Delaware Basin, and (3) low stand of sea level, which caused subaerial ...... that defined stress history and structural style of the PB, and at Vacuum field.
TIME -LAP SE , MULTIC OMP ONE NT SE ISMIC ANALYSIS OF R E SE R VO IR D Y N AMIC S
by Luca Duranti
Copyright by Luca Duranti 2001 All Rights Reserved
ii
A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Geophysics).
Golden, Colorado Date _____________
Signed: ________________________ Luca Duranti
Approved: ________________________ Dr. Thomas L. Davis Professor of Geophysics Thesis Advisor
Golden, Colorado Date _____________ ______________________________ Dr. Terence K. Young Professor and Head Department of Geophysics
iii
ABSTRACT
Time-lapse, multicomponent, surface 3D seismic at Vacuum field mapped and quantified the dynamic changes induced by a CO2 flood on the porous and fractured dolomites of the San Andres reservoir. Compliance-based effective medium theory simulated the time-lapse variations in seismic velocities in a dual porosity dolomite. Fractures were described as mechanically non-interacting, penny-shaped cracks, and pores were represented as spheres. Numerical modeling and ultrasonic velocity measurements clarified some of the physical mechanisms responsible for time-lapse seismic anomalies in a fractured reservoir. Geomechanical models for stress and saturation changes in a dual porosity rock were derived using those physical mechanisms. Poststack processing of vertical incidence, time-lapse volumes enhanced repeatability of compressional and shear waves. In processing compressional waves, the preferred technique for poststack processing was crossequalization, while a combination of layer stripping and crossequalization was employed on shear waves. Time-lapse, shear waves layer stripping revealed that the rock column at Vacuum field is composed of at least three coarse layers with different principal directions of azimuthal anisotropy. The differences in azimuthal anisotropy were quantified in terms of the orientation of the natural coordinate systems, and fracture density. In the reservoir section, fracture density and orientation changed between the baseline and the repeated seismic survey, thus showing dependency on the CO2 flood, and in general on the poroelastic changes caused by reservoir engineering operations. The Vacuum field time-lapse experiment shows a subdivision of the reservoir into at least three zones on the basis of saturation and pore pressure changes. The discrimination was made possible by the usage of multicomponent seismology in a fractured reservoir. In particular, real seismic data and numerical modeling with effective medium theory show that time-lapse shear wave splitting can be a powerful indicator of saturation changes in the presence of corrugated fracture sets.
iv
TABLE OF CONTENTS
ABSTRACT............................................................................................................................. IV TABLE OF CONTENTS ............................................................................................................. V LIST OF FIGURES ................................................................................................................ VIII SYMBOLS AND ABBREVIATIONS ........................................................................................... XIII ACKNOWLEDGEMENTS......................................................................................................... XVI CHAPTER 1 ..............................................................................................................................1
INTRODUCTION .....................................................................................................................1 1.1
Geology ....................................................................................................................4
1.2
Time-lapse multicomponent seismic monitoring ...........................................................5
1.3
Multicomponent seismic data acquisition .....................................................................7
1.4
Data processing.......................................................................................................11
1.5
Summary ................................................................................................................13
CHAPTER 2 ............................................................................................................................14
THEORY AND MODELS ..........................................................................................................14 2.1
Introduction ............................................................................................................14
2.2
Definitions and properties of porous and fractured rocks............................................14
2.3
Effective medium theory ..........................................................................................19
2.3.1
Three-dimensional single cavities .......................................................................19
2.3.2
Fractures as regions of weakness.......................................................................24
2.3.3
Cracks distribution and symmetry of the crack compliance...................................27
2.3.4
Cross-coupling compliances ...............................................................................28
v
2.4
Effective stress ........................................................................................................33
2.5
Reflection seismology over azimuthally anisotropic media...........................................35
2.6
Layer stripping ........................................................................................................38
2.7
Summary ................................................................................................................41
CHAPTER 3 ............................................................................................................................42
ROCK PHYSICS .....................................................................................................................42 3.1
Introduction ............................................................................................................42
3.2
Experimental measurements ....................................................................................42
3.2.1
Fluid properties.................................................................................................46
3.2.2
Experimental results..........................................................................................49
3.3
Modeling dual porosity .............................................................................................52
3.3.1
Modeling experimental results............................................................................52
3.3.2
Modeling lower crack symmetries.......................................................................54
3.4
Summary ................................................................................................................69
CHAPTER 4 ............................................................................................................................71
STATE OF STRESS IN THE CRUST..........................................................................................71 4.1
Introduction ............................................................................................................71
4.2
Permian Basin tectonics ...........................................................................................72
4.3
Structural domains of the Permian Basin ...................................................................82
4.4
Current state of stress .............................................................................................90
4.4.1
Patterns and orders of stress .............................................................................93
4.4.2
Pore pressure as a second-order stress field .......................................................93
4.4.3
Shear wave splitting as a stress indicator............................................................96
4.5
State of stress in the San Andres dolomites at Vacuum Field ......................................98
4.6
Summary .............................................................................................................. 103
CHAPTER 5 .......................................................................................................................... 104
P-WAVE POSTSTACK ANALYSIS ........................................................................................... 104 5.1
Introduction .......................................................................................................... 104
vi
5.2
Signal crossequalization ......................................................................................... 104
5.3
Crossequalization of Vacuum P-wave data............................................................... 109
5.4
P-wave time-lapse anomalies ................................................................................. 119
5.5
Summary .............................................................................................................. 122
CHAPTER 6 .......................................................................................................................... 123
S-WAVE POSTSTACK ANALYSIS ........................................................................................... 123 6.1
Introduction .......................................................................................................... 123
6.2
Time-lapse 2Cx2C shear wave data......................................................................... 124
6.3
Time-lapse layer stripping and crossequalization...................................................... 127
6.4
Shear wave time-lapse results ................................................................................ 136
6.5
Shear wave time-lapse relative attenuation ............................................................. 144
6.6
Summary .............................................................................................................. 145
CHAPTER 7 .......................................................................................................................... 146
TIME-LAPSE INTERPRETATION AND CONCLUSIONS ............................................................. 146 7.1
Introduction .......................................................................................................... 146
7.2
CO2 flooding: general aspects................................................................................. 146
7.3
CO2 flooding: engineering data from Vacuum field ................................................... 149
7.4
Reservoir time-lapse zonation................................................................................. 157
7.4.1
Dynamics of area 1 ......................................................................................... 157
7.4.2
Dynamics of area 2 ......................................................................................... 163
7.4.3
Dynamics of area 3 ......................................................................................... 166
7.5
Conclusions of the study and ideas for additional research ....................................... 169
REFERENCES ...................................................................................................................... 175
vii
LIST OF FIGURES
Figure 1.1. Location of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Figure 1.2. Seismic survey design and acquisition parameters . . . . . . . . . . . . . . . . . . . . . . .. 7 Figure 1.3. Surface topography and time-lapse seismic data acquisition . . . . . . . . . . . . . . . . 9 Figure 1.4. Processing flow for multicomponent seismic data . . . . . . . . . . . . . . . . . . . . . . .. 10 Figure 1.5. CMP gather of S1H1 component from pre-injection data at Vacuum field . . . . . . . 12 Figure 2.1. Coordinate system for vertical fracture planes used in the text . . . . . . . . . . . . . . 22 Figure 2.2. Thin section from Vacuum field CVU 100 well . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Figure 2.3. Symmetry of the fracture compliance matrix for a single fracture set . . . . . . . . .. 23 Figure 2.4. Fractures as a periodic array of inclined cracks . . . . . . . . . . . . . . . . . . . . . . . . . 31 Figure 2.5. Normal, tangential, and coupling compliances as a function of fracture roughness 31 Figure 2.6. Principal normal stresses and deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Figure 2.7. Example of shear wave splitting in reflection seismology . . . . . . . . . . . . . . . . . . 36 Figure 2.8. Geometry of reflection seismology over azimuthally anisotropic media . . . . . . . . 37 Figure 3.1. Properties of samples used for ultrasonic velocity measurements . . . . . . . . . . . . 43 Figure 3.2. Core plug from CVU 100 well and SEM image . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Figure 3.3. SEM photograph in the proximity of sample 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Figure 3.4. Sequence of experimental conditions for ultrasonic velocity measurements . . . . . 45 Figure 3.5. Physical properties of brine, CO2, and oil-CO2 mixes . . . . . . . . . . . . . . . . . . . . . 48 Figure 3.6. Experimental velocities and velocity changes for sample 1 . . . . . . . . . . . . . . . . . 50 Figure 3.7. Experimental velocities and velocity changes for sample 2 . . . . . . . . . . . . . . . . . 51 Figure 3.8. Crack density as a function of effective pressure . . . . . . . . . . . . . . . . . . . . . . . . 58 Figure 3.9. Experimental and computed velocities for brine and oil saturated conditions for sample 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Figure 3.10. Experimental and computed velocities for brine and oil saturated conditions for sample 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
viii
Figure 3.11. Velocity difference (%) between computed and experimental velocities for the two samples from Vacuum field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Figure 3.12. Vertical incidence compressional velocities for a dolomite matrix with an array of inclined penny-shaped crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Figure 3.13.
Vertical incidence shear-wave velocities for a dolomite matrix with an array of
inclined penny-shaped cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Figure 3.14. Compressional and shear-wave velocity response to an increase of the normal-totangential coupling compliance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Figure 3.15. Vertical incidence compressional velocities on a dual porosity dolomite rock . . . 65 Figure 3.16. Vertical incidence shear-wave velocities on a dual porosity dolomite rock . . . . . 66 Figure 3.17. Dependence of shear-wave splitting parameter on fluid saturants for a dual porosity dolomite rock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Figure 3.18. Changes of compressional velocity and shear-wave splitting parameter caused by substituting oil with CO2 in a dual porosity dolomite . . . . . . . . . . . . . . . . . . . . . . . . 68 Figure 4.1. The Permian Basin of West Texas and southeastern New Mexico . . . . . . . . . . . . 75 Figure 4.2. Early Devonian plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Figure 4.3. Upper Mississippian plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . 76 Figure 4.4. Upper Pennsylvanian plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . 76 Figure 4.5. Early Permian plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Figure 4.6. End of Permian plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Figure 4.7. Early Triassic plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Figure 4.8. Early Jurassic plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Figure 4.9. Early Cretaceous plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . 78 Figure 4.10. End of Cretaceous plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . 78 Figure 4.11. Paleocene plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Figure 4.12. Eocene plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Figure 4.13. Miocene plate tectonic representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Figure 4.14. Crustal mobility and sedimentation rates versus geologic time for the various portions of the Permian Basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Figure 4.15. Stratigraphy of the Northwestern Shelf in relation to the seismic column . . . . . . 81
ix
Figure 4.16. Basement structural style in the Central Basin Platform and Northwestern Shelf of the Permian Basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Figure 4.17. Basement structural style in the Northwestern Shelf of the Permian Basin . . . . . 86 Figure 4.18. Azimuthal strikes of the Central Basin Platform and Northwestern Shelf basement faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Figure 4.19.
Structural style of the San Andres dolomites in the Northwestern Shelf of the
Permian Basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Figure 4.20. Azimuthal strikes of the San Andres faults and Northwestern Shelf basement faults in the proximity of Vacuum field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Figure 4.21.
Effective stresses on the horizontal plane of a dolomite rock with unidirectional
vertical fractures subjected to increasing pore pressure . . . . . . . . . . . . . . . . . . . . . 91 Figure 4.22. Superposition of regional and pore pressure principal horizontal stresses . . . . . . 92 Figure 4.23. Present day stress indicators in the North and Central American regions . . . . . 100 Figure 4.24. Present day stress indicators in the Permian Basin . . . . . . . . . . . . . . . . . . . . . 101 Figure 4.25. Maximum horizontal stress in the Vacuum field San Andres dolomites . . . . . . . 102 Figure 5.1. Effects of time shift on the differencing process . . . . . . . . . . . . . . . . . . . . . . . 106 Figure 5.2. Effects of amplitude scaling on the differencing process . . . . . . . . . . . . . . . . . . 107 Figure 5.3. Effects of spectral unbalancing on the differencing process . . . . . . . . . . . . . . . 108 Figure 5.4. Effects of phase rotation on the differencing process . . . . . . . . . . . . . . . . . . . . 108 Figure 5.5.
Example of residual energy in the static portion of the time-lapse compressional
wave data from Vacuum field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.6. Repeatability of the static portion of Figure 5.5 in time and frequency domain . . 112 Figure 5.7. Crossplots of three time-lapse reflectors (A, B, and Queen) from the static portion of the Vacuum field P-wave data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Figure 5.8. P-wave average RMS amplitude as a function of reflection time for the pre- and postinjection surveys at Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.9.
Intermediate results in the crossequalization process after amplitude matching
(global + trace by trace) applied to the data of Figure 5.5 . . . . . . . . . . . . . . . . . . . 115 Figure 5.10. Final results in the crossequalization process after amplitude matching and phase matching applied to the data of Figure 5.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Figure 5.11. Repeatability of the static section of Figure 5.10 in time and frequency domain . 117
x
Figure 5.12. Repeatability of three reflectors from the static section of Figure 5.10 . . . . . . . 118 Figure 5.13.
Time-lapse changes in compressional velocity in the San Andres reservoir at
Vacuum field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Figure 5.14.
Time-lapse amplitude difference cross-section from the P-wave data volumes at
Vacuum field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Figure 6.1. Normal incidence 2Cx2C shear wave stacks after prestack processing . . . . . . . . 125 Figure 6.2. Energy as a function of reflection time for the 2Cx2C data volumes . . . . . . . . . 126 Figure 6.3.
Time delay between the two shear wave principal components as a function of
reflection time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Figure 6.4. Time-lapse shear-wave splitting at the A1-A2 anisotropy boundary . . . . . . . . . . 131 Figure 6.5. Example of the effects of layer stripping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Figure 6.6. Time delay between shear wave principal components after layer stripping . . . . 133 Figure 6.7. Example of full layer stripping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Figure 6.8. Distribution of energy as a function of reflection time for the 2Cx2C data volumes after layer stripping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Figure 6.9. Shear wave principal components energy distribution as a function of reflection time after layer stripping and time-lapse crossequalization . . . . . . . . . . . . . . . . . . . . . . 136 Figure 6.10.
Time-lapse change in reservoir interval velocity for the fast (S1) and slow (S2)
shear modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Figure 6.11. Shear wave splitting in the San Andres reservoir before and after CO2 injection 139 Figure 6.12. Time-lapse change in shear wave splitting and S1H1 polarization . . . . . . . . . . 140 Figure 6.13. Azimuthal anisotropy in the pre-injection San Andres reservoir . . . . . . . . . . . . 141 Figure 6.14. Azimuthal anisotropy in the post-injection San Andres reservoir . . . . . . . . . . . 142 Figure 6.15.
Expressions of azimuthal anisotropy in the pre- and post-injection San Andres
reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Figure 7.1.
Schematic fluid saturation and compressional velocity profiles for a CO2 flood at
constant pore pressure and temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Figure 7.2.
Schematic fluid saturation and compressional velocity profiles for a CO2 flood at
constant pore pressure and temperature above the minimum miscibility pressure . . 148 Figure 7.3. Surface injection pressure for the six CO2 injector wells at Vacuum field . . . . . . 151
xi
Figure 7.4. Volume of fluid injected for the six CO2 injector wells at Vacuum field . . . . . . . . 152 Figure 7.5. Production data for the northern portion of Vacuum field . . . . . . . . . . . . . . . . . 153 Figure 7.6. Production data for the southern portion of Vacuum field . . . . . . . . . . . . . . . . . 154 Figure 7.7. Subdivision of the San Andres reservoir in three interpreted areas of comparable dynamic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Figure 7.8. Compressional wave velocity change with subdivision of the San Andres reservoir in three interpreted areas of comparable dynamic behavior . . . . . . . . . . . . . . . . . . . . 156 Figure 7.9. Schematic model of a dynamic behavior in Area 1 (scenario 1) of the San Andres reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Figure 7.10. Schematic model of dynamic behavior in Area 1 (scenario 2) of the San Andres reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Figure 7.11. Schematic model of the possible dynamic behavior in Area 2 of the San Andres reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Figure 7.12. Schematic model of the possible dynamic behavior in Area 3 of the San Andres reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
xii
SYMBOLS AND ABBREVIATIONS
“TWO ENTITIES AND TWO ENTITIES ARE FOUR ENTITIES”. WHEN YOU HAVE TOLD ME WHAT YOU MEAN BY “ENTITY”, WE WILL RESUME THE ARGUMENT. BERTRAND RUSSELL Compliance: [1/GPa] m = compliance of the mineral phase s M = s ijm = s ijkl sC = compliance of the crack space s P = compliance of the equant (spherical) pore space s E = s ij = s ijkl = general compliance of the effective medium dry sdry = s ijdry = s ijkl = drained (dry) effective medium compliance E u = saturated effective medium compliance suE = s iju = s ijkl
Compressibility: [1/GPa] C = generic material compressibility C m = compressibility of the mineral phase
C f = compressibility of the fluid C bc = 1 K dry = dry compressibility C bp = subsidence effect compressibility C pc = formation compaction compressibility C pp = effective pore compressibility C φ = pore space compressibility (Brown and Korringa, 1975) C u = saturated (undrained) compressibility Density: [gr/cm3] ρ brine = density of brine ρoil = density of oil ρCO 2 = density of CO2 ρm = density of the mineral phase ρe = effective medium density
xiii
Elastic moduli: [GPa] K m = bulk modulus of the mineral phase
K f = fluid bulk modulus K brine = brine bulk modulus K oil = oil bulk modulus K CO 2 = CO2 bulk modulus K dry = bulk modulus of the dry rock K sat = bulk modulus of the saturated rock µ m = shear modulus of the mineral phase Pressure: [MPa] P = hydrostatic pressure Pc = confining pressure
P p = pore pressure Pd = differential pressure Pe = effective pressure Stiffness: [GPa] m = stiffness of the mineral phase c M = c ijm = c ijkl cC = stiffness of the crack space c P = stiffness of the equant (spherical) pore space c E = c ij = c ijkl = general effective medium stiffness dry = c ijdry = c ijkl = drained (dry) effective medium stiffness c dry E u = saturated effective medium stiffness cuE = c iju = c ijkl
Strain: ε ij = general strain tensor Stress: [GPa] and [MPa] σ ij = general stress tensor σ Eij = effective stress tensor σ 1 ≥ σ 2 ≥ σ 3 = principal normal stresses σV = vertical stress σ H = horizontal stress
σ H max = maximum horizontal stress σ H min = minimum horizontal stress α Eij = coefficient of effective stress
xiv
Velocity: [km/sec] or [ft/sec] V Pbrine = compressional velocity of the rock under brine saturated conditions
V Poil = compressional velocity of the rock under oil saturated conditions V PCO 2 = compressional velocity of the rock under CO2 saturated conditions V Pdry = compressional velocity of the dry rock V Sbrine = shear velocity of the rock under brine saturated conditions V Soil = shear velocity of the rock under oil saturated conditions V SCO 2 = shear velocity of the rock under CO2 saturated conditions V Sdry = shear velocity of the dry rock Volume [m3] and porosity: V = generic total volume V m = volume of the mineral phase
V b = bulk volume V p = pore volume V P = volume of equant pores VC = crack or fractures volume φ = V p V b = total porosity φC = VC V b = crack or fracture porosity φP = V P V b = equant pores (spherical) porosity α = a c = cracks or fractures aspect ratio e = crack density Locations of geologic interest PB = Permian Basin VF = Vacuum field, NM NWS = Northwest Shelf of the PB MOB = Marathon-Ouachita orogenic belt DB = Delaware Basin DP = Diablo Platform NS = Northern Shelf CBP = Central Basin Platform MB = Midland Basin NAM = North American (plate) SAM = South American (plate)
xv
ACKNOWLEDGEMENTS
I would like to express my gratitude to the ones who encouraged me in this study and in my educational journey at Colorado School of Mines. First and foremost, I am in debt to Tom Davis, my advisor, for his constant support through the years. Tom introduced me to reservoir geophysics, and constantly pushed toward directions that were, at first, not obvious to many, but valid in the end. The idea of detecting changes in fluid content through shear wave seismology is the result of years of discussions in RCP. It would not have happened without Tom. Mike Batzle taught me to question reservoir seismology, and to search constantly for an explanation in the physical interaction between rocks and fluids. Thank you to the other committee members, John Hogan, Neil Hurley, and Ilya Tsvankin, and to the Geophysics Department Head, Terry Young, for their critical reviews. I am grateful to Mariangela Capello de Passalacqua, who allowed me to use some of the experimental rock physics data she collected on Vacuum field cores. I would like to thank Dr. Seiji Nakagawa, for discussing many issues pertaining to fracture compliance, and for allowing me to use, in this work, some of his results. Interaction among students generates new ideas. In particular, I enjoyed and benefited the most from open discussions with Reynaldo Cardona and Ronny Hofmann. The industry partners of the Reservoir Characterization Project, Phase VII, were instrumental in supporting this work. It is my hope that the industrial world continues to find cooperation with academic research useful, as well as necessary.
xvi
1
CHAPTER 1
INTRODUCTION
THOUGHT SUBDUES MATTER IN THE UNDERSTANDING OF REALITY, AND REALITY IS DEFEATED IN THIS EVER BRIEF BATTLE. YET EVERYTHING STARTS AGAIN, SINCE REALITY IS INEXHAUSTIBLE. BUT, WITHOUT THOUGHT, REALITY WOULD BE FORMLESS TO US … MICHELE PATY The focus of this work is hydrocarbon exploration and development, the application of multicomponent reflection seismology to this field, including some manifestations of anisotropy, and the seismically detectable time dependent changes induced in the rock-fluid system by reservoir dynamics. The scale of interest is the seismic scale at first: frequencies from 5 to 100 Hz, and distances on the order of tens of meters to kilometers. Additionally, measurements at ultrasonic frequencies (MHz) and distances on the order of 10-3 m were used. This work applied existing theoretical models in order to understand a set of observations made in the course of a multicomponent, time-lapse seismic experiment. Theoretical models existing in reflection seismology typically consider the medium as time independent, thus in this work some theoretical aspects were adapted to the primary objective, which is time-lapse. In this introductory chapter, the reasons and the conditions of the study are explained, including the geology of the area of interest, the benefits and issues in seismic reservoir monitoring, the essential elements of seismic data acquisition and processing at Vacuum field, and the contributions that this work makes. In chapter 2, the theoretical models used to explain the experimental observations are reviewed. Particular attention is given to the relationships describing the elastic field when a rock is exposed to changes in stress and saturating fluids. Chapter 3, starting from experimental velocity measurements, investigates the consequences of pressure and saturation changes in rocks where equant porosity and fractures coexist. In chapter 4, the state of stress at Vacuum field, and its change over time, are explored. Chapter 5 details the time-lapse poststack analysis performed on compressional waves recorded at Vacuum field.
2
Chapter 6 does the same on shear-waves, using crossequalization and layer stripping routines. In chapter 7, the time-lapse seismic anomalies are compared with what theory predicts, and an overall interpretation of the time-lapse Vacuum experiment is given. The core of this study is the detection of time-lapse seismic anomalies, and how they relate to plausible rock physics models. The primary method of investigation is the analysis of two multicomponent 3D seismic surveys acquired at Vacuum field (NM) preceding and following the injection of CO2 in the San Andres dolomite reservoir rocks. The most notable result of this study is the indication that time-lapse multicomponent seismology is capable of discriminating between pressure and saturation changes in a carbonate fractured reservoir. The CO2 injection in the San Andres dolomites subdivided the reservoir into at least three discrete zones where a combination of pore pressure and saturation effects took place. Geomechanical models were built to explain the time-lapse seismic observations. Shearwave normal-incidence reflection seismology was critical in defining the azimuthal anisotropy of the rock column, as well as detecting saturation changes in the fractured San Andres dolomites.
3
NEW MEXICO
Vacuum field
TEXAS
MEXICO
NS NWS Vacuum field MB NM TX
M
EX
DB
CBP IC O
DP MOB
NORTH 100 km
ES
FIG. 1.1: Location of the time-lapse, multicomponent seismic experiment conducted by the Reservoir Characterization Project at Vacuum field (NM), which is the objective of this study. The lower figure shows Vacuum field as part of the Northwest Shelf (NWS) of the Permian Basin (PB). Thick lines represent the limit of carbonate sedimentation during Guadalupian time. The basin can be subdivided in sub-basins (DB = Delaware Basin; MB = Midland Basin), and structural highs (DP = Diablo Platform; CBP = Central Basin Platform; NWS = Northwest Shelf; NS = Northern Shelf; ES = Eastern Shelf; MOB = Marathon-Ouachita Belt). The thin lines in the CBP and in the NWS are basement regional faults. Data from: USGS for the top map; Ewing (1991), and Yang and Dorobek (1995) for the bottom map.
4
1.1
GEOLOGY Located in the southeastern corner of New Mexico (Figure 1.1), the Central Vacuum Unit
(CVU) produces hydrocarbons from depths of 1310 to 1463 m (4300 to 4800 ft) in the San Andres Formation. The reservoir is part of the Northern Shelf of the Permian Basin, and is composed of dolomitized carbonates. Vacuum field is a combined stratigraphic-structural trap. Hydrocarbons are contained in several levels spanning through the entire Permian section. Lateral and vertical facies variation provides the main mechanism for trapping hydrocarbons. Porous carbonate facies grade laterally and vertically to tight carbonates and evaporites which provide the reservoir seal. Since early Permian, the general evolution of the Northern Shelf is a progressively shallowing-upward carbonate platform. The fundamental mechanism is a cyclic intercalation of episodes of: (1) sea level high stand, which caused aggradation of the carbonate platform, (2) still stand of sea level, which caused progradation of the carbonate platform towards the Delaware Basin, and (3) low stand of sea level, which caused subaerial exposure of the platform, erosion and clastic deposition pathways from the carbonate platform into the Delaware Basin. The San Andres Formation is the result of progradation of supratidal and intertidal lithologies over intertidal and subtidal facies. Two major depositional sequences, with the same type of sedimentation, compose the San Andres: the Lower San Andres and the Upper San Andres. During episodes of low stand, the carbonate factory was interrupted, and the platform exposed to an arid environment. The main consequences were: (1) erosion of the platform carbonates, which took place differentially, attacking structural lows more than structural highs, (2) karstification, and (3) deposition of evaporites. This cyclicity generated stacked reservoir layers isolated by non-reservoir rocks (evaporites, or supratidal dolomites) determining the mechanism of reservoir and seal. Additionally, the conditions described above resulted in lateral and vertical variability in porosity and permeability distribution. Porosity developed due to diagenetic events along with episodes of anhydrite infill and evaporite dissolution. Average porosity is 0.11. Permeability averages 22 md. The reservoir oil is 38 API, with a viscosity of 0.96 cp at the bubble-point pressure (764 psi). Reservoir temperature and pressure average 40°C (104°F) and 11 MPa (1600 psi), respectively.
5
The source of the San Andres oil is Wolfcampian shales. A suggested migration path for Vacuum hydrocarbons indicates that oil migrated laterally updip from the Delaware Basin toward the basin margin and then vertically through fractures along the shelf margin permeating the San Andres intervals on the shelf edge. 1.2
TIME-LAPSE MULTICOMPONENT SEISMIC MONITORING Vacuum field is a mature field. Production and field development started in the late
1930’s. Secondary recovery, by means of water flood, began in 1978. During the 1980’s, infill drilling reached the present density of wells at 10-acre spacing. Recently (1997), a CO2 flooding program was initiated with the intent of almost doubling the present oil production. For the operators, stimulating production of otherwise unrecoverable hydrocarbons may make the difference between economic success and failure. On a larger scale, stimulating hydrocarbon recovery and increasing production efficiency equates to generating energy reserves. The concept of enhanced oil recovery (EOR) is not new, nor are the methods of EOR (gas flood, CO2 flood, etc.). What has changed recently is the possibility to monitor the recovery process with non-invasive, high-resolution techniques. Time-lapse reflection seismology repeatedly images the producing horizons at a time interval such that detection of fluid movement is possible. Thus, the ultimate goal in time-lapse industrial geosciences is to reconstruct the permeability of the subsurface. The fluid phase may vary (CO2, water, steam, hydrocarbons), but in all the cases, the objective is the detection of changes in the rock-fluid system. The main operational benefit of reservoir monitoring is in the possibility to correct fluid production strategies. Examples are discovery of bypassed reservoir zones, unknown compartmentalization, permeability barriers, fluid saturation changes, need for additional drilling, avoiding early water or gas breakthrough, up to complete redefinitions of reservoir and flow models. The benefits are quantified by their economic impact and, although the initial decision of implementing full monitoring programs presents some risk, the outcome often justifies the investment. For the scientific community, reservoir monitoring allows us to address a level of complexity in poroelastic media that we are just beginning to estimate. For example, a classically time-independent rock parameter like porosity is now becoming a time variable. For reservoir
6
engineers, stress, pore pressure, and effective pressure have always been time-dependent variables. They were not for geoscientists, accustomed to a more static, time-independent view of porous media. Thus, reservoir monitoring is forcing at least three different disciplines (geology, geophysics, reservoir engineering) to seek common solutions in dynamic porous media. In time-lapse reservoir monitoring, every reservoir must be considered a thermoporoelastic body whose physical properties are space and time dependent. Currently, reflection seismology is the only technology providing extensive 3D coverage of the reservoir interwell space. Implications for reservoir definition in space are extraordinary even with no time dependence, but, with time-lapse seismic monitoring, every seismic observable becomes also time-dependent. Thus, there are two essential directions of research to follow in order to interpret time-lapse seismic data. First, it is necessary to understand the relationship between rock parameters and seismic attributes (static imaging). Because rock parameters are spatially varying, this is a space-dependent problem. Second, it is necessary to understand which seismic attributes can image time-dependent changes in rock parameters. This is a time-dependent problem (dynamic imaging), which relies on space dependency. The bulk of sedimentary rocks is anisotropic. A medium is anisotropic if the measured values of a particular parameter depend on the direction of measurement. In elasticity, one of the parameters commonly used to characterize medium anisotropy is velocity of seismic waves. Multiple physical mechanisms may cause velocity anisotropy in a continuum, but in all the cases, a specific symmetry of the medium exists at the scale of interest (Tsvankin, 2001; Helbig, 1994). When a property (e.g. velocity) depends on position, the medium is heterogeneous, and heterogeneity is also scale dependent. Small-scale heterogeneity (e.g. grain size) may produce an effectively anisotropic medium at larger scales (e.g. seismic wavelength), thus the concepts of anisotropy and heterogeneity are strongly related (Tsvankin, 2001; Helbig, 1994). Extensive geological analysis has established that the San Andres reservoir at Vacuum field is a porous and fractured medium (Scuta, 1997; Pranter, 1999). Thus, from a rock physics standpoint, the interest is in detecting the dynamic evolution of a dual porosity system (here intended as coexistence of equant pores and fractures) subjected to changes in pore pressure and saturation. At the same time, the presence of vertical fractures makes the San Andres reservoir an azimuthally anisotropic medium. Thus, from a multicomponent reflection seismology standpoint, the interest is in understanding the time-lapse changes detectable in an azimuthally anisotropic medium.
