A SPECTRAL METHOD OF LITHOFACIES DIFFERENTIATION WITHIN A HYDROCARBON RESERVIOR UNIT USING SEISMIC AND WELL DATA FROM TOMBOY FIELD NIGER DELTA

Eze Stanley*, Emujakporue .O. Godwin, Williams Ofuyah, Nnorom .S. Lotanna Department of Geology, University of Port Harcourt, Rivers State, Nigeria Department of Marine Geology, Nigeria Maritime University Warri South-West Delta State. Department of Physics, University of Port Harcourt, Rivers State, Nigeria Department of Earth Sciences, Federal University of Petroleum Resources, Effurun, Nigeria *Corresponding Author: Eze Stanley ABSTRACT Seismic facies analysis is a key component of Seismic interpretation workflow, as much information on depositional process, environment, reservoir architecture and potential can be determined from the seismic data. This enhances the seismic visibility of subtle stratigraphic features, and prediction of new prospects for drilling due to lateral continuity of sand bodies (the hydrocarbon reservoir) deposited within the sedimentary column. This study presents the results of the application of seismic amplitude inversion and spectral decomposition to differentiate lithofacies within a thin-sand reservoir and show their lateral and vertical continuity using amplitudederived attributes (rock properties) in the interpretation of 3D seismic and well log data from “TOMBOY” field Niger Delta. A thin-sand reservoir was delineated from lithologic log signatures within the interval 11,135.6111,210.35ft which corresponds to the time window 2.752 2.768secs on the seismic data along an arbitrary line drawn to connect the six wells (01-06) in the field. Crossplot of acoustic impedance against density across the reservoir bed showed three compartments interpreted as gas filled sand, oil filled sand and shale. The interpretation was enhanced via spectral analysis by computing frequency maps of acoustic impedance, density and velocity using discrete Fourier transform (DFT) technique at top (2.752sec) of the reservoir in terms of magnitude, phase and frequency. Phase response for the three attributes (acoustic impedance, density and velocity) showed lateral continuity and discontinuity of sand lithofacies at the various well locations which were not evident on their original amplitude time slice, while frequency response showed bed thickness, with low frequency indicating presence of hydrocarbon or sand rich beddings, while high frequency indicates thin shale beddings. It was observed that the top (2.752sec) of the reservoir for wells 02, 05, 01 and 04 showed low frequency values for the three attributes (acoustic impedance, density and velocity) which indicates potential zones for hydrocarbon production and development in the field, while wells 03 and 06 within the same time slice (2.752sec) showed a higher value in acoustic impedance frequency, density frequency and velocity frequency and suggests the presence of thin shale facies at the top (2.752sec) of the thin-sand reservoir. By defining the lateral and vertical continuity of sand facies within the reservoir bed, hydrocarbon fairways were better defined and knowledge of this can be incorporated into drilling decisions for field development. The results gave enhanced structural disposition of the reservoir bed and more insights into the variation of sand lithofacies with depth.


