4D QUANTITATIVE INTERPRETATION OF JUBARTE FIELD (BRAZIL) - AN
INTEGRATED APPROACH
by
c
Copyright by Andrea Damasceno, 2020 All Rights Reserved
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 Master of Science (Geo-physics). Golden, Colorado Date Signed: Andrea Damasceno Signed: Dr. Ali Tura Thesis Advisor Golden, Colorado Date Signed: Dr. Paul Sava Professor and Head Department of Geophysics
ABSTRACT
The use of time-lapse (4D) seismic data and quantitative interpretation is essential in the characterization and monitoring of oil reservoirs. This information reduces reservoir management risk, allows better well designs and placement, and improves history-matching. This work studies the application of 4D quantitative interpretation on the post-salt reservoir of the Jubarte field, a Brazilian deep-water oil field.
In this project, I face the challenge of conducting a 4D study using seismic acquisitions only one year apart, which is a short interval to observe significant time-lapse changes. However, a high repeat permanent reservoir monitoring system (PRM) helps detect small time-lapse signals. Conventionally, 4D interpretation is conducted with only PP-wave re-flection data. In this thesis, I use 4D PS-wave rere-flection data as well. I present a novel integrated interpretation of joint PP-PS elastic inversion, as well as PP and PS time-shift volumes. Further, I build a rock physics model from well and core data.
A detailed comparative analysis of PP and joint PP-PS inversion shows that the joint inversion results are superior in terms of noise content and spatial continuity. Also, the 4D PP-PS joint inversion estimates show a better match with the rock physics models, allowing for more reliable interpretation. 4D time-shifts are integrated with 4D inversion results to discriminate between pore pressure and fluid saturation changes. I observe that time-shifts and inversion estimates provide information on reservoir properties at different scales.
The integrated interpretation of the different 4D seismic attributes brings a much broader view, since it uses independent data with complementary information to differentiate the effects of saturation and pore pressure changes as the field produces. The information gener-ated in this project can be used to update Jubarte’s flow simulator, for placing new injection and producers wells (which can bring significant savings, considering the high cost of drilling offshore wells), in addition to the improved production.
TABLE OF CONTENTS
ABSTRACT . . . iii
LIST OF FIGURES . . . viii
LIST OF TABLES . . . xvii
LIST OF ABBREVIATIONS . . . xviii
ACKNOWLEDGMENTS . . . xix
DEDICATION . . . xx
CHAPTER 1 INTRODUCTION . . . 1
1.1 From Seismic Amplitudes to Earth Properties . . . 1
1.2 Objectives and Added Value of Research . . . 5
1.3 Jubarte Field . . . 6
1.4 Geological Setting . . . 7
1.5 Data Available . . . 12
1.5.1 Seismic . . . 12
1.5.2 Well Logs, Petrographical and Petrophysical Data . . . 13
1.5.3 Laboratory Core Measurements . . . 16
1.5.4 Horizons . . . 16
1.5.5 Engineering Data . . . 17
CHAPTER 2 ROCK PHYSICS MODELS . . . 18
2.1 Jubarte Sandstones: Depositional and Mineralogic Settings . . . 18
2.3 4D Rock Physics Template . . . 24
2.3.1 Modeling Water Salinity Difference Effects on 4D Response . . . 28
2.4 Compressibility Measurements and Biot’s Coefficient Estimation . . . 30
2.5 Modeling Time-shifts . . . 38
2.5.1 Pore Pressure Changes: Compaction Effect . . . 39
2.5.2 Pore Pressure Changes: Velocity Effect . . . 40
2.5.3 Water Saturation Changes . . . 41
2.6 Final Remarks . . . 44
CHAPTER 3 PRE-STACK SEISMIC INVERSION: PP AND JOINT PP-PS . . . 45
3.1 PRM Seismic Acquisition . . . 45
3.2 4D Seismic Processing . . . 46
3.3 NRMS Error between Monitor 1 and 2 . . . 47
3.4 Fundamentals of Seismic Amplitude Inversion . . . 49
3.4.1 Seismic Wave Modes . . . 49
3.4.2 PP Elastic Inversion . . . 51
3.4.3 Joint PP-PS Elastic Inversion . . . 53
3.4.4 Solving Inverse Problems . . . 56
3.4.5 4D Inversion . . . 57
3.5 4D Elastic Inversion Workflows . . . 58
3.6 Common steps for PP and PP-PS Inversion . . . 60
3.6.1 Seismic Data Loading and QC . . . 60
3.6.2 PP Seismic Alignment . . . 65
3.6.4 Wavelet Estimation . . . 68
3.6.5 Low-Frequency Model (LFM) . . . 69
3.6.6 PP Seismic Inversion . . . 71
3.6.7 Joint PP-PS Seismic Inversion . . . 71
3.6.8 Inversions Results . . . 72
CHAPTER 4 4D SEISMIC TIME-SHIFTS . . . 87
4.1 Data Preparation . . . 87
4.2 Time-Shifts Extraction . . . 87
4.3 PP Time-Shifts . . . 89
4.4 PS Time-Shifts . . . 94
CHAPTER 5 INTEGRATED 4D INTERPRETATION . . . 99
5.1 4D Interpretation of PP-PS Joint Inversion . . . 99
5.2 Coordinate Transformation to Obtain Pressure and Saturation Estimates . . 106
5.3 Integration of Sw and Pp Estimates with PP and PS Time-shifts . . . 108
5.4 Integration with Production Data . . . 116
CHAPTER 6 DISCUSSION AND CONCLUSIONS . . . 119
6.1 Rock Physics Models . . . 119
6.2 PP and Joint PP-PS Seismic Inversion . . . 120
6.3 4D Interpretation . . . 120
6.4 Recommendations . . . 122
REFERENCES CITED . . . 123
APPENDIX A INVERSION ADDITIONAL INFORMATION . . . 128
A.2 PP-PS Seismic Alignment . . . 130
A.3 PP and Joint PP-PS Seismic Inversion Parameters . . . 131
A.4 PP and PS Stacks NRMS Maps . . . 131
A.5 Inversion Results NRMS maps . . . 139
LIST OF FIGURES
Figure 1.1 Diagram showing the energy partitioning of a P seismic wave at the interface between two media. A fraction of the incident P-wave is reflected as P (PP-wave), another is converted to S (PS-wave), and the remaining energy is transmitted as P or S wave. Snell law states the
relationship between θ, θS, θ1, and θ1,S. . . 2
Figure 1.2 Map showing the geographical location of Jubarte field. . . 8
Figure 1.3 Graph showing the 20 largest daily oil and gas production fields in Brazil. Jubarte is highlighted in both graphs by the red arrow (ANP, 2019). . . 9
Figure 1.4 Stratigraphic chart of the Campos basin. The red rectangle highlights the interval where the Jubarte post-salt reservoir occurs. Modified from Castro & Picolini (2015). . . 10
Figure 1.5 Schematic geological cross-section (Bastos, 2017). . . 11
Figure 1.6 Description of the data available for the project. . . 12
Figure 1.7 Seismic project design (modified from Dariva et al. (2016)). . . 14
Figure 1.8 Map showing the position of the wells compared to the area covered by the seismic. . . 15
Figure 1.9 List of logs available for the wells located inside the area covered by the seismic. DT is the compressional sonic, DTS is the shear sonic, RHOB is the density, GR is the gamma ray, RES is the deep resistivity, CAL is the caliper, NEU is the neutron, SW is the water saturation, and VCL is the clay volume log. . . 16
Figure 2.1 Original composition of 55 samples from Jubarte Field, plotted in Folk (1968) diagram. Modified from Fontanelli et al. (2009). . . 19
Figure 2.2 Optical photomicrographs illustrating the texture and framework for Jubarte sands: (A) poorly sorted sandstone; (B) sub-angular quartz grains. Modified from Fontanelli et al. (2009). . . 20
Figure 2.3 Plots of P-Impedance (left) and S-Impedance (right) versus confining pressure and porosity for all Jubarte samples. The surface exhibited in the figure is the best fit for the samples considering the function in
equation 2.2. . . 22 Figure 2.4 Plots of P-Impedance (left) and S-Impedance (right) with pore pressure
and porosity for all Jubarte samples. The surface shown in this figure
is the best fit for the samples considering a function such as 2.2. . . 24 Figure 2.5 Percentage changes in S-impedance and P-impedance, showing all
possible changes in the reservoir from its original state (water saturation increase – red lines, gas saturation increase – green lines,
and pore pressure increase/decrease – blue lines). . . 26 Figure 2.6 4D RPT with the NRMS polygons for 4.5%, 10%, and 20% plotted on
it. . . 29 Figure 2.7 Table showing the sensitivity of the reservoir properties to changes in
seismic NRMS values. . . 29 Figure 2.8 Comparison between the reservoir’s sensitivity to changes in water