7
Seismic azimuthal anisotropy manifests itself in multiple ways. For example, it causes shear wave splitting into two modes, a phenomenon which is not observed in compressional waves. On the other hand, P-wave velocity in azimuthally anisotropic media may change with source-receiver azimuth. In this work, the focus was on S-wave vertical birefringence as a manifestation of azimuthal anisotropy, on its evolution with time (time-lapse), and on the possible geomechanical models that justify such evolution. 1.3
MULTICOMPONENT SEISMIC DATA ACQUISITION Two, three dimensional (3D), multicomponent seismic surveys were acquired by the
Reservoir Characterization Project (RCP) at Vacuum field. The baseline survey was conducted before the CO2 flood started (December 1997). The CO2 injection program was initiated in April 1998, and the repeated seismic survey was acquired in December 1998. A pattern of six injector wells was selected for the CO2 flood at an average spacing of 600 ft in a given injector row (Figure 1.3). In addition to the multicomponent surface seismic, the RCP monitoring program
Survey geometry: Source points: Source line interval: Source interval: Vertical source:
Horizontal source:
Receiver points: Receiver array: Total # recording channels: Receiver line interval: Receiver interval: Recording instrumentation: Subsurface bin size:
circular, with 7400 ft diameter source lines orthogonal to receiver lines 2322 total (774 vertical, 774 N-S, 774 E-W) 150 ft (source lines on E-W direction) 110 ft 2 P-wave vibrators with 30 ft separation 8-120 Hz sweep, 10 sec sweep, 3 sec listen 4 sweeps per vibration point 1 S-wave vibrator 6-60 Hz sweep, 10 sec sweep, 4 sec listen 6 sweeps per vibration point on the N-S direction 6 sweeps per vibration point on the E-W direction 840 point receiver (3 elements, 3 ft spacing inline) 2520 (840 x 3C) 495 ft (receiver lines on N-S direction) 110 ft I/O System II, 2 msec sample rate 55 x 55 ft
FIG. 1.2: Design and acquisition parameters used in the time-lapse, multicomponent seismic surveys at Vacuum field.
8
included two time-lapse vertical seismic profiles (VSP) at well VGWU127 (Michaud, 2001; see Figure 1.3 for well location). Compressional and mutually orthogonal shear wave vibrators were employed at each source point, and the reflected wavefield was recorded by three-component receivers, resulting in two time-lapse, nine-component datasets (Alford, 1986). Surface conditions at Vacuum are topographically very regular (Figure 1.3). Notice the two slightly depressed areas in Figure 1.3, coinciding with playa lakes (Hernandez, 1999), which constituted a major source of surface heterogeneity. Due to soil characteristics, multicomponent sources and receivers located in the playa lakes recorded anomalous wavefields, ultimately corrected during data processing. Acquisition architecture and parameters (Figure 1.2 and 1.3) were designed to achieve high fold in the center of the survey area, while having a uniform azimuth and offset distribution to enhance the quality of shear wave data reflected from the San Andres Formation (depths of 4300 to 4800 ft). Solid State Geophysical acquired the seismic data using the I/O System II recording system. Vibrators were Mertz M-13 (horizontal source) and M-18 (vertical source) Vibroseis. Each source and receiver location was surveyed. GPS was used in each of the vibrator trucks for positioning, and compasses were used to measure azimuth, although corrections to azimuth angles were necessary during data processing.
lin e
So ur ce
R ec ei ve r
lin es
9
s
CVU186 CVU94
CVU87
CVU194
NO RT H
CVU187
CVU196 CVU100
CVU93 CVU97
CVU200 CVU197
120
120
CVU99 VGWU127
100 100 80 lin e
80
ft INJECTOR
40
40
00
60
60
11
Cr o
ss
In lin e
PRODUCER VSP
elevation above sea level (feet)
3990
3985
3980
3975
3970
3965
FIG. 1.3: Surface topography at Vacuum field and essential elements of time-lapse seismic data acquisition. The large circle represents the limit of the source-receiver deployment in the field. The smaller circle represents the limit of 50 fold coverage for a San Andres reservoir located at depths of 4300 to 4800 ft below surface. Notice that the six CO2 injector wells are located within the high fold circle.
10
0 Time (msec)
750
Offset (ft)
1500
2250
3000
3750
0
Max Incidence Angle
10
20
30
40
Depth (ft)
801 997
1253
1585 1943
2315
2700 3011
3400 3837 4350
FIG. 1.4: Common mid point (CMP) gather of the S1H1 component from pre-injection data at Vacuum field. The thick dashed line marks the mute designed to eliminate far-offset energy from the final stack. The curve on the right shows the value of the angle of incidence at the mute line. The maximum angle used in the study to generate the final stack is about 30°, thus the stacked traces are an acceptable approximation of vertical-incidence traces. Similar mute patterns were designed for all the seismic modes.
11
1.4
DATA PROCESSING During the acquisition of a multicomponent surface seismic survey, the azimuthal
orientation of sources and receivers is surveyed and well known. The nine data components (9C) are in a common global coordinate system in which all sources and the three receiver components are oriented north, east, and vertically. Under conditions of horizontally layered interfaces, and near-vertical angle of incidence, the majority of the shear wave energy is contained in the four horizontal source and receiver components, and the compressional energy in the vertical component. Thus, a 9C survey can be effectively reduced to five components (5C): P, S1H1, S1H2, S2H1, S2H2. These were the five components extracted for time-lapse processing from the Vacuum 3D-9C survey. Figure 1.4 shows an example of what was considered “near vertical”. The offset-time panel represents a common mid point (CMP) gather of the S1H1 component after a constant azimuthal rotation into the 118°N natural coordinate system. The thick dashed line is the mute designed to eliminate faroffset energy from the stack, and the curve on the right side is the computed maximum angle of incidence contributing to the stack (maximum value of the angle of incidence is about 30°). Under these conditions, CMP gathers are composed of near-vertical traces, normal moveout (NMO) can be considered hyperbolic, and the resulting stacked traces are an acceptable approximation of vertical incidence. Similar mute patterns were designed for all the five components. Time-lapse data processing is an extension of conventional data processing dominated by the need to quantify and enhance repeatability. In this sense, processing a baseline data set, while waiting for the repeat survey to be acquired, almost certainly implies that both data sets will be processed together again. Every element of a conventional processing flow (filters, operators, mute patterns, velocity fields, static corrections, amplitude scaling, shear wave polarization) has to be defined to account for field acquisition time-variability. Thus a repeated survey, whose data quality is lower than that of the baseline survey, will have implications for the baseline survey. Figure 1.5 shows the time-lapse processing flows used for compressional and shear waves at Vacuum. Additional notable aspects are: (1) time-lapse, common trace-pair crosscorrelation analysis was used following Roche (1997), (2) the velocity field used for migration included stacking velocities and velocities derived from a vertical seismic profile (VSP), (3) shear-
12
wave data were immediately rotated into a natural coordinate system, with the fast shear wave (S1) polarized in 118°N azimuth and the slow shear wave (S2) polarized in the direction 28°N. Orientation of the natural coordinate system was obtained from multicomponent VSP (Mattocks, 1998), prestack shear wave polarization analysis (Roche, 1997), a breakout study in an adjacent borehole (Scuta, 1997), and the direction of regional maximum horizontal stress (σHmax) (Zoback, 1992). This orientation was later confirmed by Michaud (2001) using multicomponent vertical seismic profile (VSP) data at VGWU127 well, and by this work through shear wave poststack rotation analysis and layer stripping (chapter 6).
Compressional waves data Build geometry True amplitude correction: time0.8 Surface consistent shot and receiver amplitude Surface consistent shot and receiver flattening statics Residual statics NMO Shot domain TX dip filtering Receiver domain TX dip filtering Inverse NMO Q compensation Minimum phase filter Convolve receiver deconvolution filters Convolve shot deconvolution filters Residual statics NMO final Mute CDP stack FXY filter 8-120 Hz TXY filter Migration
Shear waves data Build geometry (S1H1, S1H2, S2H1, S2H2) Alford rotation into natural coordinate system True amplitude correction: time0.8 Surface consistent shot and receiver amplitude Surface consistent shot and receiver flattening statics Residual statics NMO Shot domain TX dip filtering Receiver domain TX dip filtering Inverse NMO Bandpass filter: 6-18-60-72 Hz Minimum phase filter Notch filter at 30 Hz Convolve receiver deconvolution filters Convolve shot deconvolution filters Residual statics NMO final Mute CDP stack FXY filter 8-50 Hz TXY filter Migration
Fig. 1.5: Processing flow for multicomponent seismic data at Vacuum field.
13
1.5
SUMMARY At Vacuum field, a porous and fractured dolomitized carbonate was subjected to a CO2
flood. Multicomponent, time-lapse, surface 3D seismic was considered a technology capable of detecting the changes taking place in the reservoir rock following the CO2 injection. 3D-9C seismic data were acquired to detect time-dependent seismic observable, and processed to achieve: •
maximum repeatability between the time-lapsed surveys
•
near-vertical stack, time-lapse volumes of the five components containing the majority of the reflected seismic energy (P, S1H1, S1H2, S2H2, S2H1).
Under these conditions, the objectives of this work were: •
to understand the physical mechanisms responsible for time-lapse seismic anomalies in a dolomitized reservoir, and build a geomechanical model for stress and saturation changes
•
to enhance the poststack repeatability and the clarity of the time-lapse anomalies for compressional waves
•
to maximize the energy of the shear-wave principal components (S1H1 and S2H2) through poststack layer stripping targeted at the San Andres reservoir, estimating the changes in the vertical and lateral distribution of the shear wave polarization azimuth, and enhancing the shear wave, time-lapse anomalies by increasing the poststack repeatability of the data.
14
CHAPTER 2
THEORY AND MODELS
IT IS THEORY WHICH DECIDES WHAT WE CAN OBSERVE. ALBERT EINSTEIN 2.1
INTRODUCTION Vacuum field is a porous and fractured reservoir. Thus, in this chapter, the relationships
describing a dual porosity (i.e., equant pores + fractures) elastic medium, exposed to variations in pore pressure and fluid content, are presented. In the second part, the theoretical background necessary to understand time-lapse reflection seismology over azimuthally anisotropic media is reviewed. 2.2
DEFINITIONS AND PROPERTIES OF POROUS AND FRACTURED ROCKS A solid material, with no pores and fractures, has a single compressibility C = −
1 dV
V dP
,
where V is the volume of the body and P is the hydrostatic pressure over the outer surface. In situ, a porous or fractured rock is complicated by the existence of an external confining pressure ( Pc ), an internal pore pressure ( P p ), a bulk volume (V b ), a pore volume (V p ), and a volume of the mineral phase (V m ). The last three variables are linked by V b = V p + V m , and porosity is defined as φ = V p V b . At this stage, there is no need to distinguish pores from fractures, which are combined in the concept of void space. Because we have two pressure and two volume variables, four different compressibilities are associated with a porous rock (Zimmerman, 1991):
the
drained,
or
dry
compressibility
(C
bc
= 1 K
dry
),
the
subsidence
effect
compressibility ( C bp ), the formation compaction compressibility ( C pc ), and the effective pore compressibility ( C pp )
15
(2.1)
C bc
(2.2)
C bp =
(2.3)
C
pc
= −
(2.4)
C
pp
=
= −
Pp
1 ∂V b V b ∂P c
1 ∂V b V b ∂P p
Pc
1 ∂V p V p ∂P c
1 ∂V p V p ∂P p
(drained)
(subsidence)
Pp
Pc
(compaction)
(pore space)
The first index refers to the type of volume which is likely to change as a function of the second index, which is pressure. The first index is “b” for bulk volume (V b ), or “p” for pore volume (V p ), while the second index is “c” for confining pressure ( Pc ), or “p” for pore pressure ( P p ). The term compressibility is strictly valid for elastic deformations, although equations (2.1) to (2.4) are valid for any type of deformation. The pore ( P p ) and confining ( Pc ) pressures are assumed to be mathematically independent variables, implying that a variation in confining pressure does not cause the pore pressure to change (drained or dry conditions). We define here a porous and cracked rock as a solid composed of an isotropic, homogeneous, elastic matrix containing discrete voids. The mineral matrix is intended as the totality of the mineral components, and its compressibility is defined as the compressibility of a non-porous material: C m = −
1 dV m
Vm
dP
. We will not consider for the moment the grain shape
and size of the mineral matrix, although the matrix forms a completely connected network, permeated with pores and cracks of various sizes and shapes. The void space may consist of a connected network of pores and cracks (effective porosity), or isolated pores and cracks (non effective porosity), or some combination of the two types. Notice that this pore-type distinction is not important for the mechanical behavior of the rock, but it becomes crucial for transport properties like permeability. The voids do not need to be homogeneously distributed throughout the material, nor random in their spatial orientation, or to maintain constant pore pressure. For
16
this idealized porous solid the four compressibility equations (2.1) to (2.4) are not independent, and three relationships can be derived using elasticity theory (Zimmerman, 1991): (2.5)
C
bp
= C
bc
− C
m
(2.6)
C
pp
= C
pc
− C
m
(2.7)
C bp = φC
pc
with φ and C m as the only other parameters explicitly involved. Using C bc , C m , and φ , the other compressibilities become: (2.8)
φC
(2.9)
C
(2.10)
C
= C
pc
pc
=
pp
=
C
− C
bc
bc
− C
m
m
φ
C
bc
− 1 + φ C
m
φ
Equations (2.8) to (2.10) and their derivations assume isotropic and homogeneous mineral phases. These conditions are referred to as microscopic isotropy and homogeneity. On the length scale of distances between pores, the matrix material is often a single particle of a possibly anisotropic crystal, and rocks are typically made of more than just one mineral phase. This idealized rock model may not be a realistic representation of any geologic material, but it is useful to start with the assumption of matrix isotropy and homogeneity. Firstly, the calculations to relate compressibility to pore shape become intractable without these assumptions. Secondly, the compressibilities of the major mineral phases of most rocks do not differ by large amounts when compared to pores (Simmons and Wang, 1971). Equations (2.1) to (2.10) are associated with drained or dry conditions, where pore pressure and confining pressure are independent variables. Under other conditions, confining pressure and pore pressure are coupled and not independent. These conditions are defined as undrained (or saturated), where the pore fluid is not free to move in and out of the pore space in order to equilibrate the pore pressure. The pore pressure is no longer an independent variable but is related to the confining pressures, compressibilities of pores, and compressibilities of pore fluids. Undrained conditions are typical of wave propagation problems. The viscosity of the pore fluid will not allow the fluid to travel between the pores, at least within the time frame of the
17
stress oscillation typical of seismic waves (i.e. one period of the wave propagation): the fluid is locked in the pore space. The undrained or saturated compressibility is: (2.11)
Cu
=
1
K
= −
sat ( LF )
1 ∂V b V b ∂P c
m fluid
where the mass of the fluid is kept constant. Notice that the subscript of the saturated bulk modulus refers specifically to low frequency approximations. The underlying assumption is that the pore pressure is in equilibrium throughout the pore space, and again this happens at low frequency conditions. The concept of C u (or K sat ) prompted Gassmann’s (1951) equation which estimates C u starting from porosity ( φ ), drained compressibility of the rock ( C bc ), compressibility of the pore fluid ( C f ), and compressibility of the rock matrix ( C m ): (2.12)
Cu =
C bc φ (C f − C m
φ (C f − C m
) + C m (C bc − C m ) ) + (C bc − C m )
or, in terms of bulk moduli, we obtain the equivalent expression:
(2.13)
+ 1 − 1 K dry Km 1 1 1 − + − K f K m K m
1 1 φ − K Kf m
K sat = φ
K dry
1 K m
1
K dry
Brown and Korringa (1975) relaxed the assumptions on which Gassmann’s equation is based in order to generalize the computation of C u to polymineralic and anisotropic rocks. Gassmann considered a solid to be homogeneous on a macroscopic scale, and composed of a microhomogeneous and microisotropic matrix out of which a pore space is carved. Brown and Korringa (1975) argued that sedimentary rocks do not satisfy the conditions of microhomogeneity and microisotropy, and they estimate the variations of Gassmann’s equation for various and more realistic rock models. The result is that, by just adding one new parameter ( C φ ), the assumptions of microhomogeneity and microisotropy of the mineral phase can be dropped. The requirements that still persist are: (1) the porous solid is perfectly elastic for small deformations, (2) the measurements are made over a time scale long enough for equilibration of pore pressure ( P p ) throughout the pore space, (3) all the liquid inclusions not connected with the pores are part of
18
the solid bulk volume (V b ), and (4) the solid is under an external confining pressure ( Pc ) such that an effective pressure Pe = Pc − P p exists. An additional compressibility of the pore space is introduced as (2.14)
C
= −
φ
1 ∂V p V p ∂P p
Pd
Notice that C φ ≠ C pp as defined by equation (2.3). To understand the meaning of equation (2.14), imagine experimental conditions where a rock sample is subjected to a change in pore pressure ( P p ) by an amount δP p , and a change in confining pressure ( Pc ) by an amount δPc = −δP p . The differential pressure ( Pd ) has no net change, yet a change in the pore volume δV p is indicated by equation (2.14). However, under the condition that the rock is homogeneous
C m = C φ (monomineralic rock). A change in P p with constant Pd means applying the same incremental pressure δP to the outside (confining) and inside (pore space) surfaces of the rock sample. In the case of homogeneous solids, irrespective of how complex and anisotropic they are, the application of such incremental pressure ( δP ) does not produce a change in porosity. The ratio φ = V p V b does not change, in spite of a net change of V p and V b . Thus, bulk and pore volumes will be different before and after the application of pressure, but no porosity change is induced. Brown and Korringa (1975) show that it is typical of heterogeneous rocks to experience a change of porosity with stress even at a fixed effective pressure. This is the equivalent of a porous medium composed of different crystallographic materials with different elastic properties. Brown and Korringa’s relationship is: (2.15)
C bc − C u =
(C bc
φ (C f − C φ
− Cm
) + (C
)2 bc
− Cm
)
In the tensor notation equation (2.15) becomes: (2.16)
s
bc ijkl
− s
u ijkl
=
(s
bc ij
− s ijm
φ (C f − C φ
)(s
bc kl
) + (C
− s klm bc
)
− Cm
)
u bc where s ijkl is the saturated effective medium compliance, s ijkl is the dry effective compliance, m and s ijkl is the compliance of the mineral phase.
19
2.3
EFFECTIVE MEDIUM THEORY The mechanical behavior of rocks is controlled by mineral composition, pores and cracks
structure. Mineral composition can be accounted for by knowing the volume fractions and the elastic moduli of the various minerals. The main factor, which controls the elastic moduli of a rock, and in particular the variation of elastic moduli with stress, is the pores and cracks structure. If the exact structure of the pore space were known, the elastic moduli could be calculated by solving the equations of elasticity for the rock, with the appropriate boundary conditions. In practical terms, this is usually not possible. In three-dimensional space, (1) the elasticity equations can be solved analytically only for simple regular pore geometries (spheres, ellipsoids, etc.), and (2) analytical solutions for conceptual rock bodies with many (more than one) pores or cracks cannot be obtained even if the geometry is regular. Because of these difficulties, a porous and fractured rock is usually treated as a homogeneous effective medium. Two approaches to effective medium are used here. The first considers cracks and pores as non-interacting objects immersed in a mineral matrix. Elastic parameters of a single object are computed, then cracks and pores with random and non-random orientations are distributed in the rock matrix (Eshelby, 1957; Walsh, 1965; Hudson, 1980; Hudson, 1981). The second approach considers fractures as regions of weakness, establishes linear slip boundary conditions for a single fracture, and computes the averaging for an effective medium where multiple fracture planes exist (Schoenberg, 1980; Schoenberg and Douma, 1988). These two different lines of reasoning produce similar results in terms of fracture compliance matrix, thus suggesting that fracture microstructural details are not detectable by elastic waves (Bakulin et al., 2000a). 2.3.1 THREE-DIMENSIONAL SINGLE CAVITIES One approach to modeling the deformation of the pore space is to find an analytical solution for an isolated pore or crack of idealized shape, and then account for many pores and cracks whose stress and strain fields may interact. One three-dimensional pore shape that is analytically treatable is the ellipsoid (Zimmerman, 1991). Eshelby (1957) studied the general problem of elastic inclusions, and solved the case involving an ellipsoidal pore with three axes of
20
different lengths. The outcome is an effective medium model based on ellipsoidal inclusions in an infinite medium. A spheroid is generated from the revolution of an ellipse around one of the axes of symmetry. Revolution around the ellipse minor axis generates an oblate spheroid, and the most classical example of oblate spheroid in rock physics is a penny-shaped pore, where a σHmin σ1 = σv
Normal Faulting with Strike-Slip (NS) σV > σHmax > σHmin σ1 = σv
σ2 = σHmax
σ3 = σHmin
σ2 = σHmax
σ3 = σHmin
Strike-Slip Faulting (SS) σHmax > σV > σHmin σ2 = σv
σ1 = σHmax
σ3 = σHmin Thrust Faulting (TF) σHmax > σHmin > σV σ3 = σv
σ2 = σHmin
Thrust Faulting with Strike-Slip (TS) σHmax > σHmin > σV σ2 = σHmin σ3 = σv
σ1 = σHmax
FIG. 2.6: Principal normal stresses and deformations
σ1 = σHmax
33
2.4
EFFECTIVE STRESS At any point of a medium, stress is characterized by a combination of six independent
parameters that form a second-rank tensor ( σ ij ). Each component has dimensions of [σ ij ] = [force ] /[area ] . Compressive stresses are positive, and tensional stresses negative. Because the stress tensor is symmetric (Auld, 1989), a rectangular coordinate system exists such that the tensor is reduced to a diagonal form: σ ii = (σ 1 , σ 2 , σ 3 ) , and σ ij = 0 for i ≠ j . In this case, the shear (off-diagonal) components of stress vanish on the three orthogonal coordinate planes, and σ 1 ≥ σ 2 ≥ σ 3 are defined as the mutually orthogonal principal normal stresses, acting in the direction of the principal axes. The coordinate system chosen to decompose the stress field is arbitrary (stress is invariant to the coordinate system), but in geomechanics the vertical and horizontal planes are favored. The reason is that evidence from orientation of fault planes, earthquake focal mechanisms, and deep in situ stress measurements shows that the principal components of the lithospheric stress field typically lie in the horizontal and vertical planes (Zoback, 1992). Thus follows an assumption extensively used in geomechanics: the orientation of the in situ principal components of stress can be inferred from the maximum horizontal stress ( σH max ) azimuth. Then, consider the horizontal plane of Figure (2.6) as the plane in which any horizontal stress ( σ H ) will act, and the normal to that plane as the direction of the vertical stress ( σV ). Following the assumption above, σ H max , σ H min , and σV are principal normal stresses, and their arrangement determines tectonic and faulting regimes in the lithosphere (Figure 2.6). All the structures shown in Figure 2.6 have been documented in the crust. Thus the stress field in the crust is not only three dimensional, but also anisotropic. Crustal rocks may have never been exposed to three equal principal stresses, and isotropic stress, if measured in situ, may simply be a temporary state in a dynamic system (Yin, 1992). The implication is that an effective medium whose stiffness tensor is isotropic, may still exhibit anisotropy when subjected to anisotropic stress conditions. Nur (1971) showed how a rock sample, populated with randomly oriented cracks, becomes progressively anisotropic by applying increasing magnitudes of uniaxial stress. The
34
mechanism invoked for stress-induced anisotropy is closure of microcracks whose plane is normal to the direction of maximum principal stress. Opposite conditions to Nur (1971) are found in studying the effects of pore pressure (isotropic by definition) on anisotropic porous rocks (Chen and Nur, 1992; Yin, 1992). The link between anisotropy of the effective medium and stress can be expressed with an anisotropic form of the effective stress law (Chen and Nur, 1992): (2.30)
σ Eij
= σ ij − P p α Eij
where σEij is the effective stress tensor, σij is the applied or total stress tensor, Pp is the pore pressure, and α Eij is the effective stress coefficient. Notice that equation (2.30) is a constitutive equation for a linear, poroelastic medium (Biot, 1941; Rice and Cleary, 1976) usually written as: (2.31)
σ ij
= c
ijkl
ε kl + P p α Eij
where c ijkl is the effective medium stiffness, and ε kl is the strain. For linear, elastic deformations of poroelastic media, α Eij can be derived using the superposition procedure from Nur and Byerlee (1971), or Carroll (1979), who show that: (2.32)
α Eij
= δ ij − c
ijkl
s
m klmn
m where δ ij is the Kronecker delta, s klmn is the compliance of the rock matrix describing the
mineral (intrinsic) anisotropy of the material, and c ijkl is the effective medium stiffness describing the structural anisotropy of the rock. Neglecting the intrinsic anisotropy of the mineral phase, the effective stress coefficient for structurally anisotropic rocks in an isotropic mineral matrix becomes: (2.33)
α Eij
= δ ij − c ijkk
Km
where K m is the isotropic mineral bulk modulus. Thus the effective stress relationship is now: (2.34)
σ Eij
c ijkk = σ ij − P p δ ij − 3K m
When the medium is isotropic, α Eij reduces to α E δ ij , where α E is a scalar. Then the effective stress relationship becomes: (2.35)
σ Eij
= σ ij − α E P p δ ij
35
Equation (2.35) shows that for isotropic porous materials the pore pressure only affects the normal stress components. 2.5
REFLECTION SEISMOLOGY OVER AZIMUTHALLY ANISOTROPIC MEDIA Normal-incidence reflection seismology over azimuthally anisotropic media is reviewed in
this section. Acquisition geometry and processing of multicomponent data at Vacuum field were described previously. Under the assumption that a conventional CMP gather generates an acceptable approximation of a normal-incidence trace (Alford, 1986; Willis et al., 1986; Thomsen, 1988), the manifestation of azimuthal anisotropy is on shear-wave birefringence1. A shear wave propagating through an azimuthally anisotropic medium will split into two orthogonally polarized waves traveling at different speeds in the same direction (Figure 2.7). Consider data sets generated by two horizontal and mutually orthogonal sources, where two horizontal and mutually orthogonal receivers have the same azimuthal orientation as the sources (Figure 2.8A). For each horizontal source, two receiver components are recorded (2Cx2C). Each horizontal source will, upon entering the azimuthally anisotropic medium, split into two modes. The only shear waves that propagate vertically are polarized in the medium’s natural coordinate system. In Figure 2.8A, two layers have unidirectional, but azimuthally different, vertical fracture sets, each one causing shear-wave splitting. The fracture strike and its normal are the natural coordinate systems of the two layers (Figure 2.8B). The SH, or N-S source, is vectorially decomposed in the two principal components S|| and S⊥ of Figure 2.8D. The split is instantaneous, with the S|| polarized wave traveling faster (S1) than the S⊥ polarized wave (S2). In sedimentary rocks, the reason for different speed of the two shear modes is that the effective shear modulus is anisotropic: the rock is stiff to horizontal shear stress in the S|| azimuth, while weak (compliant) to horizontal stress in the S⊥ azimuth. The two shear waves propagate vertically down to the first interface and reflect independently with reflection coefficients R|| and R⊥. In the presence of weak anisotropy in the two media, reflection coefficients, geometric spreading, and attenuation will be similar for the two shear modes. Because the two layers have different fracture orientation, each shear wave transmitted from layer 1 to layer 2 will split again into the principal components of layer 2. This 1
Shear wave birefringence is also known as shear wave splitting, or shear wave double refraction.
36
will happen again at the same interface, on the way up after reflection from the bottom of layer 2, and at the surface into the receiver components: a situation that Thomsen et al. (1999) described as chaotic. The first objective of shear wave data analysis should be to quantify subsurface birefringence. This means to find the natural polarization directions of the two S-waves and the time delays between them. In the case of depth-invariant orientation of azimuthal anisotropy, the analysis is relatively simple. Winterstein and Meadows (1991a, b), though, showed that in general the orientation of azimuthal anisotropy varies with depth (as in Figure 2.8). Because Swave splitting is cumulative, effects of anisotropy above an interface will persist, unless removed, in the lower medium, thus confusing the analysis. To remove the effects of shear wave splitting above a particular event and permit the analysis of polarization changes with depth, Winterstein and Meadows (1991a, b) introduced the concept of layer stripping. Thomsen et al. (1999) presented a vector convolutional model of wave propagation for a model like Figure 2.8, and generalized layer stripping. The 2Cx2C surface reflection case of Thomsen et al. (1999) is reviewed here below.
0
S1 S2
S1 S2
S1 S2
100
msec
200
300
FIG. 2.7: Example from the Vacuum field illustrating the shear wave splitting phenomenon as it can be observed in reflection seismology. In every pair of traces, the top one records horizontal particle motion along an azimuth of N118°, while the lower one records horizontal particle motion with an azimuth of N28°. With the exception of the peaks at 90 msec (single arrow), the top traces show reflection peaks and troughs arriving earlier in time (S1) than the lower traces (S2). At about 250 msec, the amount of shear wave splitting is 20 msec (double-arrows).