INTRODUCTION
A facies is a body of rock with specific characteristics, which can be any observable attribute of a rock such as overall appearance, composition, or condition of formation. Seismic facies are mappable 3D seismic units composed of groups of reflections whose parameters differ from those of adjacent facies unit (Mitchum et al., 1997). Seismic facies interpretation is the geologic interpretation of seismic attributes (coherence, amplitude, frequency, and interval velocity); these attributes determine variations of seismic properties within individual seismic sequences in order to determine lateral and vertical continuity in lithofacies and fluid type. (Mitchum et. al., 1997). Lithofacies differentiation within a hydrocarbon reservoir unit is the lateral and vertical distribution of rock facies within the reservoir. This technique is aimed at improving reservoir characterization to optimize hydrocarbon production (Ofuyah et al., 2015).
The seismic reflection method ever since its discovery in the late 1920s, has and still remains one of the most effective tools in the search for hydrocarbons. Reflections are due to contrast in acoustic impedance in the subsurface caused by difference in physical properties of rocks which can be density and compressional wave velocity and can be interpreted in terms of lithology, porosity and porefill (Hansen et al., 2008, Ukaigwe, 2000. The ultimate goal of the seismic method is to delineate structural and stratigraphic structures suitable for hydrocarbon accumulations. Structural traps are usually more evident in the seismic records, while Stratigraphic traps on the other hand are not so evident but subtle on seismic records (Telford et al., 1990, Yilmaz, 2001. With advancement in technologies, the use of seismic data has extended to other areas such as stratigraphic imaging, pore-fluid estimation, and lithofacies differentiation e.t.c, and these applications have led to the discovery of huge oil and gas reserves often confined within subtle stratigraphic features. These subtle stratigraphic features are thin beds defined by Widess (1973) as having a thickness of less than a quarter of the wavelength of the dominant frequency present. Thin beds usually depict gradual and gentle geologic variations that are not so obvious in conventional seismic interpretation because they fall below the limit of seismic resolution. Seismic analysis workflow can help improve vertical resolution and identify thin beds on seismic reflection data, which can lead to accurate stratigraphic interpretation (Castagna et al., 2003). In analyzing seismic facies (lithofacies as it were), seismic attributes are usually combined to obtain meaningful results for reservoir characterization. Seismic attribute was introduced as part of the seismic interpretation process in the early 1970's, and since then has remained the most reliable interpretation tool for reservoir characterization and lithofacies analysis from seismic data. This is because seismic attributes can be used to predict rock properties which are sensitive to lithology changes within the subsurface. The process of computing rock properties from seismic attributes is called "inversion". Acoustic impedance inversion involves conversion of seismic traces to a reflection coefficient time series, and then into acoustic impedance (Lavergne and William, 1977;Lindseth, 1979). These impedance traces can enhance accuracy of interpretation and correlation with properties measured in well logs. In this sense, inversion can be considered a sophisticated method of integrating well logs and seismic data for thin bed delineation, lithofacies differentiation within thin beds, and reservoir characterization. Lithofacies differentiation within hydrocarbon reservoirs before now have been done by formation evaluation using geophysical well logs, facies associated with fluid separation using well logs, and hydrocarbon reservoir mapping (Opara 2010;Aigbedion and Iyayi, 2007;Adeoye and Enikanselu, 2009). The use of seismic amplitude-derived attributes and well data for Lithofacies differentiation within a reservoir unit (such as thin beddings) have not been properly documented in literatures because thin beds often fall below the level of seismic resolution (Castagna et al., 2003). This study presents the results of a new technique which uses seismic amplitude-derived attributes (interval velocity, density, acoustic impedance & porosity) and well logs for lithofacies differentiation across a thin-sand reservoir bed. The technique uses amplitude inversion of seismic trace and geologic transform of seismic amplitude derived attributes followed by spectral decomposition using discrete Fourier transform (DFT) technique to increase the seismic bandwidth of the seismic-derived attributes to improve their resolution in spectral domain. This will in implication contribute to the existing debate on thin bed analysis, lithofacies differentiation and presence of lateral continuity of sands. The study area is Tomboy field located within the Niger Delta.

GEOLOGIC SETTING
The field under study is "TOMBOY FIELD" located in a transitional environment around Port Harcourt axis of the Niger delta. The Niger Delta is situated in the Gulf of Guinea in the West coast of Africa. Sandwell, 1997, as cited in Corredor et al., 2005).
The Niger Delta basin evolved in early tertiary times where rapid deposition and subsidence have occurred over time (Doust and Omatsola, 1990). Generally, the delta prograded over the subsidizing continental-oceanic lithospheric transition zone, and during the Oligocene spread into oceanic crust of the Gulf of Guinea (Short and Stauble 1967). Thickness of sediments in the Niger Delta averages at 12 km covering a total area of about 140,000 km 2 . The early Niger Delta is interpreted as being a river-dominated delta, however the post-Oligocene delta is a typical wave-dominated delta with well-developed shoreface sands, beach ridges, tidal channels, mangrove and freshwater swamps. It is one of the world's largest deltas and shows an overall upward transition from marine shales (Akata Formation) through a sand-shale paralic interval (Agbada Formation) to continental sands of the Benin Formation. Depending on relative sea level changes, local subsidence and sediment supply, the delta experiences episodes of regressions and transgressions. Tectonics in the Niger delta rifting diminished in the Late Cretaceous. After rifting ceased, gravity tectonics became the primary deformational process. The stratigraphic sequence of the Niger Delta comprises three broad lithostratigraphic units namely; a continental shallow massive sand sequence -the Benin Formation, a coastal marine sequence of alternating sands and shales -the Agbada Formation and a basal marine shale unit-the Akata Formation. The Akata Formation consists of clays and shaleswith minor sand alternations. The sediments were deposited in prodelta environments. The sand percentage here is generally less than 30%. The Agbada Formation consists of alternating sand and shales representing sediments of the transitional environment comprising the lower delta plain (mangrove swamps, floodplain and marsh) and the coastal barrier and fluvio marine realms. The sand percentage within the Agbada Formation varies from 30 to 70%, which results from the large number of depositional off lap cycles. A complete cycle generally consists of thin fossiliferous transgressive marine sand, followed by an offlap sequence which commences with marine shale and continues with laminated fluvio marine sediments followed by barriers and/or fluviatile sediments terminated by another transgression cycle (Weber and Daukoru 1975;Ejedawe, 1981). The Benin   Doust and Omatsola (1989).
Petroleum occurs within the Agbada Formation of the Niger Delta basin however, several directional trends form an "oil-rich belt" having the largest field and lowest gas:oil ratio (Ejedawe, 1981;Evamy et al., 1978;Doust and Omatsola, 1990). Hydrocarbon distribution was originally attributed to timing of trap formation relative to petroleum migration (earlier landward structures trapped earlier migrating oil).

