Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

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CHAPTER 3. INVERTING SHEAR-WAVE SPLITTING MEASUREMENTS FOR FRACTURE PROPERTIES Parameter Brine CO 2 Frequency (ω) 100Hz 100Hz Fluid viscosity (η) 1×10 −3 Pa.s 1×10 −4 Pa.s Fracture aperture (c) 5×10 −4 m 5×10 −4 m Fracture aspect ratio (a) 0.0005 0.0005 Porosity (ϕ) 0.2 0.2 Fluid bulk modulus (K fl ) 3GPa 0.1GPa Permeability (κ) 50mD 50mD Rock shear modulus (µ r ) 12GPa 12GPa P i 500 16.7 P ep 1.6×10 −6 5×10 −6 Table 3.2: Generic values of P ep for brine and CO 2 filled fractures, and the parameters used to calculate them where a ijkl is the elastic tensor normalised by ρ, n i is the wave normal, p i v n , and v n is the n-th phase velocity. I use the Christoffel equation to compute ψ and δV S for each S-wave arrival azimuth (θ) and inclination (ϕ) that is present in the observed dataset. The modelled ψ and δV S values are compared with the observed values, and the RMS misfit computed. Note that in all cases, ψ refers to the fast wave polarisation in ray-frame coordinates, there is no rotation into geographical or other coordinate systems as is often done when interpreting SWS. Also, I assume that in all cases splitting does occur, and that there are no null results caused by coincidence of a symmetry axis with the initial S-wave polarisation (e.g., Wüstefeld and Bokelmann, 2007). This is because I have not systematically identified null results in the data from Weyburn. Furthermore, the inclusion of null result information would require extra parameters, in the form of initial S-wave polarisations, to be included in the inversion algorithm. I compute the misfit between ψ and between δV S separately, and normalise both by their minimum values, before summing them to give the overall misfit. Conceptually, there is no reason why this sum could not be weighted such that fitting either δV S or ψ was given priority in the inversion (for instance, if one was more accurately known than the other), however, I have no reason to treat them differently here. The outcome of this process is that a misfit surface is defined throughout the 4-parameter space. This surface describes how well constrained a result is. Where many different models provide a reasonable fit to the data, the misfit minima will be broad and shallow. Where there is a well constrained best-fit model, the misfit surface will show a clearly defined minimum. I conduct an F-test (see, for e.g., Silver and Chan, 1991, in appendix) to numerically delineate this constraint. The workflow for this process is outlined in Figure 3.4. I anticipate that with sufficient data (i.e., a sufficient range of S-wave arrival angles), models will be well constrained. When arrival ranges are limited, results may be poorly constrained, with multiple models able to fit the data. 36
3.2. INVERSION METHOD Loop over γ, ξ and α Compute stiffness tensor C ijkl ⇓ Loop over number of SWS measurements For each measured θ and ϕ compute δV S and ψ using Christoffel equation ⇓ Compute the difference between observed and measured ψ and δV S ⇓ Sum the differences for each SWS measurement to give the RMS misfit for ψ and δV S ⇓ Normalise the ψ and δV S misfits by their respective minima ⇓ Sum the two normalised misfit surfaces to give the overall misfit surface ⇓ Select the values of γ, ξ and α that minimise the misfit surface ⇓ Use an F-test to compute the 90% confidence interval, and normalise the misfit surface by this value Figure 3.4: Workflow for inverting for rock physics parameters from SWS measurements. An assumption implicit in this approach is that all the rock mass through which the shear waves have travelled has similar physical properties. If there is significant spatial variation in the anisotropic system along a single - or between different - raypaths then this approach may break down. Tomographic techniques are being developed that invert for spatial variations in anisotropy (e.g., Abt and Fischer, 2008; Wookey, 2010). However these tend to run into under-determination problems, where the number of free parameters available (the spatial distribution of each area with differing anisotropy, as well as the anisotropic parameters for each area) serve only to introduce trade-offs and non-uniqueness to the solutions. Where no significant variations in anisotropic system are anticipated this approach has the advantage of ease of application and much reduced computational requirements - the tomographic approach of Wookey (2010) requires a cluster to perform the computations! In practise, I anticipate that for real cases where significant spatial variation exists our approach would fail to find significant minima. This could be used as an indication that spatial variations are present, and that tomographic techniques are necessary. 37
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Microseismic Monitoring and Geomech
Page 5 and 6: Abstract Capture of CO 2 produced a
Page 7 and 8: Author’s Declaration I declare th
Page 9 and 10: Acknowledgments There are many thin
Page 11 and 12: Table of Contents Abstract Author
Page 13 and 14: TABLE OF CONTENTS 5.4 Results . . .