NSr
ece
ive
r
37
A
E-W receiver
E-W source
Ss
ou
rce
Layer 1
N-
Layer 2
re ctu Fra sL
es
r2
ct ur
aye
Fr a
La
ye
NORTH
y0
B
r1
C
y1
y0
y2 x0
x0
θ1
ϕ1
y1
ϕ2
θ2 y2
x1
x2
x1
x2
Fr a
SH
ct ur
es
La
ye
D
S⊥
S
r1
NORTH y0
x0 Acquisition Coordinate System
N-S source
La y
y1
er
1
Co
or
di na
te
Sy x1 st em
FIG. 2.8: Geometric elements of reflection seismology over azimuthally anisotropic media.
38
2.6
LAYER STRIPPING A scalar convolution of a scalar function f (t ) with a filter h (t ) produces an output
function g (t ) = h ⊗ f . When the input is a vector f (t ) , the output is also a vector
g (t ) = H ⊗ f , and the filter H is a convolutional matrix. Wave particle motion can be written as u m (t ) , where m is the coordinate system of the physical medium. For example, particle motion at surface is u 0 (t 0 ) = w (t )u 0 , which stands for medium zero at time zero, w (t ) is the wavelet, and u 0 is the vector source. If u is a scalar representing the source strength, the two orthogonal shear sources pointing in the + x and +y u 0 u 0 directions are u 0 = ux = and u 0 = uy = , and become U 0 = in a compact form. 0 u 0 u The idea is to follow a ray propagating vertically through the layers with variable orientation of azimuthal anisotropy of Figure 2.8. For a shear source u 0 = ux
at surface, the split polarizations in the two principal
directions of medium 1 natural coordinate system correspond to a rotation θ1 (angle between the + x direction of the source and the + x direction of medium 1: see Figure 2.8C). The cos θ1 rotation is written as Θ (θ1 ) = − sin θ1
sin θ1 , and the initial source pulse in terms of the cos θ1
coordinate system of medium 1 is u 1 (t 0 ) = w (t )u 1 = Θ (θ1 )w (t )u 0 . At the bottom of layer 1, the wavefield u 1 will be u 1 (t 1 ) = P1 ⊗ u 1 (t 0 ) = P1 ⊗ Θ (θ1 )w (t )u 0 , where
(
(2.36)
A F ⊗ δ t − t 1F P1 = 1 0
)
0 S 1
(
A ⊗ δt −t
S 1
)
is an operator accounting for propagation through medium 1, t 1i = z 1 v 1i
is the one-way
traveltime, and A1i is a mode specific filter accounting for propagation related energy changes like geometric spreading, attenuation, and dispersion ( i = F, for fast shear wave, or S, for slow shear wave). At the bottom of layer 1, at time t 1 + an infinitesimal increment, the reflected wavefield is: (2.37)
u 1 (t 1 + ) = R1u 1 (t 1 ) = R 1P1 ⊗ Θ (θ1 )w (t )u 0
39
where R1 is the reflection coefficient at normal incidence. Now the ray travels back towards the receiver after reflection, and at the receiver the wavefield is: (2.38)
u 1 (2t 1 ) = P1 ⊗ u 1 (t 1 + ) = P1 ⊗ R1P1 ⊗ Θ (θ1 )w (t )u 0
and in terms of the receiver coordinate system it can be expressed as: (2.39)
u 0 (2t 1 ) = 2Θ (− θ1 )P1 ⊗ R1P1 ⊗ Θ (θ1 )w (t )u 0
At the top of layer 2, at time t 1 + an infinitesimal increment, the transmitted wavefield is: (2.40)
u 1 (t 1 + ) = T 12u 1 (t 1 ) = T 12P1 ⊗ Θ (θ1 )w (t )u 0
where T 12 is the transmission coefficient at normal incidence from medium 1 into medium 2, and in terms of the principal coordinate system of layer 2: (2.41)
u 2 (t 1 + ) = Θ (θ 2 − θ1 )u 1 (t 1 + ) = Θ (θ 2 − θ1 )T 12P1 ⊗ Θ (θ1 )w (t )u 0
The term Θ (θ 2 − θ1 ) accounts for the second shear wave splitting given by a rotation of the wavefield into the principal components of layer 2 (Figure 2.8C). Following the same logic of the first reflection, a wavefield reflected by the interface at the bottom of layer 2 is: (2.42)
u 1 (2t 1 + 2t 2 ) = P1 ⊗ Θ (θ1 − θ 2 )T 21P2 ⊗ R 2P2 ⊗ Θ (θ 2 − θ1 )T 12P1 ⊗ Θ (θ1 )w (t )u 0
and in terms of the receiver coordinate system: (2.43)
u 0 (2t 1 + 2t 2 ) = 2Θ (− θ1 )u 1 (2t 1 + 2t 2 ) = 2Θ (− θ1 )P1 ⊗ Θ (θ1 − θ 2 )T 21P2 ⊗ R 2P2 ⊗ Θ (θ 2 − θ1 )T 12P1 ⊗ Θ (θ1 )w (t )u 0
Here, the factor 2 is the free-surface effect, T 21 is the transmission coefficient from medium 2 into medium 1, P 2 is the propagation filter through medium 2, and R 2 is the reflection coefficient at the bottom of layer 2. The tensor convolutional model of Thomsen et al. (1999) combines all the arrivals at the receiver into a single expression. Additionally, it shows how difficult it may be to interpret the signal at the receiver in terms of the anisotropic characteristics of a particular medium, because the wavefield u 0 (2t 1 + 2t 2 ) went through multiple splitting and rotations. Layer stripping wants to remove the effects of the first anisotropic layer to extract the coordinate system and the anisotropic characteristics of the second layer. This is accomplished with corrections in time and 0 δ(t ) amplitude. Thomsen et al. (1999) defined a time advance operator as D 1 = , 0 δ(t + ∆t 1 ) which applies a forward time shift to the slow shear mode to equalize the reflection times.
40
Additionally, a filter is designed to equalize the two shear modes at the first interface, eliminating the mode differential attenuation: B 1SF ⊗ T1222 A1S = T1211 A1F . Notice that the filter operates on the slow shear wave to make it equal to the fast, and it uses propagation properties of the first medium combined with transmission coefficient at the first interface. Winterstein and Meadows (1991a) describe this operation as “bringing the shear source down to the interface”. As a tensor, δ(t ) 0 the mode balancing operator is defined as B1 = SF 0 B1
, and the layer stripping procedure
can be summarized in: (2.44)
uˆ1 (2t 1 + 2t 2 ) = B1 ⊗ D1 ⊗ u 1 (2t 1 + 2t 2 ) ⊗ D1 ⊗ B1 u 11 (t ) u 112 (t ) = B1 ⊗ D1 ⊗ 121 ⊗ D1 ⊗ B1 22 u 1 (t ) u 1 (t ) u 11 (t ) u 112 (t + ∆t 1 ) = B 1 ⊗ 21 1 ⊗ B1 22 u 1 (t + ∆t 1 ) u 1 (t + 2∆t 1 )
where u 1 (2t 1 + 2t 2 ) = Θ (θ1 )u 0 (2t 1 + 2t 2 )Θ (− θ1 ) , is the Alford (1986) rotation of the shear components into the natural coordinate system of medium 1. In chapter 6, the layer stripping algorithm will be applied to the Vacuum field data. The result of a layer stripping procedure should make it possible to interpret the anisotropic characteristic of the lower interval (e.g. layer 2 in Figure 2.8). If the interval of interest is located below several anisotropy boundaries, layer stripping can be continued downward. It is important to emphasize the interpretive nature of the layer stripping procedure. The analyst will decide, on the basis of energy considerations in the shear wave volumes, where an anisotropy boundary has to be placed, if and where an anisotropy boundary corresponds to a lithology and reflectivity boundary, and the plausible reasons for such a choice. Aside from the interpretational aspect, layer stripping can, and often should, be applied randomly to the shear wave time series to check the validity, for example, of the rotation angles which define the natural coordinate system of a particular layer. Some of these aspects will be addressed in chapter 6 with real data examples.
41
2.7
SUMMARY The fundamental relationships describing an elastic medium with equant pores and
fractures were reviewed. The interest is primarily in introducing an effective medium model suitable to treat saturation changes in the pore space, as well as deformation of the most compliant elements (fractures). The dual porosity model will be used in later chapters to establish the physical basis of time-lapse seismic anomalies. The usage of multicomponent seismology on a fractured reservoir requires an understanding of shear wave splitting, which is a manifestation of azimuthal anisotropy. The essential elements of the work of Thomsen (1988), Winterstein and Meadows (1991a, b), and Thomsen et al. (1999) were reviewed, with particular emphasis on shear wave layer stripping, which will be applied in chapter 6.
42
CHAPTER 3
ROCK P HY S ICS
THE VALIDITY OF THE LAW OF CAUSATION, FOR THE WORLD OF REALITY, IS A QUESTION THAT CANNOT BE DECIDED ON BUT ON GROUNDS OF ABSTRACT REASONING, EXPERIMENTATION.
MAX PLANCK 3.1
INTRODUCTION Porosity in rocks has a large range and is exhibited in virtually any size and shape. In
spite of this diversity, many reservoir rocks can be reduced to a dual porosity system, given by the coexistence of matrix and fracture porosity. This reduction maintains the elastic and transport properties of reservoir rocks (Berryman and Wang, 2000). Elastically, matrix porosity is composed of spherical, and relatively incompressible equant pores, while fracture porosity is composed of low aspect ratio, and highly deformable fractures. Hydraulically, equant porosity provides fluid storage capacity, while fractures often introduce high permeability fluid flow. In this chapter, the attention is focused on the elastic properties of dual porosity systems. The starting point is experimental, with ultrasonic velocities of two reservoir rock samples from the Vacuum field measured under various conditions of pressure and saturation. The observations are then modeled using the compliance-based effective medium theory developed in Chapter 2. Specific symmetries (HTI and monoclinic) of the crack compliance tensor are also modeled under various conditions of pressure and saturation. 3.2
EXPERIMENTAL MEASUREMENTS Ultrasonic velocity measurements conducted on two cylindrical core samples, provide a
direct measure of the impact of saturant fluids and effective pressure regimes on the velocities of
43
dolomitized rocks of the San Andres formation. The core samples were cleaned prior to the experiment using pentane and decane. Porosity, permeability and density were measured at ambient temperature and pressure. Figure 3.1 summarizes the properties of the two samples. Figure 3.2 and Figure 3.3 show details of sample 2, whose primary features are high porosity and permeability. Note in Figure 3.3 the computation of porosity on the basis of the SEM image histogram ( φ = 0.198), and compare it with the value of porosity measured on the entire core sample ( φ = 0.233). The reasons for the different values can be attributed to the different methodologies of porosity estimation, as well as the different area and volume of investigation that contributed to porosity. For velocity measurements, the core samples were jacketed in a plastic holder to avoid loss of the injected fluids, with transmitting and receiving ultrasonic transducers (one compressional and two shear) attached to the two bases of the cylinders, and then placed in a pressure vessel. Temperature in the vessel was maintained at 104°F (40°C), which is the reported temperature of the San Andres reservoir at Vacuum field. Velocities for sample 1 were measured for dry, oil, and brine saturated conditions, while for sample 2 measurements were obtained for dry, oil, and CO2 saturated conditions. A schematic sequence of the experiment is detailed in Figure 3.4.
Sample 1: CVU 345 well
Sample 2: CVU 100 well
Depth
1407 m (4617 ft)
1331 m (4366 ft)
Sample diameter
38.1 mm (1.5 in)
24.8 mm (0.976 in)
Sample length
51.6 mm 2.03 in)
23.7 mm (0.935 in)
Porosity
0.157
0.233
Permeability (md)
-
933.1
Matrix density (gr/cm3)
2.833
2.834
FIG. 3.1: Properties measurements.
of samples used for ultrasonic velocity
44
40 µm 24.7 mm
FIG. 3.2: Core plug from CVU 100 4366 ft depth and SEM image from a sample in the proximity of the core plug. Notice the rhombohedral structure of the dolomite in the SEM picture. A small inclusion of kaolinite is also present (photos from Pranter, 1999).
φ = 0.198
50 µm
FIG. 3.3: SEM photograph in the proximity of sample 2 at 4366 ft depth used for ultrasonic velocity measurements and fluid substitution. The right picture is the histogram of the left picture, highlighting dark, high aspect ratio pore space. The sample is a peloidal-intraclastic dolopackstone, characterized by abundant interparaticle and intercrystalline porosity. Porosity is 0.233 from measurements on the core plug, and 0.198 on the SEM image (SEM photo from Pranter, 1999).
45
Sample 1: CVU 345 – 4617
Temperature = 40°C
1. Ultrasonic velocity measurements (≈ 800 kHz) were recorded at dry conditions with a confining pressure regime varying from 0 to 3500 psi (0 to 24.13 MPa) 2. After measurements at dry conditions, sample 1 was vacuumed, and then saturated with brine. Pore pressure in brine saturated conditions was then kept at 500 psi (3.44 MPa), and confining pressure was then varied to obtain a differential pressure from 0 to 3500 psi (0 to 24.13 MPa). Seismic velocities were recorded at each differential pressure regime. 3. After recording the brine saturated conditions, the sample was washed with fresh water, then dried in a vacuum oven, and finally saturated with oil. Seismic velocities were recorded at each differential pressure regime of 0 to 3500 psi (0 to 24.13 MPa). Sample 2: CVU 100 – 4366
Temperature = 40°C
1. Ultrasonic velocity measurements (≈ 800 kHz) were recorded at dry conditions with a confining pressure regime varying from 0 to 4500 psi (0 to 31.02 MPa) 2. After measurements at dry conditions, sample 2 was set at a confining pressure of 4500 psi (31.02 MPa) and injected with oil from the Vacuum field. Pore pressure was kept at 1600 psi (11.03 MPa), which is the reported average pore pressure of the San Andres reservoir at Vacuum field. Confining pressure was then varied to obtain a differential pressure from 500 to 4500 psi (3.45 to 31.02 MPa). Ultrasonic velocities were recorded at each differential pressure regime. 3. After recording the oil saturated conditions, the sample was set at a pore pressure of 1000 psi (6.89 MPa). Then CO2 was injected in the sample at an injection pressure of 2000 psi (13.79 MPa). The output flow-line from the sample was then opened resulting in the displacement of the oil in the sample. A volumetric measurement of the amount of oil displaced by the flooding process was not recorded, and the sample was considered fully flushed by CO2 when no more oil was visually present in the output flow-line from the sample.
4. After CO2 flooding, pore pressure was set at 1600 psi (11.03 MPa), with CO2 fully saturating the pore space. Then confining pressure was varied to obtain a differential pressure from 500 to 4500 psi (3.45 to 31.02 MPa), and ultrasonic velocities were recorded at each differential pressure step. FIG. 3.4: Schematic sequence of experimental conditions during ultrasonic velocity measurements on the two samples.
46
3.2.1 FLUID PROPERTIES The two samples were subjected to fluid substitution with air, brine, oil, and carbon dioxide. In every instance, ultrasonic velocities were measured at fluid pressure and temperature equal to the reported reservoir conditions at Vacuum field, which are 1600 psi (11.03 MPa) of fluid pressure (RP), and 104°F (40°C) of temperature (RT°). Air density and bulk modulus (i.e. dry conditions) are considered zero for our practical purposes. The brine used in the experiment was a solution of 27000 ppm of NaCl in water, and its physical properties (density, compressional velocity and bulk modulus) are represented in Figure 3.5 as a function of pressure at RT° (at ambient conditions ρ brine = 1.05 gr/cm3,
K brine = 2.2 GPa). The oil used in the experiment came from Vacuum field, and its physical properties are also represented in Figure 3.5 as a function of pressure at RT° (at ambient conditions ρoil = 0.827 gr/cm3, K oil = 1.5241 GPa). Carbon dioxide is certainly the fluid that exhibits the largest dynamic range of physical properties and the more complex phase behavior. The physical properties of carbon dioxide are shown in Figure 3.5 as a function of pressure at RT°. The critical point of CO2 is 1070 psi (7.4 MPa), and 88°F (31°C). For any pressure and temperature higher than the critical point, CO2 is technically in a dense gas zone, designating an intermediate state between gas and liquid. At temperatures below the critical temperature and pressures above the critical pressure, CO2 is in a liquid state, and conversely it’s in the gas phase below the critical pressure. The large and rapid shift in values of carbon dioxide physical properties visible at about 10 MPa is associated with the gas to dense gas phase transition. Carbon dioxide cannot be a liquid at this temperature, but it exhibits high density similar to the liquid phase, while the bulk modulus always remains lower than oil. Additionally, we can expect that the injection of carbon-dioxide in an oil reservoir will result in some degree of miscibility of CO2 with oil. The miscibility process is also temperature and pressure dependent. The lowest pressure at which carbon dioxide can develop complete miscibility with the reservoir crude oil at reservoir temperature is defined as the minimum miscibility pressure (MMP). The definition implies that for any given system composition, there is
47
a pressure below which miscibility will not develop. In general, all other factors being equal, higher temperatures result in higher MMP. For the Vacuum oil, at reservoir conditions, MMP was estimated theoretically (MMP = 1304 psi (9 MPa) at RT°) using an expression from Orr and Taber (1984), and with laboratory tests (MMP = 1250 psi (9 MPa) at RT°) by the engineering group operating Vacuum field. Although the present study is not intended to quantify the degree of miscibility reached by CO2 in the Vacuum oil reservoir, it is necessary to highlight the conditions at which such phenomenon takes place, to understand the dynamic range of fluid physical properties possible in a carbonate rock hosting hydrocarbons and exposed to CO2 flooding. Here, the discussion is confined to pressure regimes above the MMP. In this approximation, relationships determined by Batzle and Wang (1992) can be used to compute the physical properties of three oil-CO2 mixes: 75% oil – 25% CO2, 50% oil – 50% CO2, and 25% oil – 75% CO2. The physical properties of the mixes are also shown in Figure 3.5. At pressure regimes below the MMP, oil and CO2 are not completely miscible, and most importantly they are not a single phase. Above MMP, oil and CO2 are miscible and form a single, liquid phase whose properties are determined by the overall composition. In synthesis, the physical properties of the mixes between oil and CO2 are confined by maximum and minimum values given by the 100% oil case and the 100% CO2 case.
48
brine
CO 2 100%
MMP 100% oil
100% oil
25% CO 2 50% CO 2
10 0%
CO
2
75% CO2
brine
brine
MMP
l 100% oi
MMP oil 100%
CO 2 25%
CO 2 25%
CO 2 50% O2 C 75% O2 C % 0 10
CO 2 50% O2 C % 75 CO 2 100%
FIG. 3.5: Physical properties of brine, CO2, and oil-CO2 mixes as a function of pressure for a constant temperature of 104°F (40°C). Minimum miscibility pressure (MMP) is plotted at 1304 psi (9 MPa). Data source NIST.
49
3.2.2 EXPERIMENTAL RESULTS The top portions of Figure 3.6 and 3.7 show compressional (Vp) and shear (Vs) wave velocities for the two samples under dry and saturated conditions, as a function of effective pressure. The lower parts of Figure 3.6 and 3.7 show the relative change (%) of Vp and Vs for the fluid saturated conditions with respect to dry velocities. The Vp general behavior shows the expected increase in velocities for saturated versus dry conditions, although at low effective pressure oil saturated Vp are higher than brine saturated Vp, while the opposite is more commonly observed. CO2 saturation decreases Vp with respect to oil, showing the decrease in fluid bulk modulus that occurs between oil and CO2. Fluid saturation reduces Vs with respect to dry conditions in all cases. The density effect is visible for shear wave velocities in the sequence dry, oil, brine saturated conditions, with Vs(brine) < Vs(oil) < Vs(dry) and ρ(dry) < ρ(oil) < ρ(brine). Shear wave velocities for the CO2 saturated case are smaller than the corresponding oil saturated case. Wang et al. (1998), analyzing a set of ultrasonic measurements on carbonate samples from the Mc Elroy field (TX), made similar observations on the oil-CO2 fluid substitution problem, with a decrease in both Vp and Vs attributed to a combination of fluid properties and fluid pressure change. In spite of the similarity with Wang et al. (1998), a decrease in Vs for CO2 saturated conditions, after CO2 flushing an oil saturated sample, highlights an increase in the pore fluid effective density which is difficult to explain using conventional volumetric mixing criteria. Wang et al. (1998) computed a flood efficiency of about 63% for CO2 injection, thus implying that 37% of the pore space was still saturated with oil at the time that CO2 was supposed to fully occupy the pore space. At a pore pressure of 1600 psi (11.03 MPa) the density of pure CO2 (0.6444 gr/cm3) is lower than the corresponding oil density (0.8272 gr/cm3), and miscibility between oil and CO2 is favored over coexistence of separate phases (MMP = 1300 psi (9 MPa)). Using the flood efficiency figures from Wang et al. (1998), a volumetric mix (37% oil + 63% CO2) between the two fluid constituents gives an effective fluid density of 0.7120 gr/cm3, which cannot explain the decrease in Vs between oil and CO2 saturated conditions. In synthesis, the experimental measurements can be summarized in:
V Pbrine > V Poil > V Pdry
V Sdry > V Soil > V Sbrine
(sample 1)
V Poil > V PCO2 > V Pdry
V Sdry > V Soil > V SCO2
(sample 2)
50
FIG. 3.6: Experimental velocities and velocity changes for sample 1: CVU 345 (4617 ft).
51
FIG. 3.7: Experimental velocities and velocity changes for sample 2: CVU 100 (4366 ft).
52
3.3
MODELING DUAL POROSITY The theoretical section highlighted a strategy for velocity forward modeling of porous and
fractured rocks. The framework is given by the tensor representation of the dual porosity rock and by the linear slip model. The formalism allows us to treat fractures and pores as noninteracting cavities immersed in a mineral matrix. Normal ( Z N ) and tangential ( Z T ) compliances of the cavities are the parameters that characterize equant and fracture porosity. Fracture and equant porosity compliance tensors are built with a particular symmetry, and then coupled to the background compliance to obtain the dry compliance of the effective medium: (3 .1 )
sE
= s R + φP s P + φC sC
The effective compliance for saturated models is computed using Brown and Korringa (1975), and inverted to obtain the stiffness of the saturated effective medium c ijkl sat . Seismic velocities are finally predicted using Christoffel’s equation for any combination of fluids, equant pores, and crack symmetry. 3.3.1 MODELING EXPERIMENTAL RESULTS The experimental velocities measured at dry conditions on the two samples from Vacuum field are used in this section to (1) obtain a population of cracks as a function of effective pressure, and (2) to predict velocities under saturated conditions. Measured and modeled saturated velocities are then compared. Crack density from dry velocity measurements. Under the assumptions that: (1) the mineral matrix of a sample is known, (2) pores are randomly distributed spheres, and (3) fractures are randomly distributed penny-shaped cracks, the total crack density of a sample can be derived of as a function of pressure by using compressional and shear velocity measurements under dry experimental conditions. The compressibility of a spherical pore is: (3 .2 )
Cpc =
3K + 4 µ 4 Kµ
The spherical porosity can be written as a function of effective pressure as: (3 .3 )
dφ P = − φ P0 (C pc − C m )dP e
53
where φP0 is the initial porosity of a sample, usually recorded at ambient conditions. The compliance matrix of an isotropic distribution of dry spheres ( s dry sphere ) can be computed using equation (2.30) and (3.2). Then, the dry background compliance matrix is computed at each effective pressure step as: (3 .4 )
dry
dry
s back
= s R + φ P s sphere
The compliance of a random distribution of penny-shaped cracks ( s C ) is computed using equation (2.30) and (2.17), and, at each effective pressure step, the theoretical effective dry compliance ( s Edry( T ) ) is: (3 .5 )
dry
sE
dry
= s back +
(T )
4 3
es C
where e is the unknown that we want to solve for. Inverting for stiffness c dry E (T )
(
= s dry E (T )
)
-1
,
the theoretical effective dry stiffness is obtained, which is an isotropic matrix with two independent parameters, from which the theoretical bulk and shear effective dry moduli
K Edry and µ dry E (T ) are extracted. Notice that they are both dependent on crack density, e . From the (T ) dry velocity measurements we extract experimental bulk and shear effective dry moduli: (3 .6 )
K Edry( E )
(3 .7 )
µE
(
= ρ dry V P2dry
dry
3
V S2dry
)
= ρ dry V S2
dry
(E )
Then setting K Edry( T
− 4
)
= K Edry( E ) , and µ dry E (T )
= µ dry we search for a value of crack density e E (E )
that best fits the two relationships at each pressure. Figure 3.8 (top) shows the magnitude of crack density at every effective pressure step in the two samples. Estimation of saturated velocities. Crack densities were used to estimate the saturated velocities. Equant porosity was introduced as spherical porosity. The compliance for a set of randomly distributed, non-interacting spheres was constructed using (2.18) and (2.30). The fracture compliance matrix was constructed using the crack density data. Cracks were randomly distributed in the rock matrix using (2.17) and (2.30), under the assumption of no interaction with spherical pores and among cracks. Porosity measured at ambient conditions was
54
taken as the total porosity, spherical and fracture porosity were computed at each pressure step and their sum constrained to the total porosity. The resulting effective dry compliance was then numerically inverted for stiffness and inserted into equation (2.16) to compute the effective saturated compliance. Seismic velocities at vertical incidence were computed using Christoffel’s equation. The procedure was adopted for both samples and for all the saturants (oil, CO2 and brine). Figures 3.9 and 3.10 show a comparison among the experimental saturated velocities, the saturated velocities predicted by Gassmann’s equation, and the saturated velocities obtained by modeling the pores’ and fractures’ excessive compliance in both samples. Figure 3.11 shows the difference between the computed and experimental velocities for the two samples. Solid symbols represent the difference for compliance-based model, while empty symbols represent the difference for the Gassmann-based model. The differences between theoretical and experimental velocities are reduced by using the compliance-based computation, as opposed to Gassmann’s equation, thus highlighting the impact of low aspect ratio cracks on compressibility and rigidity of the effective medium. 3.3.2 MODELING LOWER CRACK SYMMETRIES The previous results relate to isotropic distribution of penny-shaped cracks in isotropic background composed of spherical pores and isotropic mineral matrix. In this section, the symmetry of the cracks is lowered by introducing a single set of fractures. The resulting effective medium is characterized by (1) horizontal transverse isotropy (HTI), and (2) monoclinic symmetry. The interest is in the conditions under which a variation in the fluid bulk modulus is detectable with shear waves. Bakulin et al. (2000), indicate that a single set of fractures, where at least one of the normal-to-tangential coupling compliances is allowed to be non-zero, makes the shear wave
[
splitting parameter ( γ = V S21 − V S2 2
]
2V S2 2 ) dependent on the fluid content. Normal-to-
tangential coupling compliance is introduced here following Nakagawa et al. (2000) by means of a set of cracks at an angle from the mean fracture plane (Figure 2.4). The background medium contains an isotropic distribution of spherical pores in an isotropic dolomite matrix.
55
For θ = 0 , the normal-to-tangential coupling compliance in the X1-X3 plane is zero, and fractures are rotationally invariant around the X1 axis (HTI). In this case, normal and tangential compliances are introduced as Z N and Z T of a penny-shaped crack (Figure 2.3). For θ > 0 , the normal-to-tangential coupling compliance is positive and the crack system has monoclinic symmetry. Effective pressure controls crack density through e = 0.85 exp
−Pe0.65
, a relationship
obtained from a least-squares fit of the crack density values derived from sample 1 (Figure 3.8). Velocities are computed for wave propagation along the X3 axis (vertical velocity), using values of the crack angle ( θ ) at zero (HTI symmetry), 30 and 60 degrees (monoclinic symmetry). In addition, the background equant porosity is systematically changed (0%, 1%, 10% and 20%), and within each model, confining pressure controls the change in spherical porosity. Conditions of fluid saturation are varied from dry, to carbon-dioxide, to oil (fluids have the same specifications as the ones from Vacuum field). All of the cavities are introduced as if non-interacting. The dry effective compliance is computed first, saturation effect is introduced with Brown and Korringa (1975), and velocities are computed using Christoffel’s equation. Figures 3.12 and 3.13 show computed velocities at vertical incidence for compressional and shear waves in the HTI case ( θ = 0 ). Equant porosity increases from top to bottom row. The impact of an aligned set of cracks on compressional velocities is detectable only at high crack densities typical of low effective pressures. At zero and low (0.01) equant porosity, high bulk modulus and high density fluids (oil) produce higher compressional velocities. Between 0.01 and 0.1 equant porosity, the dependence is reversed, and an increase in porosity generates saturated velocities lower than dry velocities. Shear wave velocities are dominated by the crack density parameter expressed through shear-wave splitting. The fast shear wave velocity decreases with increasing equant porosity and density of the saturant. The slow shear wave follows the same pattern, although superimposed on the crack density dependence. Notice that at zero and low (0.01) equant porosity, the different saturants cannot be distinguished for both the fast and slow shear wave velocities. Figures 3.14 to 3.17 show the results of modeling the same single set of fractures with the addition of a coupling component between normal and tangential compliances. An increase in the coupling compliance is achieved by increasing the angle between open cracks and mean
56
fracture plane. Thus, a measurement of the angle ( θ ) is directly proportional to the magnitude of normal-to-tangential coupling, or fracture roughness. Compressional velocities at vertical incidence decrease in response to increase of background equant porosity (Figure 3.15). For a given value of spherical porosity, P-wave velocities increase with an increase of the coupling compliance (Figure 3.14: upper part). Thus, for P-waves, propagating in the vertical direction, a vertical fracture plane with many uncorrelated asperities results in stiffening the effective medium. Shear wave velocities exhibit the opposite behavior. The fast shear velocity is insensitive to roughness, and, for a given equant porosity, the fast shear wave velocity in a monoclinic medium is equal to that for HTI symmetry (Figure 3.14: lower part). On the contrary, an increase in the normal-to-tangential coupling term decreases the slow shear wave velocity, irrespective of the background equant porosity (Figure 3.14 and 3.16). Additionally, for a given magnitude of normal-to-tangential coupling, the slow shear wave is influenced by the fluid content (Figure 3.16). The dependency is regulated by the background equant porosity. With no spherical pore space, stiffer fluids (high bulk modulus, high density: oil) increase the slow shear wave velocity. Introducing background spherical porosity reverses the dependence: stiffer and higher density fluids decrease the slow shear wave velocity. The dependence of the shear wave splitting parameter γ on fluid saturants is shown in Figure 3.17. Three variables govern this plot: the symmetry of the fracture system (HTI or monoclinic with θ = 60 o ), the amount of background equant porosity, and the saturants in the pore system. The dependence on crack density is equivalent to effective pressure (high effective pressure corresponds to low crack density). In all the cases, γ is directly proportional to crack density, but its magnitude is increased by the coupling compliance. Additionally, there is a dependence of γ on the bulk modulus of the saturant and on background equant porosity. In HTI symmetry, γ is not sensitive to saturants. At any given crack density, an increase in equant porosity makes the background rock more compliant, thus decreasing shear wave splitting. In monoclinic symmetry, where no equant porosity is present, high bulk modulus fluids decrease γ . Notice that the dependence is on the fluid bulk modulus and not on the fluid density, or in a combination of the two, because fluid density does not enter the computation of
57
γ . Introducing equant porosity in the system decreases γ , and the differentiation of γ based on saturants bulk modulus observed at zero equant porosity condition is cancelled. The fluid physical properties plots (Figure 3.5) show that significant differences exist in substituting oil with CO2 at any pressure condition. Figure 3.18 shows the changes for vertical incidence P-wave velocity and shear-wave splitting parameter γ caused by substituting oil with CO2 in a dual porosity dolomite, where a fracture set with monoclinic symmetry is present. The different curves in each plot refer to different values of equant porosity. Larger changes are achieved for larger fracture densities in both plots, and for smaller background equant porosity. For a given set of conditions, the shear wave splitting parameter γ shows changes larger than Pwave velocity. Considering that any vertical fracture set is made of surfaces exhibiting some degree of roughness, conditions of monoclinic symmetry appear to be more common than not. In this case, the shear wave splitting parameter γ may reveal changes in saturating fluids better than P-wave velocities at vertical incidence.
