i SEISMIC LITHOFACIES PREDICTION AND RESERVOIR CHARACTERISATION IN DEEP-OFFSHORE NIGER DELTA, NIGERIA BY EBERE BENARD (119078152) (B.Sc. (Geology) and M.Sc. (Exploration Geophysics), University of Port Harcourt) A THESIS SUBMITTED TO THE SCHOOL OF POST GRADUATE STUDIES UNIVERSITY OF LAGOS, AKOKA LAGOS, NIGERIA FOR THE AWARD OF DOCTOR OF PHILOSOPHY (Ph.D.) DEGREE IN GEOPHYSICS. DECEMBER, 2016 ii iii DEDICATION To my late father and grand father In memoriam iv ACKNOWLEDGEMENTS I wish to express my sincere gratitude to my supervisors: Prof. E. A. Ayolabi, Dr. C. O. Dublin- Green and Dr. A. Akinmosin; for their support and contributions towards the success of this research work. I also want to thank the Head of Department, Prof. S. B. Olabaniyi; Dr. L. Adeoti, Dr. S. Bankole, Dr. A. Opatola, Dr. S. Oladele, all the academic and non-academic staff of the Geosciences' Department, who had assisted me for the successful completion of the Ph.D research work. I give special thanks to Sarah Kabon, Glen Penfield, and Prof. N. F. Ukaigwe for their immense support and inspiration in the course of this project work. May I also acknowledge the management of SAPETRO, Total, Petrobras, Chinese National Oil Company (CNOOC), Nigerian National Petroleum Company (NNPC) and, the Department of Petroleum Resources (DPR) for providing the data set for this project with permission to publish the research results. My appreciation also goes to Schlumberger for providing Petrel software for this research. I will not forget to acknowledge my friends: Gabriel Omolaiye, Clement Onyekwelu; my younger brother King Benard and many other persons for their encouragement. Finally, I thank my wife Rosita Benard, my son Jeremy Benard, and my daughter Tiffany Benard for their sacrifice of time and love. v TABLE OF CONTENTS Title Page i Certification ii Dedication iii Acknowledgements iv Table of Contents v List of Tables vii List of Figures viii Abstract xii CHAPTER ONE: INTRODUCTION 1.0 Introduction 1 1.1 Background to the Study 1 1.2 Statement of the Problem 4 1.3 Aim and Objectives of the Study 5 1.4 Significance of the Study 6 1.5 Definition of Terms 7 1.6 Abbreviations 10 vi CHAPTER TWO: LITERATURE REVIEW 2.0 Literature Review 11 2.1 Introduction 11 2.2 Location of the Study Area 14 2.3 Geology of Niger Delta 17 2.4 Stratigraphy and Depositional Environment of Deepwater Niger Delta 20 2.5 Petroleum Geology and Petroleum System of Deepwater Niger Delta 26 2.6 Deepwater Depositional Process and Environments 31 2.7 Deepwater Architectural Elements 37 2.8 Deepwater Exploration History in Niger Delta, Nigeria 41 2.9 Theoretical Concepts 45 CHAPTER THREE: MATERIALS AND METHODS 3.0 Materials and Methods 60 3.1 Well Log and Rock Physics Analysis 63 3.2 Post-Stack Seismic Attribute Analysis 66 3.3 Core and Sedimentary Facies Analysis 73 3.4 Geostatistical Facies Modeling 76 CHAPTER FOUR RESULTS AND DISCUSSION 4.0 Results and Discussion 78 4.1 Qualitative Well Log Data 78 4.2 Petrophysical Estimation Results 81 4.3 Rock Physics Estimation Results 82 4.4 Post Stack Seismic Attribute Data 92 vii 4.5 Core and Sedimentological Facies Results 119 4.6 Geostatistical Facies Modeling 126 4.7 Discussion of Results 145 CHAPTER FIVE: CONCLUSION AND RECOMMENDATION 5.0 Conclusion and Recommendation 153 5.1 Summary of Findings 153 5.2 Contributions to Knowledge 154 5.3 Conclusions 156 5.4 Recommendations 158 References 159 Appendices 176 List of Tables 1. Niger Delta and Anambra Basins Geologic Formations 17 2. Some Niger Delta Deepwater Discoveries and their water depth 34 3. Wireline logs and core suites 49 4. Variance of empirically derive shear wave velocity 67 5. Seismic attributes and elastic rock property correlation 90 6. Principal component analysis for neural network classification 97 7. Correlation analysis for neural network classification 98 8. Zonal facies proportion for sand and shale 110 9 Zonal object-based modeling geometrical measurements 118 viii List of Figures 1. Map of Niger Delta showing the study location, the depobelts, and five offshore structural province 12 2. Geologic cross section of the Niger Delta continental shelf and offshore setting 12 3. Bathymetry sea floor and Niger Delta Stratigraphic column 16 4. Principal architectural elements of deepwater clastic systems 29 5. World map showing the deepwater Golden triangle 32 6. Schematic diagram of sandstone and shale deformation 35 7. Base map of the study area showing the 3D seismic and data coverage 48 8. Reference well template showing the individual logs used for qualitative analysis 52 9. Well template showing the basic log inputs, generated acoustic impedance log, reflection coefficient, synthetic seismogram and seismic trace 54 10. 3D seismic grid volume showing inlines, crosslines, time slices and wells 57 11. 3D grid showing typical seismic attribute (RMS amplitude) 57 12a. Typical core photographs from 3318.50 m to 3327.30 m 59 12b. Typical core photograph from 3327.30 m to 3334 m 59 12c. Core photographs showing typical sedimentary features 60 13. Well log analysis template 64 14. Well log sand correlation template 64 15. Petrophysical estimation of shale volume and porosity 65 16. Primary wave velocity versus shear wave velocity plot and correlation 67 17. Measured and empirically derived shear wave velocity comparison 68 ix 18. Lithofacies and elastic rock property logs 68 19. Lambda-Rho-Vp/Vs-Gamma Ray Cross Plot 70 20. Lambda-Rho-Vp/Vs-Porosity Cross Plot 70 21. Lambda-Rho-Vp/Vs-Mu-Rho Cross Plot 71 22. Lambda-Rho-Vp/Vs-Acoustic Impedance Cross Plot 71 23. Lambda-Rho-Mu-Rho-Lithofacies Cross Plot 72 24. Lambda-Rho-Mu-Rho-Closure stress Scalar (CSS) Cross Plot 73 25. Lambda-Rho-Poisson's Ratio-Closure Stress Scalar (CSS) Cross Plot 74 26. Primary Wave velocity-Porosity-Closure Stress Scalar (CSS) Cross Plot 74 27. Spectral analysis of seismic data within 2.6 seconds and 4.0 seconds 76 28. Well synthetic seismogram to seismic tie 77 29. Depth structural map of the sea bed 79 30. Depth converted arbitrary seismic section across the wells 80 31. Inline 1590 showing anticlinal high over the reservoir interval 80 32. Crossline 2400 showing anticlinal high over the reservoir interval 81 33. Depth structural map of the top seismic horizon 82 34. Seismic stratigraphic facies and channel detection on seismic 84 35. Variance attribute and channel geometry 85 36. Seismic stratigraphic facies and depositional fan detection 87 37. Architectural fan lobe with lateral amalgamation 88 38. Sweetness attribute versus mu-rho cross plot 91 39. A typical seismic attribute grid filtered to show seismic facies contrast in three dimension 92 40. A typical seismic attribute property layer along the vertical direction 93 41. Seismic attribute inverted porosity grid 95 x 42. Porosity histograms for the modeled and Seismic derived porosity 96 43. Near Sea Bed Discrete facies classes showing lobate fan architecture 100 44. Near Sea Bed Seismic facies probability volume for Class 2 100 45. Discrete facies classes showing lobate fan architecture within the reservoir interval 101 46. Seismic facies probability volume of lobate fan at reservoir interval 101 47. Core section showing deformed shale and mudstone overlying fine grain sandstone unit 103 48. Cored shale interval with evidence of sand injectite 104 49. Cored sandstone section with floating mudclast 104 50. Cored fine grain sandstone with vertica burrows 105 51. Cored sandstone with inverse graded bedding and floating pebbles 105 52. Cored sandstone interval showing normal grading with horizontal lamination and lag deposits 106 53. Core sedimentological log, description and sedimentary structures 108 54. Global lithofacies histogram and facies proportion curve 109 55. Zone by zone porosity histogram from well log 110 56. Zone by zone volume of shale histogram from well log 111 57. Global porosity and volume of shale histogram from well log 111 58. Zone 1 lithofacies model using indicator kriging algorithm 112 59. Zone 2 lithofacies model using indicator kriging algorithm 113 60. First realization of lithofacies model using SIS 114 61. Second realization of lithofacies model using SIS 115 62. Third realization of lithofacies model using SIS 115 63. Lithofacies model using truncated Gaussian simulation with trend 116 xi 64. Lithofacies model using truncated Gaussian simulation without trend 117 65. First realization of Channel-sand facies distribution and morphology 119 66. Second realization of Channel-sand facies distribution and morphology 119 67. Seismic facies classes and facies probability as training image for multiple point geostatistical facies modeling 121 68. Deepwater fan sand model using seismic attributes as training image for multiple point geostatistical technique 122 69. Sand facies probability property grid 124 70. Deepwater Sand lithofacies model 125 71. Seismic attribute constrained porosity model 126 72. Seismic attribute constrained volume of shale model 126 73. Mixed Deepwater fan and Non-fan conceptual depositional model 132 xii ABSTRACT The deepwater Niger Delta is associated with local mud diapirism and complex sand distribution. Hence, sequence stratigraphic prediction of reservoir sands and seal, as well as geostatistical reservoir characterisation, have not been effective in the deepwater environments due to the isolated nature of the reservoir sand bodies dispersed in shale-prone environments. Consequently, the exploration risk of drilling dry holes and the challenges of deepwater field development are very high. Hence, this study is aimed at predicting and characterising deepwater reservoir systems, as a means of reducing geologic uncertainties in the study area. About 600 km2 of three dimensional seismic data, log suite from seven