saturation, considering three scenarios: brine replacing oil - red line; injected water (with lower salinity than brine) replacing oil - cyan line; and injected water replacing brine - purple. Pore pressure change line
is also shown (blue). . . 30 Figure 2.9 Workflow to estimate compressibility from well logs and core data. . . 34 Figure 2.10 Compressibilities and Biot’s coefficient estimated for EXT-1. Track 1
exhibits SW overlaid on VCL. Track2 shows density and porosity logs overlaid. Track 3 displays Kdry from core and well logs, compared to Ksat (derived from density and sonic logs). The Biot’s coefficient calculated from well logs and core data are shown in track 4. The derived Kp uniaxial and hydrostatic from logs, core, and direct
measurements are shown in track 5 (uni) and 7 (hydro). Tracks 6 and 8 show the calculated compressibilities, uniaxial in track 6 and
hydrostatic in track 8. The confining pressure that was used as a reference to choose the direct compressibility measurement value is
Figure 2.11 Compressibilities and Biot’s coefficient estimated for EXT-3. Track 1 shows the VCL log. Track2 shows deep resistivity log. Track 3 displays the density log. The Biot’s coefficient calculated from core data is shown in track 4. The derived Kp uniaxial and hydrostatic from core and lab measurements are shown in track 6 (uni) and 8 (hydro). Tracks 7 and 9 show the calculated compressibilities, uniaxial in track 7 and hydrostatic in track 9. The confining pressure that was used as a reference to choose the direct compressibility measurement value is
shown in track 10. . . 36 Figure 2.12 Compressibilities and Biot’s coefficient estimated for JMP-4. Track 1
shows the VCL log. Track2 shows deep resistivity log. Track 3 displays the density log. The Biot’s coefficient calculated from core data is shown in track 4. The derived Kp uniaxial and hydrostatic from core and lab measurements are shown in track 6 (uni) and 8 (hydro). Tracks 7 and 9 show the calculated compressibilities, uniaxial in track 7 and hydrostatic in track 9. The confining pressure that was used as a reference to choose the direct compressibility measurement value is
shown in track 10. . . 37 Figure 2.13 Estimates of time-shifts with P p change assuming different R values. . . 40 Figure 2.14 Plot of estimated time-shifts versus ∆P p. . . 41 Figure 2.15 Schematic diagram illustrating the calculation of depth reference
interval for water saturation changes time-shifts estimation. h is the reservoir thickness, zb and zm, are the water columns for base and monitor, respectively, and ∆Sw is the change in water saturation
between base and monitor. . . 42 Figure 2.16 Plot of estimated time-shifts versus ∆Sw for different water columns
values. . . 43 Figure 3.1 NRMS map between monitor 1 and monitor 2 PP full-stack, for a 200
ms time window above the top of reservoir. In the left corner a plot of
the NRMS histogram shows the mean value. . . 48 Figure 3.2 Plot of NRMS versus source and receiver positioning differences. This
is a modified version from the original plot from Brown & Paulsen
(2011) with PRM Jubarte data inserted for comparison. . . 49 Figure 3.3 Illustration showing the relationship between the particle displacement
Figure 3.4 Plot of the trigonometric coefficients of each term in equation 3.3 versus angle of incidence (VP
VS is assumed to be equal to 2). . . 52 Figure 3.5 Plot of the trigonometric coefficients of each property contrast in
equation 3.7 versus angle of incidence (to build the plot VP
VS is assumed
equal to 2). . . 55 Figure 3.6 Simplified ilustration of the workflow used to perform PP elastic
inversion. . . 59 Figure 3.7 Simplified ilustration of the workflow used to perform joint PP-PS
elastic inversion. . . 59 Figure 3.8 Seismic line showing data from PP monitor 1 and 2 partial stacks. . . 61 Figure 3.9 Seismic and synthetic data for well EXT-1. The graph on the right side
of the figure shows amplitudes of synthetic seismic, field seismic, and reflectivity plotted with the average incidence angle for each stack for top of Cretaceous reflection (indicated by the arrow). The wavelet used to model the synthetic data was extracted from mid-stack. . . 62 Figure 3.10 Seismic line showing data from PS monitor 1 and 2 partial stacks. . . 63 Figure 3.11 Seismic line showing data from PP and PS data for monitor 1. . . 64 Figure 3.12 Diagram summarizing the 3D and 4D alignment steps. The numbers in
the arrows indicate the step order in the sequence. . . 66 Figure 3.13 Comparison between PP and PS synthetics AVO curves for well
EXT-1, both AVO curves are for the Top of Cretaceous. . . 67 Figure 3.14 Wavelets estimated for PP angle-stacks. . . 68 Figure 3.15 Wavelets estimated for PS angle-stacks. . . 69 Figure 3.16 LFM for P-impedance overlaid on M1 Mid stack for comparison. On
the top, it is shown the model in its original frequency content, and on the bottom the model is shown after applying a high-cut filter centered at 6 HZ. Map view shows displayed line location. . . 70 Figure 3.17 Comparison between P-impedance estimates from PP data only (top)
and joint PP-PS data (bottom) inversion. . . 73 Figure 3.18 Comparison between S-impedance estimates from PP only (top) and
Figure 3.19 Comparison between band-passed S-impedance estimates from PP only (top) and joint PP-PS (data bottom) inversion. The frequency limits
of the bandpass filter is 8-12-55-65 Hz. . . 76 Figure 3.20 Comparison between band-passed density estimates from PP only
(top) and joint PP-PS (bottom) inversion. The frequency limits of the
bandpass filter is 8-12-55-65 Hz. . . 77 Figure 3.21 Comparison between the IP well log and the estimations of this
parameter from PP and joint PP-PS inversion. The comparisons are made in full-band (high-cut 55Hz) and band-limited (low-cut 8-12 Hz) frequency ranges. At the right-side it is shown a table with the
correlations between the well log and the inversion result to each
frequency range analyzed. . . 78 Figure 3.22 Comparison between the IS well log and the estimations of this
parameter from PP and joint PP-PS inversion. The comparisons are made in full-band (high-cut 55Hz) and band-limited (low-cut 8-12 Hz) frequency ranges. At the right-side it is shown a table with the
correlations between the well log and the inversion result to each
frequency range analyzed. . . 79 Figure 3.23 Comparison between the density well log and the estimations of this
parameter from PP and joint PP-PS inversion. The comparisons are made in full-band (high-cut 55Hz) and band-limited (low-cut 8-12 Hz) frequency ranges. At the right-side it is shown a table with the
correlations between the well log and the inversion result to each
frequency range analyzed. . . 79 Figure 3.24 Comparison between ∆IP (IPM 2 - IPM 1) estimates from PP only
(top) and joint PP-PS (bottom) inversion. . . 80 Figure 3.25 Comparison between ∆IS (ISM 2 - ISM 1) estimates from PP only (top)
and joint PP-PS (bottom) inversion. . . 81 Figure 3.26 RMS maps of ∆IP and ∆IS attributes in the reservoir interval. PP
inversion results are shown on the left side and joint PP-PS on the
right side. . . 83 Figure 3.27 For the PP stacks, it is shown a comparison between input data, PP
stacks residuals generated from PP inversion, and PP stacks residuals generated from joint PP-PS inversion. The workflow illustrates the generation of the outputs for PP and joint PP-PS inversion that are
Figure 3.28 For the PS stacks, it is shown a comparison between residuals and
synthetics for each angle-stack from joint PP-PS inversion. . . 85 Figure 3.29 Cross-plots between normalized ∆IP and ∆IS for PP (left side), and
joint PP-PS inversion (right side). The graphs on the top are for the entire data, and the ones on the bottom are for the anomaly close to INJ-10 (which was injecting water in the reservoir between the
acquisitions). The pore pressure (blue) and water saturation lines (red) from 4D rock physics template (Section 2.3.) . . . 86 Figure 4.1 Histograms of PP time-shifts and calculated quasi-correlation. . . 89 Figure 4.2 Calibrated rock-physics model estimate of PP time-shifts. The dashed
red rectangle highlights the regions from the expected changes in field
