The identification of formations in anisotropic reservoirs using seismic reflection data and logging data may lead to misrepresentations of the actual formations. Lithofacies discrimination intrinsically has ambiguity, and the depositional sequences of the study area comprise shales, fine-grained sands, and silts. So it needs to reduce the uncertainty of the lithofacies discrimination using anisotropic parameters. This study proposes an approach involving seismic anisotropic parameters to discriminate between different lithofacies. We calculate four anisotropic parameters (ε, δ, γ, η) from logging data (V p, V s, and density) and then employ these for lithofacies discrimination. We compared our results to lithofacies discrimination based on traditional parameters such as V p/V s ratio, clay volume, and water saturation. Using field data from Muglad Basin in South Sudan, we show how the suggested parameters could be used to identify eleven zones with distinct lithofacies. According to the anisotropic parameters, the lithofacies discrimination results are similar to other logging data, and it is easier to separate the lithofacies than petrophysical data. Furthermore, we introduce a new parameter, i.e., the difference between the normalized anisotropic δ parameter and clay volume, which can be used as a possible indicator for heavy oil reservoirs. The new parameter matches well with water saturation in the field data application.
Lithofacies is the basic unit for the analysis of sedimentary environments. It refers to any subdivision of a sedimentary stratigraphic unit with different characteristic lithologic features such as rock type, grain size, physical and biological origin, and stratigraphic structures [1,2,3,4,5,6]. These lithologic parameters can be used to analyze sedimentary environments and are essential for reservoir prediction and characterization. One can discriminate between lithofacies by analyzing the reservoir parameters obtained from core samples [7,8,9] and well logging data. Reservoir characterization from lithofacies and reservoir parameters is an important factor in the exploration and development of hydrocarbon. Therefore, lithofacies discrimination is a fundamental process in well logging interpretation. Conventional reservoir parameters included in the analysis are V p/V s ratio, impedance, λ–μ–ρ variable, bulk density, and Poisson’s ratio [10,11,12,13,14,15,16,17]. Several efforts have used impedance and Lamé parameters for lithofacies discrimination and reservoir characterization [18,19]. In addition, crossplot of reservoir parameters (e.g., density vs velocity, porosity vs velocity, acoustic impedance vs density, acoustic impedance vs porosity, velocity vs Poisson’s ratio, Poisson’s ratio vs gamma log) is an essential tool to discriminate between lithofacies [20,21,22,23,24]. In the case of the acoustic impedances of shale and gas sends like in the Gulf of Mexico are almost identical, Poisson’s ratio is often used to identify the lithofacies . Mukerj et al. attempted to separate rock formation at the interface between sand and shale based on slight difference in acoustic impedance . Xie et al. performed lithofacies discrimination and fluid prediction in a carbonate reservoir . Karbalaali and Riahi tried to identify different lithofacies using seismic attributes [28,29,30]. Other work employed crossplots of impedance vs various reservoir parameters, discrimination of fluid content in the reservoir for the characterization, and identification of promising reservoirs [20,25,30,31]. Recently a machine learning for rock classification algorithm using well logs is successfully used to group reservoir rocks into various clusters [32,33]. Avseth et al. proposed a statistical method based on prestack seismic data and well logging data for lithofacies identification . In the clastic reservoir of the Orinoco Oil Belt in Venezuela, Torres and Infante employed a support vector machine (SVM) algorithm for lithofacies classification .
Seismic anisotropic parameters have different physical properties depending on the directions, affecting the elastic moduli. These are essential factors when determining the correct reflectors and to image the subsurface at a high vertical resolution [36,37,38,39,40,41,42]. As a result, the characterization of reservoirs using seismic reflection data and logging data without anisotropy often yields a misrepresentation of the actual formations. Considering anisotropic parameters can reduce this difference. Since anisotropic parameters vary in physical properties such as elastic properties, permeability, porosity, and petrofacies, it is an important factor for accurate reservoir characterization. There are studies on lithofacies identification in the point of elastic properties [41,42]. Babasafari et al.  estimated the anisotropic parameters (ε, δ, γ) values according to the offset and compared these to elastic properties logging data for clastic reservoir characterization. These parameters reduced the uncertainty of elastic properties for reservoir characterization. Asedegbega et al.  tried to find out anisotropic parameters for improving pore pressure prediction in 3D seismic data. Alkhalifah and Rampton found a strong correlation between the anisotropic η parameter and a smoothed gamma log . They applied it to discriminate between shale and sand layers. Since a high η coincided with a high gamma log, they tried to identify shale with high anisotropy using surface seismic data. This method can distinguish a highly anisotropic shale layer (in the case of high η values in gas fields) as well as isotropic sand layers from layers with η = 0. In addition, this approach was also applied to lithologic discriminations using the seismic anisotropic parameters η and δ .