wells, and 60 m sedimentological core footage were utilized in the study. The methodology combined qualitative log analysis, petrophysics, rock physics, seismic attribute analysis, sedimentology, and geostatistics. Sedimentological evidence from core including sand injectite, floating mudclast, faint normal grading, parallel lamination, lenticular beddings, normal and inverse grading, has shown that the sedimentation mechanisms in the deepwater Niger Delta comprises of sediment slumping, sliding, debris flow, turbidity current flow, pelagic and hemipelagic settling, with no diagnostic support for hyperpycnal flow. Also, the study has shown the depositional model to be a hybrid of turbidite fan, debrite lobes and channel sands dispersed in background shale. The predicted reservoir facies include channels sands and fan lobes having good to excellent reservoir qualities, with porosity ranging between 0.21 and 0.36. The reservoir sands are easily distinguished from the background shale based on diagnostic elastic properties which measure stiffness, rigidity, and incompressibility. The reservoir sands are characterised by low lambda-rho, low Poisson's ratio, low primary versus shear wave velocity ratio, low closure stress scalar; and high mu-rho. This study has also shown the diagnostic post-stack seismic attributes for reservoir characterization in the study area to include: sweetness, envelope, reflection intensity, and root mean square amplitude. These diagnostic seismic attributes have correlation of between 0.66 and 0.8 with elastic rock properties in predicting lithofacies. Also, the use of seismic attributes as training image for geostatistical modeling of channel sands and fan lobes reconstruct reservoir geometries much better for field development than variogram and object-based geostatistical techniques. Finally, this study has proved that the integration of rock physics, post-stack seismic attributes and sedimentology is very effective in addressing the inherent challenges of predicting and characterizing geometrically complex reservoir facies in the shale-prone deepwater setting of the offshore Niger Delta. Key words: Characterisation, deepwater, geostatistics, seismic attribute, seismic lithofacies. 1 CHAPTER ONE 1.0 INTRODUCTION 1.1 Background to the Study The ability to discriminate lithofacies based on rock physics properties and diagnostic seismic attributes, is key to deepwater siliciclastic reservoir facies prediction and characterisation. Sandstones and shales in siliciclastic Formations have been observed to deform differently at specific burial depth (Bjorlykke, 2010). This implies that rock physics analysis of critical changes in the gross rock rigidity and incompressibility can be used to discriminate between lithofacies types in siliciclastic depositional setting like the deepwater Niger Delta (Avseth and Mukerji, 2002; Goodway et al., 2010). Primary wave velocity, shear velocity, density, elastic moduli, and their associated derivatives have been proved to be reliable in discriminating between hydrocarbon sand, wet sand and shale in siliciclastic environments. On the order hand, seismic waveform and multi-attribute analysis of three dimensional (3D) seismic data are useful in mapping the morphology of deepwater clastics (Avseth et al., 2000; Hart, 2008). Seismic attributes are derivatives from the original amplitude seismic that can be used to characterise lithological variation, stratigraphy, faults and fractures, hydrocarbon responses, as well as subtle detection of depositional facies architecture from seismic in three dimension (Hart, 2002). Several attributes have been formulated over the years including, stratigraphic, structural, and complex trace attributes. The complex trace analysis mathematically involves the Hilbert transformation of a real seismic trace to its imaginary component. While the real seismic trace represents the kinetic energy of particles that oscillate with respect to seismic wave energy; the imaginary signal measures the potential energy within the rock medium (Taner et al., 1979). 2 According to Ulrych et al. (2007), seismic attributes can be extracted instantaneously from common mid-point seismic data to review subtle geologic features. Of particular interest to this study, is the fact that deepwater clastics and turbidite systems in the deepwater Niger Delta and similar depositional settings are associated with diapiric structural evolution and complex sand distribution (Corredor et al., 2005). This has strong implication in exploration, lithofacies prediction, reservoir characterisation, inter-well property modeling and field development (Deptuck et al., 2003; Adeogba et al., 2005, Corredor et al., 2005; Heino and Davies, 2006; Connor et al., 2009; Stevenson et al., 2012; and Celik, 2013). Hence, it is obvious that to reduce exploration risk associated with reservoir prediction; and to reduce uncertainty in the reservoir characterisation of deepwater clastics, it is important to establish a quantitative relationship between siliciclastic reservoir properties with seismic responses. According to Avseth et al. (2001), there is a link between amplitude characteristics and depositional patterns. Hence it is possible to discriminate lithofacies and fluid changes in attribute maps and strata cubes. The focus of this study is to integrate quantitative rock physics, 3D seismic attributes data and core in order to reduce geologic risk and uncertainties inherent in the offshore Niger Delta. This is necessary as deepwater reservoir systems have been recognized as complex and variable. The complexity is reflected in the depositional mechanism, depositional environment, external morphology and geometry, sand distribution and reservoir quality of deepwater deposits (Stow et al., 1999; Caers et al., 2001; Strebelle, 2002). Massive sand bodies of economic importance are usually associated with deepwater systems in siliciclastic basins of West Africa (Shanmugam, 2006). Also, notable petroleum producing sandstone reservoirs have been reported in the North Sea, Norwegian Sea, Gulf of Mexico, Offshore Brazil, and Offshore West Africa including the 3 Offshore Niger Delta (Shanmugam, 2006). But, irrespective of the economic importance of the deepwater systems, the technical challenges associated with the exploration and the recovery of hydrocarbon in related reservoir types still remain very high (Wood et al., 2000). 1.2 Statement of the Problem The study area lies within the mud diapir, inner fold and thrust belts of the deep offshore Niger Delta, characterised by interplay of local mud diapirism and complex sand distribution pattern. Hence, exploration and reservoir characterisation methods including: regional seismic and sequence stratigraphic techniques, seismo-structural mapping, and the use of outcrop analogs, have not been very effective in the study area (Lawrence and Bosman-Smith, 2000; Bakke et al., 2013). The reason being that deepwater depositional facies exhibit different external geometries on seismic data that are not diagnostic of unique depositional systems tracts. Hence, reservoir and seal prediction is difficult in the deepwater and ultra-deepwater (Posamentier et al., 1991; Steffen, 1993; Shanmugam, 2006). Consequently, inter-well lithofacies and property prediction using variogram and object-based geostatistical methods are unreliable in deepwater channel and turbidite environment due to their complex depositional geometries and architectures (Caers et al., 2001; Strebelle, 2002). This depositional environment consist of isolated reservoir sand bodies encased in background shale. Hence, there is therefore the need to integrate rock physics, 3D seismic attributes and sedimentology, in order to address the inherent reservoir prediction challenges in the study area, and therefore reduce geologic uncertainties. 4 1.3 Aim and Objectives of the Study The aim of this study is to characterise deepwater reservoir systems and predict lithofacies types by integrating rock physics, seismic attributes, and sedimentological core data, as a means of reducing geologic uncertainty in exploration and field development in the study area. The specific objectives of the study are to:- i. investigate the mechanisms of deepwater sedimentation; ii. characterise and define the depositional model for sand distribution; iii. identify deepwater reservoirs and discriminate their elastic rock physics properties; iv. determine the most appropriate post-stack seismic attributes for reservoir characterisation; and v. compare results of calibrated seismic attributes as input for multiple point geostatistics, with two-point variogram and object-based facies modeling techniques. 1.4 Significance of the Study The integration of rock physics, seismic attributes and core sedimentological analysis will provide information on the processes and mechanism of sandstone deposition, architectural facies patterns and depositional environment in the study area. These information will aid reservoir characterisation and conceptual geological modeling of the study area. These knowledge will in turn aid the direct prediction of hydrocarbon sands using seismic data, as well as the geostatistical modeling of sandstone facies for reservoir characterisation and field development studies. 