pore pressure and water saturation between M1 and M2. . . 90 Figure 4.3 Cross-section through the PP time-shift volume. . . 91 Figure 4.4 Maps from PP time-shifts volume. On top, as a reference, is shown the
top of reservoir. On the top-left, is the map calculated above the top of reservoir representing the background time-shift. On top-right the map at the time-shift extraction at the base of the reservoir. At the bottom, the differential time-shift map is shown. The red ellipse shown in the map is a slow-down anomaly, while the blue ellipses show speed-up
anomalies. . . 92 Figure 4.5 Cross-section through the time-shift anomalies from the base of the
reservoir time-shift map (shown on top). . . 93 Figure 4.6 Map view of the anomaly section locations on PP (top-left) and PS
(top right) time-shifts. Cross-section showing the PP and PS
time-shifts as labeled. . . 95 Figure 4.7 Amplitude-frequency cross-sections comparing PP and PS time-shifts
with the PP and PS full-stacks for monitor 2. . . 96 Figure 4.8 Maps from PS time-shifts volumes. On top, as a reference, is shown
the top of reservoir. Top-left is shown the background time-shift. Top-right is shown the time-shift extraction at the base of the
reservoir. The bottom map is the differential time-shift. . . 97 Figure 4.9 Differential time-shift maps from PP (left) and PS data. . . 98
Figure 5.1 Table summarizing the relationship between changes in the
petrophysical properties and variations in the 4D seismic attributes. It is also shown in the table a qualitative comparison between the
frequency content of each 4D attribute. . . 100 Figure 5.2 RMS amplitude maps extracted across the whole reservoir interval for
time-lapse IP (∆IP ) and time-lapse IS (∆IS) from 4D joint PP-PS
inversion. . . 101 Figure 5.3 Cross-section showing the anomalies identified in ∆IP map. . . 102 Figure 5.4 Maps showing the extracted amplitudes from ∆IP and ∆IS attributes
for the horizon mapped across the 4D anomaly indicated in Figure 5.3. 103 Figure 5.5 4D Rock Physics Template with the ∆IP and ∆IS values from field
data close to INJ-10 well and from the region between the producer wells (PROD-3 and PROD-19) displayed on top. Note the alignment of the injector well (red) with the Sw axis and the producers (blue) with
the pressure axis. . . 105 Figure 5.6 Top left corner is shown the original cross-plot between ∆IP and ∆IS
for the points in the region close to INJ-10 well. Lower right side corner is the ∆P p and ∆Sw cross-plot. Note large Sw changes with
4D time-shifts. . . 107 Figure 5.7 Top left corner is shown the original cross-plot between ∆IP and ∆IS
for the points in the region between PROD-3 and PROD-19 wells.
Lower right side corner is the ∆P p and ∆Sw cross-plot. . . 107 Figure 5.8 Maps from amplitudes extracted from ∆Sw and ∆P p attributes at the
anomalous mapped horizon. . . 108 Figure 5.9 Cross-section through ∆Sw and ∆P p attributes (cross-section line is
shown in the maps in the top of figures). The back dashed horizon plotted in the cross-lines is the same used to extract the maps. It is
possible to see the strong anomaly in Sw volume. . . 109 Figure 5.10 Comparison between ∆Sw, ∆P p, PP, and PS differential time-shifts
Figure 5.11 On top it is shown the differential time-shifts map (with opacity applied) overplayed the ∆Sw and ∆P p maps. Bottom, a cross-plot between ∆Sw and ∆P p, with the points colored by the PP time-shifts values. From this we can see that mostly of the most negative PP time-shifts (speed-ups) are associated to small pressure changes and
large Sw increases. . . 112 Figure 5.12 Cross-section from the seismic ∆Sw volume intersecting the region
where the time-shifts indicate a slow-down. The cyan dashed line
shows the Sw decrease that I believe is related with the slow-down. . . 114 Figure 5.13 Comparison between a map of pressure line contours for monitor 1 and
monitor 2 (derived form the flow simulator) with the PS differential time-shifts map. Both maps show the same pressure change behavior, what indicates PS time-shifts map can be used as an indicator of 4D
regional pressure changes. . . 115 Figure 5.14 Production data displayed over the attributes maps. The blue circles
radii are proportional to the volume of water injected by the injector wells, and the red circles radii are proportional to the produced oil
volume between acquisitions. . . 118 Figure A.1 Regional line displaying PP and PS seismic stacks. . . 128 Figure A.2 Time-shifs and correlations for the pairs Ultrafar-Near (top) and
Far-Near (bottom). The asterisk indicates in each experiment which is the reference volume. . . 129 Figure A.3 Time-shifs and correlations for Far-Mid. in this case, Mid was set the
reference volume. . . 130 Figure A.4 Comparison between seismic and synthetic for 5◦-25◦ PS stacks to:
original stacks (left), stacks after alignment using time-shifts from IS
volumes (center), and stacks after all PP-PS alignment steps (right). . 131 Figure A.5 Comparison between seismic and synthetic for 20◦-40◦ PS stacks to:
original stacks (left), stacks after alignment using time-shifts from IS
volumes (center), and stacks after all PP-PS alignment steps (right). . 132 Figure A.6 Comparison between seismic and synthetic for 35◦-55◦ PS stacks to:
original stacks (left), stacks after alignment using time-shifts from IS
volumes (center), and stacks after all PP-PS alignment steps (right). . 132 Figure A.7 Parameters used for PP inversion. . . 133
Figure A.8 Parameters used for joint PP-PS inversion. . . 133
Figure A.9 Table comparing the average NRMS error to PP stacks. . . 134
Figure A.10 Table comparing the average NRMS error to PS stacks. . . 134
Figure A.11 NRMS error maps for PP full stack. . . 134
Figure A.12 NRMS error maps for PP near stack. . . 135
Figure A.13 NRMS error maps for PP mid stack. . . 135
Figure A.14 NRMS error maps for PP far stack. . . 136
Figure A.15 NRMS error maps for PP ultra-far stack. . . 136
Figure A.16 NRMS error maps for PS full stack. . . 137
Figure A.17 NRMS error maps for PS near stack. . . 137
Figure A.18 NRMS error maps for PS mid stack. . . 138
Figure A.19 NRMS error maps for PS far stack. . . 138
Figure A.20 NRMS error maps for P-impedance (IP) to PP only and joint PP-PS inversion results. On the left side side, the IP NRMS map from PP inversion is shown. On the right side, the IP NRMS map from joint PP-PS inversion is shown. Both maps were calculated in a window 70 ms above the top of reservoir. . . 139
Figure A.21 NRMS error maps for S-impedance (IS) to PP only and joint PP-PS inversion results. On the left side side, the IS NRMS map from PP inversion is shown. On the right side, the IS NRMS map from joint PP-PS inversion is shown. Both maps were calculated in a window 70 ms above the top of reservoir. . . 140
LIST OF TABLES
Table 1.1 Key to correlate well name and type. . . 15
Table 2.1 Average mineralogy for Jubarte sands. . . 20
Table 2.2 Modeled fluid properties. . . 23
Table 3.1 Incidence angle range, and average angle for PP data stacks. . . 60
Table 3.2 Amplitude ratios between stacks for field and modeled data, and correction factors for PP data. . . 62
Table 3.3 Incidence angle range and average angle for PS data stacks. . . 63
Table 3.4 Amplitude ratios between stacks for field and modeled data, and correction factors for PS data. . . 65
LIST OF ABBREVIATIONS
Amplitude Variation with Angle . . . AVA Permanent Reservoir Monitoring . . . PRM X-ray difraction . . . XRD Petro-Elastic model . . . PEM Normalized Root Mean Squared . . . NRMS Low Frequency Model . . . LFM Pressure, Volume, and Temperature . . . PVT Gas-oil ratio . . . GOR Vertical Transverse Isotropy . . . VTI
ACKNOWLEDGMENTS
Firstly, I would like to pay my special regards to Petrobras for financial support so that I could pursue this master’s degree. I would also like to thank the Esp´ırito Santo production asset, especially the geophysicist Paula Dariva and the petroleum engineer Felipe Micchi for all the information made available about the Jubarte field. Also, I want to acknowledge
´
Alvaro Arouca for recommending my name on this opportunity and for the help provided when I needed it.