58
FIG. 3.8: Top: crack density as a function of effective pressure for the two samples from Vacuum field. Bottom: crack density relationship (solid line) used in velocity modeling obtained from an exponential best fit to the experimental data of sample 1 (dots).
59
Sample 1: CVU 345 (4671 ft) BRINE saturated
OIL saturated
FIG. 3.9: Experimental and computed velocities for brine and oil saturated conditions for sample 1.
60
Sample 2: CVU 100 (4366 ft) OIL saturated
CO2 saturated
FIG. 3.10: Experimental and computed velocities for oil and CO2 saturated conditions for sample 2.
61
Sample 1: CVU 345 (4671 ft)
Sample 2: CVU 100 (4366 ft)
FIG. 3.11: Velocity difference (%) between computed and experimental velocities for the two samples from Vacuum field. Empty symbols are for Gassmann to experimental difference. Filled symbols are for compliance-based model to experimental difference.
62
velocity (km/sec)
compressional waves OIL CO2
DRY
velocity (km/sec)
φP = 0.0
OIL DRY
velocity (km/sec)
CO2
φP = 0.01
DRY
OIL CO2
φP = 0.1
velocity (km/sec)
DRY
CO2
OIL
φP = 0.2
FIG. 3.12: Vertical incidence compressional velocities for a dolomite mineral matrix with an array of penny-shaped cracks as in Figure 2.4, and θ = 0 (HTI symmetry). Equant porosity increases from top to bottom. Velocities for dry conditions are red, CO2 saturated velocities are blue, and oil saturated velocities are black.
63
shear waves OIL = CO2 = DRY
OIL = CO2 = DRY
DRY
S1
OIL CO 2
OIL CO 2
DRY
S1
S2
S2
φP = 0.0
S1
φP = 0.01
DRY CO2
DRY CO 2
OIL Y R D
S1
OIL
CO2 OIL
S2
Y R D
CO 2
OIL
S2
φP = 0.1
φP = 0.2
FIG. 3.13: Vertical incidence shear-wave velocities for a dolomite mineral matrix with an array of penny-shaped cracks as in Figure 2.4, and θ = 0 (HTI symmetry). Equant porosity increases from top to bottom. Velocities for dry conditions are red, CO2 saturated velocities are blue, and oil saturated velocities are black.
30
θ=
60
64
θ=
compressional waves
θ=
0
φP = 0.0
θ = 0 θ = 30 θ = 60
30 60
θ=
θ=
θ=
0
S1
shear waves
φP = 0.0 S2
FIG. 3.14: Compressional and shear wave velocity response to an increase in the normalto-tangential coupling compliance (ZNT) obtained by increasing the crack angle (θ) from zero to 60°. Velocities are related to dry conditions with no background equant porosity. Crack density decreases with increasing effective pressure.
65
velocity (km/sec)
compressional waves OIL CO2
DRY
velocity (km/sec)
φP = 0.0
OIL DRY CO2
velocity (km/sec)
φP = 0.01
DRY
OIL CO2
φP = 0.1
velocity (km/sec)
DRY
CO2
OIL
φP = 0.2
FIG. 3.15: Compressional velocities at vertical incidence on a dolomite rock with dual porosity. Spherical porosity increases from top to bottom. Fracture porosity is introduced by means of a single vertical fracture set with monoclinic symmetry (θ = 60°). Fracture density decreases with increasing effective pressure. Velocities are computed for dry, CO2 and oil saturated conditions.
66
shear waves S1
OIL CO2 DRY
OIL CO2 DRY
S1
OI L
CO 2
DR Y
DR Y
CO
2
L OI
S2
S2
φP = 0.0
S1
φP = 0.01
DRY CO2 OIL
DRY
Y DR
CO 2
S1
OIL
CO2 OIL
S2
Y R D
2 CO
OIL
S2
φP = 0.1
φP = 0.2
FIG. 3.16: Shear wave velocities at vertical incidence on a dolomite rock with dual porosity. Spherical porosity increases from top-left to bottom-right. Fracture porosity is introduced by means of a single vertical fracture set with monoclinic symmetry (θ = 60°). Fracture density decreases with increasing effective pressure. Velocities are computed for dry, CO2 and oil saturated conditions
67
FIG. 3.17: Dependence of the shear wave splitting parameter γ on fluid saturants for a dolomite rock with dual porosity. Spherical porosity increases from top-left to bottomright. Fracture porosity is introduced by means of a single vertical fracture set with HTI (circles) or monoclinic symmetry (θ = 60°: triangles).
68
FIG. 3.18: Changes in compressional velocity and shear wave splitting parameter γ caused by substituting oil with CO2 in a dual porosity dolomite. Spherical porosity is shown on the side of the curves. Fractures have monoclinic symmetry (θ = 60°).
69
3.4
SUMMARY Compressional and shear wave ultrasonic velocities acquired on two core samples from
Vacuum field showed their dependence on effective pressure and saturating fluids. Generalizing the experimental results, at a given effective pressure, stiffer (high bulk modulus) and denser fluids tend to increase compressional velocities and to decrease shear velocities. The exception comes from shear wave velocities under carbon dioxide saturation, which were found to be up to 2% lower than those for the oil saturated case. Wang et al. (1998) detailed similar observations on carbonate rocks from McElroy field. Overall, the two samples exhibit a behavior typical of rocks in which equant porosity coexists with low aspect ratio cracks. Thin sections, SEM images, and other techniques confirm this dual porosity nature of most sedimentary rocks. Mechanical models of these rocks also require a dual system of spherical pores and low aspect ratio cracks. Cavities were described as non-interacting, randomly distributed, penny-shaped cracks and spheres. The elastic response of the effective medium was computed, and saturated velocities were estimated with Brown and Korringa (1975). This method improved the prediction of saturated velocities by reducing the difference between experimental and modeled velocities. The same method was applied to modeling fluid substitution of a lower symmetry fracture set in an equant porosity background. The hypothesis is that, in a fractured rock, the shear wave splitting parameter is more sensitive to changes in saturating fluids than compressional wave velocity at vertical incidence. Bakulin et al. (2000) recently modeled a rock with a single fracture set, where one of the normal to tangential coupling compliances is non-zero (monoclinic symmetry). Their model exhibits a shear wave splitting parameter γ sensitive to saturated conditions. One difficulty in applying the corrugated (rough) crack model of Bakulin et al. (2000) is the unknown value of the normal-to-tangential fracture compliance. Nakagawa et al. (2000) recently provided relationships among normal, tangential, and coupling compliances based on numerical modeling. Building on these concepts, we calculated the dry and saturated velocities of a dolomite matrix with a single fracture set for HTI and monoclinic symmetry for various saturating fluids. The results show that, in the case of a corrugated (rough) fracture set (and no background equant porosity), an increase in the fluid bulk modulus decreases the shear wave
70
splitting parameter. Introducing background equant porosity in the system decreases γ , and ultimately the sensitivity of γ to the fluid bulk modulus is cancelled.
71
CHAPTER 4
STATE OF STRESS IN THE CRUS T
UT TENSIO SIC VIS. ROBERT HOOKE 4.1
INTRODUCTION The multicomponent time-lapse monitoring program at Vacuum field (VF) was conducted
on a portion of the crust subjected, on a regional scale, to the tectonic stress field of the Permian Basin (PB). Stresses generated by relative plate motion, magmatic and thermal processes, regional crust and lithospheric thickness and density variations, topography and lithospheric flexure, are reflected in the present state of tectonic stress. Reservoir engineering operations, such as fluid injection and production, may alter the local state of stress, which is linked to its regional expression by a general, anisotropic, effective stress law. Thus, a knowledge of the regional and local state of stress is a prerequisite to any seismic monitoring program intended to record the evolution of the rock-fluid interaction. In this chapter, the conditions contributing to the current state of stress in the PB, and at Vacuum field in particular, are reviewed. The starting point is the plate interaction chronology that defined stress history and structural style of the PB, and at Vacuum field. Structural mapping of the basement at Vacuum field shows consistency with the regional structural trends detected in the basement intervals of the PB. Late-Pennsylvanian, compressional tectonics is believed to be the main cause of this structural architecture. The same structural style is also detected in the younger, post-tectonic, Guadalupian levels of the San Andres, which are the focus of this study. Thus, the deformation of the basement was somehow instrumental in determining the structural style of the higher levels. The exact mechanism of structural imprinting from the basement to younger intervals is not understood, although measured fault displacement in the San Andres is essentially vertical and not lateral.
72
Recent work on measurements of tectonic stress is also reviewed, and, on the basis of the structural style, the present state of stress of the area is modeled. The present state of stress is believed to result from the superposition of a regional, first-order, tectonic stress, with a local stress induced by reservoir engineering activities in the porous and fractured levels of Vacuum field. The superposition mechanism between the two orders of stress is reviewed here on the basis of classical poroelastic models. The outcome shows that pore pressure changes in vertically fractured reservoirs may alter the magnitude and the directions of the maximum and minimum horizontal stress. 4.2
PERMIAN BASIN TECTONICS Vacuum field is located on the Northwest Shelf (NWS) of the PB (Figure 4.1).
Geologically, the PB of West Texas and southern New Mexico represents the foreland of the Marathon-Ouachita orogenic belt (MOB). The general structure is composed of foreland subbasins separated and surrounded by intraforeland uplifted areas (Figure 4.1). The Delaware Basin (DB) is bounded to the west by the Diablo Platform (DP), to the north by the Northern Shelf (NS) and NWS, and to the south by the MOB, while the north-south trending Central Basin Platform (CBP) separates the DB from the Midland Basin (MB). Recently compiled tectonic maps of the PB (GEOMAP, 1983; Gardiner, 1990; Ewing, 1990) show that this region has not been subjected to significant deformation since the late Paleozoic (265 Ma). Consequently, the present structural characters can be considered essentially unchanged since that time (Hills, 1984; Ward et al., 1986; Frenzel et al., 1988). The tectonic evolution of the PB is composed of long periods of quiescence separated by short periods of rapid crustal movement (Horak, 1985), where the tectonic pulses are directly connected to plate interactions. The tectonic history is reviewed here (Figures 4.2 to Figure 4.13) showing relative plate motion, tectonic forces, paleoenvironments, and large scale depositional processes. From Cambrian (570 Ma) to Pennsylvanian (310 Ma) the ancestral PB is part of a passive margin (Figures 4.2 and 4.3). West Texas and southern New Mexico were the site of the Tobosa basin (Galley, 1958), a shallow marine basin occupying approximately the same area as the later PB. Tectonically, this is a phase of slow and weak crustal extension, low subsidence and low sedimentation rates. Deposits are primarily shallow-water shelf, dominated by carbonates with
73
episodes of shales and sands. There is no important structural component at this time, but the pre-Pennsylvanian source and reservoir rocks of the PB are deposited in this period. During Upper Mississippian (Figure 4.3) the southeastern portion of the North American (NAM) plate is bounded by a subduction zone caused by the rapid northwestern advance of the South American (SAM) plate. Oklahoma and southeastern Texas obduct oceanic crust under the NAM plate. By Pennsylvanian time (310 Ma), the NAM and SAM plates are in full continentalcontinental collision (Figure 4.4), which progresses geographically from east to west, reaching West Texas and southern New Mexico in the early Permian. This is a suture zone, characterized by compressional tectonics, whose effects in terms of crustal deformation extended for at least 1000 km into the northwestern foreland. On a planetary scale, this event is instrumental in the formation of Pangea, and on a regional scale, the continental collision generates the MOB. The ancestral PB is fragmented into major crustal blocks by high-angle faults, which separate areas of structural depression (Midland Basin and Delaware Basin) from areas of tectonic relief (Northern Shelf, Northwestern Shelf, Central Basin Platform and Diablo Platform). By Middle Permian time (270 Ma), the collisional pulse is extinguished and the essential PB structural framework is established (Figure 4.5). Notice that the NAM-SAM suture zone runs along the Equator, which made this area an ideal location for carbonate sedimentation. Because of the tropical environment, broad carbonate shelfs were established on the structural highs delimiting the DB and the MB. From Middle Permian (270 Ma) to early Triassic (230 Ma) the areas of structural depression of the PB became depocenters of sedimentation and were filled with clastics (Figure 4.6 and 3.7). At the margins of the basins, the development of reef-fringed carbonate platforms and shelfs continued until the DB remained as the only deep water depocenter. The hydrocarbon reservoir rocks of the Upper Permian (Leonardian and Guadalupian) are deposited at this time. The final stage was given by evaporites that filled the basin and covered the surrounding shelfs. High rates of crustal mobility characterize this period, with crustal subsidence as the dominant cause (Figure 4.14). All the basins subsided differentially and crustal recoupling is achieved by the end of this phase. Figure 4.14 shows the remarkable increase in depositional rate that occurred from the beginning to the end of the Permian in the basinal areas. From Early Triassic (230 Ma) to Late Cretaceous (80 Ma), all elements of the PB remained coupled and acted as an integrated unit. Mobility rate of the crust was low, and postPermian deposition was not substantial (Figure 4.7 to Figure 4.10).
74
Starting in Late Cretaceous (80 Ma) and up to Middle Miocene (50 Ma), uplift and compressive stress developed from west to east across the entire PB in response to the Laramide orogeny (Figure 4.11). Development of faulting affecting the basement and uplift of the western part of the PB is found in West Texas along the Rio Grande River, but in general the PB records very little evidence of tectonic movement during Laramide. Nonetheless, a weak compressive stress is imposed on the region, and the PB is permanently raised over sea-level. From the Middle Eocene (50 Ma) to the Middle Olocene (30 Ma), the southwestern portion of the PB is exposed to crustal thinning and extension with development of volcanic activity and increased regional heat flow (Figure 4.12). This thermal activity is a precursor to the basin and range extensional phase that followed (25 to 0 Ma). During this last tectonic pulse, basin and range tectonism extended from the western DB across the southwestern US to California (Figure 4.13). This phase is characterized by rifting, extension and crustal thinning, with high values of heat flow and low gravity. The general uplift increases from east to west across the PB. The depositional response to the various tectonic phases is shown in Figure 4.14, portraying the differences in thickness of the sedimentary columns between areas of depocenters (DB, MB) as opposed to structural highs (DP, ES, CBP). Figure 4.15 shows the seismic expression of the depositional activity during the Permian on the NWS. The seismic line runs N-S and captures the shelf break between the NWS to the north and the DB to the south.
75
NS
NWS VF
MB
ES
NM TX DB CBP
M EX IC O
DP
MOB
NORTH
100 km
FIG. 4.1: The Permian Basin of West Texas and southeastern New Mexico. Thick lines represent the limit of carbonate sedimentation during Guadalupian time. The basin can be subdivided in sub-basins (DB = Delaware Basin; MB = Midland Basin), and structural highs (DP = Diablo Platform; CBP = Central Basin Platform; NWS = Northwest Shelf; NS = Northern Shelf; ES = Eastern Shelf; MOB = Marathon-Ouachita Belt). Notice Vacuum field (VF) located on the edge of the NWS. The thin lines in the CBP and in the NWS are basement regional faults (data from: Ewing, 1991; Yang and Dorobek, 1995).
76
FIG. 4.2: Early Devonian: 400 Ma. The ancestral PB is part of a passive margin characterized by slow and weak crustal extension, low subsidence and sedimentation rate. NAM
AFR SAM
400 Ma 5000 km at Equator
FIG. 4.3: Upper Mississippian: 340 Ma. While the ancestral PB remains unaffected by tectonic deformation, the eastern and southeastern portions of the NAM plate are bounded by a subduction zone caused by the north-northwest advance of the SAM and AFR plate (Gondwana).
340 Ma 5000 km at Equator
FIG. 4.4: Upper Pennsylvanian: 300 Ma. The NAM and SAM plates are in full continental-continental collision.
NAM
(general plate data are from PGISMac, a plate tectonic presentation program from Malcom Ross and Chris Scotese, University of Texas at Arlington)
SAM AFR 300 Ma 5000 km at Equator
77
FIG. 4.5: Early Permian: 270 Ma. The collisional phase is extinguishing. What is left is the essential structure of the Permian Basin, characterized by depocenters of future sedimentation, and structural highs. Notice the position of Vacuum field on Equatorial latitudes.
NAM
AFR SAM 270 Ma 5000 km at Equator
FIG. 4.6: End of the Permian: 245 Ma. Permian Basin phase of sedimentation.
NAM
245 Ma 5000 km at Equator
FIG. 4.7: Early Triassic: 230 Ma. Crustal mobility in the Permian Basin is reported to be extremely low. The entire basin acts as a single recoupled unit.
NAM
(general plate data are from PGISMac, a plate tectonic presentation program from Malcom Ross and Chris Scotese, University of Texas at Arlington)
AFR
SAM
230 Ma 5000 km at Equator
78
FIG. 4.8: Early Jurassic: 200 Ma. Stable platform phase.
NAM
AFR
SAM
200 Ma 5000 km at Equator
FIG. 4.9: Early Cretaceous: 120 Ma. Stable platform phase.
NAM
AFR
120 Ma 5000 km at Equator
SAM
FIG. 4.10: End of the Cretaceous: 90 Ma. Stable platform phase.
NAM
AFR
SAM
90 Ma 5000 km at Equator
(general plate data are from PGISMac, a plate tectonic presentation program from Malcom Ross and Chris Scotese, University of Texas at Arlington)
79
FIG. 4.11: Paleocene: 60 Ma. Laramide orogeny.
60 Ma 5000 km at Equator
FIG. 4.12: Eocene: 40 Ma. Volcanic phase.
NAM
40 Ma 5000 km at Equator
FIG. 4.13: Miocene: 15 Ma. Basin and range phase.
NAM
AFR
15 Ma 5000 km at Equator
(general plate data are from PGISMac, a plate tectonic presentation program from Malcom Ross and Chris Scotese, University of Texas at Arlington)
80
km SL
DP
-1
CBP
-2
ES
Passive margin
-3
Continental collision
-4
MB DB
Foreland basin
-5
Structural stability
-6
Laramide orogeny
-7
Volcanic phase
-8
Basin and range extension
-9 C 600
O 500
S
D
400
M
P Perm
300 Time (Ma)
T 200
J
K 100
T 0
FIG. 4.14: Crustal mobility and sedimentation rates versus geologic time for the various portions of the Permian Basin (from Horak, 1985). Vacuum field, located in the Northwestern Shelf, has a curve similar to the CBP.
81
Period Epoch
Formation and Tops
245 Ma
OCHOAN
N
Time-Lapse Area
S sec
SALADO 0.5
255 Ma YATES
PERMIAN
GUADALUPIAN
265 Ma
QUEEN GRAYBURG UPPER SAN ANDRES LOWER SAN ANDRES GLORIETA PADDOCK 1.0
BLINEBRY TUBB LEONARDIAN
275 Ma
ABO REEF
TOP WOLFCAMPIAN
PENNSYLVANIAN
WOLFCAMPIAN 290 Ma
1.5
BASE WOLFCAMPIAN TOP PENNSYLVANIAN
5 km
FIG. 4.15: Stratigraphy of the NWS, in relation to the seismic column and the identified seismic markers of the region. Correlations between geologic tops and seismic reflections were obtained through a combination of synthetic seismograms, vertical seismic profiles (VSP), and recently published seismic lines (Montgomery, 1997). Notice that the time-lapse area of Vacuum Field is practically located on the edge of the NWS. The shelf is defined by a major vertical discontinuity running continuously from Pennsylvanian to Guadalupian rocks. This is one of the high-angle faults discussed in the text, and initially established by the Pennsylvanian tectonic pulse.
82
4.3
STRUCTURAL DOMAINS OF THE PERMIAN BASIN Knowledge of the deformation and structural styles in the PB is partly incomplete
because of the paucity of outcrop exposure. But tens of thousands of wells have been drilled, and extensive seismic coverage has been acquired in the PB. Consequently, it has been possible to map the deep structural levels, and to characterize the general structural style of this region (GEOMAP, 1983; Ewing, 1991). Figure 4.16 shows the present regional structural trends reconstructed for the basement of the CBP and NWS. Regional faults are mapped at top of the Ellenburger Group (Lower Ordovician), and have tens of kilometers in length. The timing of deformation is late Pennsylvanian to Early Permian (Galley, 1958; Hills, 1970; Walper, 1977; Elam, 1984; Ewing, 1984; 1991; Reed and Strickler, 1990; Yang and Dorobek, 1991; 1992; 1993; 1995; Shumaker, 1992), which links the presently observed structural style to the compressive stresses of the continental-continental collision between NAM and SAM that created the MOB. The end of the crustal shortening pulse in the MOB is early Wolfcampian (Yang and Dorobek, 1995). Structurally, the basement of the CBP consists of a series of fault-bounded crustal blocks arranged in a general, left-stepping, en enchelon pattern (Gardiner, 1990; Ewing, 1991). These domains are separated from each other, and from adjacent basinal areas, by boundary fault zones. Yang and Dorobek (1995) subdivided the CBP in two dominant crustal blocks, recognizing similar structural relief, style, and fault orientation in each block (Figure 4.16). The area north of the CBP is the NWS, often defined as the Tatum ridge (Ewing, 1991). Flower structures have been identified on east-west seismic lines across the area illustrating the N-S strike-slip style of deformation that characterizes the NWS immediately north of the CBP (Yang, 1993). The N-S trending faults on the eastern and western flanks of the CBP are steeply dipping. They exhibit highly variable trends along strike, but are reconciled in a general behavior of a right-lateral shear deformation due to the compressive stress from the MOB (Shumaker, 1992; Yang and Dorobek, 1995). The E-W trending faults, separating the CBP in two blocks, and defining the southern margin of the NWS, are left-lateral strike-slip (Shumaker, 1992; Yang and Dorobek, 1995). The continental-continental collision which began to affect the PB in the early Permian, released its compressive stress along Proterozoic, north-south trending lines of weakness
83
established with the development of a north-northwestern trending trough (Hills, 1984). According to Hills (1984), this may have been an aulacogen on the edge of the NAM craton during the Grenvillian orogeny (about 1000 Ma). The late Pennsylvanian compressive stress was transmitted from the MOB to the PB as a right-lateral shear, along the N-S faults bounding the CBP (Figure 4.16). The CBP was segmented in blocks which rotated clockwise (Shumaker, 1992; Yang and Dorobek, 1995), thus impressing a left-lateral sense of displacement to the E-W cross faults that separate the blocks (Figure 4.16). In synthesis, a stress-strain pattern is recognized in the PB: right-lateral shear displacement along N-S faults caused clockwise block rotation, which in turn caused E-W, leftlateral shear displacement. The scale of the deformation progressively diminished from south to north, as the distance from the area of continental-continental collision increased, and the tectonic pulse decreased in intensity. Yet, the same stress-strain pattern is still recognizable north of the CBP, in the NWS. Figure 4.17 shows a coherency image (Bahorich and Farmer, 1995) from a 3D reflection seismic survey acquired along the Guadalupian carbonate shelf margin of the NWS in 1993, and including VF. The location of the 3D survey is shown in Figure 4.16. The upper image in Figure 4.17 is from the basement of the NWS, extracted at top of Pennsylvanian (about 1.5 sec in Figure 4.15). The lower image in Figure 4.17 shows the interpreted basement faults. Figure 4.18 shows a statistical view of the basement structural style in the CBP and NWS. The data for the CBP are regional faults derived from Ewing (1991), Shumaker (1992), and Yang and Dorobek (1995) in Figure 4.16. The data for the NWS are the interpreted faults of Figure 4.17. Although the lengths of the faults used to construct Figure 4.18 are extremely different for the two locations (tens of kilometers for the CBP, kilometers for the NWS), the two sets of diagrams show the same structural style: a predominant set of faults striking NW-SE, and a second set of faults, striking at about 55° counterclockwise from the first set. Notice that the NWS fault system is rotated counterclockwise by about 25° with respect to the CBP fault system, but the main directions of stress relief are maintained. Figure 4.19 (top) shows a coherency image from the same 3D reflection seismic survey as in Figure 4.17, horizontally sliced on the San Andres carbonates of the NWS (about 0.8 sec in Figure 4.15). The lower image in Figure 4.19 shows the interpreted faults. Figure 4.20 shows the statistics for the San Andres fault sets, and compares them with the deeper basement faults of the same survey.
84
The structural style of the San Andres faults is similar to the NWS basement faults. But, while the late Pennsylvanian, northwest directed, compressive stress is a cause of basement deformation, a different mechanism has to be responsible for the San Andres structural style, because the deposition of Guadalupian sediments occurred after the MOB tectonic pulse had already extinguished. Galarraga (1999), analyzing the same seismic data as in Figure 4.19 interpreted the San Andres structural style as a strike-slip, right lateral shear deformation along the E-W fault system. In Galarraga (1999), the main evidence for strike-slip deformation is: (1) interpreted flower structures cutting through the Leonardian and Guadalupian rocks, and (2) a relative sense of right-lateral displacement inferred from time slice coherency volumes. Unfortunately, a tectonic cause for this deformation is not given, nor is it speculated upon. Notice also that, for the E-W trending faults, the right lateral, strike-slip shear deformation of Galarraga (1999) contradicts the left-lateral shear deformation reported by Shumaker (1992), and Yang and Dorobek (1995) for the CBP and NWS. At the time of deposition of the Guadalupian rocks, the PB is already fragmented into structural highs and depocenters. Crustal rebound and recoupling are also taking place, following the compressive tectonic pulse of the MOB. Notice that, from 3D seismic coherency data, there is almost no evidence of deformation above the Queen (Middle Guadalupian). Instead, below the Queen, faults defining the southernmost part of the carbonate shelf edge have vertical displacement of about 40 msec. There is no conclusive evidence of horizontal displacement in the Permian section from 3D seismic data (no obvious piercing points on the two sides of the faults). In conclusion, Figures 4.17 to Figure 4.20 show that the MOB tectonic event fractured the basement of the CBP and NWS with two conjugate sets of faults. The same directions of fracturing are also present in the sedimentary rocks deposited after the end of the MOB tectonic event. In the thick sedimentary column overlying the basement, vertical offset of faults is measurable while horizontal offset is not. Thus a definite vertical adjustment of the crust took place between the end of the Pennsylvanian and the Middle Guadalupian, with the main directions of stress relief imposed by the fractured basement on the overlying sedimentary column. However, horizontal displacements along the existing fault trends should not be ruled out as a possibility. In particular, the Laramide orogeny, which permanently raised the PB above sea level, acted on the PB also with compressive stresses from west to east. In any case, if strike slip deformation acted on the PB any time after the MOB tectonic event, it must have followed directions of stress relief imposed by the basement.
85
NWS VF MIDLAND BASIN
NM TX
DELAWARE BASIN 50 km
CBP NORTH
NWS
NWS VF
VF MIDLAND BASIN
DELAWARE BASIN 50 km MOB
MOB
FIG. 4.16: Basement structural style in the CBP and NWS of the PB. Datum is top of Ellenburger Group (Lower Ordovician). The basement is arranged in fault-bounded crustal blocks. The Early Permian compressive stress from the MOB was released along N-S trending faults with right lateral shear displacement. This caused clockwise rotation of the blocks and left-lateral shear displacement along E-W trending cross-faults (data from Yang and Dorobek, 1995). Notice Vacuum field (VF) on the extreme upper left of the figure. The rectangle around VF is the limit of a 3D seismic survey used to assess the structural style of the NWS.
86
NORTH
NORTH
Vacuum Field Time-lapse area
1 km
FIG. 4.17: Basement structural style in NWS of the PB. Datum is top of Pennsylvanian. Top image is extracted from a coherency cube. Bottom picture shows the interpreted basement faults. Notice the square surrounding injector and producer wells in the Vacuum field time-lapse area.
87
CBP Basement Faults
82°N
139°N
NWS Basement Faults
58°N
114°N
FIG. 4.18: Azimuthal strikes of the CBP and NWS basement faults. Arrows on the left circles show all the faults in the data sets normalized by the maximum length. Arrows on the right circles show the mean values of strike, and are normalized by the total length of the fault sets.
88
NORTH
NORTH
Vacuum Field Time-lapse area
1 km
FIG. 4.19: Structural style of the San Andres dolomites in NWS of the PB. Datum is ≅ 4500 ft from surface. Top image is extracted from a coherency cube. Bottom picture shows the interpreted San Andres faults. Notice the square surrounding injector and producer wells in the Vacuum field time-lapse area.