5 1.5 Definition of Terms Attribute: Specific information set used to describe a property. Complex Seismic Trace: Representation of seismic data as real and imaginary amplitude data through a 90 degrees phase shift. Deepwater: Water depth greater than 200 m below the offshore continental shelf. Diapir: Massive low density flow structure such as shale (mud) and salt. Elastic Rock Property: Rock property derived from the combination of primary wave velocity, secondary wave velocity and density. Facies: A body of rock that can be defined by specific properties and characteristics. Fault: Vertical displacement of rock layers along the plain of movement. Formation: Mappable geological units. Fold: Structural deformation that results to bending of planner surfaces. Geostatistics: A subset of statistics used to describe and analyze spatial variability of subsurface geological variable. Lithofacies: A rock unit that is defined by the lithological composition. Lithology: Rock unit defined by specific physical characteristics such as colour, texture, grain size and mineral composition. Meandering channel: A bending river landscape. 6 Primary Seismic Wave: The first seismic signal that is reflected through a subsurface rock layer. Post-Stack Seismic: Seismic data volume that is processed after the individual traces have been merged. Reservoir: A porous rock unit that can house fluid and allow it to flow. Seismic: Energy waves that travels through the earth layers as a result of rock vibration. Seismic Lithofacies: A rock unit that is characterised by unique acoustic and elastic seismic properties. Siliciclastic: Silica rich sedimentary rocks formed and deposited through mechanical processes. Sedimentary Rock: Aggregate of minerals derived from pre-existing rocks through weathering, transportation, deposition and burial. Sandstone: Sedimentary rock composed of aggregate of quartz-rich grains with particle size between 1/16 mm and 2 mm. Shale: Fine grained clastic sedimentary rock composed of clay rich minerals and mud. Shear Seismic Wave: The second seismic signal that is reflected through a subsurface rock layer. Seismic Trace: Collection of seismic wavelets characterised by basic physical properties such as amplitude, wavelength and frequency. Stratigraphy: The description of different rock layers. Sedimentology: The study of the processes of formation and environments where sandstone, shale, and mud and deposited. 7 Turbidites: This refers to sediments deposited by sediment-laden water currents along a slope or channel. Variogram: Bivariate statistical measure of spatial relationship between variables. Wavelet: Basic unit of a seismic trace. 1.6 Abbreviations 3D: Three Dimension AVO: Amplitude Variation with Offset CSS: Closure Stress Scalar GR: Gamma Ray Max: Maximum Min: Minimum MPS: Multiple Point Statistics PEF: Photo Electric Factor RI: Reflection Intensity RMS: Root Mean Square Vp: Primary Wave Velocity Vs: Shear Wave Velocity 8 CHAPTER TWO 2.0 LITERATURE REVIEW 2.1 Previous Work Most research works in the deepwater Niger Delta were focused on the understanding of the structural complexity in the fold and thrust belts (Wu and Bally, 2000; Corredor et al., 2005; Connor et al., 2009). Published articles in the Niger Delta offshore belts are scarce in the area of quantitative seismic facies prediction and geostatistical modeling of channels and turbidite reservoir systems been a frontier exploration province (Adeogba et al., 2005; Heino and Davies, 2006; Stevenson et al., 2012; and Celik, 2013). In similar geologic setting of the deepwater Gulf of Mexico, seismic geometries are more indicative of local basinal processes such as diapirism and slumping than extrabasinal controls including: sea level change, regional subsidence and provenance (Lawrence and Bosman-Smith, 2000; Bakke et al., 2013). The implication is that the deepwater environment is characterised by several minibasins having differential supply of clastic sediments. Hence, within a depositional episode, some minibasins will receive large volume of sand, while others may receive only mud. Hence, regional sequence stratigraphic criteria for reservoir and seal prediction in deepwater sediments are difficult to define (Posamentier et al., 1991; Steffen, 1993). Consequently, regional data base of the continental shelf, shallow slope, shallow analog and outcrop studies of turbidite systems have not been very effective for deepwater facies prediction. In the deep-water fold and thrust belts, depositional facies including more distal basin fans are associated with structural traps formed by contractional folds as in the case of Agbami, Bonga, Chota, Ngolo and Nnwa deep-water fields (Corredor et al., 2005; Biloti and Shaw, 2005). 9 Turbidite and deepwater channel reservoir systems are associated with complex sand distribution (Caers et al., 2001). They can simply be defined as isolated sand facies surrounded by shale in characteristic slope, basin floor, and channel setting. These facies types constitute technical challenge in reservoir characterisation and deepwater development studies, including: reservoir and seal prediction as well as inter-well sand correlation (Wood et al., 2000). Also, the mechanism of deepwater sedimentation has been a subject of debate. In marine and lacustrine environments, meandering channel levee systems and distal fan lobes have been attributed to powerful hyperpycnal flow over long distances on the sea bed (Mutti et al., 1996; Zavala et al., 2006; Mulder and Chapron, 2011). Turbidity current and debris flow models have also been proposed respectively for the deepwater Niger Delta and Angola (Graue, 2000; and Abreu et al., 2003). Incorrect use of these models have implication in frontier exploration (Shanmugam, 1998). The technical challenges of deepwater hydrocarbon exploration, development and production, still remain high due to inherent complex depositional pattern of turbidite and channel sands. According to Pettingill and Weimer (2001), over 70% of unrecovered hydrocarbon are trapped in turbidite and related reservoir systems. Consequently, two-point geostatistical methods using variogram analysis are not very efficient in modeling reservoir properties in depositional settings associated with complex geometrical trends such as turbidite lobes and sinuous channels (Strebelle, 2002). Variogram estimation is inherently affected by insufficient data pairs, extreme values, presence of outliers, and biased geological sampling for effective averaging and prediction of unsampled locations (Kelkar and Perez, 2002). However, to accurately represent complex geologic features such as turbidites and channel sands, a measure of correlation between multiple spatial locations is required. 10 Some authors have reported the application of seismic attributes as being very useful in predicting reservoir properties such as lithology, volume of shale, net-to-gross sand and porosity in complex depositional environments (Leiphant and Hart, 2001; Meyer et al., 2001; McGrory et al., 2006). This implies that lithology sensitive seismic attributes can serve as training image for facies classification and multiple point facies modeling of complex reservoirs. Hence, the use of high resolution seismic attributes as training images, can be integrated as a complimentary technique to the use of variogram, in modeling complex curvilinear reservoirs systems (Journel, 2005). 2.2 Location of the Study Area The field under study is situated within the mud diapir, inner fold and thrust belt of deepwater Niger Delta, at water depth greater than 1000 m. The area of study covers approximately 600 km2 in areal extent. The geology is very complex, and is characterised by rapid deposition of prograding sands on over-pressured mobile shale of the Akata Formation. The sedimentary succession of the slope and basin floor deepwater setting, is considered to be dominated by pelagic and hemipelagic marine shales (>80%); with interbedded sandstone deposits of debris flow, turbidites and channel-levee complexes (Graue, 2000). According to Corredor et al. (2005), the offshore Niger Delta has been subdivided into five structural zones with distinct depositional framework (Figures 1 and 2). These zone include the following:- i. Extensional province: This zone lies beneath the continental shelf and is characterised by both basinward-dipping and counter-regional growth faults, associated rollovers and depocenters. 11 ii. Mud diapir zone: This is located beneath the upper continental slope, and is characterised by passive, active and reactive mud diapirs. The mud diapirs include shale ridges and massifs, shale overhangs, vertical mud diapirs, and interdiapir depocenters. iii. Inner fold and thrust belt: This zone extends in an actuate path across the center of the offshore delta. It is characterised by basinward verging thrust faults and associated folds. It consist of Tertiary to Holocene deep marine sediments. iv. Transitional detached fold zone: This zone lies beneath the lower continental slope, and is characterised by large areas of little or no deformation. It is interspersed with large detachment folds above structurally thickened Akata Formation. v. Outer fold and thrust belt: It consists of northern and southern sections that define two outer lobes of the delta. It is characterised by both basinward and hinterland-verging thrust faults and associated folds. Growth sedimentation rates are low relative to uplift. 