This study presents logging data-based lithofacies discrimination of reservoirs in a sedimentary basin with anisotropic characteristics. Since it is difficult to characterize the physical properties like seismic anisotropic parameters due to their varying degree of anisotropy, simplified models are usually employed, with the vertical transversely isotropy (VTI) model being the most well-known example . To determine the anisotropic parameters of individual layers, one used coring plugs in three different directions (at 0°, 45°, and 90° to the vertical) , full-wave sonic logging data , and multi-component seismic data. Core plug data can be used to determine the relevant petrophysical parameters in the laboratory. However, this approach is time-consuming (acquisition of core plugs) and requires adequate technology to perform the analysis. Moreover, the use of multi-component seismic data requires certain data acquisition and highly technical processing efforts. One can use P- and S-wave velocities from full-wave sonic logging data to measure anisotropic parameters. Anisotropy in the earth layers mainly results from micro-fractures, multiple stacks of isotropic thin layers, and intrinsic anisotropic properties. One uses Backus averaging  to measure the petrophysical properties in multiple stacks of thin layers. The main objective of this study is to distinguish lithofacies using anisotropic parameters. Moreover, we suggest an empirical indicator for heavy oil reservoirs. We present an approach for the petrophysical delineation using anisotropic parameters and suggest the use of the anisotropic δ parameter and clay volume for lithofacies identification. We calculate the anisotropic parameters from acoustic logging data including compressional sonic, shear sonic, and density log. The logging data set used to demonstrate this new approach was obtained in the Muglad Basin in South Sudan. Field data for the study were obtained from Muglad Basin in the central northern part of South Sudan [48,49,50,51,52,53,54]. The reservoir consists of finely layered shale and sand, and it is a heavy-oil reservoir . The tectonic regime of the study area is primarily controlled by rifting, which produces normal faulting, fault blocks, and horst graben structures . In addition, the basin contains potential hydrocarbon produced from the sands of the Bentiu formation [55,56].
2 Location and geological setting
The Muglad Basin in South Sudan is considered part of the Late Jurassic to Early Cretaceous rift basin. That covers an area of about 112,000 km2 and vertically consists of 10–15 km of Jurassic-Tertiary continental sediments (Figure 1) [56,57]. The basin forms part of the well-known Western-Central African Rift System that comprises the Muglad Basin, Melut basin, Bongor Basin in Chad, and Termit Basin in Niger. Several authors have described the geology of Western-Central Africa [53,58,59,60]. All these basins have been targeted for exploration and yielded significant oilfield discoveries. Giedt described the regional aspects of the interior Muglad Basin petroleum geology . There are three rifting phases in sediments with each phase consisting of lacustrine facies at the bottom and fluvial and fluvial-deltaic facies at the top. Many authors have contributed to the currently accepted Muglad Basin stratigraphy shown in Figure 2 [48,61,62,63]. The depositional sequences include the primary source of rich organic lacustrine claystone and shales interbedded with fine-grained sands and silts in the Abu Gabra formation of Early Cretaceous [60,63,64]. The Bentiu formation consists of deposits of Bentiu sands that originated from the uplifted flanks during the Albian period . The Bentiu formation is the main oil-bearing unit with an average thickness of several hundred meters. This formation overlies the Aradeiba formation and is comprised of interbedded sequences of mudstone, sandstone, and siltstone. It is similar to the Aradeiba formation. The Zarga formation was deposited in a lacustrine environment with fluvial-deltaic channels. The Baraka formation was identified as the topmost part of the arenaceous strata and recognized as a non-contributor to the reservoir zones due to an absence of adequate sealing. The Amal formation is characterized by thick massive sandstones deposited in alluvial fans and braided streams. During the Late Eocene-Oligocene, deposition was caused by the reactivation of extensional tectonism . This formation is similar to Nayil in that deposition was caused by the reactivation of extensional tectonism and that they share similar depositional characteristics. The Adok formation originated during the Late Oligocene to Middle Miocene. The Zerf formation and Quaternary are Tertiary–Quaternary sediments known as the Umm Ruwaba formation which is characterized by widespread unconsolidated to semi-consolidated gravels, sands, clay sands, and clays from fluvial and lacustrine environments.
