Frequency distribution curves from the three wells (WX, WY and WZ) indicate the distribution of the descriptive statistical curves for the three wells and show peak constituents and uniformity of sediment fraction for the study location (Figure 6). The curves are primarily unimodal with a dominating peak around 2 ϕ (Figure 6(F)) and 1 ϕ (Figure 6(J) and Figure 6(K)), whereas, a few of the samples exhibit bimodal behaviour with distinct peaks at 3 ϕ (Figure 6(C), Figure 6(D), Figure 6(H), Figure 6(G), Figure 6(J)-(O)), 4 ϕ (Figures 6(A)-(G), Figuress 6(P)-(Q)), 5 ϕ (Figure 6(E), Figure 6(K), Figure 6(O) and Figure 6(P)), 6 ϕ (Figure 6(H), Figure 6(J), Figure 6(K), Figure 6(M) and Figure 6(N)), 7 ϕ (Figures 6(A)-(L), Figures 6(O)-(R)) and 8 ϕ (Figure 6(D)). This is explained by the occurrence of both unimodal and bimodal populations, indicating the presence of both types of sediments (i.e., pure sand without any silt particles and sand mixed with some finer particles). For sediments depicting unimodality, sediments settled throughout a uniform depositional process. Bimodality is attributed to the mixing of populations of various sizes from the source areas, variations in the velocities of depositional, or differences in the modes of transportation, such as rolling, saltation, or suspension ([19]). The bimodality is also most likely as a result of the low energy present during sediment deposition.

Figure 6. Frequency distribution curves for facies of the study area: A) IRregularly Laminated Heterolithics, B) Planar Laminated Heterolithics, C) Sandy Heterolithics, D) Bioturbated Heterolithics, E) Muddy Debrite, F) Sandy Debrite, G) Ripple Cross-Laminated Sandstone, H) Structureless Sandstone, I) Weakly Stratified Sandstone, J) Pebbly Sandstone, K) Planar Stratified Sandstone, L) Dewatered/Deformed Sandstone, M) Bioturbated Sandstone, N) Fine Grained Sandstone, O) Mudstone, P) Slump Deformed Mudstones/Heterolithics, Q) Conglomerate and R) Injectite.

Additionally, phi values were plotted against the cumulative frequencies. The cumulative frequency plot highlights the various ways that the sediments were transported and deposited as well as their significance in the origin of the rock samples. The curve typically exhibited an S-shaped pattern when plotted on an arithmetic scale (Figure 7) and the slope of the central portion of the curve can be used to predict sorting. Low velocity and rapid rate of deposition leads to poor sorting and a broader and gentle slope in the distribution curves. In contrast, a very steep slope is an indication of good sorting ([19]; [27]; [12]; [4]). From the cumulative frequency curves, the samples are predominantly silt, with few samples being medium to fine grain and very few being coarse in nature. The broadness and gentleness of the slope indicates that the grains are poorly sorted to very poorly sort (Figure 7). The cumulative frequencies also revealed that most of the sediments was transported by the process of saltation which is dependent on the rate of deposition followed by suspension population which reflects conditions above the depositional interface ([36]) and a few indications of the traction process.

Figure 7. Cumulative frequency curves for facies of the study area: A) Irregularly Laminated Heterolithics, B) Planar Laminated Heterolithics, C) Sandy Heterolithics, D) Bioturbated Heterolithics, E) Muddy Debrite, F) Sandy Debrite, G) Ripple Cross-Laminated Sandstone, H Structureless Sandstone, I) Weakly Stratified Sandstone, J) Pebbly Sandstone, K) Planar Stratified Sandstone, L) Dewatered/Deformed Sandstone, M) Bioturbated Sandstone, N) Fine Grained Sandstone, O) Mudstone, P) Slump Deformed Mudstones/Heterolithics, Q) Conglomerate and R) Injectite.

On the [14] sediment classification ternary diagram, the samples generally form a tight grouping along the sand, silty sand and sandy silt side for the fine plot. Of the 18 samples, one, (Sm) about 6% of the total is classified as sand, eight others (Sb, Sf, Sp, Sxr, Hs, I, Hb and Dm) which is about 44% are classified as silty sand and four samples, (Hp, Hi, M, MHd) making up 22% of the sample total are classified as sandy silt (Figure 8(A)).