12 Figure 1: Map of Niger Delta showing the study location, the depobelts, and five offshore structural provinces (Adapted from Corredor, et al., 2005) Figure 2: Geologic cross section of the Niger Delta continental shelf and offshore setting (After Corredor et al., 2005) 13 2.3 Geology of Niger Delta The Niger Delta Basin is situated on the passive margin of West Africa. The sub-aerial part of the delta covers about 75,000 km2 and extends for more than 300 km from the apex to the mouth (Figure 3). The basin started as a proto-Niger Delta following the tectonic evolution of the Benue- Abakaliki Trough (Bustin, 1988). This tectonic episode occurred in the Early Cretaceous as a failed arm of a rift triple junction associated with the opening of the South Atlantic (Burke, 1972; Weber and Daukoru, 1975; Whiteman, 1982). The Niger Delta is characterised by major regressive phase from the Eocene to Holocene; this was initiated by the uplift of the Benin and Calabar flanks during the Paleocene to Early Eocene (Murat, 1972). Following the Miocene uplift of the Cameroon Mountains, the Niger Delta has prograded with the seaward shift of the coastline (Whiteman, 1982). The modern Niger Delta records major regressive-transgressive sequences in the Late Pleistocene; this is related to eustatic sea level changes during the late glaciation (Allen, 1965; Oomkens, 1974). Cretaceous tectonic elements of the Benue Trough had influenced the drainage pattern in the lower Anambra Basin. Consequently, the early Niger Delta in the Eocene to middle Miocene began to advance southwards along three distinct sedimentary axes. The Niger Delta continued to grow in the Eocene in response to the epeirogenic movements along the Benin and Calabar flanks (Murat, 1972). According to Allen (1963), about 22 distributaries discharges radially into the basin in the modern Niger Delta. These river systems serve as fairway for sand transportation into the deepwater settings. Three of these rivers: Ramos, Forcados in the west and Nun River at the delta nose carry over 70% of sediments into the sea. Erosional canyons of early to middle Miocene age were incised in the Niger Delta shelf and slope during periods of sea level fall (Doust and Omatsola, 1990). Several large submarine fan channels extend down slope across the continental rise from erosional submarine canyons on the upper slope (Damuth, 1994). Major 14 canyons in the offshore Niger Delta include, Lagos, Avon, Mahin, Niger, Qua-Ibo and Calabar canyon. The Niger Delta Basin is characterised by three main lithostratigraphic units, the Akata, Agbada, and Benin Formation from the oldest to the youngest (Short and Stauble, 1967). Sediment deposition in the Tertiary prograding Niger Delta Basin is complicated by depositional patterns restricted to series of fault-controlled sub-basins, referred to as depobelts that strike northwest to southeast, sub-parallel to the present shoreline (Knox and Omatsola, 1989). The depobelts were associated with increasing deltaic sediment loads that forced underlying marine shale to move upward and basinward. The depobelts represent different offlapping siliciclastic sedimentation cycles in the Niger Delta (Stacher, 1995). Each depobelt is a separate unit defined by a break in the regional dip of the prograding delta, and is bounded landward and basinward by growth faults and counter regional faults or growth faults of the next seaward belts respectively (Evamy et al.,1978; Doust and Omatsola,1990). As shown in Figure 1, five depobelts have been recognized in the Niger Delta based on their sedimentology, deformation and petroleum history. According to Doust and Omatsola (1990), the northern delta depobelts which include the Northern and Greater Ughelli depobelts overly relatively shallow basement and have the oldest faults. The central delta depobelts consisting of Central swamp I, Central swamp II, Coastal swamp I and Coastal Swamp II have well defined structures. While the distal depobelts including: the Shallow offshore and deep offshore depobelts are structurally complex due to internal gravity tectonics on the modern continental slope. 15 2.4 Stratigraphy and Depositional Environment of Deepwater Niger Delta The Niger Delta is a prograding delta with three main lithostratigraphic units: Akata, Agbada, and Benin Formation in ascending order (Figure 3b). The Formations are stratigraphyically related in space and time, having ages between Eocene and Holocene. These Formations also have lateral equivalent in the Anambra Basin of the Lower Benue Trough (Table 1). The stratigraphy of Niger Delta is subdivided into the following units: an upper sequence of massive sand and gravel deposited under continental condition, transitional series of sandstone and shale intercalation deposited under a parallic condition, and a basal marine shale section with isolated sand lenses and turbidite deposits (Evamy et al., 1978). According to Nwachukwu and Chukwura (1986), the depositional environments for the Niger Delta clastics span from the delta plain in the continental setting, through a transitional delta front environment, to the prodelta and submarine fan environment typical of the deepwater Niger Delta. 16 Figure 3: (a)Bathymetry sea floor (After Corredor et al., 2005) and (b) Stratigraphic column (After Tuttle et al., 1999) 17 Table 1: Niger Delta and Anambra Basin Geologic Formations ( Modified from Short and Stauble, 1967). SUBSURFACE OUTCROP FORMATI ON AGE M.A FORMATION AGE M.A BENIN Oligocen e- Recent <33. 9 BENIN Miocene? Pleistocene/Pliocene 23.0- 0.01 AGBADA Eocene- Recent <56 OGWASHI- ASABA AMEKI Oligocene - Miocene Eocene 33.9-23.0 56 -33.9 AKATA Eocene- Recent <56 IMO Paleocene - L. Eocene 66 -56 EQUIVALENT NOT KNOWN NSUKKA AJALI MAMU NKPORO Maastrichtian - Paleocene Maastrichtian Campanian-Santonian Campanian/Maastrichtian 72.1 -56 72.1 - 66 83.6-72.1 86.3 - 66 AWGU EZE-AKU SHALE ASU RIVER GROUP Turonian- Coniacian/Santonian Turonian Albian 93.9-83.6 93.9- 89.8 113 -100 18 The delta plain environment is generally associated with sandstone units representing braided stream, point-bar, channel-fill, and crevasse splays, as well as back-swamp shale deposits (Frankl and Cordry, 1967; Weber, 1971). The depositional environments within the delta front are characterised by tidal channel, distributary mouth bar, lagoon, barrier bar deposits, and beach sands. The prodelta and submarine fan environments are peculiar to the deepwater Niger Delta, with continuous deposition of pelagic and hemipelagic shale. This shale unit is mainly under- compacted and over-pressured, and also contains isolated sand lenses and turbidite (Avbovbo, 1978). 2.4.1 Benin Formation The Continental Benin Formation is the uppermost unit in the Niger Delta and is composed of Late Eocene to Holocene continental deposits. These include alluvial and coastal plain sands that are about 2000 m (6600 ft) in thickness (Avbovbo, 1978). Onshore in some coastal regions, the Benin Formation overlies the Agbada Formation (Kulke, 1995). Offshore, the continental sands of the Benin Formation become thinner and disappear near the shelf edge (Cohen and McClay, 1996) as illustrated in Figure 2. On seismic sections, the Benin Formation exhibits parallel reflection configurations that are associated with variable frequency and amplitude; as well as low discontinuities that decrease landwards. 2.4.2 Agbada Formation This formed the major petroleum-bearing unit in the Niger Delta. The paralic clastic sequence known as the Agbada Formation is present in all the depobelts and ranged in age from Eocene to Pleistocene. It is more than 3500 m (11,500 ft) thick and represents the actual deltaic sequence that 19 accumulated in the delta-front, delta-topset, and fluviodeltaic environments (Doust and Omatsola, 1990). Channel and basin floor fan deposits in the Agbada Formation formed the primary reservoirs in the Niger Delta. On seismic, they are characterised by parallel, hummocky, acoustically chaotic, slightly divergent, highly divergent and sigmoid/oblique clinoform (Adeogba et al., 2005). 2.4.3 Akata Formation This is composed of clays, shales and silts which occur at the base of the delta sequence. The Akata Formation is generally believed to contain source rocks; and might also contain some turbidite sands. On seismic sections, the Akata Formation is generally devoid of internal reflections, with the exception of a strong, high-amplitude reflection that was locally present in the middle of the formation (Bilotti and Shaw, 2005). On the other hand, the mid-Akata Formation served as an important structural marker for defining detachment levels, and is recognized on seismic section as transparent and chaotic reflections. The Akata Formation exhibited low primary wave seismic velocities (≈2000 m/s; ≈6600 ft/s), and in addition reflects regional fluid overpressures (Bilotti and Shaw, 2005). The Formation has a thickness range of about 2000 m (6,600 ft) to 7000 m (23,000 ft). In deep-water, it is up to 5000 m (16,400 ft) thick (Doust and Omatsola, 1990). The Akata Formation, being composed of massive shale deposits and turbidite sands would likely occur on seismic as acoustically chaotic and transparent facies (Adeogba et al., 2005). 20 2.5 Petroleum Geology and Petroleum System of Deepwater Niger Delta 2.5.1 Petroleum Geology The classification scheme of Worrall et al. (2001) has been used to describe the petroleum geology of deepwater systems and to divide the plays into four types of basins: a. Basins with large mobile substrates, fed by large rivers: These basin types are associated with large volume of sediments transported into the deepwater environments. They have high potential for reservoir presence, and may have multiple play types and migration pathways. Large volume of sedimentary fill deposited within extensional and contractional domains, in this type of basin favours hydrocarbon generation. The mobile substrate in deepwater Angola (Congo Basin) and northern Gulf of Mexico consists of salt, while the deepwater Niger Delta has mobile shale substrate. b. Basins with mobile substrates fed by small rivers: These are common along steep margins, where high-sediment-load smaller rivers flow into the basin. Typical examples include the Island of Borneo and the Campos Basin in Brazil. Neocomian lacustrine source rocks occur below mobile Aptian salt in the Campos Basin. c. Basins with non-mobile substrates fed by small rivers: These basins type are characterised by the reservoirs draping over basement highs, which directly affects petroleum migration. The Wet Shetland island, More and Voring Basins in Offshore Norway fall under this basin type (Gjelberg et al., 2001) d. Basins containing non-deepwater reservoirs: These basin type contain reservoirs that were not originally deposited in deepwater setting. The paleo-environment may have been fluvial, deltaic or shallow marine. Jurassic and Cretaceous fluvial-deltaic syn-rift strata in the north-west shelf of Australia, carbonate reservoirs in the Maampaga Field of 21 Philippines, and some Albian discoveries in the Campos Basin, Brazil, are typical examples of non-deepwater reservoir in deepwater basins. 