3 Material and methods
The anisotropic parameters of rocks can be obtained from the full-wave sonic log and density log data by an approach that yields the stiffness matrix in terms of P- and S-wave velocity and density. Multiple isotropic thin layers (e.g., shale) represent the simplest anisotropic media in the Vertical Transverse Isotropy model (VTI) . In these VTI media, the relationship between stress and strain, which is normally expressed as an 81-coefficient comprising stiffness tensor, takes a much simpler isotropic form of a 6 × 6 stiffness matrix that is applied to various areas. The anisotropic petrophysical properties contain more information than these isotropic media. The seismic wave characteristics for each layer in the horizontal, isotropic multiple stacks of thin layers intrinsically vary. When a long wavelength seismic wave propagates in multiple stacks of isotropic thin layers, the physical properties naturally have anisotropy, and the variation is getting smaller in the vertical direction. The anisotropic parameters can be obtained through the stiffness matrix formulated in terms of the Lamé parameter and shear modulus which can both be obtained from velocity and density data contained in the logging data [44,65]. Our approach thus involves:
V p, V s, density log,
Lamé parameter (λ) and shear modulus (μ),
Stiffness coefficients (A, C, F, L, M), and
Anisotropic parameters (ε, δ, γ, η).
Anisotropic parameters (ε, δ, γ) and vertical wave speeds (V p and V s) are functions of the stiffness matrix c ij and density . Typically the anisotropic parameters in VTI media can be expressed as follows:
According to Alkhalifah and Tsvankin , the anisotropic parameter η can be expressed in terms of (ε, δ):
The layer properties of the multiple isotropic thin layers and wave speeds ( , ) as well as elastic moduli (A, C, F, L, M) can be defined as follows:
Here, “ < > ” refers to the volume average of a quantity in the simple layered medium . Since the Lamé parameters and shear modulus are expressed in terms of V p , V s , and density, we can also express the stiffness matrix using the same parameters:
4 Application to field data
A seismic stack image of the study area shows target reservoir reflectors around CDP #545 with a 1.6 s two-way travel time (TWT) (Figure 3). The CDP spacing was 12.5 m and the shot interval 50 m. The seismic travel time along the wellbore was used to determine the approximate depth and calculate the expected depth based on formation velocities. The approximate time–depth relationship yields a depth of about 1,320 m for a TWT of 1.6 s (Figure 4). Figure 5 is a general workflow from logging data to lithofacies discrimination and a Direct Hydrocarbon Indicator (DHI) for heavy oil reservoirs. First, we calculate clay volume, porosity, and water saturation from input logging data. These calculated logging data are input data for the anisotropic parameters and then apply it to facies discrimination and DHI indicator.