89
San Andres Faults
73°N
110°N
NWS Basement Faults
58°N
114°N
FIG. 4.20: Azimuthal strikes of the San Andres faults (top) and NWS basement faults (bottom) in the proximity of Vacuum field. Arrows on the left circles show all the faults in the data sets normalized by the maximum length. Arrows on the right circles show the mean values of strike, and are normalized by the total length of the fault sets.
90
4.4
CURRENT STATE OF STRESS Stresses are difficult to measure directly. Typically, some aspect of strains are measured
from which the state of stress is inferred. In a general sense: (1) measurable deformations are not functionally related to a unique stress, and (2) a measurable deformation is the result of superposition of a series of incremental strains, where each strain is related to an instantaneous state of stress by a specific set of material properties, which changes during the sequence. Thus, the final, measurable deformations in a rock may have no relationship with any particular state of stress. Complex geologic settings, with superposition of several tectonic phases, are likely to show the effects of (1) and (2). But, growing experimental evidence shows that a direct correlation exists between strain-derived in situ stress orientations and relative magnitudes, with plate characteristics (Zoback, 1992). The World Stress Map project (WSM) currently uses six types of geological and geophysical data in four different categories to infer the tectonic stress (Mueller et al., 2000): (1) earthquake focal mechanisms, (2) well bore breakouts, (3) in situ stress measurements (hydraulic fracturing and overcoring), and (4) neotectonic events (recent fault slip and volcanic alignments). Details, assumptions, uncertainties, and difficulties in reconstructing in situ stress orientations from each method are extensively explained in Zoback and Zoback (1989), Zoback et al. (1989), Zoback and Zoback (1991), and Zoback (1992). The WSM project does not include stress orientations inferred from shear wave splitting.
91
Z
X Y
e = 0.01
e=
e
0.0
=
5
e
0. 1
=
0. 01
e = 05 0. 0.1 = e
FIG. 4.21: Effective stress σHmax and σHmin, according to equation (2.31), on the horizontal plane of a dolomite rock with unidirectional vertical fractures subjected to increasing Pp. Fractures are approximated to penny-shaped cracks (top). An initial (Pp = 0), first-order, tectonic stress of 60 MPa is imposed on the system with σHmax = σHmin. Maximum Pp is 30 MPa. Increase in Pp causes a differential decrease in effective stress such that σHmax and σHmin are developed. The different curves refer to various fracture densities (e) imposed on the dolomite isotropic matrix. Notice that changes in principal horizontal stresses are larger for higher crack densities.
92
Z
X
Z’
θ Y Y’
X’
Increasing Pp
Decreasing Pp
0.1 0.3 0.5
-0.1 -0.3 -0.5
0.7 0.9 1.0
-0.7 -0.9
-1.0
FIG. 4.22: Superposition of regional and pore pressure principal horizontal stresses. The regional stress is imposed to be compressive (x, y, z). The Pp system (x’, y’, z’) may be extensional or compressive. When Pp increases in the fractures, the effective stress decreases in magnitude, its horizontal principal components rotate according to the curves on the right part of the figure, and the reservoir undergoes volume expansion. When Pp decreases in the fractures, the effective stress increases in magnitude, and its horizontal principal components rotate according to the curves on the left part of the figure, with an overall contraction of reservoir volume.
93
4.4.1 PATTERNS AND ORDERS OF STRESS The first important observation emerged from mapping the distribution of the lithospheric stress is that broad intraplate regions are characterized by uniformly oriented ( ± 15 o ) horizontal stresses. Consistent intraplate stress orientations are documented over distances up to 5000 km. Zoback (1992) defined these global trends as first-order stress provinces. In particular, midplate regions are dominated by compression, where the maximum principal stress is horizontal (Zoback, 1992). The source of the midplate compressive stress field are ridge push and continental collision at the plate boundaries. Thus, the effects of these forces are felt for thousands of kilometers from the source. This is equivalent to an upper bound of 50+ times the thickness of the upper part of the lithosphere. Then, it is reasonable to imply that the distribution of first-order tectonic stresses in the upper lithosphere of midplate regions is laterally and vertically homogeneous. Once the first-order stress fields are identified, it is possible to search for second-order stress distributions, or local anomalies to the regional stress field. Second-order variations in stress orientation and relative magnitude are documented at every scale: localized tectonic forces in the lithosphere, like buoyancy and plate flexures (103 km), thermal anomalies, topography, anomalies related to fluids in the crust, and other site specific anomalies (< 1km). 4.4.2 PORE PRESSURE AS A SECOND-ORDER STRESS FIELD Among the localized anomalies to the state of stress are the effects induced by changes of pore pressure ( P p ). The subject is relevant here because production of fluids (water, steam, hydrocarbons), as in the case of Vacuum field, is likely to change P p , thus possibly changing the local state of stress. The evolution of the stress field as a function of P p can be estimated with poroelastic models. The fundamental work on isothermal porous media is from Biot (1941). Rice and Cleary (1976) added straightforward physical meaning to Biot’s work. McTigue (1986) expanded the treatment to thermoelasticity, thus dropping the isothermal assumption. Segall (1992), and Segall and Fitzgerald (1998) found specific solutions for hydrocarbon and geothermal reservoirs. Their treatment considers a reservoir as an ellipsoid, flat on the horizontal plane (plane section is a
94
circle), and with aspect ratio α res = thickness / diameter of the reservoir. The distribution of stresses associated with changes in P p is obtained inside and outside the reservoir by using the model of Eshelby (1957) for the determination of the elastic field of ellipsoidal inclusions. The important outcome is that the magnitude of the local stress changes, due to reservoir engineering operations, is such that P p indeed constitutes a second-order stress field. In Segall (1992), and Segall and Fitzgerald (1998), linear poroelasticity and isotropy are assumed. Conditions of poroelastic structural anisotropy are of interest though, because changes in P p may occur in intervals of the crust where azimuthal anisotropy is caused by vertical fractures and aligned pores. In this case, the general form of effective stress has to be used (equation 2.30). Chen and Nur (1992) derived equation (2.30), and investigated the conditions of pore pressure buildup or decline that may change the local state of stress, leading to fault instability and microearthquakes. Their work shows that changes in P p are a second-order stress field that locally superimposes on the tectonic stress. The variations in the principal horizontal stresses induced by changes in P p can be computed quite simply as shown here below for the case of a reservoir where vertical fractures are present. The treatment is two-dimensional and limited to the horizontal plane, thus the assumption is made that one of the principal normal stresses is always vertical. The results show that variations of P p in fractured intervals may lead to significant changes in the magnitude and orientation of the maximum and minimum horizontal stresses. Consider a portion of the crust where vertical fractures, approximated to ellipsoidal shapes, are embedded in a rock matrix (Figure 4.21). The rock matrix is a dolomite ( K m = 80 GPa, µ m = 45 GPa), and the vertical penny-shaped fractures strike along the Y direction. A uniform pore pressure exists in the reservoir, but production operations like injection and extraction of fluids will change P p . Figure 4.21 shows the changes in the principal horizontal stresses induced by changes in P p for an azimuthally anisotropic medium. Fractures have a fixed aspect ratio ( α = 10 −3 ) and fracture density is changed from e = 10 −1 to e = 10 −2 . The behavior of σEH max and σ EH min is shown in response to increasing PP from 0 to 30 MPa. At initial conditions PP = 0 , and the tectonic stress on the horizontal plane is hydrostatic with σ ij = 60 MPa in every direction. Because PP is increased, the effective stress decreases
95
according to equations (2.30) and (2.31) developing the two principal horizontal stresses σEH max and σ EH min . If σ H max and σ H min already exist in the horizontal plane due to tectonic stress, the change of PP in the fractures will introduce a second stress system. In general, the two stress systems will not have the same orientation, but they will be at an angle θ (Figure 4.22). The regional stresses are in the unprimed coordinate system [x, y, z]: (4 .1 )
σXR
= σ HR
σY R
min
= σ HR
σZ R
max
= σVR
The local stresses due to changes in PP are in the primed coordinate system [x’, y’, z’] (4 .2 )
σ ′X
= σ HL
σ Y′
min
= σ LH
σ ′Z
max
= σ HL
max
Notice that equations (4.1) and (4.2) refer to principal stresses only, thus implying that the tangential stresses ( σ XY ) are zero. Confining the analysis to the horizontal plane only, the local stress field can be expressed in the regional coordinate system as (Jaeger and Cook, 1976): (4 .3 )
σX L
= 1 2 (σ′X + σ′Y
)+
1 2 (σ′X − σ′Y
) cos 2 θ
(4 .4 )
σY L
= 1 2 (σ′X + σ′Y
)−
1 2 (σ′X − σ′Y
) cos 2 θ
(4 .5 )
σ XY L
= − 1 2 (σ′X − σ′Y
) sin 2 θ
Notice that the local tangential stress ( σ XY L ) is not zero anymore. Superposition of the two stress fields results in the effective stress field in the coordinate system of the regional stress field, as: (4 .6 )
σ EX
= σXR
(4 .7 )
σYE
= σY R
(4 .8 )
σ EXY
+ σXL + σY L
= σ XY R
+ σ XY L
Because the regional stresses are taken as principal stresses, then σ XYR = 0 . When θ ≠ 0 , the local stress has σ XYL ≠ 0 , then σ EXY ≠ 0 . In this case, the effective stress field expressed by equations (4.6), (4.7), and (4.8) is not a principal coordinate system. The principal coordinate system for the effective stresses is given by (Jaeger and Cook, 1976): (4 .9 )
tan 2 ϕ =
2 σ EXY σ EX − σYE
=
(σ
(
2 σ XY R XR
+ σX L
+ σ XY L
) − (σ
YR
)
+ σY L
)
96
where ϕ is the angle of the principal effective stress system from the regional coordinate system. In equation (4.9) the terms with the subscript
L
are a function of PP . Thus PP will
influence the total effective stress in magnitude and direction of its principal normal components. Figure 4.22 shows the results from the superposition of second-order principal horizontal stresses, induced by PP changes, on a regional principal compressive stress system. The PP change acted on a vertically fractured dolomite. The various curves correspond to the magnitude of the PP change, expressed as fractions of the tectonic σ H max . Significant rotations (up to 50°) of the effective stress principal components can be induced by large PP increase even for small angles between the regional and the pore pressure stress systems. On the contrary, during episodes of pore pressure decline acting on a tectonic compressive system, significant rotations of the effective stress principal components are achieved only for large misalignments between the regional and the pore pressure principal stresses. The important message, from examples like Figure 4.22, is that pore pressure variations acting on structurally anisotropic levels of the crust (fractures, aligned pores) may result in anisotropic distributions of effective stress. Thus, it is conceivable that any kind of time-lapse activity monitoring of the state of stress associated with actively producing intervals, where pore pressures are likely to change, may experience time variations in magnitude and orientation of the principal components of the effective stress. 4.4.3 SHEAR WAVE SPLITTING AS A STRESS INDICATOR Evidence of shear-wave splitting is found in multicomponent surface and borehole seismology (e.g. Alford, 1986; Lynn and Thomsen, 1990; Martin and Davis, 1987; Mueller, 1991; Winterstein and Meadows, 1991a; 1991b), and laboratory studies (Rai and Hanson, 1987; Ebrom et al., 1990; Sondergeld and Rai, 1992; Lo et al., 1986; King et al., 1995; Rathore et al., 1995). Crampin and Lovell (1991) suggested a number of possible sources of anisotropy in the rock mass which could cause shear-wave splitting: (1) aligned crystals, (2) direct stress-induced anisotropy, (3) aligned grains (or lithology anisotropy), (4) fine layering, and (5) stress-aligned crack-induced anisotropy. The last two decades of exploration seismology have accumulated convincing evidence of the fact that the first 10 to 20 km of the lithosphere are pervaded by
97
vertical fractures and cracks whose strikes are aligned with the local σH max . Thus, fractureinduced orientation of stress is likely to be the most important cause of seismic azimuthal anisotropy. Two additional lines of evidence support seismic azimuthal anisotropy aligned with stress direction. First, consider the results of about thirty years of experimental studies of ultrasonic velocity anisotropy induced from applied stress. In crystalline rocks: Bonner (1974), Lockner et al. (1977), and Granryd et al. (1983) worked on Westerly granite, Nur and Simmons (1969) on Barre granite, Hadley (1975) on Westerly granite and San Marco gabbros. In sedimentary rocks: Gupta (1973) worked on Indiana Limestone, Lo et al. (1986) on sandstone and shale, Rai and Hanson (1987) on shale, sandstones and limestone, Sammonds et al. (1989) on Darley Dale sandstone, Sayers et al. (1990), and Scott et al. (1993) on Berea sandstones. In a recent set of experiments, Rathore et al. (1995), and Holt et al. (1996) synthetically created samples of sandstones. The samples were uniaxially loaded and unloaded several times, and ultrasonic velocities were measured along different directions to compute anisotropy. The results show that crack opening and closure is induced by stress load and unload, mostly in the grain contact area. The cracks tend to be oriented with respect to the stress field, with more cracks opened perpendicular to the direction of maximum stress reduction. Velocity is faster in the direction of σH max , and slower in the direction of σH min . Thus velocity anisotropy appears to be closely related to stress anisotropy (Holt et al., 1991; Holt and Kenter, 1992; Holt et al., 1993). Stress-aligned fracture-induced anisotropy has also been justified theoretically. Zatsepin and Crampin (1997), and Crampin and Zatsepin (1997) developed an anisotropic poroelastic model that predicts stress-dependent velocity and permeability anisotropy. An additional model of porous media containing combination of pores of various aspect ratios (cracks and pores) was developed by Xu (1998). The author successfully applied his theory to the laboratory results of Rathore et al. (1995). In summary, an upper portion of the sedimentary basins pervaded by stress-sensitive vertical fractures may be the reason for shear-wave splitting as a manifestation of azimuthal anisotropy. The polarization of the fast shear waves is usually observed to be parallel or subparallel ( ± 15 o ) to σH max (Crampin and Lovell, 1991; Crampin, Evans, and Atkinson, 1984). Thus, in the extensive dilatancy anisotropy (EDA) model of Crampin and co-authors, a measurement of
98
the azimuth of the fast (S1) and slow (S2) shear waves is equivalent to a determination of σH max azimuth. Thus we expect that shear-wave splitting in the earth reflects the in situ stress field, and that changes in the stress associated with reservoir engineering operations (e.g. pressure buildup and depletion) may result in changes in shear-wave splitting, both in azimuth and magnitude. 4.5
STATE OF STRESS IN THE SAN ANDRES DOLOMITES AT VACUUM FIELD The PB and Vacuum field are located in a first-order midplate stress province
characterized by compressive stress (Zoback, 1992). The western portion of the PB is proximal to the limit between the active extensional tectonics of the western Cordillera and the mid-continent region of the NAM plate (Figure 4.23). Compressive stress converges towards the PB in a radial sense from the eastern side (NAM plate) and southern side (Mexico), with azimuthal directions of
σH max ranging from 60°N to 160°N (Figure 4.23). The driving mechanisms for the present state of stress are the tectonic activities of the western coast of Central America (south), the complex Gulf of Mexico-Caribbean system (southeast), and the North Atlantic spreading centers (eastnortheast). Additionally, the northwestern portion of the state of New Mexico is dominated by the Rio Grande rift, which imposes compressive stress from northwest to southeast on the PB region. Figure 4.23 shows the complete set of available directions of σH max in the North and Central American region, reflecting the first-order stress imposed on the crust by large-scale tectonic processes. Figure 4.24 shows a regional perspective of all the available stress indicators in the PB. Classical stress indicators, shear wave splitting, and structural style have been combined. All the stress indicators are compressive, an observation initially noticed by Zoback (1992) as a general pattern for midplate provinces. In the PB, the structural style accommodates the present state of stress, with the most convincing feature being the co-alignment between σH max azimuth and the strike of the main faults. Figure 4.25 shows a model reconstruction of the azimuthal distribution of σH max in the San Andres dolomites at a depth of 4500 ft in the Vacuum field area. The plot is built using all available indicators: (1) data from the World Stress Map project (Mueller et al., 2000) on the first-order
σH max , (2) azimuthal directions of the fast shear wave obtained from two
99
multicomponent vertical seismic profiles (VSP) acquired by the RCP at Vacuum field (Mattocks, 1998; Michaud, 2001), (3) azimuth of σH max obtained from borehole breakout analysis on the WS-2-26 well (Scuta, 1997), and (4) fault geometry and fault displacement data obtained from 3D seismic in the area of the carbonate shelf. After building the geometry of the San Andres dolomites, the main faults were introduced along with measured vertical offsets ranging from zero to a maximum value of 350 ft. Then stresses were imposed on the system: a compressive stress σH max of 70 MPa with an azimuth of 120°N, a σ H min of 33 MPa (source of data: World Stress Map), and a vertical lithostatic stress σV of 33 MPa obtained from density logs in the area of interest. Finally, the distribution of σH max was modeled using Poly3D (Thomas, 1993). The results show that the uniform direction of compressive stress (120°N) can be locally modified in the proximities of faults with significant vertical displacement. However, the state of stress in the time-lapse area appears to be uniform, with principal direction of σH max at 120°N. The modeled distribution of σH max is based on an isotropic dolomite rock, thus the effects of azimuthal anisotropy on stress, caused by aligned fractures, are not taken into account. In addition, the effects of pore pressure in equant pores and in fractured zones are not included, thus in this approximation effective stress is equal to compressive stress. As it will be shown in the rest of this work, one of the significant observations made at Vacuum field is the fact that, by using shear wave splitting from 3D surface seismic, the San Andres dolomites showed azimuthal anisotropy in some areas, thus making Figure 4.25 only a first-order reconstruction of the state of stress.
100
40 N
VF 30 N
NORTH 120 W 20 N
10 N
0 110 W
100 W
90 W
80 W
FIG. 4.23: Present day stress indicators in the North and Central American regions. Stress data are from the World Stress Map project (Mueller et al., 2000).
101
NORTH 100 km NWS
MIDLAND BASIN
VF
ES
NM TX
DELAWARE BASIN DP
CBP MOB
TX MEXICO
FIG. 4.24: Present day stress indicators in the Permian Basin. Arrows (blue) show azimuth of maximum horizontal stress, which is compressive in all cases. Notice the consistency between present stress measurements and the basement faults (black lines) in the CBP. Stress indicators comprise all the classical sources + shear wave splitting at Vacuum field. Stress data are from the World Stress Map project (Mueller et al., 2000).
102
INJECTOR PRODUCER CVU94 CVU196 CVU194
CVU97
CVU100
CVU200 VGWU127
CVU93 CVU197
NO RT H 100 0f t
WS2-26
CVU99
Fig. 4.25: Azimuth of maximum horizontal stress in the San Andres dolomites of Vacuum field at a depth of 4500 ft. The top figure shows the available measurements of σHmax at three well locations (blue). The lower figure shows the results of modeling the lateral distribution of σHmax on the basis of all the existing stress indicators, the geometry and displacements of the faults (red lines), and isotropic elastic constants of a dolomite rock. Symbols for CO2 injectors and producers refer to the time-lapse experiment monitored by the RCP with multicomponent reflection seismology.
103
4.6
SUMMARY The reconstruction of the state of stress in the crust is an important aspect of any
program intended to monitor the time evolution of at least three variables: fluid pressure, temperature, and fluid content. Any engineering operation, such as fluid injection and extraction, has the potential to alter the local state of stress, which in turn is linked to first-order stress distributions set by large-scale tectonic processes. Stress is rarely isotropic in its distribution, thus the effective elastic properties of a geologic material subjected to anisotropic stress are structurally anisotropic. Fractures in particular are a cause of structural anisotropy and, when exposed to pore pressure changes, are capable of changing the local state of stress in magnitude and direction. Several types of stress indicators are used today. Among them, shear wave polarization has the potential to detect the time-lapse variation of azimuthally anisotropic rocks where the magnitude and the orientation of fracture systems is altered by pore pressure changes. A review of all the available stress indicators in the PB and at Vacuum field shows that the measurements of present σH max are consistent with large-scale tectonic processes that are located far away from the PB but still influence this region. On a local scale, the rock-fluid system in the San Andres dolomites, if considered within the context of engineering activities linked to production of hydrocarbons, has the potential to be a source of second order stress field. For the sake of monitoring the evolution of the stress field in the San Andres with multicomponent reflection seismology, the two most important variables are the variation of pore pressure and the symmetry of the effective medium.
104
CHAPTER 5
P-WAVE POSTSTACK ANALYSIS
THE DETERMINIST SHOULD NOT PROTEST BUT EXPERIMENT. MAX BORN 5.1
INTRODUCTION In spite of the efforts in acquisition and processing to obtain perfect match and
repeatability, two time-lapsed seismic sections exhibit differences in time, amplitude, frequency, and phase in the static portion above the reservoir. The magnitude of the changes may be comparable to the differences in the dynamic reservoir section, thus making time-lapse imaging and its rock physics implications questionable. To obtain meaningful differences of time-lapsed volumes, crossequalization schemes were developed, forcing the static portion of the repeated data to match the static portion of the baseline data. The approach is not new (e.g. Ross et al., 1996) although application to time-lapse shear waves and layer stripping is unique (chapter 6). In this chapter, the general techniques for signal crossequalization are discussed, irrespective of the seismic mode of wave propagation. Simple models are built to show the sensitivity of the differencing process to each one of the crossequalization filters. Finally, the two time-lapse compressional volumes from the 3D survey at Vacuum field are crossequalized, then differenced in various domains, revealing time-lapse anomalies in velocity, amplitude, and frequency. 5.2
SIGNAL CROSSEQUALIZATION The idea of measuring time-dependent changes of a particular physical property is well
established in several disciplines: time-lapse tomography in medical imaging, the multiple scans of a satellite over the same region of the Earth, and many more. One aspect common to all these techniques is to ensure replication of what has not, or should not, have changed with time. In
105
time-lapse reflection seismology, the baseline and all the additional monitoring surveys should be acquired and processed with repeatability in mind, but, even in the best scenarios, significant differences occur between the baseline and repeated surveys. Hence, the direct difference between time-lapse volumes may result in seismic differencing errors, which may be corrected using equalization schemes. Crossequalization is a poststack processing technique applied to the repeat data so that time-lapse 3D imaging is possible. Crossequalizing the base and repeated surveys requires us to generate one or more wavelet operators which, once convolved with the repeated data set, will match the two surveys. Operators are generated as match filters to equalize time shifts, amplitude, frequency and phase. Operators are calibrated on a static section of the surveys, where changes are not expected, and intentionally exclude the dynamic section, where changes are expected. In theory, a successful application of crossequalization schemes would produce a difference between the two surveys equal to zero in the static section, and equal to the time-lapse change in the dynamic section. Equalizing time series is a correction methodology consisting of four separate elements: (1) time-shift corrections, (2) amplitude or energy balancing in time domain, (3) spectral equalization, and (4) phase matching. Each separate correction is evaluated below using simple models and limited portions of the Vacuum field data. TIME
CORRECTIONS:
Obtaining a global time-alignment of common reflectors
between the baseline and the repeated survey is crucial to interpret correctly the amplitude anomalies in the difference volume (difference = repeated - base). Figure 5.1 shows a wavelet extracted from a static portion of the Vacuum field P-wave data set delayed by 1, 2, 4 and 6 samples (sampling rate is 2 msec). In the lower part of the figure, the differences between the base and the delayed wavelets are plotted. A 2-sample delay results in an amplitude difference similar to the amplitude of the base wavelet. AMPLITUDE EQUALIZATION:
Time-lapse acquisition and processing focus mostly on
prestack repeatability in amplitude and energy distribution for the final stacks. Nonetheless, differences in amplitude are a reality even in carefully controlled conditions. Simple differences in amplitude scaling of the entire volumes may be expected, as well as more complex time-variant scaling functions embedded in time-lapse data. The objective of poststack amplitude and energy equalization is to remove time-constant and time-variant scaling differences to enhance the repeatability of the time-lapse seismic volumes so that their subtraction results in zero energy in the static section. An example of the effects of different scalar coefficients applied to a wavelet is
106
amplitude -4
-3
-2
-1
0
1
2
3
4
0
wavelets 10
Base 1 sample shift
time (msec)
20
2 sample shift 30
4 sample shift 6 sample shift
40
50
60 -4
-3
-2
-1
0
1
2
3
4
0
difference wavelets 10
time (msec)
20
30
1 sample shift 2 sample shift
40
4 sample shift 50
6 sample shift
60
FIG. 5.1: Effects of time shift on the differencing process. A wavelet from the Vacuum field 3D survey is time-shifted by one, two, four, and six samples (top). The differences between the base and the time-shifted wavelets are plotted in the lower part. For a two-sample shift, the amplitude of the difference is comparable to the amplitude of the original wavelet. given in Figure 5.2, where the same base wavelet shown in Figure 5.1 is scaled by 80%, 60%, 40% and 20%. The lower part of Figure 5.2 shows the differences between the base and the scaled wavelets. Significant amplitude anomalies result from subtracting incorrectly scaled versions of the same wavelet. Additional and more complex erroneous patterns may be generated if different time-variant scaling functions embedded in the data are not recognized and corrected. SPECTRAL
BALANCING:
Differencing traces with different bandwidths causes
significant differencing errors. Figure 5.3 shows unit amplitude Ricker wavelets with different peak frequencies (30, 35, 40, 45, and 50 Hz), and the subtraction of the higher frequencies from the base 30 Hz wavelet. A change of the central frequency of only 5 Hz may cause a 10% residual amplitude in the differencing process. PHASE MATCHING:
Figure 5.4 shows the effects of phase rotation on a base wavelet
from the Vacuum field 3D survey, and the differences between base and phase-rotated wavelets. Differencing without phase matching results in erroneous residual reflector energy. A phase
107
amplitude -4
-3
-2
-1
0
1
2
3
4
0
wavelets 10
Base wavelet
time (msec)
20
80% amplitude
30
60% amplitude
40
40% amplitude 20% amplitude
50
60 -4
-3
-2
-1
0
1
2
3
4
0
difference wavelets
time (msec)
10
80% amplitude
20
60% amplitude
30
40% amplitude
40
20% amplitude
50
60
FIG. 5.2: Effects of amplitude scaling on the differencing process. A wavelet from the Vacuum field 3D is scaled by 80%, 60%, 40%, and 20% (top). The differences between the base and the scaled wavelets are plotted in the lower part. mismatch of only 10° to 20° can generate residual reflector amplitude of 10% to 20%. As Ross et al. (1996) pointed out, the human eye cannot detect phase mismatches lower than about 20°, thus there is the need for an efficient and accurate phase matching algorithm. Among the four possible sources of time-lapse imbalance (time, amplitude, frequency, and phase), phase is the most sensitive to small corrections, and it is practically impossible to obtain good results in crossequalization without phase matching.
108
amplitude -1
1
0 wavelets
-1
30 Hz 20
40
40 time (msec)
time (msec)
1
difference wavelets
35 Hz 40 Hz 45 Hz 50 Hz
20
amplitude 0
60
60
80
80
100
100
FIG. 5.3: Effects of spectral unbalancing on the differencing process. Ricker wavelets of unit amplitude (left) have peak frequency of 30 (base wavelet), 35, 40, 45, and 50 Hz. The differences between the base and the higher frequency wavelets are plotted on the right.
amplitude 0
-1
1
-1
on rotati hase on 60° p rotati e s a h 30° p
20
40 20° p hase rotati on 10° ph ase ro tation
80
100
time (msec)
time (msec)
40
60
1
difference wavelets
wavelets 20
amplitude 0
60
80
se 0 pha
100
FIG. 5.4: Effects of phase rotation on the differencing process. A unit amplitude wavelet from the Vacuum field 3D is rotated in phase by 10°, 20°, 30°, and 60° (left). The differences between the base and the phaserotated wavelets are plotted on the right. A phase shift of only 10° to 20°, may result in 10% to 20% amplitude difference.
109
5.3
CROSSEQUALIZATION OF VACUUM P-WAVE DATA The ultimate objective in signal crossequalization is to cancel energy in the static portion
of the difference section and to detect anomalies in the reservoir. Thus, the amount of residual energy in the difference volumes is a measurement of the effectiveness of the crossequalization filters. Figure 5.5 shows the reasons for crossequalization at Vacuum field. Three panels of timelapse compressional wave data from the 3D survey refer to pre-injection, post-injection, and difference. Data are obtained from prestack processing and final migration, with no crossequalization applied. The static section above the reservoir has a considerable amount of residual energy which has not been cancelled by the subtraction process, while ideally this should result in no residual energy. On the contrary, there is more anomalous energy in the static section than in the reservoir. The static portion of the data in Figure 5.5 is analyzed in Figure 5.6. The lower part of the figure shows amplitude spectra of the pre- and post-injection data, as well as their difference. While there is certainly a general level of good repeatability, there are also amplitude differences on the order of 20% of the original amplitude for a given frequency. Figure 5.7 shows the time-shift expression of the lack of repeatability in the P-wave Vacuum data. Three timelapse events (A, B, and Queen) from the static portion of the P-wave data are crossplotted. A perfect repeatability in reflection time would correspond to data falling along the 45° diagonal of the plots. The departure from the diagonal is a measurement of the time-lapse uncertainty of the data in time domain. Crossequalization is intended to remove the differences in the static portion shown in Figure 5.5, 5.6, and 5.7. AMPLITUDE EQUALIZATION:
Amplitude was equalized in a two-step process. First in
a global sense, I used RMS amplitude ratios from the entire volumes for the base and repeated survey (Figure 5.8). Then amplitudes were equalized on a trace-by-trace basis among identical reflectors from the two surveys. The time window length over which the equalization operators are built is the most sensitive parameter. Multiple, short and overlapping matching windows give better results compared to single, long, matching windows. The best results were obtained with seven 100 msec time windows, 50% overlapping, applied in a layer stripping form, starting from the top of the section and moving toward the reservoir zone. For each time window, a matching
110
filter is computed and then convolved with the repeated survey to generate the crossequalized volume. Figure 5.8 shows the results of amplitude equalization for the entire P-wave time-lapse data set (global equalization). The repeatability in RMS amplitude of the static section has improved to a difference of less than 1%. The reservoir section and the static section below the reservoir were not included in the equalization process. Figure 5.9 shows the results of the entire amplitude matching process (global + trace by trace) for the same data of Figure 5.5. A considerable amount of residual energy has been cancelled in the static section, and some residual amplitude begins to appear in the reservoir zone. PHASE MATCHING:
After amplitude equalization, data were phase matched in a layer
stripping mode starting from the top of the section toward the reservoir. Three time windows were used, 200 msec in length, 50% overlapping. A phase match filter was computed for each trace pair (base and repeated) in a given time window, and then convolved with the postinjection trace. Figure 5.10 shows the results of phase matching the data of Figure 5.9. TIME CORRECTIONS AND SPECTRAL BALANCING:
Figure 5.11 and 5.12 show the
repeatability of the static section in the frequency domain, and for the same three reflectors analyzed in Figure 5.7, after phase matching. In both domains, crossequalization has increased repeatability with respect to the initial conditions of Figure 5.5, 5.6 and 5.7. The overall repeatability for P-waves after crossequalization can be estimated within one msec (half of a sample) in reflection time, and within 5% of any original reflector amplitude. Additional corrections in reflection time and spectral balancing were attempted but did not improve the results of Figure 5.10, 5.11 and 5.12.