THEORY OF SEISMIC INVERSION AND GEOLOGIC TRANSFORM 3.1 Seismic amplitude inversion
In this study acoustic impedance and interval velocity (Vi) were derived from seismic amplitude via seismic inversion technique Boisse (1978). The instantaneous amplitude (envelope or reflection strength), and its derivatives, are key seismic attributes which are diagnostic in resolving hydrocarbon bearing reservoir units.
Amplitude inversion is a 1-D inversion of seismic data which visualizes the earth as made up of composite of layers at each CMP location. Each composite layer has a characteristic density, velocity, and layer thickness and similar two-way time intervals. The procedure that converts estimates of reflection coefficients into an image of acoustic impedance with depth has been discussed meticulously by Lavergne and William (1977), Lindseth (1979) and Dobrin (1988 151 For a normal incident acoustic pressure wave, the reflection coefficients for layer interfaces are related to acoustic impedance by:

RC=
(1) Where RC is the reflection coefficient of the i th interface and ρiVi is the acoustic impedance of the i th layer.
Therefore the acoustic impedance for the next (i + 1) th layer is, In this study, seismic amplitude traces were extracted from the geologic window defined from well logs. Therefore the scaling factor K is given by; Where Ao is the seismic amplitude values from traces extracted from the geologic window under analysis.
Finally the estimated interval velocity is; Where RCe is the amplitude dependent reflection co-efficient.
In the absence of density values, the internal velocity can be estimated by equating the density parameters, hence the interval velocity is Equation (6) was in turn used to determine the interval velocity at the reservoir window.

Geologic transforms
These are transforms in time domain used in the estimation of dense 3-D volume of pseudo-sections from 3-D seismic data (amplitude) and well logs using neutral networks, statistical or non-linear estimator and calibration techniques. However, the process to go from seismic data and existing well logs to a dense 3-D cube of pseudowell logs de pends on the appr aisal of ma n y critical sub-pr oce ss and non-tr ivial c hoice s. These have not been well documented in literatures (Branchs and Michelena, 2002). The t e c h n i q u e offers important 152 advantages such as the ability to incorporate spatial and temporal variations in the relationship between seismic data and well logs. In this study, the following pseudo-well logs were estimated:

Pseudo Acoustic impedance log
Gardner et al., (1974) showed an empirical linear relationship between acoustic impedance ( ) and interval velocity (V) given as = (V -3460)/ 0.308 (7) Where V is interval velocity in ft/sec, and v is the acoustic impedance value. A reflection coefficient sequence RCi, can be computed from a borehole sonic log. H o w e v e r , i f density information is available (conditional), a better approximation to the reflection coefficient can be obtained using RCi= (8) Where and are the density and velocity at specified time index. The inversion of seismic data is board upon rearranging the terms in the (i th ) interface to give the acoustic impedance log series.

Pseudo-Porosity log
The relation for the computation of pseudo-porosity log series is: This empirical equationis based on field observations (Schlumberger, 1987). This relation was adopted for use because of its applicability to uncompacted sands in the tertiary Niger Delta, where this study is being carried out. In terms of significance, porosity usually decreases with increasing velocity although the velocity-porosity relations are not always unique.

Pseudo-Density log
The pseudo-density log series was estimated from acoustic-impedance log from the expressions: The density log series also called Acoustic-Impedance derived density was found closets to the well log density values (in time), and was therefore used in this study.