I wish to express my deepest gratitude to Dr. Ali Tura for being such a dedicated and patient advisor, who shared with me his vast experience and technical knowledge. I also thank the members of my thesis committee: Dr. James Simmons, Dr. Manika Prasad, Dr. Hossein Kazemi, and Dr. Guilherme Vasquez for generously offering their time and support throughout this work.
I would like to acknowledge the assistance of Frank Pereira and Diane Witters, who, in different ways, have made important contributions to the realization of this project.
I would also like to thank the“little Brazil team” (Odette, ´Atilas, Lu´ıza, Moacyr, Lucas, and J´ulia) for welcoming me and making me feel at home.
This project would never have succeeded without the help of my family. I thank my par-ents, Raimundo Damasceno e Severina Damasceno, and my brother, Adriano Damasceno, for all the support and affection received by me over the years. I also thank my husband, Max Velasques, and my daughter, Beatriz Velasques, who were my companions in this ex-traordinary adventure. I also thank my mother-in-law, Vera Velasques, who helped us so much during this time.
CHAPTER 1 INTRODUCTION
In this thesis, I present the integration of seismic attributes, obtained from PP and PS (converted) wave data, and their calibration to rock physics models and production data, using data from Jubarte field (Offshore Brazil). The guiding principle of this work is to extract as much information as possible from the whole set of available data for the field (including core measurements, well logs, seismic, and production data) in order to reduce uncertainties in the management of this producing reservoir.
Here, I summarize the work previously carried out in the field, briefly discuss the applied methodology, and present general information about the geology and the data available for carrying out this work.
1.1 From Seismic Amplitudes to Earth Properties
In 1919, Zoeppritz published a set of equations (Zoeppritz & Erdbebenwellen (1919)) de-scribing the relationship between the amplitude of the seismic waves reflected or transmitted at an interface and the contrasts between the properties of the media across this interface (Figure 1.1). These equations were not widely used in practice because they do not allow an easy interpretation of the energy partition phenomenon.
Almost 60 years later, in 1980, Aki and Richards published their famous equation, causing a paradigm shift in the interpretation of hydrocarbon reservoirs (Aki & Richards (1980))1
. This equation, a linearized version of Zoeppritz, made it possible to associate the seismic amplitudes with the contrasts of the elastic and acoustic properties of the rocks in a more intuitive way. According to Russell (2010), before the publication of this equation, the interpretation of seismic data was limited to the search for geological structures that pre-1
Besides Aki-Richards’s equation, there were other important approximations to Zoeppritz’s equations pub-lished in the same period, such as Shuey (1985), Fatti et al. (1994).
Figure 1.1: Diagram showing the energy partitioning of a P seismic wave at the interface between two media. A fraction of the incident P-wave is reflected as P (PP-wave), another is converted to S (PS-wave), and the remaining energy is transmitted as P or S wave. Snell law states the relationship between θ, θS, θ1, and θ1,S.
sented similarities with models of consolidated petroleum systems (such as that of anticline traps). The oil and gas industry realized at this point that information contained in seismic amplitudes could be explored to infer important characteristics of reservoirs. Ostrander is considered the first to introduce a practical application of the AVA effect, showing an ampli-tude variation with offset at the interface between a shale and a gas sand layer (Ostrander, 1984).
Initially, these amplitude analyses were performed over stacked data (post-stack), where anomalously high or low amplitudes (called “bright-spots” and “dim-spots”, respectively) could indicate the presence of hydrocarbon saturating the rock. Despite having some impact on reducing uncertainty, these analyses on stacked data still had many ambiguities.
Going beyond amplitude analysis in stacked data, the use of amplitude variations with angle of incidence to infer changes in rock properties is called AVA (or amplitude varia-tion versus angle) analysis in the energy industry. AVA analysis is done over pre-stack or partial-stacks (stacks by range of incidence angles), and can strongly contribute to further
reducing interpretation uncertainties. For example, with this methodology, one can differ-entiate the seismic response of high-porosity sandstone saturated with water from a similar rock saturated with light hydrocarbon.
Despite all its benefits and potential applications, AVA analysis is limited to a qualitative description of the phenomenon. The method can indicate changes in rock properties of the reservoir, but does not quantify them. For example, AVA analysis can give an indication that the porosity of the reservoir increases laterally (or spatially) in a certain direction, but does not allow to access the porosity values at the different locations or even measure the magnitude of the variation.
Quantitative analysis can be done via the inversion of seismic data amplitudes (known as AVA inversion). Seismic AVA inversion is a mathematical process that uses the same fundamentals of AVA to quantify the properties of the rock. Although the first publication on the topic dates from 1983 (Cooke & Schneider, 1983), inversion of seismic amplitudes started to be effectively developed in the 1990’s. Compared to AVA, this process involves greater use of computational resources.
Acoustic inversions were the first to be developed, using post-stack data to estimate acoustic properties of the reservoir (Cooke & Schneider (1983), Russell & Hampson (1991) and Martinez et al. (1991)). Connolly (1999) work presents the concept of elastic impedance, introducing an extension of the post-stack inversion for different angles of incidence. How-ever, this inversion proceeding is not simultaneous (it does not invert all angle-stacks at the same time) and needed post-processing to derive the elastic properties itself. Between the end of the 1990s and the mid-2000s, the first simultaneous elastic inversions were carried out (Rasmussen et al. (2004), Ma (2002), and Hampson et al. (2005)). In these inversions, all partial stacks are inverted at the same time, directly generating volumes of elastic rock properties as a product.
The next step in terms of improving seismic inversions was the combined use of PP and PS data (Figure 1.1 ). Algorithms capable of simultaneously inverting both data were created.
This increased the quality of the elastic property estimates. The first studies involving the PP-PS joint inversion were published in the early 2000s (Pendrel et al. (2000) and Hampson et al. (2005)). Although it has been under development for two decades, this topic is still active, attracting a lot of interest in the geophysical community. Recent advances in seismic acquisition and processing techniques for converted wave data have generated more reliable volumes, increasing the potential for successful multi-component inversions.
Elastic seismic inversions greatly increase the potential to get useful features from seismic data. They can provide essential information not only in the context of hydrocarbon ex-ploration, but also generating inputs for reservoir geological modeling and characterization. The inversion products can also be used to provide volumetric estimates reservoir static properties, such as porosity, clay volume, lithological and facies distribution, etc. Reservoir models, in turn, are used to simulate the flow of fluids in the porous medium, generating essential information for decision making related to the management of an oil field.
