.3. RESULTS Marl Vugg 0.8 0.8 Norm
Page 173 and 174: 8.3. RESULTS 15 10 Injector Produce
Page 175 and 176: 8.3. RESULTS 2000 15 2000 15 1500 1
Page 177 and 178: 8.4. A SOFTER RESERVOIR 8.4 A softe
Page 179 and 180: 8.4. A SOFTER RESERVOIR 2000 15 200
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8.4. A SOFTER RESERVOIR 2000 Max SW
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8.5. DISCUSSION pore-pressure being
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8.6. SUMMARY 8.6 Summary • I appl
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9 Conclusions Geological storage wi
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calibrate. This model has been cali
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9.1. NOVEL CONTRIBUTIONS techniques
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9.2. FUTURE WORK Finally, the compa
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Bibliography Abt, D. L., Fischer, K
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BIBLIOGRAPHY Gassmann, F., 1951. Ub
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BIBLIOGRAPHY Kendall, J.-M., Pilido
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BIBLIOGRAPHY Sayers, C. M., 2002. S
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BIBLIOGRAPHY White, D., 2009. Monit
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A List of Symbols The table below l
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B In Support of Carbon Capture and
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Both China and India are aggressive
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Utsira rock properties vary signifi
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