111
Inline 68 Post-injection
Pre-injection CVU200
S
CVU97
CVU200
CVU194
N S
CVU97
Difference CVU200
CVU194
NS
CVU97
CVU194
N msec
400
A
B Yates
Queen
500
600
GB USA
700 CY1
FIG. 5.5: Example of residual energy in the static portion of the time-lapse compressional wave data from Vacuum field. The rectangular box delimits top and bottom of the reservoir. Pre-injection, post-injection, and difference (= repeated – base) sections were prestack processed and migrated according to the flow in Figure 1.4. No poststack enhancement was applied. The amount of residual energy in the static section is locally higher than the anomalies in the reservoir section.
112
Inline 68 Post-injection
Pre-injection CVU200
CVU97
CVU200
CVU194
CVU97
Difference
N S
S
CVU200
CVU194
CVU97
CVU194
NS
N msec
400
500
600
Post-injection
Pre-injection CVU200
CVU97
CVU200
CVU194
CVU97
Difference
N S
S
CVU200
CVU194
CVU97
CVU194
NS
N Hz
20
40
60
amplitude zero
amplitude max
zero
amplitude difference max
min
zero
max
FIG. 5.6: Repeatability of the static portion of Figure 5.5 in time and frequency domain. Spectral cross-sections (lower part of the figure) were obtained by applying spectral decomposition techniques to the time-domain data (upper part of the figure). While there is generally a good level of repeatability, some amplitude differences are about 20% of the original reflector amplitude. Notice that most of the static residual energy is concentrated between 30 and 50 Hz.
113
FIG. 5.7: Crossplots of three time-lapse reflectors (A, B, and Queen) from the static portion of the Vacuum field P-wave data.
er ro r e sa m pl -1
0
er ro r
sa m pl e
er ro r
+ 1
Post-injection TWT (msec)
Event A
-1
sa m pl e
Post-injection TWT (msec)
er ro r
+ 1
sa m pl
0
e
Event B
er ro r
er ro r
Pre-injection TWT (msec)
-1
sa m pl
e
Post-injection TWT (msec)
er ro r
+
1
0
sa m pl e
Queen
er ro r
er ro r
Pre-injection TWT (msec)
Pre-injection TWT (msec)
114
1.6
P-wave RMS Amplitudes Before Crossequalization
1.6
P-wave RMS Amplitudes After Crossequalization
Reservoir
Reservoir 1.2 RMS Amplitude
RMS Amplitude
1.2
0.8
0.4
Base RMS
0.8
0.4
Repeat RMS
Repeat RMS 0.0 200
400
Base RMS
600 Time (msec)
800
1000
0.0 200
400
600
800
1000
Time (msec)
Fig. 5.8: P-wave average RMS amplitude as a function of reflection time for the pre- and postinjection surveys at Vacuum. The plot on the left refers to data before any crossequalization scheme was applied. The plot on the right shows distribution of amplitudes after a global amplitude equalization filter was applied to the post-injection data.
115
Inline 68 Post-injection
Pre-injection CVU200
S
CVU97
CVU200
CVU194
N S
CVU97
Difference CVU200
CVU194
NS
CVU97
CVU194
N msec
400
A
B Yates
Queen
500
600
GB USA
700 CY1
Fig. 5.9: Intermediate results in the crossequalization process after amplitude matching (global + trace by trace) applied to the data of Figure 5.5.
116
Inline 68 Post-injection
Pre-injection CVU200
S
CVU97
CVU200
CVU194
N S
CVU97
Difference CVU200
CVU194
NS
CVU97
CVU194
N msec
400
A
B Yates
Queen
500
600
GB USA
700 CY1
FIG. 5.10: Final results in the crossequalization process after amplitude matching (Figure 5.9) and phase matching were applied to the data of Figure 5.5.
117
Inline 68 Post-injection
Pre-injection CVU200
CVU97
CVU200
CVU194
CVU97
Difference
N S
S
CVU200
CVU194
CVU97
CVU194
NS
N msec
400
500
600
Post-injection
Pre-injection CVU200
CVU97
CVU200
CVU194
CVU97
Difference
N S
S
CVU200
CVU194
CVU97
CVU194
NS
N Hz
20
40
60
amplitude zero
amplitude max
zero
amplitude difference max
min
zero
max
Fig. 5.11: Repeatability of the static section of Figure 5.10 in time and frequency domain after crossequalization. Compare this plot to Figure 5.6 to see the effects of crossequalization.
118
Fig. 5.12: Repeatability of three reflectors (A, B, and Queen) from the static section of Figure 5.10 after application of the crossequalization scheme. The crossplots should be compared to Figure 5.7 to see the effects of crossequalization.
er ro r e sa m pl -1
0
sa m pl
er ro r
e
er ro r
+ 1
Post-injection TWT (msec)
Event A
-1
sa m pl e
Post-injection TWT (msec)
er ro r
+ 1
sa m pl
0
e
Event B
er ro r
er ro r
Pre-injection TWT (msec)
-1
sa m pl
e
Post-injection TWT (msec)
er ro r
+
1
0
sa m pl e
Queen
er ro r
er ro r
Pre-injection TWT (msec)
Pre-injection TWT (msec)
119
5.4
P-WAVE TIME-LAPSE ANOMALIES The reservoir time-lapse anomalies of P-wave data at Vacuum field are presented in
terms of change of reservoir interval velocity (1), and reflection amplitude (2). ANOMALIES
IN
INTERVAL
VELOCITY:
Reflectors in the reservoir zone and
immediately below were affected by the velocity changes that took place in the reservoir caused by CO2 injection. In time-lapse, a reflector at the bottom of the dynamic interval is mapped on the repeated data set as being slower or faster than the equivalent reflector in the base survey. The difference in interval reflection-time between the base and repeated horizons is proportional to the velocity difference in the reservoir. Figure 5.13 shows interval velocity increase and decrease in the reservoir section between the base and repeated survey after crossequalization. ANOMALIES IN REFLECTION AMPLITUDE
( T I M E D O M A I N ) : Differencing seismic
volumes after crossequalization resulted in the creation of a three-dimensional distribution of seismic amplitude anomalies (= repeated – base). Figure 5.14 shows three cross-sections extracted from the time-lapse P-wave amplitude difference volume. The sections have a northsouth trend and cross injector and producer wells. In general, the distribution of amplitude anomalies appears to confirm the velocity anomalies of Figure 5.13 (interpretation of the anomalies is the subject of chapter 7).
120
INJECTOR
N80
PRODUCER
CVU94
N55
CVU196
CVU194
CVU97
90
NO RT
H
N69
90
CVU100
CVU93
80
80
CVU200
S80
CVU197
70
70
IN LI N E
S69 CVU99
60
N LI SS O CR
E
60 55 0
ft
S55 50
50
P-wave velocity change zero
-5%
Fig. 5.13: Time-lapse changes in compressional velocity (= post – pre injection) in the San Andres reservoir at Vacuum field. Reservoir top and bottom are the top of the Upper San Andres Formation (USA) and a marker at approximately 4800 feet depth (CY1). Black lines are fault planes cutting through the reservoir section.
121
CVU93
N55
CVU99
CVU197
S55 600
msec
USA
CY1
720 CVU194
N69
CVU97
CVU200
S69
600
msec
USA
CY1
720 CVU94
N80
CVU196
CVU100
S80
600
msec
USA
CY1
720
FIG. 5.14: Time-lapse amplitude difference cross-sections (= repeat – base) from the P-wave data volumes at Vacuum field. Cross-section traces are indicated along the map border in Figure 5.13.
122
5.5
SUMMARY Many disciplines attempt to reconstruct the dynamic behavior of physical properties by
using time-lapse measurements. Once the measurements have been acquired and processed, it is necessary to apply techniques capable of enhancing the differences in the dynamic zone. In reflection seismology, crossequalization minimizes the lack of repeatability which may affect timelapse data. The assumption is that a portion of the data was not affected by any time dependent change, thus digital filters are constructed to equalize the time-lapsed data sets in the static section, and then applied to the dynamic section. In this chapter, the effects of time-lapse data mismatches were reviewed using simple examples. In addition, the need to apply crossequalization operators to P-wave data at Vacuum field was shown. Finally, after application of matching filters, P-wave anomalies in velocity and amplitude at Vacuum were presented.
123
CHAPTER 6
S-WAVE POSTSTACK ANALYSIS
FALSE FACTS ARE HIGHLY INJURIOUS TO THE PROGRESS OF SCIENCE, FOR THEY OFTEN ENDURE LONG. BUT FALSE VIEWS, IF SUPPORTED BY SOME EVIDENCE, DO LITTLE HARM, FOR EVERYONE TAKES A SALUTARY PLEASURE IN PROVING THEIR FALSENESS. CHARLES DARWIN 6.1
INTRODUCTION Vertical fractures are the most probable cause of azimuthal anisotropy in the San Andres
dolomites. A primary objective of the Vacuum field experiment was the seismic detection of fracture parameters in the San Andres reservoir and the change induced by CO2 injection. The analysis of normal-incidence shear wave data in this chapter provides an estimate of reservoir fracture density and orientation, as well as their evolution over time. The analysis required an application of Winterstein and Meadows (1991a, b) layer stripping technique, implemented following Thomsen et al. (1999). As a first outcome, a coarse sequence of azimuthally anisotropic layers at Vacuum field was revealed. Then, the anisotropic effects above the San Andres reservoir were stripped away, and spatially varying fracture density and orientation of the carbonates were quantified. Layer stripping was applied independently to the pre- and post-injection shear wave data sets, so that the time-lapse evolution of fracture density and orientation could be studied. As a final poststack enhancement step, a crossequalization routine, comparable to the P-wave case, was calibrated on the static section above the San Andres reservoir and applied to the shear wave principal volumes. The final, interpretable products of this analysis are time-lapse fracture density maps (shear wave splitting γ), shear wave polarization and velocity maps, as well as shear wave amplitude and differential attenuation cross sections.
124
6.2
TIME-LAPSE 2CX2C SHEAR WAVE DATA In the prestack processing sequence of Figure 1.4, a first Alford rotation was applied to
the shear wave CMP gathers. The underlying assumption is that the four component gathers exhibit time- as well as space-invariant azimuthal anisotropy, implying that there is only one natural coordinate system in the entire rock column. At Vacuum field, this coordinate system was estimated as 118°N (direction of S1 particle motion) and 28°N (direction of S2 particle motion). After this step, data processing continued all the way to produce normal-incidence 2Cx2C shear wave stacks, an example of which is shown in Figure 6.1 from the post-injection volumes. A note on nomenclature is required. The first global Alford rotation applied during prestack processing put the shear wave data in the best natural coordinate system that could be detected, albeit depth-invariant. Sources and receivers are now effectively rotated to produce a fast (S1) and a slow (S2) shear mode. When horizontal particle motion at the source is along the 118°N, and is recorded by a horizontal geophone oriented with the same azimuth, the resulting trace is labeled S1H1. If the same particle motion is recorded by a horizontal geophone oriented on the 28°N azimuth, the resulting trace is S1H2. Thus, for horizontal source particle motion on an azimuth of 28°N, two traces are recorded: S2H1 and S2H2. It follows that S1H1 and S2H2 are the principal components (fast and slow shear waves), while S1H2 and S2H1 are the crossdiagonal components. Figure 6.2 shows the time-lapse distribution of energy as a function of reflection time for the 2Cx2C stacked volumes. The initial prestack Alford rotation has successfully minimized the reflection energy in the crossdiagonal components, although additional energy is expected to be recovered in the principal components by using depth-dependent four-component rotation and layer stripping. Additionally, in Figure 6.2, a comparison of the distribution of energy between pre- and post-injection shows the need for time-lapse crossequalization of the data in the static portion.
125
Inline 68 2Cx2C S1H1
S1H2
msec
800
1000
1200
1400
1600
USA CY1
1800
S2H1
S2H2
msec
800
1000
1200
1400
1600 USA CY1 1800
FIG. 6.1: Normal incidence 2Cx2C shear wave stacks after prestack processing. The example is from the post-injection volumes. At this stage, shear wave data are rotated in a single, depth-invariant, natural coordinate system (118°N for S1H1 and 28°N for S2H2).
126
Pre-injection 2Cx2C before layer stripping 4
RMS amplitude
3
2
San Andres Reservoir
S1H1
S1H2
S2H2
1
S2H1
0
800
1000
1200
1400
1600
1800
Reflection two-way-time (msec)
Post-injection 2Cx2C before layer stripping 4
San Andres Reservoir
RMS amplitude
3
S1H1 2 S2H2 1
S1H2 S2H1
0
800
1000
1200
1400
1600
1800
Reflection two-way-time (msec)
FIG. 6.2: Distribution of energy as a function of reflection time for the 2Cx2C data volumes. Top diagram refers to the pre-injection, lower diagram refers to the postinjection volumes.
127
6.3
TIME-LAPSE LAYER STRIPPING AND CROSSEQUALIZATION Figure 6.3 shows the time delay between the shear wave principal components for the
pre- and post-injection data sets, and clarifies the need for layer stripping. In rock columns where azimuthal anisotropy is not constant with depth, it is possible to detect anisotropy boundaries, defined as locations where shear wave polarization changes. When a wave enters a region with different natural polarization directions, the change is instantaneous. On the other hand, the recorded wavelets change slowly, and shear wave splitting cannot be detected unless the two S-waves have traveled long enough in the birefringent medium, accumulating enough time delay. For these reasons, a change in the slope of principal components time delay curves tends to be a robust indicator of anisotropy boundaries. In contrast, calculated azimuth angles as a function of depth are comparatively more scattered indicators of polarization change. In summary, the search is for a model of the rock column made of discrete layers of azimuthal anisotropy. In each layer, S-wave polarization is assumed to remain constant. The change in polarization occurs discontinuously at layer boundaries. Additionally, the time delay
Principal components time delay (msec)
San Andres Reservoir A1
A2
A3
Post injection
20
10
0 Pre injection -10
800
1000
1200
1400
1600
1800
Reflection two-way-time (msec)
FIG. 6.3: Time delay between the shear wave principal components as a function of reflection time. Error bars are the standard deviations on time delay. At this stage, data are in a single, depth-invariant, natural coordinate system. The shape of the curve suggests the presence of at least three discrete layers with different characteristics of azimuthal anisotropy (A1, A2, and A3).
128
between the principal components in a given layer follows a monotonic increase from zero (at the top) to a finite value (at the bottom). Figure 6.3 shows three interpreted anisotropy layers at Vacuum field (A1, A2, A3), and the position of the anisotropy boundaries. Layers A1 and A2 have to be stripped away to reveal the anisotropic characteristics of A3, which is the San Andres reservoir. Following equation 2.44 (Thomsen et al., 1999), the steps for stripping away the anisotropic effects of layer A1 are: (1) rotate the 2Cx2C data into the natural coordinate system of layer A1 (2) apply a static shift to the cross-diagonal components ( ∆t 1 ), and to the slow shear wave component ( 2∆t 1 ) (3) equalize the shear wave components using a balancing filter As in Winterstein and Meadows (1991a, b), the best rotation angle and shear wave polarization were estimated, trace by trace, using Alford (1986). The best results were obtained by searching for the rotation angle that minimizes the crossdiagonal energy in a 200 msec time window above the anisotropy boundary. Figure 6.4 shows the anisotropic parameter γ computed from the time delay between the S1H1 and S2H2 principal components, and the polarization direction of the S1H1 component, at the A1-A2 interface after residual rotation. Figure 6.5 shows an example of the effects of residual rotation and time-shifting on the four shear components of the A1 layer. Figure 6.6 shows the general behavior of the principal components time delay after the anisotropic effects of A1 have been stripped away. The second discrete interval A2 shows no time delay and, with respect to the effects of shear wave birefringence, it was interpreted as behaving isotropically. No additional rotation and time shift were applied to the data between 1100 and 1600 msec. The third step in the layer stripping scheme of Thomsen et al. (1999), involving equalization of the shear components at the interface to compensate for differential attenuation, was moved from the A1-A2 interface to the A2-A3 interface. The reason was simply in the interest of a clean reservoir section not affected by anisotropic effects in the higher intervals. Figure 6.7 shows an example of shear wave balancing at the A2-A3 anisotropy boundary. The way B 1SF was computed and applied is summarized here below. The two principal component traces are: (6 .1 )
(t ) = w (t ) ⊗ e F (t ) u 22 (t ) = w (t ) ⊗ e S (t )
u
11
129
This means that the same wavelet w (t ) is convolved with the Earth’s impulse response for the fast ( e F ), and slow ( e S ) shear wave, containing the propagation and attenuation properties of a particular medium in the two principal directions of anisotropy. For the purpose of eliminating the differential anisotropic effects we could write equation (6.1) such that the difference in the two time series resides in the wavelets only: (6 .2 )
u 11 (t
) = w F (t ) ⊗ e (t ) u 22 (t ) = w S (t ) ⊗ e (t )
This means to impose a single Earth’s impulse response ( e ), and two different mode-related wavelets ( w F and w S ). The advantage is in the fact that wavelets can be derived from the two principal components time series using conventional wavelet extraction techniques, and their differences analyzed. Thus a filter B 1SF is obtained as: (6 .3 )
w
F
= B 1SF ⊗ w
S
(t )
which implies that the filter is: (6 .4 )
B 1SF
= w
F
(t ) ⊗
(w (t )) S
−1
Then the slow shear wave time series is convolved with the B 1SF to obtain a balanced S2 trace. In the case of the A2-A3 anisotropy boundary, wavelets were extracted for the S1H1 and S2H2 modes after layer stripping, trace by trace, such that a volume of B 1SF was computed. Figure 6.7 shows the two extreme points of the process, before and after mode balancing. At the end of the layer stripping procedure, the important aspect to notice is that S1H1 and S2H2 at the A2-A3 interface have the same reflection time. The 2Cx2C data have been rotated into the natural coordinate system of the A1 layer. These polarization directions (Figure 6.4) are maintained in the A2 layer because no additional azimuthal anisotropy could be detected. Also, the reflection amplitude of the two principal components at the A2-A3 interface has been equalized with the application of the mode balancing filter. From the top of A3, continuing down into the reservoir section, note the development of time delay between S1 and S2 (e.g. Figure 6.7), revealing azimuthal anisotropy in the San Andres dolomites. Then, an additional Alford rotation was done using the 2Cx2C time-lapse data in the A3 layer, searching for the natural coordinate system of the San Andres dolomites.
130
Figure 6.8 shows the time-lapse distribution of energy as a function of reflection time for the 2Cx2C stacked volumes after layer stripping. Comparing Figure 6.8 to Figure 6.2, the improvement given by poststack four-component rotation and layer stripping is noticeable, with less energy in the crossdiagonal volumes of Figure 6.8. A time-lapse comparison of the two diagrams in Figure 6.8, though, shows that the principal components are not equalized in the static section above the San Andres reservoir. Thus, a crossequalization scheme, similar to the one used for P-waves (chapter 5), was applied to the principal components. The best results were obtained with global amplitude equalization and phase matching. All the other equalization steps did not improve the repeatability of the data. Figure 6.9 shows the energy distribution of the principal components after crossequalization, with a noticeable improvement in time-lapse repeatability.
131
INJECTOR PRODUCER CVU94
NO RT
H
Pre-injection CVU196
CVU194
CVU97
90
80
90
CVU100
CVU93
80
CVU200 CVU197
70
70 IN LI N E
N LI SS O R C
CVU99
E
60
60 55 0
ft
50
50
Shear wave splitting γ (%)
0
2
4
6
8
10
INJECTOR PRODUCER CVU94
CVU196
CVU194
CVU97
90
NO RT
H
Post-injection
80
90
CVU100
CVU93
80
CVU200 CVU197
IN LI N E
70
70
N LI SS O CR
CVU99
E
60
60 55 0
ft
50
50
FIG. 6.4: Time-lapse representation of the lateral distribution of shear wave splitting γ, for the whole layer A1, at the A1-A2 anisotropy boundary. Arrows show the azimuthal orientation of the S1H1 polarization.
132
Before layer stripping S
Inline 69
N
msec
800
1000
A1 A2
1200
After layer stripping S
Inline 69
N
msec
800
1000
A1 A2
1200
FIG. 6.5: Example of the effects of layer stripping. Each group of four traces represents the 2Cx2C shear wave components (from left to right: S1H1, S1H2, S2H1, S2H2). Alford rotation transformed the traces in the top panel into the traces in the lower panel. Additionally, a time shift ∆t was applied to the S1H2 and S2H1, and 2∆t to the S2H2 components.
133
Principal components time delay (msec)
San Andres Reservoir A1
A2
20
A3
Post injection
10
0 Pre injection -10
800
1000
1200
1400
1600
1800
Reflection two-way-time (msec)
FIG. 6.6: Time delay between shear wave principal components after layer stripping. The three layers (A1, A2, and A3) are now in their own natural coordinate system.
134
Before balancing the shear wave principal components S
Inline 69
N
1500
A2 A3
1600
Top San Andres
1700
1800 After balancing the shear wave principal components S
Inline 69
N
1500
1600
A2 A3
1700
Top San Andres
1800
FIG. 6.7: Example of full layer stripping. The trace couples in the top panels are shear wave principal components (S1H1 and S2H2) before layer stripping. In the lower panel, traces have been rotated into their natural coordinate system, time-shifted, and mode-balanced. As a result, at the A2-A3 interface, principal components have the same reflection time and very comparable amplitude. Notice the development of time delay between S1H1 and S2H2 from the A2-A3 interface downward, revealing the presence of azimuthal anisotropy in the reservoir section.
135
Pre-injection 2Cx2C after layer stripping 4
RMS amplitude
3
2
San Andres Reservoir
S1H1
S2H2
1
S1H2 S2H1 0
800
1000
1200
1400
1600
1800
Reflection two-way-time (msec)
Post-injection 2Cx2C after layer stripping 4 San Andres Reservoir
RMS amplitude
3
S1H1 2 S2H2 1
S1H2 S2H1
0
800
1000
1200
1400
1600
1800
Reflection two-way-time (msec)
FIG. 6.8: Distribution of energy as a function of reflection time for the 2Cx2C data volumes after layer stripping.
136
Pre- and Post-injection principal components after crossequalization 4 San Andres Reservoir
RMS amplitude
3 S1H1 pre and post injection 2
1 S2H2 pre and post injection 0
800
1000
1200
1400
1600
1800
Reflection two-way-time (msec)
FIG. 6.9: Shear wave principal components energy distribution as a function of reflection time after layer stripping and time-lapse crossequalization.
6.4
SHEAR WAVE TIME-LAPSE RESULTS Several final products can be interpreted from a shear-wave time-lapse survey. A
summary of the various levels of interpretation achievable with multicomponent data is given by Lynn (1996). The core issue in this study is to usefully represent azimuthal anisotropy and its time-lapse evolution. Interpretation of the data will be the subject of chapter 7. Figure 6.10 shows the time-lapse change (= post – pre) in the reservoir interval velocities of the two shear modes. Figure 6.11 shows the anisotropic parameter γ (or shear wave splitting) for the pre- and post-injection survey. The overlying arrows represent the azimuthal direction of polarization of the fast shear wave (S1H1 component) in the San Andres, resulting from the final four-component rotation in the reservoir section. Figure 6.12 shows the computed time-lapse change (= post – pre) in shear wave splitting γ and the location of shear wave polarization change. Shear wave polarization is effectively an amplitude related measurement derived from four-component Alford rotation. Velocities and shear wave splitting γ are derived from reflection time and horizon picking at the top and bottom of the San Andres section, but they are also affected by amplitude distribution because of Alford rotation.
137
Thomsen (1988) established the basis for detection of lateral variation of azimuthal anisotropy using normal-incidence reflection coefficients of shear wave principal components. Since the most likely cause of changes in azimuthal anisotropy is fracture density, Mueller (1991) compared amplitudes from S1 and S2 stacked sections in the Austin Chalk to detect lateral variations in fracture density. The essential idea is that S1 reflectivity senses the velocity of the unfractured rock, while S2 reflectivity is sensitive to the fractured rock, decreasing from an unfractured value as a function of fracture density. In Mueller (1991) the comparison between the shear mode reflectivity is visual, searching for zones of S2 amplitude dimming as a fracture indicator. The success of the technique supports the argument that shear wave principal components amplitude differences show azimuthal anisotropy with great spatial resolution, while traveltime differences between S1 and S2 show robust average azimuthal anisotropy over thick intervals, albeit with lower resolution (Thomsen, 1988). A set of figures (Figure 6.13 and 6.14) shows cases where shear wave splitting γ and reflection amplitude of the principal components validate each other. Thus, lateral variation in azimuthal anisotropy, by means of vertical fractures, is indicated by simultaneous increase in shear wave splitting γ and S2 amplitude dimming. Figure 6.13 shows cross sections of shear waves principal components related to the pre-injection survey. The sections are chosen to intersect injector and producer wells as well as the locations of the main shear wave splitting anomalies. Figure 6.14 shows the same cross sections from the post-injection survey.
138
INJECTOR PRODUCER
Fast shear wave S1
CVU196
CVU194
CVU97
90
NO
RT H
CVU94
90
CVU100
CVU93
80
80
CVU200
CVU197
70
70
IN LI N E
CVU99
CR
60
E N LI SS O
60 55 0
ft
50
50
Time lapse shear wave velocity change (%)
-5
-4
-3
-2
-1
0
2
1
3
4
5
INJECTOR PRODUCER
Slow shear wave S2
CVU97
90
CVU100
CVU93
80
NO
CVU196
CVU194
90
RT H
CVU94
80
CVU200
CVU197
70
70
IN LI N E
CVU99
CR
60
E N LI SS O
60 55 0
ft
50
50
FIG. 6.10: Time-lapse change (= post – pre) in reservoir interval velocity for the fast (S1) and slow (S2) shear modes. Black lines are fault planes cutting through the reservoir section.
139
INJECTOR PRODUCER
Pre-injection
CVU196
CVU194
CVU97
90
NO RT H
CVU94
80
90
CVU100
CVU93
80
CVU200
CVU197
70 IN
LI N
70
E
60
60 55 0
ft
50
50
Shear wave splitting
1
0
E N LI SS O CR
CVU99
3
2
γ (%) 4
5
6 INJECTOR
Post-injection
PRODUCER
CVU196
CVU194
CVU97
90
NO RT H
CVU94
80
90
CVU100
CVU93
80
CVU200
CVU197
70 IN
LI N
70
E
E N LI SS O CR
CVU99
60
60 55 0
ft
50
50
FIG. 6.11: Lateral variation of shear wave splitting γ in the San Andres reservoir before (top) and after (bottom) CO2 injection. Arrows show the azimuthal direction of polarization of the S1H1 component. Black lines are fault planes cutting through the reservoir section.
140
Area of time-lapse polarization change
INJECTOR PRODUCER
OR TH
CVU94
N
CVU196
CVU194
CVU97
90
90
CVU100
CVU93
80
80
CVU200
CVU197
70 IN
LI N
70
E
E N LI SS O CR
CVU99
60
60 55 0
ft
50
50
Time lapse change in shear wave splitting
-4
-3
-2
-1
0
1
γ (%) 2
3
4
FIG. 6.12: Time-lapse change (= post – pre) in shear wave splitting γ and S1H1 polarization. This is the final result after layer stripping and crossequalization. Black lines are fault planes cutting through the reservoir section.
141
CVU94
CVU196
CVU194
CVU97
CVU93
CVU100
CVU200
INLINE 81
CVU197
Pre-injection CVU99
INLINE 69
INLINE 57 S1 INLINE 57 CVU99
CVU197
S2 INLINE 57 CVU99
CVU93
N
1650
CVU93
S
N
San Andres
San Andres
S
CVU197
1700
1750
1800 S2 INLINE 69
S1 INLINE 69 CVU200
CVU97
CVU200
CVU194
N
1650
CVU194
S
N
San Andres
San Andres
S
CVU97
1700
1750
1800 S1 INLINE 81 CVU100
S2 INLINE 81 CVU100
CVU94
N
1650
1700
1750
S
CVU196
CVU94
N
San Andres
San Andres
S
CVU196
1800
FIG. 6.13: Azimuthal anisotropy in the pre-injection San Andres reservoir rocks. Panels are NS sections indicated on the shear wave splitting map. Left column shows the fast shear component (S1), right column shows the slow shear component (S2). Areas in the map with high shear wave splitting correspond to S2 amplitude dimming in the cross sections.
142
CVU94
CVU196
CVU194
CVU97
CVU93
CVU100
CVU200
INLINE 81
CVU197
Post-injection CVU99
INLINE 69
INLINE 57 S2 INLINE 57
S1 INLINE 57 CVU99
CVU197
CVU99
CVU93
N
1650
CVU93
S
N
San Andres
San Andres
S
CVU197
1700
1750
1800 S2 INLINE 69
S1 INLINE 69 CVU200
CVU97
CVU200
CVU194
N
1650
CVU194
S
N
San Andres
San Andres
S
CVU97
1700
1750
1800 S1 INLINE 81 CVU100
S2 INLINE 81 CVU100
CVU94
N
1650
1700
1750
S
CVU196
CVU94
N
San Andres
San Andres
S
CVU196
1800
FIG. 6.14: Azimuthal anisotropy in the post-injection reservoir rocks. See Figure 6.13 for time-lapse comparison.