2.5.2 Petroleum Systems Six basic elements of the petroleum systems of the deepwater and ultra deepwater settings as described by Pettingill and Weimer (2002), are summarized below: i) Reservoir Most deepwater discoveries were made in reservoirs of Cenozoic age, with the remaining contributions from Cretaceous reservoirs. About 90% of deepwater reservoirs are sandstone of deepwater origin, while the remaining 10% include shallow marine and fluvial sandstones, as well as carbonates. Deepwater reservoirs generally have good reservoir qualities, with over 30% porosity and thousands of milliDarcy permeability respectively. The good reservoir quality of deepwater reservoirs is a function of sedimentary processes of mature river systems transporting the sediments. High porosity of deepwater sandstones is attributed to low geothermal gradient and unconsolidation resulting from overpressure. Generally, deepwater reservoir connectivity and continuity ranges from poor to excellent. Also, high net-to-gross channel-fill and basin floor sheet sands, have excellent reservoir quality, while low net-to-gross channel-fill and thin-bed levees have poor reservoir quality. Low net-to-gross reservoirs pose more technical challenges in deepwater exploration and development. Consequently, the ability to predict deepwater reservoirs prior to drilling is critical. 22 ii) Traps Trapping style in deepwater plays varies with basin type and tectonic regime. Significant proportion of turbidite plays have stratigraphic component to their traps. Common to the deepwater Niger Delta and other West African Basins, is a combination of structural-stratigraphic traps (Pettingill, 1998). Other trapping styles include: structural traps in emerging fold belts plays, and depositional mounding in unconfined settings (Kirk, 1994). Pure stratigraphic traps are also possible in unconfined setting due to lateral pinch out (Clemenceau et al., 2000). iii) Seal The deepwater marine environment is mud-prone and therefore associated with adequate top seals. However, seal integrity may pose serious risk due to overpressures and crestal faulting. Reservoir pressure, overburden pressure, and rock strength are critical elements for evaluating seal integrity. iv) Source Rock According to Duval et al. (1998), the deposition of potential marine source rocks in the deepwater environment, is associated with major marine transgressions and favourable oceanographic conditions. The source rock type may include Type I, II and III kerogens, which differ for different offshore basins. Different source rocks had been reported along the West African margin. In the deepwater sections of Niger Delta and northern Equatorial Guinea, the Akata Shale, Eocene to Oligocene in age, is considered the main source rock. It is progressively younger basinward with variation in efficiency towards the ultra deepwater setting (Doust and Omatsola, 1990; Tuttle et al.,1999). Deepwater related source rocks include Jurassic, Cretaceous and Tertiary strata. Lacustrine source rocks are common in the syn-rift setting such as the Campos Basin of Brazil and 23 part of West African margin (Schiefelbein et al., 2000). Also, Tertiary terigenous gas-prone materials have good source rock potentials. These materials initially deposited in coastal and shallow marine settings, are transported into deepwater environment during Tertiary lowstands to form oil-prone source rocks (Schiefelbein et al., 1999; Peters et al., 2000). There have been much discussion on the nature and distribution of source rock in the Niger Delta. The Akata Formation is considered the main source rock for hydrocarbon in the Niger Delta up to the deepwater environment in water depth of 2500 m (Bustin, 1988; Duost and Omatsola 1990; Haack et al., 2000; and Cobbold et al., 2008). However, Cretaceous source rocks have also been identified in the Niger Delta (Schiefelbein et al., 1999; Haack et al., 2000; Morgan, 2003; Saugy and Eyer, 2003). v) Generation and Migration Most source rocks in the deepwater environments are considered to have recently reached the hydrocarbon generation window, hence timing is of very high risk. Adjacent depocenters and faults serve as migration pathways for entrapments. The Cenozoic mobile shale in the deepwater Niger Delta are over-pressured with a system of fluid trapping and leaking that favours oil migration into fault traps. Faults and piercement structures can provide adequate vertical migration. 2.6 Deepwater Depositional Process and Environments Common deepwater depositional processes include the following:-  Gravity-driven flow (slides, slumps, debris flows, and turbidity currents)  Deepwater bottom current 24  Liquidization  Clastic injection  Mud diapirism  Sediment plumes, wind transport, etc  Pelagic and hemipelagic settling  Tsunamis The deepwater depositional environments associated with the processes listed above include: the deep-lacustrine environment, sub-marine slope environments, submarine canyon and gully environments, submarine fan environments, submarine non-fan environments, and submarine basin-plain environments. 2.6.1 Deepwater Depositional Processes According to Shanmugam (2006), gravity-driven processes remained the most important mechanism for deepwater sediment transport into the deep marine environments. The gravity- driven processes include: slides, slumps, debris flows, and turbidity currents, commonly associated with shelf edge sediment failures. The mechanism of deepwater sedimentation typical of the different depositional processes, are best inferred from sedimentary features observed in core and outcrops. It is almost impossible to use plan morphological features on seismic data to interpret the mechanism of deepwater deposition. Typical gravity-driven deepwater processes and their associated features are presented thus. 25 i. Sediment slides: This refers to the process and also the mass of sediment transported along a glide plane without any internal deformation. Large scale slides are seen in high-resolution seismic profile of modern systems. Diagnostic features of sediment slides include the following:-  Gravel to mud lithofacies  Clastic injections  Sheet-like geometry  Salt and shale diapirism ii. Slumps: This refers to mass of sediments transported along concave-up glide plane, with significant internal deformation due to rotational movement. Large scale modern slump occur as chaotic facies. Diagnostic features of deepwater slumps in sedimentary core include the following:-  Gravel to mud lithofacies  Basal zone of shearing  Contorted layers interbedded with non-contorted layers at core scale  Irregular upper contact  Sand injections  Steeply dipping and truncated layers  Lenticular to sheet-like geometry with irregular thickness iii. Debris flow: 26 This refers to slow moving mass of sediments that breaks up into smaller blocks at the axis of advance. Both muddy and sandy debris flow deposits (debrites) show the following features on core.  Gravel to mud lithofacies  Floating mudstone clast  Planar clast fabric in muddy matrix  Projected clast in mudstone  Brecciated mudstone clasts in sandy matrix  Planar clast fabric in sandy matrix  Inverse grading of rock fragments  Inverse grading, normal grading, inverse to normal grading  Floating quartz granules in sandy matrix  Inverse grading of granules in sands and pocket of gravel iv. Turbidite: This refers to deposits of turbidity currents. They are classified into coarse-grained, medium- grained and fine-grained turbidites with a standard sequence of structures within individual depositional units. Most turbidite deposits are associated with partial sequences (top-absent, mid-absent, base-absent). Important diagnostic features for recognition and interpretation of turbidites include the following:-  Fine-grained sand to mud  Normal grading without floating clasts or granules  Reverse grading at base of thick coarse-grained beds 27  Sequential grading within silt laminae in fine-grained beds  Sharp or erosional base contact  Gradational upper contact  Thin layer (centimeter scale)  Sheet-like geometry in basinal setting  Lenticular geometry in channel-fill settings  Parallel elongated clast  Random orientation of clay particles  Bioturbation at the top of beds Generally, turbidity current versus debris flow models are used to predict reservoir sand distribution. Incorrect use of the models have implication in frontier exploration (Shanmugam, 1998). In the deepwater lower Miocene of offshore Angola, the origin of sinuous channel forms has been explained by turbidity currents (Abreu et al., 2003). v. Sand injectite: This results from the injection of sand into fine grained shale. It is caused by possible sedimentary slumping, depositional loading, glacial loading, tectonic stress, seismic induced liquification, igneous intrusion, and vertical migration of fluid. vi. Mud diapirism: This refers to sediment flowage and deformation due to rapid sedimentation caused by gravity instability. Sediment loading and rapid burial of cohesive sediments will commonly result to overpressure of the underlying mud. 28 vii. Pelagic and hemipelagic settling: This refer to the settling of mud fractions derived from continental materials and shells of microfauna through the water column to the ocean floor. Common diagnostic features include the following:-  Mudstone and shale lithofacies  Parallel lamination  Faint normal grading  Bioturbation  Deep-marine body and trace fossils 2.7 Deepwater Architectural Elements Siliciclastic deposits in the deepwater environments have been classified into gravel-rich, sand- rich, mixed sand-mud, and mud-rich facies, based on grain size and sediment delivery systems (Reading and Richards, 1994; Richards et al., 1998). A three end-member sediment delivery systems have been defined for the deepwater systems which includes: single point-fed source fan, multiple point-source submarine ramp, and line-source submarine slope aprons. These depositional systems are characterised by five principal architectural elements: wedges, channels, lobes, sheets and chaotic mounds (Figure 4). 