Page 15 and 16: Preface ‘Research is not an end i
Page 17 and 18: 6. D. Angus, J-M. Kendall, J.P. Ver
Page 19 and 20: 1 Introduction A technology push ap
Page 21 and 22: 1.2. CCS OVERVIEW Figure 1.2: CCS s
Page 23 and 24: 1.3. THESIS OVERVIEW for CO 2 to be
Page 25 and 26: 1.3. THESIS OVERVIEW as microseismi
Page 27 and 28: 2 The Weyburn CO 2 injection projec
Page 29 and 30: 2.2. WEYBURN GEOLOGICAL SETTING Fig
Page 31 and 32: 2.2. WEYBURN GEOLOGICAL SETTING N F
Page 33 and 34: 2.4. EVENT TIMING AND LOCATIONS 500
Page 35 and 36: 2.4. EVENT TIMING AND LOCATIONS 500
Page 37 and 38: 2.4. EVENT TIMING AND LOCATIONS Nor
Page 39 and 40: 2.4. EVENT TIMING AND LOCATIONS Fig
Page 41 and 42: 2.5. DISCUSSION 500 1000 1100 North
Page 43 and 44: 2.6. SUMMARY 2.6 Summary • CO 2 s
Page 45 and 46: 3 Inverting shear-wave splitting me
Page 47 and 48: 3.2. INVERSION METHOD the additiona
Page 49 and 50: 3.2. INVERSION METHOD 1. P-wave inc
Page 51 and 52: 3.2. INVERSION METHOD 180 160 140 C
Page 53: 3.2. INVERSION METHOD 2800 2800 260
Page 57 and 58: 20 10 5 5 1 20 30 40 80 100 60 40 1
Page 59 and 60: 3.4. SWS MEASUREMENTS AT WEYBURN th
Page 61 and 62: 3.4. SWS MEASUREMENTS AT WEYBURN ei
Page 63 and 64: 3.4. SWS MEASUREMENTS AT WEYBURN ξ
Page 65 and 66: 3.4. SWS MEASUREMENTS AT WEYBURN da
Page 67 and 68: 4 2 2 3.4. SWS MEASUREMENTS AT WEYB
Page 69 and 70: 1 1 1 1 1 1 1 1 1 1 3.5. DISCUSSION
Page 71 and 72: 3.6. SUMMARY 3.6 Summary • I have
Page 73 and 74: 4 A comparison of microseismic moni
Page 75 and 76: 4.2. EVENT LOCATIONS 2400 Velocity
Page 77 and 78: 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
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5.3. NUMERICAL MODELLING 5.3.1 Flui
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5.3. NUMERICAL MODELLING MORE FLUID
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5.3. NUMERICAL MODELLING (a) (b) Fi
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5.4. RESULTS 0 500 1000 Depth (m) 1
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5.4. RESULTS 1 0.9 0.8 Soft Med Sti
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5.4. RESULTS Overburden Extension i
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5.4. RESULTS 1z:100x:100y 1z:100x:5
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5.5. SURFACE UPLIFT 1 0.9 0.8 Soft
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5.5. SURFACE UPLIFT Figure 5.17: Ma
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6 Generating anisotropic seismic mo
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6.2. STRESS-SENSITIVE ROCK PHYSICS
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6.3. A MICRO-STRUCTURAL MODEL FOR N
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6.4. CALIBRATION WITH LITERATURE DA
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6.4. CALIBRATION WITH LITERATURE DA
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6.5. COMPARISON OF ROCK PHYSICS MOD
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6.5. COMPARISON OF ROCK PHYSICS MOD
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7 Forward modelling of seismic prop
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7.2. SEISMODEL c⃝ WORKFLOW time s
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7.3. RESULTS FROM SIMPLE GEOMECHANI
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7.4. SUMMARY 7.4 Summary • I have
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8 Linking geomechanical modelling a
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8.2. MODEL DESCRIPTION Layer Thickn
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8.2. MODEL DESCRIPTION Unit E (GPa)
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8.3. RESULTS Marl Vugg 0.8 0.8 Norm
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8.3. RESULTS 15 10 Injector Produce
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8.3. RESULTS 2000 15 2000 15 1500 1
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8.4. A SOFTER RESERVOIR 8.4 A softe
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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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Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

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