For the coarse plot, four samples, (Cgl, Sc, Sd and Ss) about 22% grouped around slightly gravelly sand with only one sample (Ds) constituting 6%, plotted in the gravelly muddy sand (Figure 8(B)).

Figure 8. Ternary diagrams of sediment classification scheme from [14], Produced by program SEDPLOT: A) samples with no gravel and B) samples with GREATER THAN 0.1% gravel.

On the [33] sediment classification ternary diagram, the samples generally form a tight grouping along the sand, silt and clay (gravel < 10%) side for the coarse plot. Of the 18 samples, five samples, (Cgl, Ss, Sc, Sd and Ds) constituting 28% plotted in the sand, silt and clay (gravel <10%) region (Figure 9(A)).

For the fine plot, four samples, (Hi, Hp, MHd and M) about 22.2% grouped around sandy silt, additional four, (Hb, Hs, Dm and I) which makes up 22.2% of the samples plotted in the silty sand portion with ten other samples (Sb, Sd, Sf, Sc, Sp, Sxr, Ss, Sm, Ds and Cgl) which is about 55.6% grouping in the sand region (Figure 9(B)).

Figure 9. Ternary diagrams of sediment classification scheme from [33] and modified by [32], produced by program SEDPLOT: a) samples with gravel and b) samples with no gravel.

According to the graphic median, at a given value, half of the particles are coarser and the other half are finer. The values in this sample range from 0.87 to 6.09, with an average of 2.91 (Table 2) which shows that the grains are typically fine. The median class yielded several fairly high results, indicating that the sediments are abundant in a particular grain size.

The results of the mean demonstrates that the reservoir unit is primarily composed of medium to silt sand deposits, with a range of 1.01 to 6.29 and an average of 3.26 (Table 2). According to [19], the peculiar size distribution of very fine sand may be the result of the low energy environment that occurred at the time of deposition. The results of some samples, such as MHd, M, Hp, Hi, Hb, Hs and Dm (Figure 10(A)) are relatively high since that kind of sediment class predominates. On the other hand, some samples such as Cgl, Sc, Sm, Sd and Ss (Figure 10(A)) however, is low because there are about equally many fine and very fine sediments, and they are poorly sorted since there is a large variation in grain size.

Table 2. Results for moment statistical parameters using GSSTAT software.

Figure 10. Histograms plotted with respect to the moment method: A) mean size, B) standard deviation, C) skewness and D) kurtosis.

Standard Deviation assesses the homogeneity or sorting of the grains, which reveals the energy conditions present during transport and deposition. Majority of the samples denotes poor sorting, with only a few other samples, Hb, Hi, Hp, Hs, MHd, M, Dm, Ds and I showing very poor sorting (Figure 10(B)). It ranges from 1.27 to 2.78 with a mean of 1.98 (Table 2). The poorly sorted sediments show a mixing of sediments of different sizes as well as a little variation in the mode of transporting current velocity. Although it reflects the energy state of the environment of deposition ([19]), it does not primarily assess the degree to which the sediment has been mixed.

Skewness evaluates the degree of asymmetry in the frequency curves in terms of the dominance of fine or coarse-grained fractions and thus evident of deposition energy. The skewness values for the sand samples range from 0.06 to 0.55 with an average skewness of 0.34 (Table 2). Almost all the samples are very fine skewed or exhibits positive skewness, suggesting that the sample accumulated in a low-energy environment with only one sample, MHd being near symmetrical and M being fine skewed (Figure 10(C)). This denotes that a higher percentage of particles is present in the fine tail of the sediments.

Kurtosis denotes the sharpness of the grain size frequency distribution which compares sorting of the middle portion to the tail spread and indicates whether the distribution is relatively narrow and peaked (leptokurtic) or broad and flat (platykurtic). With an average value of 1.32, the peak of the samples ranges from 0.80 to 1.87 (Table 2). The grains occupy the very leptokurtic zone with better sorting at the tails (Figure 10(D)).

Based on the presumption that distinct depositional settings represent various fluid mechanisms for sediment transport and deposition, bivariate plots are produced to discriminate between them ([34]). The majority of the sample clusters in the field of medium and silt sand grains and are very poorly sorted to poorly sorted as shown by the mean size and standard deviation plot (Figure 11(A)). The very fine-grained sediments are an indication of low-energy conditions of deposition ([11]).