143
INLINE 57 CVU99
2.0
CVU197
CVU93
S
N Pre-injection
1.6
1.2
D
Post-injection 0.8
0.4
0.0
INLINE 69 CVU200
2.0
CVU97
CVU194
S
N
1.6
Pre-injection
D
1.2
0.8
Post-injection
0.4
0.0
INLINE 81 CVU100
2.0
CVU196
S
CVU94
N
1.6
D
1.2
0.8
0.4
Pre-injection
Post-injection
0.0
FIG. 6.15: Expressions of azimuthal anisotropy in the pre- and post-injection San Andres reservoir. Panels are related to the N-S sections indicated in the two shear wave splitting maps of Figure 6.13 and 6.14, and show shear wave differential attenuation (D) computed using equation (6.8). In general, zones of higher differential attenuation correspond to higher shear wave splitting.
144
6.5
SHEAR WAVE TIME-LAPSE RELATIVE ATTENUATION In the presence of vertical fractures, the differential amplitude dimming of S2 with
respect to S1 indicates that the medium is elastically weak along the direction perpendicular to fracture strike. This observation can be further exploited by computing the differential attenuation between the shear modes. Cliet et al. (1991) successfully applied the method to VSP data in the Romashkino reservoir, showing that, at a given location, larger time delays between the shear-wave principal components coincide with higher differential attenuation. On the Vacuum field data, the time-lapse differential attenuation between the two shear modes in the reservoir section was computed using the spectral ratio method. The essential theory is summarized here. Consider the amplitude spectra of the two shear wave principal component traces at a given location. The spectra can be written as: (6 .5 )
A 11 (f
)
1 = A0 e − α ( f ) z
A 22 (f
)
2 = A0e − α ( f )z
where A0 is the initial amplitude, f is the frequency, α1 and α 2 are shear modes attenuation coefficients, and z is the distance traveled over the reservoir section. The assumption is that, over the frequency range at which shear waves propagate, α is a linear function of frequency. This results in α (f (6 .6 )
Q =
)
= ϕf , where ϕ is a constant related to the quality factor ( Q ) as: π
ϕv
Taking the natural logarithm of the ratio of the amplitude spectra we obtain: (6 .7 )
A 11 11 ln = ln A 22 A
[ ] − ln [A ] = (ϕ 22
2
)
− ϕ 1 fz ≈
1
Q2
−
1
Q1
Amplitude spectra of the shear wave principal components were computed, trace by trace, in the San Andres reservoir section. Then RMS shear waves differential attenuation was computed as:
145
(6 .8 )
[ [
n 11 ∑ ln A i (f i = 1 D =
)] − n
[ (f )]]
ln A
22 i
2
1 / 2
The computation effectively cancels the frequency dependence by RMS averaging over a fixed bandwidth ( i = 1 ,..., 40 Hz in the Vacuum case). Figure 6.15 shows differential attenuation for pre- and post-injection shear wave data along the same cross-sections as in Figure 6.12. 6.6
SUMMARY The 2Cx2C shear wave data from Vacuum field were analyzed with the objective of
quantifying the change of fracture density and orientation in the San Andres reservoir. The primary technique employed was layer stripping, which revealed a coarse sequence of three azimuthally anisotropic layers in the rock column. Once the effects of azimuthal anisotropy above the San Andres were stripped away, the reservoir section exhibited complex patterns of shear wave splitting and polarization. Independent application of layer stripping to the pre- and post-injection data sets, along with crossequalization, resulted in imaging the evolution of fracture density and fracture orientation in the San Andres dolomites. The final products of this analysis will be interpreted in the final chapter.
146
CHAPTER 7
TIME-LAPSE INTERP RETATION AND CONCLUSIONS
NATURAL SCIENCE DOES NOT SIMPLY DESCRIBE AND EXPLAIN NATURE, IT IS PART OF THE INTERPLAY BETWEEN NATURE AND SCIENTISTS. WERNER HEISENBERG 7.1
INTRODUCTION In this chapter, the theoretical components and observational elements developed in the
previous sections are combined in the form of a final interpretation. The Vacuum field time-lapse zone is subdivided into three areas where observation and theoretical predictions appear to coincide. The result is an image of a highly dynamic reservoir where the interplay between saturation and pore pressure changes is the main cause of the observed time-lapse anomalies. The capability to discriminate between saturation and pressure changes is currently one important area of research in reservoir studies. In this sense, the Vacuum field case study represents a successful example. The key to the pressure-saturation discrimination in many cases may be the usage of multicomponent seismology. In particular, two of the three interpreted areas of the San Andres reservoir indicate that time-lapse shear wave splitting may be a powerful indicator of saturation changes. 7.2
CO2 FLOODING: GENERAL ASPECTS The primary objective of enhanced oil recovery (EOR) is to mobilize residual oil by
modifying the viscous and interfacial tension forces existing in a rock-oil-water system. CO2 flooding is one of the EOR methods whose objective is to displace oil with a fluid that is miscible with oil at the conditions existing at the interface between the injected fluid and the oil bank being displaced. Microscopic displacement efficiency is a function of interfacial forces acting among oil, rock, and displacing fluid. Lowering the interfacial tension between oil and displacing
147
fluid allows oil droplets to be deformed and combined with other droplets to form a continuous oil phase. By definition, a miscible process is one in which the interfacial tension is zero, thus the displacing fluid and the residual oil are mixed to form one single phase. On the basis of how miscibility is developed, two major variations in a miscible process are recognized: first-contact miscibility (FCM), and multiple-contact miscibility (MCM). In an FCM process, the injected displacement fluid forms a single phase upon first contact when mixed in all proportions with crude oil. CO2 is not first contact miscible with most crude oils at normal reservoir temperatures and pressures, and is more correctly described by an MCM process. In the MCM process, modifications of the oil or injected solvent compositions occur to such a degree that the fluids become miscible as the solvent moves through the reservoir. Thus, miscibility does not exist initially but is dynamically developed as the process continues. From that point on, under idealized conditions, a miscible displacement will occur. Two primary physical mechanisms take place when CO2 is injected and mixed with oil (Metcalfe and Yarborough, 1979). The viscosity of the CO2-oil mix decreases compared to the original oil viscosity, thus allowing the contacted oil to flow more easily through the permeable rock. Also, because CO2 is highly soluble in oil at pressures higher than the minimum miscibility pressure (MMP), the resulting mixture is swelled, thus causing fluid migration induced by volume expansion. In Figure 3.3, the physical properties of oil, CO2, and oil-CO2 mixtures at Vacuum field were presented. Schematic fluid saturation and compressional velocity profiles for a CO2 flood where pore pressure and temperature are kept constant below MMP, are shown in Figure 7.1 (from: Metcalfe and Yarborough, 1979; Batzle et al., 1998). A complex distribution of different saturation regimes is developed during a CO2 flood. In particular, a gas bank may be in front of the CO2 enriched phase, where the volume of the gas bank is a function of pressure, temperature and original composition of the hydrocarbons in place. For pore pressure regimes above the MMP (Figure 7.2) the gas bank will disappear, and CO2-oil miscibility will develop. Conversely, the gas bank will tend to increase when pore pressure is lowered from the MMP.
Compressional Velocity
Volume % Liquid
148
100 LIQUID CO2 0
LIQUID CO2 + OIL
GAS LIQUID
LIQUID OIL + CO2
ORIGINAL OIL IN PLACE
high
low
Compressional Velocity
Volume % Liquid
FIG. 7.1: Schematic fluid saturation and compressional velocity profiles for a CO2 flood at constant pore pressure (8 MPa) and temperature (71°C). In this case CO2 and oil are below the minimum miscibility pressure (from Batzle et al., 1998).
100 LIQUID CO2 0
LIQUID CO2 + OIL
LIQUID OIL + CO2
ORIGINAL OIL IN PLACE
high
low
FIG. 7.2: Schematic fluid saturation and compressional velocity profiles for a CO2 flood at constant pore pressure and temperature above the minimum miscibility pressure. The gas bank present in the previous figure does not form, and the velocity profile reflects a gradual increase in CO2 concentration within the hydrocarbon.
149
7.3
CO2 FLOODING: ENGINEERING DATA FROM VACUUM FIELD In this section, a summary of the injection and production data gathered at Vacuum field
between January 1998 and June 1999 is presented. The relevant dates of the CO2 flooding and seismic monitoring operation are: •
December 1997: acquisition of the baseline, 3D, multicomponent seismic survey
•
April 1998: the CO2 injection operation is initiated
•
December 1998: acquisition of the monitoring, 3D, multicomponent seismic survey
The engineering data refer to six CO2 injector wells (CVU194, CVU93, CVU94, CVU99, CVU200, CVU100), and six producer wells (CVU97, CVU196, CVU197, CVU87, CVU187, CVU186), whose locations are shown on Figure 1.3. Figures 7.3 and 7.4 show details of the CO2 injection operation in terms of surface injection pressure and injected volume of fluid. Water was injected prior to CO2 until April 1998 (dashed portion of the curves in Figure 7.3 and 7.4). The CO2 injection operation was intended to maintain the existing pore pressure support, so that anomalies detected by seismic monitoring could be attributed to changes in saturation only. Unfortunately, the existing engineering data (Figure 7.3 and 7.4) do not clarify whether pore pressure changed in the reservoir during the injection. In general, surface injection pressure appears to be regular and well regimented over time (Figure 7.3). The available pressure data though, are related to surface conditions, and do not clarify bottom hole pressure conditions. Thus, it is not known whether or not injection pressure was uniform and regular during the seismic monitoring period (December 1997 – December 1998). Additional concerns regarding the uniformity of the injection process arise from the highly variable amount of injected CO2 among the six injector wells (Figure 7.4). There is an obvious imbalance among some of the wells which were essentially not capable of injecting CO2 (CVU100, CVU99, CVU194), and other wells which exceeded the expectations (CVU93). A reason for this imbalance is not presently available. Production data are presented with the intent of showing which producer wells were contacted by the injected CO2 (Figure 7.5 and 7.6). In the two figures, CO2 volumes are combined with natural gas because a separate measurement of CO2 content was not obtained in the field. Under these conditions, a well contacted by CO2 is typically detected on the basis of an increase in gas/oil ratio. The reason is that CO2, initially injected as a high pressure liquid, is later
150
produced as a low pressure gas. From Figure 7.6 the first notable peak in gas/oil ratio occurred at well CVU97, approximately coinciding with the time of the repeat 3D seismic survey. Notice also that CVU97 experienced an increase in oil production starting on November 1998, suggesting that the CO2 flooding had a positive effect at least in some portions of the field. By March-April 1999, all the producer wells show an increase in gas/oil ratio, but only CVU97 increased oil production. This observation suggests that processes more complex than direct response between injector and producer wells may have occurred at Vacuum field, and that a complete reservoir flow simulation is necessary to understand the dynamics of the CO2 injection process.
151
Northern CO2 Injectors 2500
Surface Injection Pressure (psi)
Baseline 3D Survey Dec 1997
CO2 Injection Start
Repeat 3D Survey Dec 1998
2000
CVU94
1500
CVU194 1000
CVU93
500
0
Jan-98
Mar-98
May-98
Jul-98
Sep-98
Nov-98
Jan-99
Mar-99
May-99
Mar-99
May-99
Southern CO2 Injectors 2500
Surface Injection Pressure (psi)
Baseline 3D Survey Dec 1997
CO2 Injection Start
Repeat 3D Survey Dec 1998
2000
CVU99 1500
CVU200 1000
CVU100
500
0
Jan-98
Mar-98
May-98
Jul-98
Sep-98
Nov-98
Jan-99
FIG. 7.3: Surface injection pressure for the six CO2 injector wells at Vacuum field. The CO2 injection phase started in April 1998 (continuous curves), and it was preceded by water injection (dashed curves).
152
Northern CO2 Injectors Volume of Fluid Injected (barrels, mcf)
5000
Baseline 3D Survey Dec 1997
CO2 Injection Start
Repeat 3D Survey Dec 1998
4000
3000
CVU93
2000
CVU94
1000
CVU194
0
Jan-98
Mar-98
May-98
Jul-98
Sep-98
Nov-98
Jan-99
Mar-99
May-99
Jan-99
Mar-99
May-99
Southern CO2 Injectors Volume of Fluid Injected (barrels, mcf)
5000
Baseline 3D Survey Dec 1997
CO2 Injection Start
Repeat 3D Survey Dec 1998
4000
3000
2000
CVU200
1000
CVU99 CVU100
0
Jan-98
Mar-98
May-98
Jul-98
Sep-98
Nov-98
FIG. 7.4: Volume of fluid injected (at surface) for the six CO2 injector wells at Vacuum field. The CO2 injection phase started in April 1998 (continuous curves, measured in mcf), and it was preceded by water injection (dashed curves, measured in barrels).
153
Northern Row of Producer Wells
150
CO2 Injection Start
Oil (barrels)
125 100
Repeat 3D Survey Dec 1998
Baseline 3D Survey Dec 1997
CVU186
75 50
CVU87 CVU187
25 0 300
CO2 Injection Start
Gas (mcf)
250
200
Repeat 3D Survey Dec 1998
CVU186
Baseline 3D Survey Dec 1997
150
CVU187
100
CVU87
50
0
5 CO2 Injection Start Gas/Oil Ratio
4
3
CVU186
Repeat 3D Survey Dec 1998
Baseline 3D Survey Dec 1997
CVU187
2 CVU87
1 0
Water (barrels)
1000
CVU187
CO2 Injection Start
800
Repeat 3D Survey Dec 1998
600 400
CVU87
Baseline 3D Survey Dec 1997
CVU186
200 0
Jan-98
Mar-98
May-98
Jul-98
Sep-98
Nov-98
Jan-99
Mar-99
FIG. 7.5: Production data for the northern portion of Vacuum field.
May-99
154
Southern Row of Producer Wells
150
CO2 Injection Start
Oil (barrels)
125 100
Repeat 3D Survey Dec 1998
Baseline 3D Survey Dec 1997
CVU97
75
CVU196
50
CVU197
25 0 300
CO2 Injection Start
Gas (mcf)
250
200
Repeat 3D Survey Dec 1998
Baseline 3D Survey Dec 1997
CVU97
150
CVU196
100
50
CVU197
0
5
CO2 Injection Start
Gas/Oil Ratio
4
3
Repeat 3D Survey Dec 1998
Baseline 3D Survey Dec 1997
CVU197 2
CVU97 CVU196
1
0
Water (barrels)
1000 CO2 Injection Start
800
CVU97
Repeat 3D Survey Dec 1998
600 400
Baseline 3D Survey Dec 1997
200
CVU196 CVU197
0 Jan-98
Mar-98
May-98
Jul-98
Sep-98
Nov-98
Jan-99
Mar-99
FIG. 7.6: Production data for the southern portion of Vacuum field.
May-99
155
Area 1
Area 2
INJECTOR PRODUCER
RT H
CVU94
NO
CVU196
CVU194
CVU97
90
90
CVU100
CVU93
80
80
CVU200
CVU197
70
70
IN LI N E
CVU99
O CR
60
Area 3
60 55 0
ft
50
50
Time lapse change in shear wave splitting
-4
-3
-2
E N LI SS
-1
0
1
γ (%) 2
3
4
FIG. 7.7: Subdivision of the San Andres reservoir in three interpreted areas of comparable dynamic behavior. The map is the same as Figure 6.12, representing time-lapse changes in shear wave splitting γ, after layer stripping and crossequalization. .
156
Area 1
Area 2
INJECTOR PRODUCER
CVU196
CVU194
CVU97
90
NO RT
H
CVU94
80
90
CVU100
CVU93
80
CVU200
CVU197
70
70
IN LI N E
60
Area 3
N LI SS O CR
CVU99
E
60 55 0
ft
50
50
P-wave velocity change zero
-5%
FIG. 7.8: Map of the compressional wave velocity change (same as Figure 5.13) with subdivision of the San Andres reservoir in three interpreted areas of comparable dynamic behavior.
157
7.4
RESERVOIR TIME-LAPSE ZONATION Figures 7.7 and 7.8 show the essential subdivision of the San Andres reservoir into three
zones (Area 1, Area 2, Area 3) of consistent dynamic behavior. The maps underlying the subdivision show changes in shear wave splitting γ (Figure 7.7), and changes in compressional wave velocity (Figure 7.8). The zones are the result of comparing seismic observations to rock physics models. Here, dynamic behavior simply indicates a combination of reservoir physical conditions which may be the cause of the detected seismic anomalies. The natural evolution of this zonation is reservoir flow simulation intended to validate or to disprove the dynamic model. Unfortunately, at Vacuum field, this last, integral part of the time-lapse study was not possible. In the following paragraphs, the logic behind the time-lapse zonation will be described. 7.4.1 DYNAMICS OF AREA 1 The distinctive characteristic of this area is a high value of shear wave splitting ( γ = 5% ) before CO2 injection (Figure 6.11 top). Image of the post-injection γ (Figure 6.11 bottom) shows that shear wave splitting has almost disappeared. Thus, Area 1 is spatially delimited by the timelapse decrease in shear wave splitting (Figure 7.7). In terms of individual seismic mode velocities, Area 1 is the site of a time-lapse S2 vertical velocity increase (6%), and almost no time-lapse change in S1 velocity (Figure 6.10), which explains the time-lapse reduction in shear-wave splitting. At the producer wells (CVU97 and CVU196) a time-lapse drop in V p of about 4% is observed, while in the rest of Area 1 there is no time-lapse change of compressional velocity (Figure 7.8). Shear wave polarization in Area 1 shows time-lapse changes only in the interwell space between CVU194 injector well and CVU97 producer well (Figure 6.12). Time-lapse seismic observations, engineering injection and production data, and results from effective medium theory modeling, are consistent with two plausible scenarios of reservoir dynamic behavior.
158
Area 1, scenario 1: in this model, summarized in Figure 7.9, the cause of the timelapse seismic anomaly is a reduction in fracture density caused by pore pressure ( P p ) decrease. The key element is the time-lapse decrease in crack density, which is imaged by a reduction in shear wave splitting. Before CO2 injection, Area 1 behaves as a fractured medium (Figure 7.9 a), where γ = 5% . In a fractured medium, a decrease in pore pressure ( P p ), and a consequent increase in effective pressure ( Pe ), will close the lowest aspect ratio fractures, thus decreasing fracture density (Figure 7.9 b). An example of the physical mechanism invoked here is given in Figure 7.9 (c), where a dolomite rock matrix was modeled. The carbonate is populated with penny-shaped vertical cracks resulting in an effective medium with HTI symmetry, and 0.1 background equant porosity. The relationship between crack density and Pe used in the model is taken from sample 1 of Figure 3.6. A decrease in shear wave splitting from γ = 5% toward zero requires an increase in Pe , thus a decrease in P p . The correct amount of P p drop in Area 1 could be computed only if the exact relationship between crack density and Pe was known. This example illustrates some of the difficulties existing in calibrating seismic response with realistic rock physics models, even under the assumption that seismic data are error-free. Additionally, time-lapse compressional velocity in Area 1 shows very little change. Figure 3.10 shows why this is possible. Assuming dolomite matrix with HTI crack symmetry, a background equant porosity of 0.1, and keeping saturation and saturants constant, a Pe change would result in a practically negligible increase in V p , thus matching the observations. In the proximity of the producer wells, compressional velocity in Area 1 shows a time– lapse decrease. Due to the mechanics of the fluid extraction process, P p at the producer wells was kept very low (200 psi) before and after CO2 injection. In these conditions, any amount of CO2 in the proximity of the producer wells is below MMP, and more importantly is in a gas phase. Thus, the time-lapse reduction in compressional velocity is interpreted as a local effect due to CO2-enriched fluids contacting the producer wells.
159
Before CO2 Injection
Pc
After CO2 Injection
Pc
Pp
(a)
(b)
(c)
FIG. 7.9: Schematic model of a dynamic behavior in Area 1 (scenario 1) of the San Andres reservoir. In the dolomite rock before injection (a), fractures are kept open by an existing pore pressure (Pp). The CO2 injection precess (b) occurs with a decrease in Pp. Because the confining stress (Pc) is constant, effective pressure (Pe) increases, causing fractures to close (b), and shear wave splitting γ to decrease (c). The results of (c) are obtained by modeling a dolomite rock with 0.1 background equant porosity, populated with pennyshaped vertical cracks in HTI symmetry.
160
Area 1, scenario 2: in this model, summarized by Figure 7.10, the cause of the timelapse seismic anomaly is a change in fluid saturation within the fractured rock. The key element is the time-lapse decrease in shear wave splitting caused by the presence of a less compressible fluid in the fracture space. Before CO2 injection, Area 1 behaves as a fractured medium (Figure 7.10 a), where γ = 5% . A combination of oil and water is present within fractures and pores, but permeability in the Area 1 is largely confined to the fractures. In this respect, the spherical pores are responsible for the largest amount of storage capacity, but are almost bypassed by fluid flow. The fracture network instead, has minimal storage capacity, but makes the carbonate in Area 1 a "fast flow" medium, where injected fluids do not invade the spherical pores, but are channeled through the fractures. When CO2 injection takes place, the pore pressure is maintained and fractures are as open as before, i.e. crack density is unchanged. CO2 is highly mobile and, using the existing fracture permeability framework, invades the fractures preferentially and not the spherical pores. CO2 mixes with the residual oil present along the fractures walls and displaces it moving fast from the injector wells towards CVU97 producer well. The displacement is fast to the extent that CVU97 is contacted by the miscible fluid even before prediction from the Vacuum field engineers. Notice in Figure 7.6 that CVU97 increased gas/oil ratio approximately at the same time of the acquisition of the repeated 3D seismic survey. CVU97 was also the first producer well to respond to the injection process with a quantifiable and sustained increase in oil production, not just with increase in gas/oil ratio. From a rock-fluid interaction stand point, the mixing effect of CO2 occurred mostly in the fracture space, sweeping oil away, and leaving behind a combination of fluids which is less compressible than before the injection. In essence, by taking away the oil from the fractures, CO2 differentially enriched the fractures with water, which is less compressible than oil (Figure 7.10 b). As shown by the effective modeling work of chapter 3, in the presence of corrugated (rough) fractures, shear wave splitting γ is dependent on the fluid bulk modulus ( K f ). In this specific case, shear wave splitting decreases by increasing K f , as fractures are differentially enriched with a stiffer fluid (water). The implications of this scenario are particularly important for Vacuum field. First, the time-lapse anomaly of Area 1 appears to show the most efficient portion of the reservoir fracture
161
permeability. Additionally, the fast response to CO2 injection between injector wells and the CVU97 producer well (while all the other producer wells show uncertain responses), indicates that permeability in the field is highly variable. In this respect, it is possible that the presence of fractures is actually limiting the efficiency of the CO2 injection process in terms of EOR. In Area 1, CO2 appears to be preferentially channeled through fractures, bypassing the residual oil present in the equant pores.
162
Before CO 2 Injection
After CO2 Injection
OIL
WATER
(a)
OIL
WATER
(b)
FIG. 7.10: Schematic model of dynamic behavior in Area 1 (scenario 2) of the San Andres reservoir. The cause of the time-lapse anomaly is a change in fluid saturation within the fractures. In the dolomite rock before injection (a) residual oil and water are present in the fracture network. The CO2 injection does not change the pore pressure (Pp), thus fracture density is also unchanged. CO2 mixes preferentially with oil and, because of the high mobility of the mix, effectively sweeps oil away from the fractures, leaving behind a less compressible fluid (b). In the presence of corrugated (rough) cracks, an increase in fluid bulk modulus (Kf) causes shear wave splitting γ to decrease.
163
7.4.2 DYNAMICS OF AREA 2 The lateral extent of Area 2 was imposed by the time-lapse polarization changes. This area includes P-wave velocity anomalies in the northern part of the survey, while time-lapse changes in shear wave velocities and splitting are negligible. The dynamic model for Area 2 is interpreted as a combination of P p changes and fluid substitution with CO2-enriched fluids. From Figure 4.22, a change in the orientation of shear wave polarization may be linked to local variations of the effective stress caused by a P p pulse. This could be an increase or a decrease in P p , but compressional wave velocity anomalies in Area 2 show a decrease in V p . Experimental data (Figure 3.5) indicate that P p increase is a possible cause for drop in V p . On this basis, Area 2 is interpreted as a zone of P p increase. The same experimental data of Figure 3.5 show that a direct fluid substitution of oil for CO2 is also likely to decrease compressional velocities. In an equant pore, fracture-free dolomite, the drop in velocity as a function of CO2 is more pronounced for compressional velocities than for shear velocity, thus matching seismic observations. In summary, saturation effects must be included as a possible source of the anomaly in Area 2. Figure 7.11 shows a model of what might have occurred in Area 2. The starting point is the conditions before CO2 injection (Figure 7.11 a), where a porous dolomite rock is fractured, and fractures are invaded by a brine (oil + water). The density of fractures is not very high, as shown by the small values of γ in Figure 6.10. At the time of the second seismic survey, a positive pore pressure pulse has reached the area such that fractures previously closed are now open (Figure 7.11 b). The new pressureinduced open cracks are compliant cavities, and have the effect of locally rotating the direction of
σH max . Because shear waves are sensitive to the direction of σH max , the multicomponent data detect a time-lapse change in polarization. Also it is reasonable to assume that the fluid responsible for the pore pressure pulse contained CO2 in various proportions, such that compressional velocity decreased, as shown by the seismic anomaly of Figure 7.8. A partial inconsistency is present in the dynamic model of Area 2 for which no explanation is currently clear. If an increase in P p is responsible for the time-lapse change in orientation of the horizontal effective stress, the same pressure pulse should have increased the
164
density of fractures, thus increasing shear wave splitting in Area 2. Figure 6.11 indeed shows that post-injection shear wave splitting moved from east to west, but its extension is only a fraction of the polarization change area.
165
pore
op en
cr a
NORTH
ck
ϕ1 S1 be po in for lar je e iza ct CO ti io on n 2
(a) NORTH
pore
op en
ck
ϕ2
tion lariza S1 po CO 2 after on injecti
(b)
cr a
FIG. 7.11: Schematic model of the possible dynamic behavior in Area 2 of the San Andres reservoir. The porous and fractured dolomite before CO2 injection is represented in (a), while (b) shows the rock after injection. In both cases, the rose diagrams show the S1 direction of polarization corresponding to the fracture system in the cartoon. In (a) pores and fractures are filled with oil and water (brine) resulting from years of water flooding. In (b), a pore pressure pulse has opened cracks along azimuthal directions different from the original, causing a local redistribution of the state of stress which results in a new orientation of maximum horizontal stress (σHmax). As a consequence, shear wave polarization, which responds to the azimuthal orientation of σHmax, undergoes a rotation with respect to the initial case. Because of the injection, pores and cracks in (b) are now filled with a CO2-enriched fluid, more compressible than (a).
166
7.4.3 DYNAMICS OF AREA 3 Area 3 is characterized by a time-lapse increase in shear wave splitting, while all the other variables show no sign of time-lapse change. In terms of individual seismic mode velocities, the time-lapse anomaly is entirely confined to an increase of S1 velocity after CO2 injection. Compressional velocity, S2 velocity and shear wave polarization are all unchanged by the injection process. In Figure 6.15, a time-lapse increase in shear wave differential attenuation in the proximity of CVU197 well (top cross-section) corroborates the shear wave splitting anomaly. Figure 6.11 (bottom) shows that, in the post-injection shear wave splitting data, the time-lapse increase is confined to the two sides of a fault, but in the pre-injection map of γ almost no splitting is detectable. The dynamic model for Area 3 is interpreted as the effect of CO2-enriched fluids invading a fractured portion of the San Andres dolomites. This is the equivalent of stating that changes in saturation are detectable with shear waves under particular conditions. Figure 3.16 gives an explanation to the observed seismic anomaly, and the mechanism invoked for the interpretation of Area 3 is summarized in Figure 7.12. The San Andres dolomites have to be considered, in many spatial occurrences, a dual porosity rock, where classical equant porosity interacts with fractures (Figure 7.12 a). If the elastic response of fractures can be described by low symmetry anisotropy (e.g. monoclinic as in Figure 7.12 b), then Figure 7.12 (c), suggests that vertically propagating shear waves show sensitivity to the fluid bulk modulus. In particular, shear wave splitting γ increases by decreasing K f , as in the case of oil to CO2 substitution. This is the equivalent of stating that shear wave splitting γ increases when fractures are invaded with more compliant saturants. Area 3 has a particular significance in this investigation. First, an indication is given to discriminate saturation from pressure changes: a subject of current interest. Landro (2001) used approximations of time-lapse reflection coefficient versus offset to compute changes in saturation and pressure. Because both expressions are a function of AVO gradient and intercept changes, input to the algorithm were near and far offset stacks. Landro (2001) shows a successful application on a sandstone reservoir, where spherical porosity dominates and changes in V p with water saturation and effective stress are reasonably linear. The work at Vacuum shows that
167
multicomponent seismology can differentiate saturation from pressure changes in a fractured reservoir. A second notable aspect is that shear waves are commonly considered insensitive to fluid content. The modeling work of chapter 4 and the anomaly of Area 3 indicate that, under particular symmetry classes of the effective medium, shear waves can be used as a valid indicator of saturation changes. Comparable observations were made by van der Kolk et al. (2001) in the Naith field. A notable inconsistency is present in this model, for which no explanation is available. In Figure 3.16, the model shows a change in splitting generated by a change in S2 velocity with almost no change in S1 velocity. In the time-lapse seismic data at Vacuum, the largest anomaly is in the S1 velocity, while the S2 velocity has a much smaller time-lapse change.
168
(a)
(b)
(c)
FIG. 7.12: Schematic model of the possible dynamic behavior in Area 3 of the San Andres reservoir. A fractured dolomite rock (a) is modeled as being equivalent to a periodic array of inclined cracks (b). Before CO2 injection, fractures and pores are invaded by oil and water. The compressibility of the fluid is very low (Kf is high), and such that values of shear wave splitting γ are low (Figure 6.11 top). The CO2 injection process introduces a fluid in the fractures and pores which is more compressible (low Kf) than oil and water. As shown by modeling shear wave propagation through a medium like (b), shear wave splitting γ increases when low symmetry fractured media are invaded by highly compressible fluids (c).