METHODOLOGY
The data provided for this study consists of seismic data (measured field amplitude) and a suite of well logs which includes, gamma, resistivity, spontaneous, density, sonic and deep lateral logs f o r s i x ( 6 ) Vol.9, No.3, 2019 153 was taken at depths of 11,135.61-11,210.35ft which corresponds to 2.752-2.768 seconds, following a depth to time conversion done with velocity at 4046.37ft/s. Crossplot of measured and derived density versus acoustic impedance was made across the reservoir bed using Gnuplot programme, to check for fluid content distribution.
Seismic data (field amplitude) was used to invert for acoustic impedance and interval velocity using seismic amplitude inversion technique discussed in section 3.1. Geologic transforms were equally used to compute rock attributes such as acoustic impedance, density and porosity at top (2.752sec) of the reservoir.
Spectral decomposition analysis using the discrete Fourier transform technique (DFT) was applied to transform the amplitude derived attributes in time into frequency and their mean spectral response were obtained in terms of magnitude, phase and frequency at top (2.752sec) of the reservoir. The comparison w a s m a d e between the attributes in time and their frequency equivalents, and interpreted for lithofacies differentiation and lateral continuity of sands within the top of the reservoir. The geologic t r a n s f o r m s were computed using written program scripts within MATLAB software. The entire seismic and well data were initially loaded into kingdom suite software (Shell platform), from which the base map, seismic section and digital seismic data were extracted and used.

AMPLITUDE AND PHASE SPECTRA OF ACOUSTIC IMPEDANCE, DENSITY AND VELOCITY
Amplitude and phase spectra of acoustic impedance, acoustic impedance derived density, and velocity was computed by Discrete Fourier transform (DFT) within MATLAB to obtain their mean spectral response in terms of magnitude, phase and frequency and their corresponding time slice at top (2.752sec) of the reservoir was produced. The dominant frequency spectrum in the dataset is about 50Hz as the amplitude plots (ABS. MAGNITUDE) were symmetrical at 50Hz. Spectral analysis was carried out decomposition using discrete Fourier transform (DFT) technique, to enhance our interpretation for stratigraphic studies. Stratigraphic features at the reservoir window are below seismic resolution due to low frequencies, hence will require frequency enhancement techniques to improve their frequency spectrum for detailed analysis Frequency maps of acoustic impedance, density and velocity were computed at top of the reservoir (2.752sec) by discrete Fourier transform (DFT).
(a) Amplitude and Phase Spectra of Acoustic Impedance by Discrete Fourier Transform (DFT). Plot is symmetrical at 50Hz frequency.
(b) Amplitude and Phase Spectra of Acoustic Impedance derived density by Discrete Fourier Transform (DFT). Plot is symmetrical at 50Hz frequency. Therefore for field development, drilling direction should be directed more to the west on the green zones. The phase attribute in (c) shows lateral discontinuity in sand lithofacies within the reservoir which is not evident in a, b, d above. Low density frequency is seen at well-02, well-05, well-01 and well-04 locations (green-yellow colour) and indicates sand zones while high frequency zones indicates presence of thin shale bedding.  diagnostic to presence of hydrocarbon. The low velocity frequency zones represents the sand zones while high velocity frequency represents thin shale beddings. Therefore drilling decisions should be made at the low frequency green zones (west) for field development.

DISCUSSION OF RESULTS
Figures 5 (a-d) is the plot of GR, SP and resistivity log (LLD) for wells 04, 02, 01 and 05. In well-04 (reference well) the reservoir window of interest is between 11,135.61-11,210.35ft while for the other wells (well 02, 05 and 01) the sand interval picked is from 10,000-11,000ft (in red circle). Figure 6 shows the GR log correlation for wells 02, 05, 01 and 04 within their respective intervals. The correlation shows changes in lithofacies across the Well-03