While inversion techniques were under development, in the late 1990s, the first publica-tions showing the use of 4D (or time-lapse) seismic to image the flow of fluids in the reservoir were published (see Landro et al. (1999), and Lumley et al. (1998)). 4D seismic interpreta-tion consists of analyzing the differences on a succession of 3D seismic surveys performed at different times during production (thus providing dynamic information). In the case of 4D seismic, we are interested in inferring the change of the reservoir properties over production time. The matching of reservoir flow simulation with wells production history is also facili-tated by the use of 4D seismic, which increases the flow simulator predictability (Mezghani et al., 2004).
As with conventional 3D interpretation, the use of inverted data for 4D interpretation allows to quantify the rock properties. In the case of 4D elastic inversions, it is possible to separate the effects of variation in pore pressure from changes in fluid saturation, effects that overlap when analyzing only the acoustic information (Tura & Lumley, 1998). According to Johnston (2013), modeling the sensitivity of each elastic property to changes in pressure
and fluid saturation is mandatory in 4D interpretation work.
Another attribute derived from 4D seismic data that can provide information about changes in reservoir properties through time is the time-shifts volume. These time-shifts represent changes in the seismic wave traveltimes to corresponding interfaces in the analyzed 4D seismic surveys, which in turn represent changes in seismic velocity or layer thickness (MacBeth et al. (2019) and Tura et al. (2005)). Seismic velocity changes can be associ-ated with several factors, including pressure changes, fluid saturation changes or reservoir compaction.
Both inversion and time-shifts are volumetric attributes extracted from the seismic data, and represent estimates of the elastic properties of the reservoir. Different attributes have different resolutions and also different sensitivities to changes in petrophysical and dynamic properties of the reservoir. For this reason, an integrated interpretation of this set of at-tributes may be the key to reducing uncertainty.
1.2 Objectives and Added Value of Research
The Jubarte field 4D seismic interpretation results are discussed in earlier work by Ramos Filho et al. (2017) and Thedy et al. (2015). These publications discuss the va-lidity of 4D anomalies in addition to providing relevant information for understanding the effects of injection operations performed in the field using estimated 4D elastic properties.
In this work, I extend the discussions held in previous publications. I interpret the results of a joint PP-PS inversion and time-shift volumes calculated from PP and PS data in an integrated way. This interpretation is carried out based on locally calibrated rock physics models and production data. The different attributes bring information that are complementary, and when used together, provide a broader view of the field properties distribution. Using this information, it is possible to optimize injection operations and identify prospective locations for new producer wells. Therefore, considering the high cost for drilling offshore wells, the information generated from a study like this has high added value.
Additionally, the use of inverted data has advantages over conventional amplitude data, especially in the case of amalgamated reservoirs (as is the case for Jubarte). In this work, I perform a comparative analysis of PP and joint PP-PS inversion results to verify the value of using the PS data in improving elastic inversion results. I also compare the inversions in terms of their capacity to solve P-impedance, S-impedance, and density. With this analysis, I aim to quantify the benefits of using multicomponent data in elastic inversion to reservoir characterization (3D) and reservoir monitoring (4D).
The results of this study indicate that the origins of the 4D anomalies can be distin-guished, and the method can provide information about compartmentalization of the reser-voir (which can help to place future injection and production wells). Also, integrating data from different scales and sources, helps to reduce uncertainties in interpretation. In quali-tative studies, the use of production data and models is mandatory to reduce ambiguity in interpretation. In quantitative interpretations, such as the one performed here, the separa-tion between pressure and saturasepara-tion effects is based on the differentiated sensitivity of the attributes to the contrasts of these properties.
Ultimately, the knowledge acquired here can also be applied to other oil fields with similar characteristics.
1.3 Jubarte Field
Jubarte field (meaning “humpback whale”) was discovered in 2001, but it started pro-duction in 2006. It is part of a cluster of oil fields with similar geological features, discovered in the same period, called parque das baleias (meaning “whales park”). Figure 1.2 shows the geographical location of this field, in the context of the other fields of the whales park. It is located in the northern part of the Campos Basin, 77 km offshore Espirito Santo state coast, in water depths around 1250 m.
According to the annual bulletin of the Brazilian National Oil and Gas Agency (ANP, 2019), Jubarte is the fourth largest oil producer and the sixth largest gas producer in Brazil (Figure 1.3). The field produces from two reservoir levels; from a shallow reservoir in
post-salt, whose daily production is 64 thousands barrels of oil, and a deeper reservoir in pre-salt level, which produces 150 thousands of oil barrels daily. Considering only the post-salt reservoir production itself (which is going to be the focus of this study), the field would be the ninth largest producer in the country. These numbers indicate the importance of this field to fulfill the Brazilian demand for oil. Given the importance of this field for Brazilian national oil and gas production, it is mandatory that the best technologies/methodologies be used to characterize it. Improving the understanding of reservoir static and dynamic properties distribution can increase further the production of the field by better or less well placement.
1.4 Geological Setting
The dominant regime in the formation of the Campos basin, and other sedimentary basins off the coast of Brazil, is the separation of the Gondwana super-continent and the opening of the South Atlantic.
The stratigraphy of the Campos Basin is traditionally divided into three large tectonic-sedimentary units or mega-sequences: Rift sequence, Transitional (or post-Rift sequence), and Passive Margin (or Drift sequence) (Winter et al. (2007)). Figure 1.4 shows the strati-graphic chart of the Campos basin and the intervals corresponding to the mentioned sedi-mentary sequences are highlighted. Jubarte turbiditic sandstones are part of the Carapebus Formation, while the mudstones that seal the oil accumulation are from the Ubatuba For-mation.
Figure 1.5 shows the main structural features of the basement underlying the basin. According to de Castro & Picolini (2015), this structural framework controlled the tectonic-sedimentary features of the Rift and Transitional sequences. The sedimentation of the Passive Margin Sequence was controlled by the combination of this compartmentalization with the crustal thermal subsidence and halokinetic movement.
The main source rocks were deposited during the continental rift phase, but the reservoirs deposition extends between Neo-comian fractured volcanic rocks to Miocene turbidites from
Figure 1.3: Graph showing the 20 largest daily oil and gas production fields in Brazil. Jubarte is highlighted in both graphs by the red arrow (ANP, 2019).
Figure 1.4: Stratigraphic chart of the Campos basin. The red rectangle highlights the interval where the Jubarte post-salt reservoir occurs. Modified from Castro & Picolini (2015).
Figure 1.5: Schematic geological cross-section (Bastos, 2017).
the marine regression sequence. It was during the evolution of the transgressive marine sequence that the sandstones of the Jubarte field were deposited (Fontanelli et al. (2009)). Salt-rooted growth faults allowed the accumulation of the turbiditic sandstones interbedded with mudstones, with a high net-to-gross ratio (75%). Later on, the salt movement caused a structural inversion that formed the oil trap. The field is truncated by a northeast extensional fault and also crossed by several minor northwest faults.
According to Gontijo et al. (2005), the Jubarte trough, 8 to 14 km long and 1.5 to 5.5 km wide, was filled with coarse-grained sediments deposited by highly confined density flows. The reservoir has an average thickness of 400 m and is formed by a succession of staked channel complexes. The main sedimentary facies observed are conglomerates, massive and cross-bedded sandstones, marls and chaotic debris flows. The depositional cycles are of metric thickness, fining upwards, composed by conglomerates, coarse-grained sandstones, aligned pebbles and fine-to-medium-sized sandstones. The presence of angular to sub-angular shape grains and fragments of coal and vegetables, suggests the erosion of nearby continental source rocks during large river floods (hyperpicnal flows).
