Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

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CHAPTER 6. GENERATING ANISOTROPIC SEISMIC MODELS BASED ON GEOMECHANICAL SIMULATION D −1 are ∂D ∂α ii = (1 + f 3 )(Sr jk + f 9 αm ) 2 + 2f 9 (Sr ii + α ii + f 3 αm )(S r jk + f 9 αm ) + f 3 (Sr ik + f 9 αm ) 2 + 2f 9 (Sr jj + α jj + f 3 αm )(Sik r + f 9 αm ) + f 3 (Sr ij + f 9 αm ) 2 + 2f 9 (Sr kk + α kk + f 3 αm )(Sij r + f 9 αm ) − 2f ( (Sik r + f 9 9 αm )(Sjk r + f 9 αm ) +(Sij r + f 9 αm )(Sjk r + f 9 αm ) + (Sij r + f 9 αm )(Sik r + f ) 9 αm ) −(1 + f 3 )(Sr jj + α jj + f 3 αm )(S r kk + α kk + f 3 αm ) − f 3 (Sr ii + α ii + f 3 αm ) (S r kk + α kk + f 3 αm ) − f 3 (Sr ii + α ii + f 3 αm )(S r jj + α jj + f 3 αm ) , (6.28) where i ≠ j ≠ k ≤ 3. The partial derivatives for C † ii = C iiD terms are ∂C † ii ∂α ii = 2f 9 (Sr jk + f 9 αm ) − f 3 (Sr kk + α kk + f 3 αm ) − f 3 (Sr jj + α jj + f 3 αm ) , ∂C † ii ∂α jj = 2f 9 (Sr jk + f 9 αm ) − (1 + f 3 )(Sr kk + α kk + f 3 αm ) − f 3 (Sr jj + α jj + f 3 αm ) , (6.29) where i ≠ j ≠ k ≤ 3. The partial derivatives for C † ij = C ijD (when i ≠ j) terms are ∂C † ij ∂α ii = f 9 (Sr kk + α kk + f 3 αm ) + f 3 (Sr ij + f 9 αm ) − f 9 (Sr jk + f 9 αm ) − f 9 (Sr ik + f 9 αm ) = ∂C† ij ∂α jj , ∂C † ij ∂α kk = f 9 (Sr kk + α kk + f 3 αm ) + (1 + f 3 )(Sr ij + f 9 αm ) − f 9 (Sr jk + f 9 αm ) − f 9 (Sr ik + f 9 αm ) , (6.30) where i ≠ j ≠ k ≤ 3. The partial derivatives for C ij (i, j ≤ 3) are written ∂C ij = D −1 ∂C† ij − C † ∂D ijD−2 (6.31) ∂α ii ∂α ii ∂α ii 114
6.3. A MICRO-STRUCTURAL MODEL FOR NONLINEAR ELASTICITY and the partial derivatives for C ii (i ≥ 4) terms are ∂C 44 ∂α 11 = − 4f 9 (Sr 44 + α 22 + α 33 + 4f 9 αm ) −2 ∂C 44 ∂α 22 = −(1 + 4f 9 )(Sr 44 + α 22 + α 33 + 4f 9 αm ) −2 ∂C 44 ∂α 33 = −(1 + 4f 9 )(Sr 44 + α 22 + α 33 + 4f 9 αm ) −2 ∂C 55 ∂α 11 = −(1 + 4f 9 )(Sr 55 + α 11 + α 33 + 4f 9 αm ) −2 ∂C 55 ∂α 22 = − 4f 9 (Sr 55 + α 11 + α 33 + 4f 9 αm ) −2 ∂C 55 ∂α 33 = −(1 + 4f 9 )(Sr 55 + α 11 + α 33 + 4f 9 αm ) −2 ∂C 66 ∂α 11 = −(1 + 4f 9 )(Sr 66 + α 11 + α 22 + 4f 9 αm ) −2 ∂C 66 ∂α 22 = −(1 + 4f 9 )(Sr 66 + α 11 + α 22 + 4f 9 αm ) −2 ∂C 66 ∂α 33 = − 4f 9 (Sr 66 + α 11 + α 22 + 4f 9 αm ) −2 . (6.32) This method finds the best fitting values of α at a given B N /B T value. I found that when B N /B T was included in the Newton-Raphson scheme, it was seldom possible to find stable, convergent solutions: stationary points in the objective function were too close to the desired solution. Therefore a grid search was performed over B N /B T , and for each B N /B T value the Newton-Raphson approach was used to find α. These α values were used to back-calculate velocities, and the value of B N /B T that, in conjunction with the α values computed from it, minimised the misfit between back-calculated and observed velocities was selected as the most appropriate. This approach is illustrated in Figure 6.3. The results of this inversion for the samples from the Clair reservoir are shown in Figure 6.4. Figure 6.5 shows the optimum values of B N /B T determined via this method. We also perform the inversion for Berea (Lo et al., 1986) and Penrith (Sayers, 2002) sandstone samples. Because EBSD and XRTG information is not available for these samples, S r is determined from the behaviour of the samples at high pressure following MacBeth (2004). The results are shown in Figure 6.6, with B N /B T plotted in Figure 6.7. At high pressures the observed stiffness tensors become close to S r , hence α becomes small and our inversion for B N /B T becomes less reliable. This problem is not encountered by the Clair samples, where the observed stiffness is always well below S r . Figures 6.5 and 6.7 give an indication as to how appropriate the scalar crack assumption is. For a flat crack with no infill, equation 6.15 suggests that B N /B T should be between 0.8 and 1, depending on the Poisson’s ratio of the background matrix. Although there is some spread outside these bounds, the majority of inverted B N /B T values are found close to this range, indicating that the scalar crack assumption is appropriate. It is also worth noting that there appears to be no systematic variation of B N /B T with pressure, which is implicitly predicted by the scalar crack assumption, further strengthening our confidence in making it. 115
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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
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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 131: 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
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Page 181 and 182: 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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