4.1 Log data analysis
We prepared the wireline logging data for a single borehole to perform a petrophysical evaluation and identify key facies, using the lithology model for lithological analysis and facies description. The main steps focused on (i) shale volume calculation, (ii) porosity, (iii) resistivity, and (iv) water saturation (estimated using the Indonesian saturation model, cf., Poupon and Leveaux ). The usual methods to determine the log-derived shale volume involve gamma-ray (GR) responses and the difference between the neutron- and density-log-derived porosities [69,70]. Since the study area is a clastic environment, the rock properties vary in grain size and shale content. In a clastic reservoir, one uses the gamma-ray log for shale volume calculation [71,72,73,74]. However, minerals with a concentration of potassium or thorium make it difficult to identify clean sand resulting in an overestimation of shale volume. The difference between neutron- and density-log porosities is another indicator of shale volume that works well in clastic depositional sequences. Poupon and Gaymard  quantified clay content in sedimentary strata using the following clay index
where GRlog is the gamma-ray intensities acquired in each layer of the log, and GRmax and GRmin are the processed gamma-ray maximum (100% shale) and minimum (clean sand). Since the calculation of shale volume using the linear relationship of shale volume and clay index overestimates shale content reservoirs, researchers developed various non-linear equations for obtaining realistic shale volume [76,77,78,79,80]. The GR, density, and neutron log coverage of the study area are the same, mainly covering all main borehole sections. Consequently, there are no issues with shale volume calculation across the field. So the shale volume calculation is based on clay volume and silt volume. In the present study, we use an empirical equation that combines clay volume and silt volume to reduce the overestimating;
where V shale is the shale volume, V cl for the clay volume, and V silt for the silt volume. V cl is equivalent to the clay index and V silt is defined as follows:
where V wcl is the wet clay equivalent volume of V cl, φ e for effective porosity, and φ max for maximum porosity [73,81]. We can calculate the porosity with a variable matrix density model if both shale and oil affect the porosity ,
where φ N1 is the neutron corrected-porosity for matrix 1, φ N2 the neutron-corrected porosity for matrix 2, φ D1 the density-corrected porosity for matrix 1, and φ D2 the density-corrected for matrix 2. Since our study area contains both fresh formation water salinity and heavy oil, we can use the Indonesian water saturation model . The advantage of this model is its flexibility in that it can handle fresh water, heavy oil, and laminated clay . We used the following equation to calculate water saturation:
where S w is the effective water saturation, n the saturation exponent, m the cementation exponent, a the tortuosity factor, R t the true resistivity log, R w the formation resistivity, R cl the resistivity of clay, V cl the wet clay volume, and φ the porosity.
5 Results and interpretation
We calculated shale volume, porosity, and water saturation from the logging data. The parameters are conventionally the basis for lithofacies discrimination. However, the results could be subjective, and it needs to reduce ambiguity. So, first, we show the results from the traditional and anisotropic parameters. Additionally, we suggest a direct hydrocarbon indicator for heavy oil reservoirs.
5.1 Logging data and lithofacies
The log types used for this analysis include gamma-ray (GR), deep resistivity (LLD or LLS), neutron porosity (NPHI), sonic (DT), bulk density (RHOB), and caliper (CALI). Figure 6 shows the wireline logging profiles that were used to evaluate the Muglad Basin formation lithofacies. The wireline logging data were converted into meaningful rock properties such as porosity, clay volume, and water saturation. We obtained the petrophysical properties such as clay volume (V cl), effective and total porosity (PHIE and PHIT), and water saturation (S w) from the input logging data. Sandstone and shale were estimated and used as indicators to identify facies types. The GR log was used to identify the shale distribution. Although the gamma-ray log is a reliable shale indicator, it cannot be used to estimate the constituents, such as silts volume, and cannot identify the sand shale [79,83]. In some cases, the logging response was influenced by the lithological properties of the reservoir, mainly texture, mineralogy, and fluid content. This approach is, therefore, a reliable qualitative description of the reservoir properties and can be used to identify lithofacies types. Without a core data analysis, dividing the lithofacies into anything other than sand and shale is unclear. The Gamma log curve is high over shale zones and vice versa over non-shale zones. There is a significant correlation between the gamma log and bulk density log . Low-density anomalies over high gamma readings show shale zones since a significant correlation between the gamma log and bulk density log (Figure 6). Based on the logging data analysis and sedimentological reports, we conclude that the depths between 1,353 and 1,382 m mainly consist of sand and shale while the lithofacies between 1,382–1,456 m are sand-dominated. Between 1,456 and 1,528 m, the formation is dominated (∼90%) by shale, while the formation between 1,528 and 1,711 m is claystone with interbedded sand/shale layers with limited thin sands. According to the drilling reports, the oil-bearing zone is between about 1,566 and 1,620 m.