29 Figure 4: Principal architectural elements of deepwater clastic systems (After Readings and Richard, 1994) 30  Wedges: This refers to sand-prone sedimentary unit that pinches out downslope by a downlap surface.  Channels: This refers to elongate negative-relief features created by turbidity-current flow (Mutti and Normark, 1991). They represents extended linear fairway for sediment transport and depositions. Depending on grain size and sediment delivery systems, deepwater channels can be categorize as straight (chute and braided channels), and sinuous (channel- levees) geometries. Most channel-levee systems are associated with over-bank deposits. These are fine-grained, thin-bedded turbidite sediments, laterally extensive, and adjacent to the main channels in turbidite systems (Mutti and Normark, 1991).  Lobes: Mutti and Normark (1987, 1991), defined lobes as areas of sand deposition, downslope from the main channel. Channelized lobes and depositional lobes are typical of deepwater settings.  Sheets: Amalgamated and layered sand units, laterally continuous, with tabular external geometries are referred to as sheet (Mahaffie, 1994). The base of layered sheet sand is characterised by high net-to-gross, typical of the stacked assemblages of top-absent Bouma sequence. On the contrary, the upper section of sheet sands is characterised by low net-to- gross sand percentage, typical of a complete or base-absent Bouma sequence.  Thin beds: This refers to very fine sands and silt deposits which include: levee, inter- channel, and outer fan/fringe deposits (Shew et al., 1994). Thin beds generally contain ripple bedding, pinch-and-swell structures, convoluted beddings, minor bioturbation, and graded beds. 31 2.8 Deepwater Exploration History in Nigeria Niger Delta Deepwater exploration in the offshore Niger Delta began in 1990, following the first acquisition of speculative two dimensional (2D) seismic data in the deepwater and ultra-deepwater Niger Delta offshore (Ofurhie et al., 2002). This seismic campaign was followed by a second 2D seismic acquisition and 3D seismic acquisition respectively, targeted at unveiling the petroleum potential in the deepwater setting. The exploration targets were deepwater channel related sand complexes and turbidite reservoir systems. The deepwater reservoir systems are believed to be associated with large hydrocarbon accumulation (Shanmugan 1992; Stow et al., 1999).The advent of deepwater exploration and production activity in the Niger Delta, was triggered by giant deepwater discoveries in the Gulf of Mexico and the Campos Basin of Brazil, from 1975 and 1984 respectively (Shanmugam, 2006). The deepwater Gulf of Mexico, Campos Basin in Brazil, and offshore West African constitute the "Golden triangle" petroleum exploration belt (Figure 5). 32 Figure 5: World map showing the deepwater Golden triangle (Adapted from Pettingill and Weimer, 2001) 33 Bonga Field was the first deepwater discovery in the Niger Delta in 1995, immediately after the Angola west African discovery in 1994. Later deepwater discoveries include: Agbami, Chota, Ngolo, Nnwa, Usan, Nsiko and Doro (Corredor et al., 2005; Biloti and Shaw, 2005). The Bonga discovery and some of the others consists of structural and combination traps in water depths greater than 500m (Table 2). Regrettably, several dry wells were also drilled in the same water depth during this period from 1995 to 2003. Consequently, most of the oil companies operating in the deepwater and ultra-deepwater acreages had to relinquish their blocks. Several factors were considered to be responsible for the failure cases: from structural traps integrity, source rocks maturity and timing, and reservoir presence. Failure rate was greater than 50% compared to success rate in the deepwater Niger Delta (Kostenko et al., 2008). Subsequently, there have been a decline in deepwater exploration activities since 2000. 34 Table 2 Some Niger Delta Deepwater Discoveries and their water depth Field Water Depth (m) Year of Discovery Recoverable Resources Bonga 1125 1995 735MM bbl oil & 451 bcf gas Bosi 1424 1996 2.3 tcf gas Agbami 1435 1998 780MM bbl oil & 576 bcf gas Nwa-Doro 1283 1999 4.4 tcf gas Bonga SW 1245 2001 500 MM bbl oil & 500 bfc 35 2.9 Theoretical Concepts The theoretical concepts for this study involved rock physics analysis, complex seismic trace and multi-attribute analysis, sedimentology, variogram and mulitiple-point geostatistics. 2.9.1 Rock Physics Based on the stress-strain relationship , quartz-rich wet sand, oil sand, gas sand, and clay-rich shale will deform differently and therefore characterised by distinct rock physics responses (Avseth et al., 2005). Figure 6 is a schematic of siliciclastic rock deformation under normal stress, hydrostatic stress and shear stress respectively. Figure 6: Schematic diagram of sandstone and shale deformation. Tx, Ty, and Tz represent normal stresses in the x, y, and z coordinate directions respectively. While dxy and dyx represents shear stresses tangential to x and y directions respectively. 36 The basic rock physics parameters and their derivative rock physics attributes, can be expressed by the result of the three dimensional tensor relationship between stress and strain as shown in equations 1a to 1e. ijkkijijT  2 (1a) ijijT  (1b)   2 Vp (1c)   3 4   k Vp (1d)   Vs (1e) where T ij =Stress tensor,  =Lame' first parameter,  ij =Kroneka delta,  kk =volume strain, µ=second Lame's parameter or shear (rigidity) modulus,  ij =Strain tensor, k=bulk modulus,  =density, Vp= compressional velocity, and Vs=shear velocity. For i=j, equation 1a represents compressional wave equation, and for i j equation 1b represents shear wave equation. The various elastic rock properties are defined in appendix A. 2.9.2 Complex Seismic Trace Analysis The concept of complex trace analysis involves the Hilbert transform of the real seismic signal into its imaginary signal (Robertson and Nogami, 1984). The transformation is mathematical and 37 allows the seismic trace to be expressed as an analytical signal having both the real and imaginary components. Complex trace analysis decomposes the seismic signal into functions that discriminate between the original trace amplitude information, and angular frequency and phase information (Equations 2 to 6).    tiytxtU )( (2) where U(t)=Complex seismic trace x(t) = f (real seismic signal) and, iy(t) = g (imaginary seismic signal) By expressing the seismic trace as an analytical trace, specific seismic properties of a complex function can be extracted from the original seismic signal. These seismic properties include instantaneous amplitude, frequency and phase; which together with their higher order derivatives, are effective in predicting lithology variation, depositional features, reservoir properties and fluid; otherwise masked by the original amplitude signal (Hart, 2008). Typical examples of complex seismic attributes include: envelope or reflection strength, root mean square (RMS) amplitude, instantaneous frequency, instantaneous phase, acoustic impedance, sweetness, quadrature amplitude, etc (Schultz et al., 1994). Generally, these attributes are expected to capture subtle changes in waveform that can be linked to physical properties of depositional systems. The mathematical formulation of the various instantaneous attributes, and higher order derivatives, as well as their physical significance are presented below:- 38 i. Instantaneous amplitude (envelope) This is the total instantaneous energy of the analytical signal. It is independent of phase and can be used to detect bright spots, sequence boundaries and subtle changes in lithologies. Mathematically, it is represented by equation 3. Envelope = 22 gf  (3) where f and g are the real and imaginary seismic signals respectively. ii. Instantaneous phase This is related to events continuity, faults, pinch-out, dips, and seismic sequence boundaries. Mathematically, instantaneous phase is expressed as phase, ] )( )( [tan)( 1 ty tx t  (4) iii. Instantaneous frequency This is the derivative of phase, and can be used to estimate seismic attenuation. The instantaneous frequency is characterised by sharp reduction in oil and gas reservoirs. However, it is very unstable in the presence of noise. Mathematically, frequency is expressed as, dt td t )( )(    (5) iv. Sweetness This a measure of the overall energy signature changes in the seismic data. It is expressed mathematically as the ratio of envelope and instantaneous frequency. It can easily distinguish 39 channels and stratigraphic features based on seismic facies contrast. Sweetness is very useful in the detection and prediction of sand-filled channels in shaly deepwater successions (Hart, 2008). Sand prone facies are characterised by high sweetness, while shale facies will give low sweetness values. Mathematically, sweetness is expressed as )( 22 t gf Sweetness    (6) v. RMS amplitude This is defined as the square root of the average amplitude squares within a specific analysis window. It is very sensitive to extreme amplitude values, and therefore discriminate between sand and shale. Shale-prone intervals usually have low amplitude while isolated sand bodies in shale such as channel fills and frontal splays are characterised by high amplitude. Amplitude characteristic of seismic reflection have been found to be directly linked to grain size. According to Deptuk et al. (2003); Posamentier and Kolla (2003); high amplitude response correspond to coarse grained sediments. Most channel terrace and thalweg containing coarse grained turbidite deposits have been associated with high amplitude, while the inter-channel sections typical of fine grained turbidity current plume and hemipelagic sedimentation display low amplitude values (Heino and Davies, 2006). It is mathematically expressed as 2 1 1 ai N i irms N a    (7) where ai = amplitude, rms = root mean square, and N = sample number. 