1.5 Data Available
Figure 1.6 shows the data available to be used in this project. The suite of data that Petrobras made available to be used in this work is broad. It is composed of seismic data, mapped horizons and tops, logs from 43 wells, lab core velocity measurements, petrografi-cal and petrophysipetrografi-cal data, production data, and some engineering measurements. In the following sub-sections I describe each of these data and comment on how they were used in the project.
Figure 1.6: Description of the data available for the project.
1.5.1 Seismic
The seismic data used in this project comes from a PRM (Permanent Reservoir Mon-itoring) acquisition system. This type of acquisition is ideal for reservoir characterization projects, as its main objective is to maximize the similarity of seismic surveys, using fixed receivers positioned on the seabed. It is important to mention that the acquisition did not cover the entire Jubarte reservoir, being focused on the southernmost portion of the
field. In this region, stimulation operations (water injection) were active during the seismic acquisitions period.
The Jubarte PRM project is the first of its kind in ultra-deep waters. Dariva et al. (2016) describes the system as being composed by an active and a passive part. The active part of the seismic cable and receiver system (dry-end) was installed on the P-57 platform. The passive part (wet-end) is composed of 100% optical receiver cables, lead-in cables (extension), HUB (centralizer) and connectors (wet-mate). A riser connects the subsea system to the control room (“4D room”) on P-57. Figure 1.7 illustrates the design of this acquisition system and also shows the shot and receiver coverage area. Details on the acquisition and processing of these data that are relevant to this project are discussed in Chapter 3. The seismic data used as input for the seismic inversions were the partial stacks after the application of some filters to remove noise (without application of gains). For the generation of time-shifts, new full-stack volumes were generated from the post-migration gathers. Quality control and details on the generation of the stacks is discussed in Chapter 4.
1.5.2 Well Logs, Petrographical and Petrophysical Data
Forty-three wells are available for use in this project, of which only 21 are in the area covered by the 4D seismic. Figure 1.8 exhibits a map showing the region covered by the seismic in relation to the wellheads. Figure 1.9 shows a list of all available logs for the wells located within the area covered by the seismic. The last two columns of the table (SW and VCL) refer to available petrophysical logs calculated from log and core data. The wells highlighted in red in the table in the Figure 1.9 are the ones that have all the logs. I am going to deal with this issue in more detail in Chapter 3, but wells outside the area covered by seismic can not be used in some steps of the inversion (wavelet estimation, quality controls, etc.). However, the data associated with these wells can be used to enrich the rock physics models that are valid for the entire field. The wells have their original nomenclature altered, but the names chosen are correlated with the type of well like shown in Table 1.1.
Some reports containing petrographic analyzes on thin sections and lateral samples were also made available, which were used as input for the modeling presented in the Chapter 2. The information contained in these reports and XRD (X-ray diffraction) analysis made it possible to calibrate the mineralogical composition and certify the levels of cementation present in different reservoir intervals.
Figure 1.8: Map showing the position of the wells compared to the area covered by the seismic.
Table 1.1: Key to correlate well name and type. Name Prefix Meaning
PION Pioneer (Wild cat)
EXT Extension
JMP Deepest reservoir
PROD Production
INJ Injection
Figure 1.9: List of logs available for the wells located inside the area covered by the seismic. DT is the compressional sonic, DTS is the shear sonic, RHOB is the density, GR is the gamma ray, RES is the deep resistivity, CAL is the caliper, NEU is the neutron, SW is the water saturation, and VCL is the clay volume log.
1.5.3 Laboratory Core Measurements
Lab measurements of ultrasonic P and S seismic velocities on 69 samples were also pro-vided. The measurements were made under different confining pressure, ranging from 500 to 6000 psi. These measurements are the main input for the generation of the rock physics models presented in the Chapter 2.
In addition, I received hydrostatic compressibility measurements performed at different pressures for a set of samples from three wells sampling the reservoir. These measurements were used in the calculation of the Biot’s coefficient and also as an input for modeling the magnitude of time-shifts presented in Chapter 2.
1.5.4 Horizons
Three horizons mapped by the interpreters of the field were provided for use in this study. The horizons are: the top of the Cretaceous, top of reservoir and base of reservoir. These
horizons were used as input to generate the inversion low frequency models and also as a basis for the interpretations of the seismic attributes.
1.5.5 Engineering Data
PVT measurements were used as a reference to build the templates for interpreting the 4D inversion (presented in the Chapter 2).
Saturation and pressure maps for the acquisition periods, generated from the flow sim-ulator, were also given by the field reservoir engineers. Additionally, the volumes of water injected by the injector wells and cumulative volumes of oil, gas, and water produced by the producer wells were provided.
CHAPTER 2
ROCK PHYSICS MODELS
In this chapter, I present rock physics models built to represent Jubarte reservoir be-havior. Due to the short interval between the time-lapse (4D) seismic acquisitions2
, just one-year apart, small variations in reservoir elastic properties are expected. The questions that arise are as follows: Are the contrasts in elastic properties large enough to be recovered from seismic? How can we relate the elastic properties contrasts with variations in fluid saturation and pore pressure? Do 4D time-shifts have significant value?
Additionally, all these analysis must be carried out considering the level of seismic re-peatability. It is necessary to verify whether the observed contrasts exceed the 4D noise level present in the field data.
Trying to address these issues, I begin the chapter providing general information about Jubarte sands. After that, I present the steps for the construction of a Petro-Elastic model (PEM) calibrated for the field. This model is the key to interpret 4D anomalies. Also, infor-mation derived from this model is used to estimate the relationship between fluid saturation and pore pressure changes from seismic velocities and impedances (product of velocity and density). Additionally, it can be used to model the expected magnitudes for 4D time-shifts. I implemented all the models discussed in this chapter using the Python programming language. The scripts are available in Appendix B of this thesis.
2.1 Jubarte Sandstones: Depositional and Mineralogic Settings
The work of Fontanelli et al. (2009) presents a detailed provenance study for Jubarte reservoir sandstones. In this work, they show that the reservoir is composed of Arcosian sandstones, with moderate to high percentage of feldspar (plagioclase, and K-feldspar). Fig-ure 2.1 shows data from Jubarte cuttings and cores plotted in Folk’s diagram, visually 2
illustrating the proportion of quartz, feldspar and lithic fragments. The original quartz-feldspathic, lithic-poor detritic composition of Jubarte sandstones indicates a provenance from continental blocks of the uplifted basement.
The sands are fine to very coarse-grained, sometimes conglomeratic. They have poor sorting and angular to sub-angular grains (Figure 2.2). Some samples analyzed showed a large amount of fine grains, mainly kaolinite and illite-smectite. Table 2.1 shows the average mineralogy that was used as the basis for calculating the effective elastic moduli necessary for modeling.
Figure 2.1: Original composition of 55 samples from Jubarte Field, plotted in Folk (1968) diagram. Modified from Fontanelli et al. (2009).
The level of replacement and dissolution intensity associated with diagenesis was limited. Feldspar grains were more affected, being replaced by kaolinite, carbonates, pyrite, and albite. Besides, they were affected by dissolution along cleavages and twinning planes. The degree of dissolution was variable. Detrital quartz was locally replaced by blocky dolomite. Carbonate cementation was localized and occurs only as concretions.
Figure 2.2: Optical photomicrographs illustrating the texture and framework for Jubarte sands: (A) poorly sorted sandstone; (B) sub-angular quartz grains. Modified from Fontanelli et al. (2009).
Table 2.1: Average mineralogy for Jubarte sands. Mineral Fraction Quartz 0.49 K-Felspar 0.12 Plagioclase 0.24 Dolomite 0.03 Pyrite 0.03 Kaolinite 0.02 Ilite 0.03 I/S 0.03
2.2 Petro-Elastic Model
According to Wulff et al. (2008), a rock physics model provides the link between reservoir properties (such as porosity, mineralogy, shale volume, etc.) and the elastic parameters that control the seismic response (seismic velocities and density). Also, it should incorporate the dynamic effects to explain, for example, how pore pressure and fluid saturation changes affect seismic.