5.2 Anisotropic parameters and lithofacies
The logging data (V p, V s, and density) form the basis for calculating the anisotropic parameters (ε, δ, γ, and η) (Figure 7). Figure 7 shows a procedure for acquiring anisotropic parameters and DHI from logging data. First, we obtain the Lamé parameter, λ, and shear modulus, μ, from the V p, V s, and density log. Using equation (4), we obtain the stiffness coefficients (A, C, F, L, M). Then, we calculate the anisotropic parameters from equation (3) after applying Backus averaging to the logging data (Figure 7). In the resulting parameters, ε, γ, and η show similar positive trends, with different magnitudes, whereas δ exhibits a negative trend (Figure 8). There are relatively high values at depths 1,200–1,250, 1,300–1,320, 1,400–1,450, 1,500–1,550, and 1,600–1,750 m. The quantitative ranges for each parameter are 0.002–0.08 for ε, –0.12–0.02 for δ, 0.02–0.28 for η, and 0.04–0.44 for γ. The input logging data (GR, CALI, SP, and NPHI) were used to calculate S w, V cl, and δ (Figure 9). We suggest eleven prominent lithofacies zones from the anisotropic parameters (indicated by A to K in Figure 9). The eleven zones were distinguished, considering only changes in the variable anisotropy values. The tendency toward changing the four anisotropic variables (ε, δ, η, and γ) is similar. If it is divided into a value close to 0, from zone G to zone K can be one zone. However, this study classified the 1,570 m lower part into five zones, even though the absolute anisotropic variables were higher than zero. When we compare these results with petrophysical data such as V p, V s, V p/V s, V cl, and S w, we can see relatively low values (0.02–0.2) for V cl and low values (0.2–0.3) for S w in Zones B and G. In the same zones ε, γ, and η all have low positive values. At the same time, δ is negative, suggesting that the δ parameter correlates with V cl and S w. A quantitative comparison of lithofacies based on V cl (track 8 in Figure 9) and δ (track 4 in Figure 9) reveals that when V cl is low, δ is low, too, and vice versa. Zones A, B, C, F, and G represent predominantly sandy units of the formation. It should be noted that the zones with the lowest water saturation are typically the pay zones. These results are consistent with the rocks’ anisotropic contrast between layers, as shown by the similar magnitude P- and S-wave velocities. The V p /V s ratio yields low values in the zones mentioned earlier and coincides with low V cl and high S w values. Typically, this result would be consistent with a sand reservoir. Higher values of V cl in some intervals indicate high levels of anisotropy. Negative δ was found to correlate with V cl. Therefore, the zones with the lowest amount of clay (having a high S w) indicate hydrocarbon-bearing rocks. Negative δ seems to act as a possible hydrocarbon indicator. For a more reliable interpretation, we first normalized and then used this to derive a new parameter, namely direct hydrocarbon indicator (DHI), the difference between the normalized δ and V cl, to serve as a possible hydrocarbon indicator (Figure 10a). Though the assumption lacks a correlation between the δ and primary logging data, the possible relationship is explored. We found a significant negative correlation between normalized S w and DHI, showing a clear dependence of DHI on S w (Figure 10b). The resulting correlation coefficient is high and typical of hydrocarbon-bearing reservoirs. Figure 11 shows shale volume (track 8), water saturation (track 9), and normalized anisotropic parameter, δ (track 10).