40 vi. Reflection intensity This is the average amplitude over a specified seismic window multiplied by the sampled interval. It can be represented mathematically by RI. ai N i ttRI    1 12 *)( (8) where (t2 - t1) =sampled interval, ai=amplitude, and N=sample number. 2.9.3 Bayesian Probability This defines the relationship between the posterior probability and prior probability (Maiti and Tiwani, 2010).      Bp BAp BAp  | (9)  BAp | represent the probability of A, given that B has occurred (i.e. the posterior probability of A).  BAp  represents the probability that both A and B will occur.  Bp represents the probability of event B. In equation 13,  BAp  can be represented as    ApABp | (10) By substituting equation 10 in equation 9,        Bp ApABp BAp   | | (11) 41 Where  Bp is unknown, equation 11 can be expressed as  BAp | α    ApABp | (12) The above equation implies that the posterior probability of an event A is related to the prior probability of event A. Hence if the sample is comprised of n and mutually exclusive events iA , then   1| 1   n i i BAp (13) By combining equations 12 and 13, the posterior probability can always be calculated. This concept of Bayesian probability is very useful in representing and quantifying the relationship between seismic attributes and any geological facies (Maiti and Tiwani, 2010). For each facies, specific seismic attributes are defined as continuous properties. Probability of a seismic attribute to take a particular value between 0 and 1 given a particular facies is expressed by equation 1.   ji kSp | (14) Where iS =the value of seismic attribute (attribute class), jK = seismic facies In practice, the seismic attribute is divided into discrete seismic facies classes, and the probability of each seismic facies class representing a specific geologic facies is estimated. Hence, given a specific seismic attribute, the posterior probability of geological facies can be expressed with the Baye's rule in equation 15.   ij SKp | α     jji KpKSp | (15) 42 2.9.4 Variogram Estimation This involves the use of weighted arithmetic averaging to estimate unknown values at unsampled locations. Variogram is a bivariate statistical measure of spatial relationship used in the estimation of unsampled variables. Mathematically, it is defined as half the variance of the difference between two variables separated by a given distance (Kelkar and Perez, 2002).                          LuXuXVL 2 1  (16)  = variogram, L  = distance between sampled variables, V = variance,       uX and         LuX are sampled values at locations separated by distance, L  . Variogram is closely related to covariance. While variogram measures the variance between sampled data points, covariance measures the similarity between the sampled data points (Appendix B). At zero distance between sampled locations, the variogram is expected to be equal to zero. This relationship between variogram and covariance is given by equation 17.                LCCL 0 (17) where  0C =covariance at zero distance, and       LC =covariance at a given separation distance between sampled location. In practice, the estimated variogram based on the sample data is expressed as the equation 18. 43 2 12 1                                           Ln i ii Luxux Ln L (18) where  Ln =number of pairs at lag distance  L ;        iux and         Lux i =data values for the ith pair located  L lag distance apart. By rearranging equation 19,                LCLC 0 (19) The matrix equation of covariance can be written as                                                                          0 01 1 1 111 , , ,........, ,........, uuC uuC uuCuuC uuCuuC n n nnn n   (20) where              nn uuCuuC ,, 11   1000 C The covariance matrix equation can also be expressed as equation 21. cC  (21) hence, cC 1  (22) 44 where C =the covariance among the sample points, 1 C =inverse of matrix C and  =vector of weights assigned to samples By solving for 1 and  n as the weighting on sampled locations in equation 20, unknown values can be estimated using different kriging methods. In principle kriging technique can be expressed as equation 23 to estimate values at unsampled locations.         0uX          i n i i uX 1  (23) Equation 23 can be modified and expressed as equation 24.         0uX  0 +          i n i i uX 1  (24) where         0uX = the estimated value at unsampled location,  0u ,        iuX = the value at the neighboring location,  iu ,  i =the weight assigned to the neighboring value,  0 =         n i i m 1 1  , m=mean of sampled values. All kriging algorithms are based on equations 23 and 24 with minor variations depending on specific applications. The weight assigned to the individual neighboring points is derived from the covariance matrix equation as a function of different variogram models such as Isotropic, Gaussian, spherical and exponential variogram models (Appendix B). 45 2.9.5 Object-based Modeling This refer to a set of geostatistical simulation techniques used to describe geological bodies, facies and lithhofacies with objects of discrete geometry. According to Kelkar and Perez (2002), the geostatistical techniques used for object-based facies modeling involves defining probability functions for different object dimensions. Typical geologic shapes for object modeling include parallelepiped, wedge, ellipsoid, lobe, sigmoid, channel, and dune. The most commonly used object modeling technique for describing geologic bodies by discrete shapes in reservoir models is the marked point process. The marked point process involves the simulation of an empty volume over the reservoir area of interest or zone. With an initial assumption of background facies fill in the entire volume, distinct objects are randomly inserted into the volume to replace the background. The simulation process allows the objects to be first inserted at conditioning data locations to honor the presence of observed geologic facies at wells. Thereafter, the objects are inserted randomly within the reservoir volume until the target volume fractions are attained. 2.9.6 Single Normal Equation The single normal simulation equation (snesim) was reviewed and adopted for inter-well property prediction in this study in order to overcome the inherent limitations in the use of variogram and object-based facies prediction methods. The snesim equation allows the use of seismic attribute as training image for inter-well multiple-point geostatistical facies prediction. The equation uses kriging probability to quantify the joint dependency between a random binary variable (Ak) and random variable events (Su) describing facies classes (Sk) at grid locations (Ux). According to and Meyer et al. (2001) and Strebelle (2002). 46 ][ ],[ BVar BACov k (25) where λ=weight assigned to neighboring value, Cov=covariance, Var= variance, Ak= binary random variable (e.g. lithofacies and depositional facies), B=conditioning data event (binary random variable constituted by the n conditioning data e.g. discrete seismic facies).     0 1 B Ak=1 if facies class k occur and is 0 elsewhere Using equation 25, the following conditional probability is derived, P(Ak=1|B=1)=E[Ak]+λ[E[B]] (26) where E[Ak] and E[B] are the expected values of discrete random variable (X) and so, E[X]= ]1[ 1   xPx n i i (27) E[X]= Expectation value (weighted average outcome of random variables), xi= the outcome of the random variable X, P[X=xi] = probability mass function for the ith outcome of n-number of possible outcome. From equations 25 and 26, the Bayes' rule is defined in equations 28 to 30. P(Ak=1|B=1)=   ][ ][][][ BE BEAEBAE AE kk k   (28) P(Ak=1|B=1)= )1( )1,1(   BP BAP k (29) P(Ak=1|B=1)= )1( )1()1|(   BP BPABP k (30) if S(uα)=sα, α=1, . . . . , n if not 47 CHAPETER THREE 3.0 MATERIALS AND METHOD 3.1 Data Gathering An integrated data set was used to address the objectives of this study. The data set consist of approximately 600 km2 of processed 3D seismic data acquired by SAPETRO, Total and their Joint Venture partners in 2004 (Figure 7). Other data set include wireline logs for seven (7) wells and photographs of about 60 m footage of core from 2 wells. Table 3 shows the available suite of logs for the respective wells. The seismic data was acquired using air gun energy source pressurized at 2500 psi with volume capacity of 3090 cubic inch and towed at water depth of 5 m. The seismic signal was sampled every 2 ms and recorded using a 10 streamer receiver system of 600 m length each at 37.5 m spacing. Inline and crossline spacing are 18.7 m and 12.5 m respectively, with 234 m2 bin size and 160 subsurface fold coverage. The processed post stack 3D seismic data was suitable for the purpose of study. 