The samples are clustered around very fine skewed and fine skewed, with an average mean value of 1.19, according to the bivariate plot between mean size and skewness (Figure 11(B)). They all lie in the fine and very fine skewed group but encircle in medium to silt grain sizes. According to Mean vs Kurtosis bivariate analysis indicates that the medium sand to silt grain sizes is scattered in platykurtic to very leptokurtic conditions (Figure 11(C)).

Standard deviation vs skewness plot shows that the very poorly sorted sediments are near symmetrical to strongly fine skewed in nature and the poorly sorted sediments are fine to very fine skewed (Figure 11(D)). Standard deviation vs kurtosis indicates that the very poorly sorted sediments are platykurtic to mesokurtic and poorly sorted sediments are leptokurtic to very leptokurtic in nature (Figure 11(E)) and the skewness vs kurtosis plot exhibits near symmetrical to very fine skewing, revealing the sediment are scattered in the very platykurtic to very leptokurtic regions (Figure 11(F)).

Figure 11. Bivariate plots between: A) mean and standard deviation, B) mean and skewness, C) mean and kurtosis, D) sorting and kurtosis, E) sorting and skewness and F) skewness and kurtosis; CS coarse sand, MS medium sand, FS fine sand, VFS, very fine sand, MWS moderately well sorted, M.S moderately sorted, ns near symmetrical.

Bivariate is most successful at differentiating between beach and river sands as well as river and coastal dune sands according to ([23]) and ([6]), and whether quarter, half, or whole phi data are employed, the differentiation is accurate. Therefore, statistical values obtained using both graphical and moment approaches were shown in different bivariate diagrams to confirm the existing paleoenvironmental conditions. [17] created a bivariate by graphing skewness vs standard deviation to discriminate between beach and river sedimentary environments. The sample points plotted in the river (fluvial) environment when the graphical and moment measures were used (Figure 12(A)). The distinction between coastal dune and river environments was further made using the bivariate between skewness and kurtosis by ([16]) and ([19]), which supported ([17]) findings. Most of the sample plot in the river environment with only a few plotting in the coastal dune environment for both graphical and moment statistical measures (Figure 12(B)).

Figure 12. A) bivariate plot of skewness vs standard deviation (source: [18]) and B) bivariate plot of skewness vs kurtosis (source: [16]).

Using (Equations (10)-(13)), it was discovered that Y1 demonstrated that each sample belongs to the beach environment after the linear discriminate function values were calculated using statistical parameters obtained by the graphical technique (Table 3). All of the sediments are shallow marine sediments with Hb and Sf being beach sediments, according to Y2 values. Y3 was used to compare the fluvial and shallow-marine predominance, and it was found that the former predominated. According to Y4, the sediments were primarily deposited by turbidity current with only Sf being fluvial in nature.

Table 3. Results of linear discriminate function analysis using the graphical method.

B Beach, SM Shallow Marine, F Fluvial, T Marine Turbidity Current

The application of moment-method statistical parameters to the Linear Discriminant Function (Table 4) yielded consistent results. Y1 classified all samples as beach deposits while Y2 indicated a shallow-marine setting. Additionally, Y3 demonstrated the fluvial nature of the sediments, and Y4 was used to discriminate between fluvial and marine (turbidity current) environments. It showed that the marine turbidity environment predominated, with seven samples (Hb, Hi, Hp, MHd, M, Dm, and Cgl) classified as fluvial origin.

Table 4. Results of linear discriminate function analysis using the moment method.

B Beach, SM Shallow Marine, F Fluvial, T Marine Turbidity Current

The LDF plot of Y1 versus Y2 plot (Figure 13(A)) shows that the majority of samples plot in the Beach shallow agitated field, with only three samples departing into the aeolian or littoral fields. Similarly, the Y2 versus Y3 plot (Figure 13(B)) places nearly all samples in the Shallow marine agitated field, with two samples plotting as Fluvial beach. The Y3 vs Y4 plot (Figure 13(C)) shows that all samples, from both the graphical and moment techniques, fall inside the Fluvial/Turbidity current field, with no samples falling in the purely fluvial or shallow marine fields. This suggests that the sediments originated from a fluvial sand population but were eventually deposited by turbidity-current (sediment gravity flow) processes, indicating a deep-water turbidite system fed by a fluvial frontier rather than a beach or shallow-marine reworking pathway.

Figure 13. Linear discriminate function plot for the study area: A) Y1 vs Y2, B) Y2 vs Y3 and C) Y3 vs Y4.