This article discriminates lithofacies using anisotropic parameters (ε, δ, γ, and η) in the Muglad Basin, South Sudan. The results show that the Muglad Basin has significant lithological and rock property changes. Usually, ε represents the ratio of horizontal P- and vertical P-wave velocity. δ is related to P-wave velocity variations away from the symmetry axis, influencing SV wave velocity. γ includes the fractional difference between SH- and SV-waves. Therefore, ε and δ are related to the P-wave velocity. In general, anisotropic characteristic of shale is high and low levels in sandstone. η values correlate with gamma log data, which makes it a valuable parameter for the discrimination between shale and sand . Based on the variability of the anisotropic parameters, we could identify several lithofacies. The possible layer boundaries yield a total of eleven different zones labeled Zones A to K. Zone B (1,330–1,400 m) was only weakly anisotropic, while Zones C, E, H, I, and J showed high levels of anisotropy. In Zones C, F, H, I, and J, ε values were higher than in other zones. Thus, ε can serve as one of the possible indicators for lithofacies discrimination. Lithofacies discrimination based on anisotropic parameters reveals different sedimentary environments. Since drill-cuttings and cores are typically used to discriminate lithofacies in the wellbore in combination with the logging data, the continuous anisotropic values from the logging data can help to define lithofacies. Therefore, this approach will be suitable for reservoir evaluation whenever core logs, mud logs, or natural GR log data are unavailable. The logging data analysis and sedimentological reports from our study area suggest that the recognized formations in Zones F–J (1,520–1705 m) are claystone with interbedded sand/shale layers with limited thin sands. In Zone F (1,520–1,560 m), the formation was dominated (∼90%) by shale, while Zones A, C, F, and G contained sand and shale at similar percentages. At 1,325–1,353 m, there is a mixed zone. Zone B (1,340–1,400 m) is mostly sand and shale. The lithofacies in Zone C (1,400–1,455 m) were sand dominated. The Indonesian model can handle fresh water, heavy oil, and laminated clay and was therefore used to calculate the water saturation . The environment of the study area is known as fresh formation water salinity and heavy oil [55,85]. The logging data depend on the lithological properties of the reservoir, mainly texture, mineralogy, and fluid content. So this is a reliable qualitative analysis method for describing the reservoir properties and lithofacies types. Due to the lack of core data analysis, it is difficult to divide the lithofacies into finer groups other than sand and shale. However, a distinct correlation exists with low-density anomalies corresponding to high γ readings (shale). Several prominent lithofacies could be identified and were labeled Zones A to K. Zones A and B consist of low volumes of clay and low water saturation in the depth interval between 1,340 m and 1,400 m. In the same interval, ε is positive while γ and η are very low, and δ is negative. It was compared to clay volume (V cl) and an essential low saturation zone. The other anisotropic parameters (ε, γ, and η) are inversely proportional to δ. A quantitative comparison between lithofacies based on clay volume and the anisotropic parameter δ in Zone C revealed a relationship between δ and clay volume. Comparing the lithofacies obtained from the anisotropic parameters and from other logging data yields similar results, although not identical. According to Li et al. , the study area in the Muglad Basin is a heavy-oil shaly-sand reservoir. The results come from geochemical analysis of core data and petrophysical analysis of well logging data. We found a parameter, DHI, the difference between the normalized δ and S w. Since the changes in DHI are related to the S w, we suggest DHI is a possible empirical indicator for the heavy oil reservoir. However, it needs to apply the DHI parameter to other types of reservoirs, though it is applicable in these local areas.
Sedimentary layers with horizontally multiple stacked isotropic thin layers tend to have anisotropic characteristics. The anisotropic parameters reduce the ambiguity in lithofacies discrimination and enhance reservoir characterization. In this study, we applied the anisotropic parameters to lithofacies discrimination and suggested an empirical indicator for heavy oil reservoirs. First, we calculated the Lamé parameter and shear modulus from the logging data (V p, V s, and density log) in the Muglad Basin to obtain the stiffness coefficients. We then calculated the anisotropic. We proposed eleven lithofacies units for reservoirs based on the anisotropic parameters. The discrimination resulted from differences in the sedimentary environment. The suggested empirical indicator is a difference between normalized anisotropic parameter δ and clay volume. We showed that the new indicator matches well with water saturation through the field data application. In the absence of drill core data or drilling cuttings, these anisotropic parameters obtained from the logging data appear efficient for lithofacies discrimination.
This work was supported by the Energy Efficiency & Resources Core Technology of the Korea Institute of Energy Technology Evaluation & Planning (KETEP). In addition, it was granted financial resources by the Ministry of Trade, Industry & Energy (MOTIE), Republic of Korea (No. 20182510102470, KIGAM GP2020-034).
Funding information: This work was supported by the Energy Efficiency & Resources Core Technology of the Korea Institute of Energy Technology Evaluation & Planning (KETEP). In addition, it was granted financial resources by the Ministry of Trade, Industry & Energy (MOTIE), Republic of Korea (No. 20182510102470, KIGAM GP2020-034).
Author contributions: SHJ designed the study. WAD and SHJ processed the seismic data. WAD and SHH processed and interpreted log data. SHJ developed some codes for anisotropic parameters from log data and performed them to calculate anisotropic parameters. The authors prepared the draft, SHJ for Abstract, Introduction, and Conclusion, SHH for log data analysis, and WAD for Geological setting & Discussion.
Conflict of interest: The authors state no conflict of interest in this article.
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