169
7.5
CONCLUSIONS OF THE STUDY AND IDEAS FOR ADDITIONAL RESEARCH At Vacuum field, a porous and fractured dolomitized carbonate rock containing
hydrocarbons was subjected to CO2 flood. Multicomponent, time-lapse, surface 3D seismic was employed to map the dynamic changes taking place in the reservoir rock. Prestack processing focused on repeatability, and produced near-vertical stack, time-lapse volumes of the five components containing the majority of the reflected seismic energy (P, S1H1, S1H2, S2H2, S2H1). This work has focused on: •
Understanding the physical mechanisms responsible for time-lapse seismic anomalies in a fractured reservoir, and building geomechanical models for stress and saturation changes.
•
Enhancing the poststack repeatability of the time-lapse anomalies for compressional and shear waves.
•
Maximizing the energy of the shear wave principal components (S1H1 and S2H2) through poststack layer stripping targeted on the San Andres reservoir.
•
Estimating the changes in vertical and lateral distribution of shear wave polarization and fracture density.
•
Interpreting the time-lapse anomalies in terms of reservoir properties. Dual porosity reservoirs, like the San Andres, are very heterogeneous, and their intrinsic
mineral parameters exhibit the characteristics of hard, incompressible rocks. As a consequence, the detection of fluid related changes by using reflection seismology is particularly difficult, because the magnitude of elastic changes from fluid-effects is very small (only a few percent). This characteristic of incompressibility typical of many carbonate rocks was confirmed by compressional and shear wave ultrasonic velocities acquired on two core samples from Vacuum field. Generalizing the experimental results, at a given effective pressure, stiffer (high bulk modulus) and denser fluids tend to increase compressional velocities and to decrease shear velocities. The exception comes from shear wave velocities under carbon dioxide saturation, which were found to be up to 2% lower than the oil saturated case.
170
The key to a possible success in dynamic characterization of dual porosity hard rock is to explore for changes in the most compliant part of the rock-fluid system: fractures. In this work, equant pores and fractures were combined in an effective model suitable to treat saturation changes in the pore space, as well as deformation of fractures. The model is a compliance representation of an effective rock, combined with linear slip theory. One of the advantages of the model is the fact that a complex problem, like the coexistence of pores and fracture in a rock matrix, can be simulated by simply adding the individual compliances. Fractures were described as non-interacting, randomly distributed, penny-shaped cracks, and pores were represented as spheres. The elastic response of the effective medium was computed, and saturated velocities were estimated with the method of Brown and Korringa (1975). This method improved the prediction of saturated velocities by reducing the difference between the experimental and modeled velocities. The same method was applied to modeling fluid substitution of low symmetry fracture sets in an equant porosity background. The goal was to understand the behavior of the shear wave splitting parameter in the presence of various fracture scenarios and to test the sensitivity of γ to changes in saturating fluids. Dry and saturated velocities of a dolomite matrix with a single fracture set for HTI and monoclinic symmetry were computed for various saturating fluids. The results show that, in the presence of corrugated (rough) fracture sets, an increase in the fluid bulk modulus decreases the shear wave splitting parameter, thus revealing a sensitivity of shear waves to fluid saturation. One of the critical and most uncertain aspects of a fractured reservoir is to quantitatively assess, in a given lithology, the relationship between stress and strain in the presence of various degrees of fracturing. Effective medium theory can simulate distributions of fractures in space, from which particular classes of effective anisotropic symmetry may arise. But, at the core of elastic tensor manipulations are rock-specific, stress-strain relationships which have to be addressed experimentally. The detailed work of Pyrak-Nolte (e.g. Pyrak-Nolte, 1996) on isolated fractures, could be viewed as an example, but many additional experiments could potentially address the same issue, for example: ultrasonic velocity measurements on fractured rocks, ultrasonic tomography, stress-strain analysis using low frequency devices, and others.
171
On the same subject, existing experimental data published in recent years, all focusing on fractures deformation, have not been collectively analyzed. Generalized stress-strain relationships, derived from experimental data on fractured rocks, would find immediate application on simulation of fractured reservoirs. The idea should be extended to the analysis of stress-strain relationships in the presence of interacting, non-isolated fractures, and fractures and pores. In summary, there are various theoretical models capable of treating poroelastic deformations for a variety of fractures and pore scenarios. On the contrary, empirical relationships derived from experimental data are strongly needed. CO2 injection, as well as many other reservoir engineering operations, has the potential to alter the local state of stress in the reservoir, which is linked to the regional stress by a general, anisotropic, effective stress law. The tectonic stress in the area of Vacuum field was reconstructed by using structural mapping, available measurements of tectonic stress in the Permian Basin, shear wave polarization, and breakout analysis from borehole studies. Ultimately, data integration of various stress measurements resulted in a model, derived from dislocation theory, of the distribution of σH max centered on the San Andres reservoir.
To obtain meaningful differences of time-lapsed volumes, crossequalization schemes were developed for compressional and shear waves, forcing the static portion of the repeated data to match the static portion of the baseline data. The technique was applied by constructing digital filters in the static section of the data, and then propagated to the dynamic section. The benefits of crossequalization were shown by following, step by step, the increase in repeatability of the time-lapse data. Repeatability of time-lapse data is constantly enhanced by improving acquisition technology. The detection of time-lapse inconsistencies, or errors, is almost routinely done on the basis of simple models, like crossequalization, where a portion of the time-lapse data is forced to be time-invariant. A full integration of poroelastic models in geophysical processing would probably change the scenario. Following Segall and Fitzgerald (1998), a pore pressure change in a given reservoir section is likely to produce changes to the state of stress inside as well as
172
outside the reservoir boundaries. Thus, a future research path could be to include poroelastic modeling in time-lapse geophysical processing. A key objective of the Vacuum field experiment was seismic detection of fractures. Using an implementation of Thomsen et al. (1999) layer stripping algorithm on normal-incidence shear wave data, an estimate of reservoir fracture density and fracture orientation, as well as their evolution over time, was obtained. From the same analysis, it can be concluded that the rock column at Vacuum field (from surface to reservoir depth) exhibits at least three coarse layers with different azimuthal anisotropy. The natural evolution of the multicomponent data analysis technique used in this work is the study of azimuthally dependent signatures of compressional and shear waves (PP, PS, and SS). This should allow to obtain all the parameters estimated in this study (fracture density, fracture orientation, and interval velocities) and to construct a more complete picture of the anisotropic parameters of the elastic medium. The time-lapse extension of this work will quantify time-dependent elastic anisotropy. In terms of field related results, the Vacuum field time-lapse experiment shows a subdivision of the reservoir in at least three zones. The key to understanding this subdivision is the interplay between saturation and pore pressure changes. This result is a direct benefit of the usage of multicomponent seismology, which is consequently recommended for time-lapse studies. In terms of methodology, the Vacuum field time-lapse experiment shows that the discrimination between saturation and pressure changes is possible with multicomponent seismology, at least in the presence of fractured reservoirs. In this environment, possibly one of the most prominent results of this work is that time-lapse shear wave splitting is a powerful indicator of saturation changes. The usage of multicomponent seismology in the time-lapse Vacuum field experiment raises the question of understanding what is the real value of multicomponent data for time-lapse monitoring. The answer is in the increased number of independent rock parameters that may be
173
estimated. From a reservoir engineering stand point, time-lapse seismology is a valuable technology if pressure, saturation, and temperature changes are detectable over time. Even confining the changes to pressure and saturation only, multicomponent seismic data are necessary to estimate the two parameters. Additionally, the fact that rocks exhibit anisotropic stress-strain relationships implies that pressure and saturation time-lapse changes are also anisotropic. Thus, the initial estimation of two independent parameters is increased to a number which depends on the symmetry of the effective rock compliance tensor. In these conditions, only multicomponent surface seismic data, integrated with various forms of borehole seismology, may be capable of describing the anisotropic medium statically (single measurement), and dynamically (time-lapse measurements). Currently, there are several commercial implementations of multicomponent seismology, essentially revolving around PP, PS, and SS reflections, with different operating costs and environments. This work had the opportunity to explore the value of SS reflection seismology, and some of the interesting results were obtained only due to this technology. Then, what is the value of shear wave seismology? First, shear-wave reflection seismic is evolving from being considered insensitive to fluid saturation, to an expression of fluid saturation within the anisotropic rock frame. In this respect, there is a growing need to perform interesting rock physics experiments that could validate rock models where normal and tangential fracture compliance are coupled. The value of the coupling is the key to fluid saturation detection with shear waves, and the consequence of fluid discrimination within fractures is likely to lead to permeability. At least twenty years of shear wave reflection seismology have convinced a large portion of the geophysical community of the link between shear wave vertical birefringence and direction of maximum horizontal stress. Algorithms and interpretational tools dedicated to the analysis of shear wave vertical birefringence (e.g. layer-stripping, source-receiver vector rotation) are becoming more common. Yet, there are still very few reservoir characterization studies where independent measurements of stress as a function of depth, and shear wave 3D surveys are collected and monitored. In this respect, the link between maximum horizontal stress and shear wave seismology could be the key to a complete poroelastic treatment of reservoir analysis from seismic monitoring data.
174
Time-lapse seismic anomalies need to be corroborated by additional independent measurements, among which pore pressure and stress measurements at well sites are probably the most critical. For shear waves, time-lapse crossdipole logging should be included in the current methodologies. Having time-lapse multicomponent surface seismic, VSP, and crossdipole logging would constitute an exceptional data set to study fracture detection as a function of frequency. The shear wave differential attenuation analysis in chapter 6 used RMS amplitude values averaged on the entire bandwidth (0 to 40 Hz). But, it was noticed that time-lapse, frequency dependent shifts in energy are present in the data. The observation is intriguing because of the relationship that frequency has with effective medium viscosity (e.g. Jones, 1986), and it could be pursued from a theoretical and data analysis stand point.
175
REFERENCES
Alford, R. M., 1986, Shear data in the presence of azimuthal anisotropy: Dilley, Texas: 56th Ann. Internat. Mtg., Soc. Explor. Geophys., Expanded Abstracts, 476-479. Angel, Y. C., and Achenbach, J. D., 1985, Reflection and transmission of elastic waves by a periodic array of cracks: J. Appl. Mech., 53, 33-41. Auld, B. A., 1989, Acoustic fields and waves in solids: Krieger Publishing. Backus, G. E., 1962, Long-wave anisotropy produced by horizontal layering: J. Geophys. Res., 66, 4427-4440. Bahorich, M. and Farmer, S., 1995, The coherence cube: The Leading Edge, 14, 1053-1058. Bakulin, A. V., Grechka, V., and Tsvankin, I., 2000a, Estimation of fracture parameters from reflection seismic data – Part 1: HTI model due to a single fracture set: Geophysics, 65, 1788-1802. Bakulin, A. V., Grechka, V., and Tsvankin, I., 2000b, Estimation of fracture parameters from reflection seismic data – Part 3: Fractured models with monoclinic symmetry: Geophysics, 65, 1818-1830. Batzle, M. L., and Wang, Z., 1992, Seismic properties of pore fluids: Geophysics, 57, 1396-1408. Batzle, M., Christiansen, R., and Han, D-H, 1998, Reservoir recovery processes and geophysics: TLE, 10, 1444-1447. Berryman, J. G., and Wang, H. F., 2000, Elastic wave propagation and attenuation in a doubleporosity dual-permeability medium: Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 37, 63-78. Biot, M. A., 1941, General theory of three-dimensional consolidation: J. Applied Physics, 12, 155164. Bonner, B. P., 1974, Shear wave birefringence in dilating granite: Geophys. Res. Lett., 1, 217220. Brown, R. J. S. and Korringa, J., 1975, On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid: Geophysics, 40, 608-616. Carroll, M. M., 1979, An effective stress law for anisotropic elastic deformation: J. Geophys. Res., 84, 7510-7512.
176
Chen, Q., and Nur, A., 1992, Pore fluid pressure effects in anisotropic rocks: mechanisms of induced seismicity and weak faults: Pure App. Geophys., 139, 463-479. Cliet, C., Brodov, L., Tikhonov, A., Marin, D., and Michon, D., 1991, Anisotropy survey for reservoir definition: Geophys. J. Int., 107, 417-427. Crampin, S., Evans, R., and Atkinson, B. K., 1984, Earthquake prediction: A new physical basis: Geophys. J. Roy. Astr. Soc., 76, 147-156. Crampin, S., and Lovell, J. H., 1991, A decade of shear-wave splitting in the Earth’s crust: what does it mean? what use can we make of it? and what should we do next?: Geophys. J. Int., 107, 387-407. Crampin, S., and Zatsepin, S. V., 1997, Modelling the compliance of crustal rock: II, Response to temporal changes before earthquakes: Geophys. J. Int., 129, 495-506. Ebrom, D. A., Tatham, R. H., Sekharan, K. K., McDonald, J. A., and Gardner, G. H. F., 1990, Hyperbolic traveltime analysis of first arrivals in an azimuthally anisotropic medium: A physical modeling study: Geophysics, 55, 185-191. Elam, J. G., 1984, Structural systems in the Permian Basin: West Texas Geological Society Bulletin, 24, 7-10. Eshelby, J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems: Proceedings of the Royal Society of London, A241, 376-396. Ewing, T. E., 1984, Models of the Late Paleozoic structural evolution of the Permian Basin: West Texas Geological Society Bulletin, 24, 17. Ewing, T. E., 1990, The tectonic map of Texas: Austin, Bureau of Economic Geology, The University of Texas at Austin. Ewing, T. E., 1991, The tectonic framework of Texas: Text to accompany “The tectonic map of Texas”: Austin, Bureau of Economic Geology, The University of Texas at Austin. Frenzel, H. N., Bloomer, R. R., Cline, R. B., Cys, J. M., Galley, J. E., Gibson, W. R., Hills, J. M., King, W. E., Seager, W. R., Kottlowski, F. E., Thompson, S., Luff, G. C., Pearson, B. T., and VanSiclen, D. C., 1988, The Permian basin region: In: Sloss, L. L., eds.: The geology of North America, D-2, 261-306. Galarraga, M., 1999, 3-D seismic interpretation in Vacuum Field area, Permian Basin, Lea County, New Mexico: M.S. Thesis, Colorado School of Mines. Galley, J. E., 1958, Oil and geology in the Permian Basin of Texas and New Mexico: In: Weeks, L. G., eds., Habitat of oil – A symposium: Tulsa, Oklahoma, AAPG, 395-446.
177
Gardiner, W. B., 1990, Fault fabric and structural subprovinces of the Central Basin Platform: A model for strike-slip movement. In: Flis, J. E., and Price, R. C., eds., Permian Basin Oil and Gas Fields: Innovative Ideas in Exploration and Development. West Texas Geological Society, Publication 90-87, 15-27. Gassmann, F., 1951, Uber die elastizitat poroser medien: Verteljahrsschrift der Naturforschenden Gesellschaft in Zurich, 96, 1-23. GEOMAP, 1983, Pre-Pennsylvanian subcrop map of the Permian Basin of West Texas and Southeast New Mexico. GEOMAP executive reference map 502. Granryd, L., Getting, I. C., and Spetzler, H., 1983, Path independence of acoustic velocity and attenuation in experimentally deformed westerly granite: Geophys. Res. Lett., 10, 71-74. Gupta, I. N., 1973, Seismic velocity in rock subjected to axial loading up to shear fracture: J. Geophys. Res., 78, 6936-6942. Hadley, K., 1975, vp/vs anomalies in dilatant rock samples: Pure Appl. Geophys., 113, 1-23. Helbig, K., 1994, Foundations of elastic anisotropy for exploration seismic: Pergamon Press. Hernandez, E. M., 1999, Influence of shallow heterogeneities on multicomponent 4D seismic data at Vacuum Field, New Mexico: M. E. Engineering report, Colorado School of Mines. Hill, R., 1965, a self-consistent mechanics of composite materials: Journal of the Mechanics and Physics of Solids, 13, 213-222. Hills, J. M., 1970, Late Paleozoic structural directions in southern Permian basin, west Texas and southeastern New Mexico: AAPG Bulletin, 54, 1809-1827. Hills, J. M., 1984, Sedimentation, tectonism and hydrocarbon generation in Delaware basin, west Texas, and southeastern New Mexico: AAPG Bulletin, 68, 250-267. Hoenig, A., 1979, Elastic moduli of a non-randomly cracked body: Int. J. Solids Struct., 15, 137154. Holt, R. M., Fjaer, E., Raaen, A. M., Ringstad, C., 1991, Influence of stress state and stress history on acoustic wave propagation in sedimentary rocks. In “Shear waves in marine sediments”; eds. Hovem, J. et al., Kluwer Publ., 167-174. Holt, R. M., and Kenter, C. J., 1992, Laboratory simulation of core damage induced by stress release: Proc. 33rd US Symp. Rock Mechanics, A.A. Balkema, 959-968. Holt, R. M., Unander, T. E., Kenter, C. J., and Santarelli, S. J., 1993, Constitutive mechanical behavior of synthetic sandstone formed under stress: Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 30, 719-722.
178
Holt, R. M., Fjaer, E., and Furre, A. K., 1996, Laboratory simulation of the influence of earth stress changes on wave velocities. In “Seismic Anisotropy”, 6IWSA, eds. Fjaer, E. et al., SEG, 297-317. Horak, R. L., 1985, Tectonic and hydrocarbon maturation history in the Permian basin: Oil and Gas Journal, 5, 124-129. Hsu, C., and Schoenberg, M., 1993, Elastic waves through a simulated fracture medium: Geophysics, 58, 964-977. Hudson, J. A., 1980, Overall properties of cracked solids: Math. Proc. Camb. Phil. Soc., 88, 371384. Hudson, J. A., 1981, Wave speeds and attenuation of elastic waves in material containing cracks: Geophys. J. Roy. Astr. Soc., 64, 133-150. Jaeger, J. C., and Cook, N. G. W., 1976, Fundamentals of rock mechanics: Chapman and Hall, New York. Jones, T. D., 1986, Pore fluids and frequency dependant wave propagation in rocks: Geophysics, 51, 1939-1953. Kachanov, M., 1992, Effective elastic properties of cracked solids: critical review of some basic concepts: Appl. Mech. Rev., 45, 304-335. King, M. S., Chaudhry, N. A., and Shakeel, A., 1995, Experimental ultrasonic velocities and permeability for sandstones with aligned cracks: Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 32, 155-163. Landro, M., 2001, Discrimination between pressure and fluid saturation changes from time-lapse seismic data: Geophysics, 66, 836-844. Lo, T., Coyner, K. B. and Toksoz, M. N., 1986, Experimental determination of elastic anisotropy of Berea sandstone, Chicopee shale, and Chelmsford granite: Geophysics, 51, 164-171. Lockner, D. A., Walsh, J. B., and Byerlee, J.D., 1977, Changes in seismic velocities and attenuation during deformation of granite: J. Geophys. Res., 82, 5374-5378. Lynn, H. B. and Thomsen, L. A., 1990, Reflection shear-wave data collected near the principal axes of azimuthal anisotropy: Geophysics, 55, 147-156. Lynn, H. B., 1996, A geophysicist’s view on seismic anisotropy: in, Rathore, J., Seismic Anisotropy, Soc. Of Expl. Geophys., 1-4. Martin, M. A., and Davis, T. L., 1987, Shear-wave birefringence: A new tool for evaluating fractured reservoirs: The Leading Edge, 10, 22-28.
179
Mattocks, B. W., 1998, Borehole geophysical investigation of seismic anisotropy at Vacuum Field, New Mexico: Ph. D. Thesis, Colorado School of Mines. Mavko, G., Mukerji, T., and Dvorkin, J., 1998, The rock physics handbook: Cambridge University Press. McTigue, D. F., 1986, Thermoelastic response of fluid-saturated porous rock: J. Geophys. Res., 91, 9533-9542. Metcalfe, R. S., and Yarborough, L., 1979, The effect of phase equilibria on the CO2 displacement mechanism: SPE Journal, 242-252. Michaud, G. C., 2001, Time-lapse multicomponent borehole seismic monitoring of a pilot CO2 flood: Ph. D. Thesis, Colorado School of Mines. Mikata, Y., and Achenbach, J. D., 1988, Interaction of harmonic waves with a periodic array of inclined cracks: Wave Motion, 10, 59-72. Molotkov, L. A., and Bakulin, A. V., 1997, An effective model of a fractured medium with fractures modeled by the surfaces of discontinuity of displacements: J. of Math. Sci., 86, 2735-2746. Montgomery, S. L., 1997, Permian Bone Spring Formation; sandstone play in the Delaware Basin; Part I, slope: AAPG Bulletin, 81, 1239-1258. Mueller, B., Reinecker, J., and Fuchs, K., 2000, The 2000 release of the World Stress Map. Available online at www.world-stress-map.org. Mueller, M. C., 1991, Prediction of lateral variability in fracture intensity using multicomponent shear-wave surface seismic as a precursor to horizontal drilling: Geophys. J. Int., 107, 409-416. Nakagawa, S., 1998, Acoustic resonance characteristics of rocks and concrete containing fractures: Ph.D. Thesis, University of California at Berkeley. Nakagawa, S., Nihei, K. T., and Myer, L. R., 2000, Shear induced conversion of seismic waves across single fractures: Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 37, 50-66. Nur, A., 1971, Effects of stress on velocity anisotropy in rocks with cracks: J. Geophys. Res., 76, 2022-2034. Nur, A., and Byerlee, J. D., 1971, An exact effective stress law for elastic deformation of rock with fluids: J. Geophys. Res., 76, 6415-6419. Nur, A., and Simmons, G., 1969, Stress induced velocity anisotropy in rock: an experimental study: J. Geophys, Res., 74, 6667-6674.
180
Orr, F. M., and Taber, J. J., 1984, Use of carbon dioxide in enhanced oil recovery: Science, 224, 563-569. Pranter, M. J., 1999, Use of a petrophysical-based reservoir zonation and multicomponent seismic attributes for improved geological modeling, Vacuum Field, New Mexico: Ph. D. Thesis, Colorado School of Mines. Pyrak-Nolte, L. J., 1996, The seismic response of fractures and the interrelations among fracture properties: Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 33, 787-802. Rai, S. C., and Hanson, K. E., 1987, Shear-wave velocity anisotropy in sedimentary rocks: A laboratory study: Geophysics, 53, 800-806. Rathore, J. E., Fjaer, E., Holt, R. M., and Renlie, L., 1995, P- and S-wave anisotropy of a synthetic sandstone with controlled crack geometry: Geophys. Prospect., 43, 711-728. Reed, T. A., and Strickler, D. L., 1990, Structural geology and petroleum exploration of the Marathon thrust belt, west Texas: In: Laroche, M. T., and Higgins, L., eds.: Marathon thrust belt; structure, stratigraphy, and hydrocarbon potential. West Texas Geological Society, 39-64. Rice, J. R., and Cleary, M. P., 1976, Some basic diffusion solutions for fluid-saturated elastic porous media with compressible constituents: Rev. Geophys. Space Phys., 14, 227-241. Roche, S. L., 1997, Time-lapse, multicomponent, three-dimensional seismic characterization of a San Andres shallow shelf carbonate reservoir, Vacuum Field, Lea County, New Mexico: Ph.D. Thesis, Colorado School of Mines. Ross, C. P., Cunningham, G. B., and Weber, D. P., 1996, Inside the crossequalization black box: The Leading Edge, 11, 1233-1240. Sammonds, P. R., Ayling, M. R., Meredith, P. G., Murrell, S. A., and Jones, C., 1989, A laboratory investigation of acoustic emission and elastic wave velocity changes during rock failure under triaxial stresses. In “Rock at Great Depth”, A. A. Balkema, 233-240. Sayers, C. M., Van Munster, J. G., and King, M. S., 1990, Stress-induced ultrasonic anisotropy in Berea sandstone: Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 27, 429-436. Schoenberg, M., 1980, Elastic wave behavior across linear slip interfaces: J. Acoust. Soc. Am., 68, 1516-1521. Schoenberg, M., and Douma, J., 1988, Elastic wave propagation in media with parallel fractures and aligned cracks: Geophys. Prospect., 36. 571-590. Schoenberg, M., and Muir, F., 1989, A calculus for finely layered anisotropic media: Geophysics, 54, 581-589.
181
Scott, T. E., Ma, Q., and Roegiers, J. C., 1993, acoustic velocity changes during shear enhanced compaction of sandstone: Proc. 34th Symp. Rock Mechanics, A. A. Balkema, 29-32. Scuta, M. S., 1997, 3-D reservoir characterization of the Central Vacuum Unit, Lea County, New Mexico: Ph.D. Thesis, Colorado School of Mines. Segall, P., 1992, Induced stresses due to fluid extraction from axisymmetric reservoirs: Pure App. Geophys., 139, 535-560. Segall, P., and Fitzgerald, S. D., 1998, A note on induced stress changes in hydrocarbon and geothermal reservoirs: Tectonophysics, 289, 117-128. Shumaker, R. C., 1992, Paleozoic structure of the Central Basin uplift and the adjacent Delaware Basin, west Texas: AAPG Bulletin, 76, 1804-1824. Simmons, G., and Wang, H., 1971, Single crystal elastic constants and calculated aggregate properties: a handbook: M.I.T. Press, Cambridge. Sondergeld, P. G., and Rai, C. S., 1992, Laboratory observations of shear-wave propagation in anisotropic media: The Leading Edge, 11, No. 2, 38-44. Thomas, A. L., 1993, Poly3D: A three-dimensional, polygonal element, displacement discontinuity boundary element computer program with application to fractures, faults, and cavities in the earth’s crust: M.S. Thesis, Stanford University. Thomsen, L., 1988, Reflection seismology over azimuthally anisotropic media: Geophysics, 53, 304-313. Thomsen, L., Tsvankin, I., and Mueller, M. C., 1999, Coarse-layer stripping of vertically variable azimuthal anisotropy from shear-wave data: Geophysics, 64, 1126-1138. Tsvankin, I., 2001, Seismic signatures and analysis of reflection data in anisotropic media: Elsevier. van der Kolk, C. M., Guest, W. S., and Potters, J. H. H. M., 2001, The 3D shear experiment over the Naith field in Oman: the effect of fracture-filling fluids on shear propagation: Geophys. Prosp., 49, 179-198. Walsh, J. B., 1965, The effect of cracks on the compressibility of rocks: J. Geophys. Res., 70, 381-389. Walper, J. L., 1977, Paleozoic tectonics of the southern margin in North America: Gulf Coast Association of Geological Societies, 27, 230-241. Wang, Z., Cates, M. E., and Langan, R. T., 1998, Seismic monitoring of a CO2 flood in a carbonate reservoir: A rock physics study: Geophysics, 63, 1604-1617.
182
Ward, R. F., Kendall, C. G., and Harris, P. M., 1986, Upper Permian (Guadalupian) facies and their association with hydrocarbons: Permian Basin, West Texas and New Mexico: AAPG Bulletin, 70, 239-262. Winterstein, D. F. and Meadows, M. A., 1991a, Shear-wave polarizations and subsurface stress directions at Lost Hills field: Geophysics, 56, 1331-1348. Winterstein, D. F. and Meadows, M. A., 1991b, Changes in shear-wave polarization azimuth with depth in Cymric and Railroad Gap oil fields: Geophysics, 56, 1349-1364. Willis, H., Rethford, G., and Bielanski, E., 1986, Azimuthal anisotropy: Occurrence and effects on shear wave data quality: 56th Ann. Internat. Mtg., Soc. Explor. Geophys., Expanded Abstracts, 468-470. Xu, S., 1998, Modelling the effect of fluid communication on velocities in anisotropic porous rocks: Int. J. Solids and Structures, 35, 4685-4707. Yang, K. M., 1993, Late Paleozoic synorogenic stratigraphy, tectonic evolution, and flexural modeling of the Permian Basin, West Texas and New Mexico: Ph.D. Thesis, Texas A&M University. Yang, K. M., and Dorobek, S. L., 1991, The tectonic mechanism for uplift and rotation of crustal blocks in the Central Basin Platform, Permian Basin, Texas and New Mexico: AAPG Bulletin, 75, 698. Yang, K. M., and Dorobek, S. L., 1992, Tectonic mechanisms for formation of the Central basin Platform and adjacent basinal areas, Permian Basin, Texas and New Mexico: AAPG Bulletin, 76, 586. Yang, K. M., and Dorobek, S. L., 1993, Late Paleozoic synorogenic stratigraphy and tectonic evolution of the Permian Basin, West Texas and New Mexico: In: Gibbs-J., and Cromwell, D. eds., New dimensions in the Permian Basin, West Texas Geological Society, 93, 8-18. Yang, K. M., and Dorobek, S. L., 1995, The Permian Basin of West Texas and New Mexico: tectonic history of a "composite" foreland basin and its effects on stratigraphic development. In: Stratigraphic evolution of foreland basins. Special Publication - SEPM 52, 149-174. Yin, H., 1992, Acoustic velocity and attenuation of rocks: isotropy, intrinsic anisotropy, and stress induced anisotropy: Ph.D. Thesis, Stanford University. Zatsepin, S. V., and Crampin, S., 1997, Modeling the compliance of crustal rock: I, Response of shear-wave splitting to differential stress: Geophys. J. Int., 129, 477-494. Zimmermann, R. W., 1991, Compressibility of sandstones: Elsevier.
183
Zoback, M. L., Zoback, M. D., Adams, J., Assumpcao, M., Bell, S., Bergman, E. A., Bluemling, P., Brereton, N. R., Denham, D., Ding, J., Fuchs, K., Gay, N., Gregersen, S., Gupta, H. K., Gvishiani, A., Jacob, K., Klein, R., Knoll, P., Magee, M., Mercier, J. L., Mueller, B. C., Paquin, C., Rajendran, K., Stephansson, O., Suarez, G., Suter, M., Udias, A., Xu, Z. H., and Zhizin, M., 1989, Global patterns of tectonic stress: Nature, 341, 291-298. Zoback, M. D., and Zoback, M. L., 1989, Tectonic stress field of the continental United States: Mem. Geol. Soc. Am., 172, 523-540. Zoback, M. D., and Zoback, M. L., 1991, Tectonic stress field of North America and relative plate motions. In: Neotectonics of North America. Geol. Soc. Am. 339-366. Zoback, M. L., 1992, First- and second-order patterns of stress in the lithosphere: the World Stress Map Project: J. Geophys. Res., 97, 11703-11728.