When dealing with the use of time-lapse seismic to estimate changes in dynamic proper-ties, it is necessary to consider the intrinsic coupling of pressure and saturation. Increasing the pore pressure decreases the volume modulus of the rock, but increases that of the fluid. Alternatively, injection of water into the reservoir can both increase the bulk moduli, through increasing water saturation, and reducing the bulk moduli by increasing the pore pressure.
The sensitivity of rocks to pressure variation can be addressed by laboratory measure-ments performed on core samples. As already mentioned in Chapter 1, I have P and S velocity measurements available for 69 samples, from 4 wells (EXT-3, EXT-1, JMP-1, and JMP-4).
MacBeth (2004) explains that the behavior of the changes in the bulk and shear modulus (and therefore of the seismic P and S velocities) with pressure has an asymptotic behavior. This behavior is due to the presence of cracks and micro-failures in the rock, generating an “excess of compliance” in the rocks associated with its larger aspect ratio. When the rock is subjected to increments of confining pressure, these small-scale flaws are easily closed, which progressively increases the elastic modulus of the rock. This effect occurs until all the most compliant pores are closed. From this point, the rock pressure sensitivity decreases until the asymptote is reached. When this pressure is reached, the remaining pores are those with near-zero compliance, and the pressure effects become negligible. Although other representations are used, the logarithmic function provides a very suitable mathematical representation to represent this asymptotic behavior (Vasquez et al., 2005). Figure 2.3 shows a plot of P-impedance (IP) and S-P-impedance (IS) versus confining pressure and porosity for Jubarte
samples. In the same figure, I show the best fit surface of a function with the general form P rop(φ, P ) = a + bφ + (c + dφ) ln P, (2.1) where Prop is the represented elastic property (K, µ, VP, VS, IP, IS, etc.); a, b, c, and d are the coefficients to be estimated that provide the best fit; φ is the porosity; and P is the confining pressure.
Figure 2.3: Plots of P-Impedance (left) and S-Impedance (right) versus confining pressure and porosity for all Jubarte samples. The surface exhibited in the figure is the best fit for the samples considering the function in equation 2.2.
Lab velocity measurements are usually made on dry samples. Thus, to include the sensi-tivity of rock properties to changes in fluid saturation, empirical relationships are generally used, such as Gassmann (1951). The equations used to perform the fluid property calcu-lations were extracted from Batzle & Wang (1992). To estimate the mineral effective bulk modulus I used the mineralogy displayed in Table 2.1 to average the mineral K and ρ values. The other information needed to calculate the fluid properties was obtained from the PVT3 data: the reservoir original pressure is 290 kgf/cm2
(or 28 MPa), water salinity is 140.000 ppm, the temperature is 76◦C (or 169◦F ), the oil is 17◦ API, and the gas-oil ratio (GOR) is 46. Table 2.2 shows the calculated fluid properties. The function shown in equation 2.1 3
can be expanded to incorporate the effects of fluid saturation on elastic properties via a polynomial term on water saturation. The resulting function has the form
P rop(φ, P, SW) = a + bφ + (c + dφ) ln P + eSw + f Sw 2
, (2.2)
where e and f are the new coefficients, φ is the total porosity, and Sw is the water saturation.
Table 2.2: Modeled fluid properties. Fluid K(GP a) ρ(g/cc)
Oil 1.17 0.87
Gas 0.066 0.197
Brine 3.256 1.085
Injected Water 2.838 1.028
Effective reservoir pressure can be given as
Pef f = Plitho− αPp, (2.3)
where Pef f is the effective pressure, Plitho is the lithostatic pressure, α is the Biot’s coefficient, and Pp is the pore pressure.
Thus, to write the PEM as a function of pore pressure (instead of effective pressure) it is necessary to calculate the lithostatic pressure and Biot’s coefficient. The lithostatic pressure is calculated by integrating the density well log extended to the sea bottom. The Biot’s coefficient can be estimated from well logs, cores, or compressibility measurements. This calculation will be explained in detail in Section 2.4.
Figure 2.4 shows a plot equivalent to Figure 2.3, expressed in terms of pore pressure variations instead of effective confining pressure. Impedances (and velocities) decrease with increasing pore pressure.
I only considered variations of density with fluid saturation, as this property does not vary with pressure. The relationship used is the mass balance equation, where the rock
Figure 2.4: Plots of P-Impedance (left) and S-Impedance (right) with pore pressure and porosity for all Jubarte samples. The surface shown in this figure is the best fit for the samples considering a function such as 2.2.
density is determined by combining the density of its constituents as follows:
ρ = (1 − φ)ρs+ φρWSW + φρHC(1 − Sw), (2.4) where ρs is the density of the solid rock part, ρW is the density of the water, and ρHC is the density of the hydrocarbon.
2.3 4D Rock Physics Template
The 4D rock physics template is an essential tool for 4D seismic interpretation. It ag-gregates all possible scenarios in terms of the reservoir 4D response. Using this kind of plot, it is possible to associate variations in pore pressure and fluid saturation with percentage changes in P- and S-impedance (Zachariassen et al., 2006). The concept behind the use of this template is the fact that fluid changes predominantly affect the P-impedance. In contrast, changes in pore pressure affect both S-impedance and P-impedance.
The locally calibrated PEM is used to generate estimated values of P and S-impedances for different scenarios. Those values are then normalized by the average of these properties for each base-monitor pair.
To build the template, for the base scenario an average reservoir porosity of 0.24, a 28 MPa (or 4061 psi) pore pressure, which is the original virgin field pressure, and water saturation (or Sw) of 0.2, which corresponds to reservoir irreducible water saturation. Variations in pressure and saturation of fluids almost always occur simultaneously. However, to better understand the contribution of each of these effects, it is necessary to generate curves where each effect is analyzed individually. Therefore, the monitor data was simulated as follows:
1. Changing the water saturation only 2. Changing the gas saturation only 3. Changing the pore pressure only
In Figure 2.5, the template built for Jubarte reservoir is shown. The base case is shown as a black dot. The purple star corresponds to the bubble point. The monitors associated with exclusive changes in water saturation (full red line) were generated by varying the water saturation from 0.2 to 0.8. In this case, I consider a two phases system: water and oil. Oil saturation can be written as So = 1 - Sw. This curve represents the movement of the water front due to production.
For the gas saturation (full green line), I consider a three-phase system: water, oil, and gas. Water saturation is fixed at 0.2. Gas saturation varies from 0 to 0.2, with intervals of 0.025. Oil saturation is equal to So = 1 - Sw - Sg. This curve represents cases where, for example, gas is injected into the reservoir, or gas is dissociated from the oil (disregarding associated pressure variations). The bubble point (18 MPa for Jubarte field) is plotted in this figure to be used as a reference (purple star). Below this pressure, the gas begins to dissociate from the oil. The effect of changing heavy oil to light gas causes substantial changes in P-impedance, due to the large difference in bulk modulus and density of these fluids (see Table 2.2).
It is important to mention that, since the field has been produced maintaining pore pressure higher the than bubble point, there is no free gas in reservoir conditions. Actually,
Figure 2.5: Percentage changes in S-impedance and P-impedance, showing all possible changes in the reservoir from its original state (water saturation increase – red lines, gas saturation increase – green lines, and pore pressure increase/decrease – blue lines).
the gas produced by the field is dissociated from oil at atmospheric pressure. In addition, the gas produced is not re-injected into the field.
For the pore pressure variations (full blue line), ranging from 15 to 36 MPa (or 2175 to 5221 psi) were modeled, at intervals of 1 MPa (or 145 psi). As previously mentioned, the original reservoir pressure is 28 MPa. Therefore, to generate cases with pressure increase, I start from 28 MPa and increase the pressure up to 36 MPa. For pore pressure reduction, I start from 28 MPa and progressively reduce the pressure until it reaches 15 MPa. These scenarios can be the basis for a field depletion process, or the pressure increase associated with injection (disregarding variations in the saturation of the fluids phases). The reservoir has a moderate sensitivity to variations in pore pressure, being more sensitive to pressure reduction than to pressure increase.