Well-06
Journal of Environment and Earth Science www.iiste.org ISSN 2224-3216 (Paper) ISSN 2225-0948 (Online) DOI: 10.7176/JEES Vol.9, No.3, 2019 wells which differ in thickness due to erosion, faulting or differential rates of gravitational slumping that occurred at the various depth intervals. Figure 7 is a well log plot panel of GR, SP, RES, SONIC and DENSITY of the test data (well-04) used to map out the hydrocarbon bearing zones in the reference well which is from 11,135.61-11,210.35ft and is taken as the reservoir window of interest in this study. Figure 8 is a crossplot of gamma ray log against SP(mv), RES(ohm-m), density (RHOB) and sonic log(µs/ft) and was used as a control to ascertain the reservoir window chosen for well 04. The crossplot gave a convergence in interpretation (black circle) which agrees in behaviour within a reservoir window. Figure 9 is a crossplot of measured (at well location) and derived (from seismic amplitude) acoustic impedance against density dataset. The crossplot shows three distinct compartments in sand-shale lithofacies with predominant sand content across the reservoir bed and interpreted as gas filled sand, oil filled sand and shale based on table 1 proposed by Dobrin, 1988. The lithofacies showed lateral continuity across the reservoir bed. Figure 10 is the seismic section after interpretation for Inline 5970 connecting all the wells. Two faults (F1 and F2) were seen bounding the wells within the reservoir interval 2.752-2.768sec, these structures are favorable for hydrocarbon accumulation and indicates the presence of hydrocarbon within the interval. Acoustic impedance, density and porosity slice at top (2.752sec) of the reservoir is shown in figure 11 and suggests that the top of the reservoir for wells 01-06 contains low-impedance gas filled sand lithofacies which is laterally continuous across the reservoir bed. derivatives of (a) in terms of magnitude, phase and frequency. The magnitude attibute shows gas accumulations, sequence boundaries and lithofacies variations within beds. Phase attribute shows lateral continuity and discontinuity of lithfacies, it shows beddings very well along a horizon. Phase attributes is independent on amplitude, hence it should not change in principle along a horizon. However, changes arise if the lithofacies within a layer changes lateral which can be caused by "sink-holes" or changes in bedding configurations. Frequency attibute correspondes to the average frequency of the amplitude spectrum of the seismic wavelet. Low frequency is an indicator of hydrocarbon or sand rich beddings, while high frequency indicates thin shale beddings, hence frequency attribute is a bed thickness indicator. This interpretation was taken after subramanyam and Rao 2008, Jenkins and Watts 1968. In figure 13(c) (acoustic impedance phase), we noticed the lateral continuity in sand lithofacies in the various well locations which is not evident in figure 13(a,b and d). Also in figures 14(c) and 15(c) (density phase and velocity phase respectively), the lateral discontinuity and continuity of sand lithofacies were evident in both figures respectively which suggests that phase attribute is the best indicator of lateral continuity and discontinuity in beds. Also a close look at figures 13(d), 14(d) and 15(d) (acoustic impedance frequency, density frequency and velocity frequency respectively) shows that the top of the reservoir for wells 02, 05, 01 and 04 have a characteristics low values and suggests potential zones for hydrocarbon production and development in the field, while wells 03 and 06 within the same time slice (2.752sec) showed a higher value in acoustic impedance frequency, density frequency and velocity frequency and suggests the presence of thin shale facies at the top (2.752sec) of the sand reservoir. The frequency maps give better geologic image and shows lithofacies changes within stratigraphic units better than their amplitude time maps.

CONCLUSION
This study have applied an integrated approach which combines seismic amplitude inversion, geologic transform and spectral decomposition of amplitude derived seismic attributes and well-logs for lithofacies differentiation within the Niger Delta "TOMBOY" field and results obtained show improved understanding of the concept of vertical and lateral continuity of sand lithofacies within the reservoir window because geoscientists before now had few clues about the presence of lateral continuity of sand lithofacies. From the results obtained, it is evident that the reservoir interval under analysis is made up of various lithofacies which includes gas filled sands, water-sands, oil filled sands and thin shale beds. Acoustic impedance derived from seismic amplitude inversion, improved the seismic visibility and resolution of the various lithofacies delineated within a thin-sand reservoir (of 16ms in thickness). Acoustic impedance inversion improved the resolution of the interval velocity values computed within the thin-sand reservoir to a reasonable level of accuracy comparable to sonic velocity. Rock properties such as acoustic impedance, interval velocity, density, and porosity, serves as useful tools for drawing relevant geologic conclusions from the interpretation of seismic data and are theoretically the best for lithofacies differentiation, hydrocarbon delineation and reservoir characterization and particularly more in spectral (frequency) domain. The implication of this study is that by defining the lateral and vertical distribution of sand lithofacies within the reservoir bed, seismic stratigraphic studies in the field will be enhanced and hydrocarbon fairways are better defined and knowledge of this can be incorporated into drilling decisions.