48 Figure 7: Base Map showing the 3D seismic coverage and Well locations for this study. The annotated symbols W1 to W6 represents well locations. 49 Table 3: Wireline Logs Suites Well Gama Ray Caliper Resistivity Density Neutron PEF Primary sonic Shear sonic W-1        W-2        W-3       W-4      W-5         W-6        W-7       50 3.2 Data Processing 3.2.1 Well Log and Rock Physics Analysis Wireline logs including: gamma ray, deep resistivity, bulk density, neutron, photo electric factor (PEF), compressional sonic, and shear sonic, were qualitatively analyzed for lithology, pore fluid type, over-pressure, diagenetic changes and depositional facies (Rider, 1996). To ensure quality interpretation, the input logs were quality-checked and edited. Top and base of sand units were defined on the gamma ray log and attempt made to analyze similar log motif for depositional energy trend across the wells. The wireline logs were then quantitatively analyzed using standard petrophysical equations (Equations 31 to 36) and rock physics equations (Appendices A13 to A27). Shale volume (Vshale) was computed using the Larinov equation for unconsolidated Tertiary clastics (Equation 31).  108.0 2 *7.3  IGRV shale (31) GRGR GRGR IGR minmax minlog    (32) where IGR=gamma ray index, GRlog=measured gamma ray log reading, GRmin=minimum gamma ray reading and GRmax=maximum gamma ray reading. Also, porosity was calculated from density log using equation 33.     fmab  1 (33) where  b =density reading from log,  ma =density of mineral matrix,  f =density of fluid, and  =porosity. Elastic rock properties were estimated using standard rock physics equations and their derivatives (Appendices A13 to A27). Elastic rock properties, petrophysical and wireline log 51 responses were then analyzed on cross plots using linear regression and cluster analysis. In order to qualitatively and quantitatively classify the distinct property trends and cluster patterns as discrete seismic lithofacies logs, polygon were digitized over distinct data clouds to serve as discrete facies filter. The input logs for the computation of the elastic rock properties include primary sonic velocity, shear sonic velocity and density (Figure 8). However, the measured shear sonic velocity was only available for well W-5 in the study area. Hence, to estimate shear sonic velocity for the remaining six wells, an empirical equation (Benayol shear velocity equation) was derived for the study area. The empirical equations by Castagna et al. (1985); Han et al. (1986) and Castagna et al. (1993) were also used to estimate shear wave velocity in the study area for purpose of comparison. 52 Figure 8: Reference well template showing the individual logs used for qualitative analysis of facies, petrophysical property estimation, and the computation of elastic rock physics properties. 53 3.2.2 Post-Stack Seismic Attributes Analysis Different seismic attributes including: structural, stratigraphic, and instantaneous seismic attribute volumes were generated and used for multi-attribute analysis. The volume attributes were quantitatively calibrated and then screened in three dimension to reveal distinct seismic facies pattern. 3.2.2.1 Seismic Waveform and Spectral Analysis Spectral analysis was done on the original seismic amplitude volume at different windows to determine the dominant frequency of the seismic data and tuning thickness using equation 34 (Widess, 1973). The dominant frequency was estimated by computing the reciprocal of the time difference between two successive seismic peaks or trough in seconds (Period). fV  (34) where V=interval velocity, f =dominant frequency of seismic data, =seismic wavelength, and 4  =tuning thickness (seismic resolvable limit) and 8  =seismic detectable limit. 3.2.2.2 Synthetic Seismogram and Well-to-Seismic Correlation Using density and sonic velocity logs, acoustic impedance was computed as a product of density and velocity, from which reflection coefficient was derived. By convolving the reflection coefficient with a basic wavelet extracted from the seismic volume, synthetic seismograph was generated from the reference well. Figure 9 shows the basic input logs, generated acoustic impedance log, reflection coefficient, synthetic seismogram and seismic trace. 54 Figure 9: Well template showing the basic log inputs, generated acoustic impedance log, reflection coefficient, synthetic seismogram and seismic trace. 55 3.2.2.3 Seismo-structural and Stratigraphic Analysis The seismic stratigraphic and structural analysis adopted for the study include the following steps below:- i. Inlines, crossslines, and arbitrary lines, were analyzed across the 3D seismic volume using reflection termination, reflection configuration, frequency, and amplitude to identify stratigraphic elements on seismic. Also, time slices were screened for channel related morphological features. ii. The sea bed and two proximal horizons were interpreted and mapped in time. Six other marker horizons were also interpreted and mapped for the reservoir zone of interest. iii. 3D structural grids were constructed for the near surface and selected reservoir seismic windows respectively. The interpreted structure maps from seismic were used to construct 3D grid skeletons of 50 x 50 cell sizes. The structural maps and stratigraphic well tops were then combined with the 3D grid skeleton to define a geologic framework for property distribution. iv. Seismic attribute volumes were generated and re-sampled into the 3D geologic framework for multi-attribute analysis. The attributes include variance attribute, RMS amplitude, reflection intensity, envelope, acoustic impedance, instantaneous frequency, quadrature amplitude, sweetness, etc. v. A simple velocity model was used for depth conversion of the time structural maps and seismic attributes volumes. Using the time maps and well tops, a vertical velocity model was built for the zone of interest. Interval velocities from the wells were estimated by the simple interval velocity equation, V=V0=Vint . The interval velocity values were interpolated by the convergent method in a 50 x 50 grid scale to generate constant interval velocity models for all 56 the time surfaces. The V0 represents a time depth relation (TDR) which was constant for each interval. The well TDR constant is equivalent to the calculated interval velocities between each of the time surfaces, computed from the checkshots and sonic derived average velocities. Figures 10 and 11 show typical seismic amplitude sections and RMS amplitude attribute sections respectively. 57 Figure 10: 3D seismic grid volume showing inlines, crosslines, time slices and vertical well trajectories. Figure 11: 3D grid showing typical seismic attribute (RMS amplitude) 58 3.2.2.4 Multi-attribute Analysis and Correlation Several seismic attributes including complex trace attributes were re-sampled into constructed 3D grid cells and screened visually for diagnostic morphological patterns. The following steps were used for the multi-attribute analysis and correlation. i. Synthetic seismic attribute logs were extracted from the attribute strata cubes and cross- plotted with derived elastic rock property logs. ii. Seismic attributes having high correlation coefficients with elastic rock properties were identified. iii. Using unsupervised classification and conditional probability rules shown in equations 25 to 30, discrete facies classes, seismic facies probabilities, and lithofacies probabilities were respectively defined from the re-sampled attribute volumes. 3.2.3 Core and Sedimentary Facies Analysis 3.2.3.1 Core Description and Depositional Facies Analysis Core photographs of day light were described and analyzed for lithofacies variation, sedimentary structures, textural characteristics and depositional facies (Figures 12a, b and c). Observed grain size variation and sedimentary structures on core were integrated with gamma ray log motif and seismic architectural elements, to infer sedimentation mechanism, sedimentary facies. The observations were compared with sea bed and modern day depositional analogs to interpret sedimentation mechanism and facies architecture. 59 Figure 12a: Typical core photographs from 3318.50 m to 3327.30 m Figure 12b: Typical core photographs from 3327.30 m to 3334 m 60 Figure 12c: Core photographs showing typical sedimentary structures 61 3.2.4 Geostatistical Facies Modeling The following steps and methods were used for the geostatistical modeling of deepwater channel related sand bodies in the study area:- i. Seismic lithologic facies and estimated petrophysical properties were upscaled into the geologic grid framework at all the grid cells intersected by the wells. ii. Statistical histogram and facies proportion curve were used to quality-check the upscaled log properties based on different averaging methods. iii. Data analysis using variogram modeling and transforms were used to capture and quantify the spatial relationship between sampled variables (Kelkar and Perez, 2002). As a rule of thumb, half the maximum distance between sampled variables were used as ranges to fit the model variogram to the experimental variogram in the major, minor and vertical direction. Indicator and normal score transforms were applied respectively to remove outliers from discrete facies and continuous petrophysical properties distribution respectively. iv. Inter-well lithofacies modeling was carried out using different variogram estimation algorithms including: indicator kriging, SIS, and TGS techniques in five realization e