To get the time-lapse changes in P- and S-impedances (∆IP and ∆IS, respectively) in a scenario where both pore pressure and fluid saturation are changing, it is necessary to project both lines and take the intersection of the projected lines. This intersection point is the expected ∆IP and ∆IS change associated to the mixed Sw and P p variations.
The orange polygon highlighted in the upper right corner inserted in Figure 2.5 represents the elastic property changes necessary to get an NRMS of 4.5%. This is the average NRMS reference value for the Jubarte PRM acquisition4
. In order to calculate the NRMS values in this figure, it was necessary to calculate the reflectivities for each base-monitor pair, and use them in the NRMS calculation equation (shown in Section 3.3).
This polygon can be interpreted as representing the limit above which the contrasts of properties can reliably be extracted in this 4D project, since it is above the field noise level. As can be seen from the graph, small changes in fluid saturation already exceed the limit and should allow them to be reliably extracted from Jubarte time-lapse data. In the case of pore pressure changes, the limits are slightly higher, but still very low. Considering a scenario of mixed changes of saturation and pressure, it would be even easier to exceed the
4
seismic NRMS noise level.
Despite the similarities of the oil and water properties, and the limited time interval between the seismic acquisitions, the high repeatability of the PRM acquisition makes the 4D changes observable for Jubarte field post-salt reservoir. To illustrate the relation between seismic NRMS average error and the contrasts between elastic and reservoir properties, I made Figure 2.6. This figure shows the 4D rock physics template with three different NRMS average polygons plotted on it: 4.5% (Jubarte PRM PP stacks reference), 10%, and 20%. It is possible to notice that, as the seismic NRMS error increases, the region where the contrasts of the properties cannot be reliably estimated also expands. When considering changes in water and gas saturations, the impact on increasing NRMS is not very strong. However, when pressure changes are considered, the effect of the increasing seismic NRMS is substantial (especially when it comes to the sensitivity to pore pressure increments). As a reference, to quantify the sensitivity of the reservoir properties to the seismic NRMS error value, I built the table showed in Figure 2.7.
2.3.1 Modeling Water Salinity Difference Effects on 4D Response
In the time period between the seismic acquisitions, Jubarte received operations to stim-ulate production with water injection at two wells: INJ-5 and INJ-10. According to Thedy et al. (2015), the salinity of the water injected into the reservoir was 60,000 ppm, while the formation brine has a salinity of 140,000 ppm. This salinity difference is expressed in the bulk modulus and density of fluids, as shown in Table 2.2.
In well INJ-10, water is injected close to the oil-water contact. Thus, we can establish two different scenarios: injection water replacing oil, and injection water replacing brine. For well INJ-5, water was injected into the aquifer, that is, we only have the scenario where injected water replaces formation brine. To assess the effect of each scenario on the elastic properties, I generated the comparison shown in Figure 2.8.
The red curve in Figure 2.8 shows the changes for a production scenario, where brine replaces the oil. As the formation water has properties considerably different from the oil
Figure 2.6: 4D RPT with the NRMS polygons for 4.5%, 10%, and 20% plotted on it.
Figure 2.7: Table showing the sensitivity of the reservoir properties to changes in seismic NRMS values.
(see Table 2.2), the effect of this substitution on the elastic properties is significant. In the case where injected water replaces the oil (cyan curve), the effect of fluid substitution over the P-and S-impedances is slightly smaller, since both fluids have more similar properties. The scenario where the formation water is replaced by the injected water, that is, the effect of salinity contrast on elastic properties is shown in purple line. Comparing this modeling to the other cases, one can see that the effect is more subtle, but still representative (generating impedance contrasts up to 3%). The more water injected the lower the reservoir impedance. Besides, combining this effect with the pore pressure increasing due to injection can enhance the impedance decrease. However, it is important to mention that the injected water would mix with the aquifer water relatively quickly and dissipate from the well rapidly.
Figure 2.8: Comparison between the reservoir’s sensitivity to changes in water saturation, considering three scenarios: brine replacing oil - red line; injected water (with lower salinity than brine) replacing oil - cyan line; and injected water replacing brine - purple. Pore pressure change line is also shown (blue).
2.4 Compressibility Measurements and Biot’s Coefficient Estimation
In this project, it was necessary to calculate compressibilities and Biot’s coefficient to use them as inputs for time-shift modeling and pore pressure calculation. However, the
methodology presented here transcends its direct use of these properties for this project, and it can be useful for other applications.
The compressibility of materials is defined as the volume variation due to changes in the effective pressure (stress or tension) acting on it. Rock compressibility measurements can be used by reservoir engineers for: (1) calculation of oil in place by pressure decline data in undersaturated volumetric reservoirs, and (2) studies of natural water drive performance. In reservoir geophysics, these measurements can be used to estimate magnitudes of 4D time-shifts associated with pore pressure changes.
Despite all these possible applications for measurements of this property, direct mea-surements in the laboratory are scarce and very sparse. In this section, I present the im-plementation of the methodology proposed by Vasquez et al. (2019) to obtain continuous compressibility measurements from core and log data. These compressibilities are then com-pared to direct measurements of these properties obtained in the laboratory from a limited amount of samples from Jubarte field. Using the same input data, Biot’s coefficient is also determined.
For elastic porous media, there are two types porous volume: bulk volume (Vb, the total rock volume) and the porous volume (or Vp). It is also necessary to consider at least two types of pressures acting on the material: confining (Pc) and internal pore pressure (Pp). Therefore, it is necessary to define at least four different compressibilities. Following Zimmerman (1991)’s notation, in which the first subscript corresponds to the volume change, and the second is the pressure that is varied, those compressibilities can be defined as:
Cpc = 1 Vp ∂Vp ∂Pc pp, (2.5) Cbp= 1 Vb ∂Vb ∂Pp pc, (2.6) Cbc = 1 Vb ∂Vb ∂Pc pp, (2.7) Cpp= 1 Vp ∂Vp ∂Pp pc, (2.8)
where the bar with subscript in the right side of the equations represents the pressure that is kept constant during the associated experiment.
Compressibility associated with changes in porous volume due to pore pressure variations (Cpp), keeping the confining pressure constant, is the most important to reservoir engineers and geophysicists, as it emulates the process of primary production.
The direct lab compressibility measurements are hydrostatic (pressure equally distributed in all directions). Therefore, it does not reflect the process that occurs in the field, which involves a uniaxial deformation (pressure exerted in one specific axis) of the reservoir. Ac-cording to Vasquez & Rosa (2016), the compressibility estimated from geophysical data is more correlated with the uniaxial situation, because of the unidirectional wave propagation in lab and logs scale. Thus, it is possible to say that deriving this property from geophysical measurements would be more appropriate than using lab compressibility measurements to match reservoir behavior.
According to Zimmerman (2017), both Cpp compressibilities, hydrostatic and uniaxial, can be related by the following expression
CP puni ≈ α 3 1 + σ 1 − σ Cpp, (2.9)
where α is the rock Biot’s coefficient, and σ is the rock Poisson’s ratio. These two parameters can also be estimated from logs or core velocity measurements, and the relationships to derive them are going to be shown later.
The bulk modulus is defined as the inverse of the compressibility. Therefore, for each of these compressibilities, it is also possible to define their bulk modulus. Moreover, the bulk modulus is the most common parameter associated with seismic measurements, as its directly related to compressional velocities. According to Mavko et al. (2020), the dry bulk modulus of a rock is Kdry = 1/Cbc, and the dry pore space stiffness is Kφ = 1/Cpc. I am representing the bulk modulus associated with Cpp as Kp = 1/Cpp.
