Introduction

Lithology

Reservoir characterization supplies geologists and petroleum engineers with valuable information on various rock and fluid properties playing an important role in managing and developing all stages of a hydrocarbon reservoir (Cross et al. 2022). Understanding lithology correctly can be advantageous to forecasting the volume of hydrocarbon in place and lessening uncertainty over reservoir characterization, for it is directly connected to porosity and permeability (Mondal and Singh 2022). There is a wide range of methods for lithology identification, one of which is utilizing coring samples and laboratory measurements such as microscopic image analysis (i.e., thin section) or other analyses like CT scans of cores and electron microscope (SEM) (Cao et al. 2022; Temizel et al. 2022). Extensive research has long been performed through well-logging data to distinguish lithology (Das and Chatterjee 2018; Islam et al. 2021), which recently using tools such as nuclear magnetic resonance (NMR) very much considered (Singh and Ojha 2022). Seismic analysis and seismic inversion are commonly used to determine lithology (Fawad et al. 2021; Radwan et al. 2022). Artificial intelligence (AI) methods have recently played a significant role in determining lithology (Taheri et al. 2022). A myriad of AI approaches was employed, which support vector machines (SVM), convolutional neural networks (CNNs), and deep learning (DL) methods are the most commonly used (Deng et al. 2017; Wang et al. 2022a, b; Xu et al. 2022). This point must be mentioned that in AI methods, information such as core, well–logging data, images, and seismic data are employed as data sets for input data. Electrofacies and geostatistics approaches are other techniques used to evaluate and identify lithology (Karimian Torghabeh et al. 2022; Mirhashemi et al. 2022). The mentioned methods are more likely to demand a great deal of money or be costly in some situations. In order to deal with the problems, rock physic techniques (RPT) can provide fast, easy, and accurate discrimination for underground projects. Many researches utilized PRT to discriminate lithology, some of which are listed as follows: (Huang et al. 2021; Hossain et al. 2022; Albakr et al. 2022).

Pore fluid saturation

Recognizing pore fluid distribution is a fundamental goal in oil and gas studies as it can control some vital parameters, such as pore pressure which is crucial in all stages of hydrocarbon investigations, especially for gas storage, enhanced oil recovery (EOR), and 4D seismic surveys (Elyasi et al. 2016; Pang et al. 2019). Various methods have been employed to pore fluid distribution in porous media. Laboratory test through coring samples is one of these, but it takes a lot of time and expenditure, and above all, maybe the fluid content of the samples will change due to the depth displacement and pressure changes (Wang et al. 2020). Well-logging information has another way (Das and Chatterjee 2018; Teillet et al. 2021). Numerous studies show that seismic-based methods were also used extensively to discriminate fluids. These methods use the impacts of fluids on seismic and elastic features, including velocities (Xu et al. 2021; Xie et al. 2022), amplitudes using amplitude versus offset (AVO), and impedances (Foster et al. 2021; Wang et al. 2022a, b), and frequency (Yang and Malcolm 2021; Lan et al. 2022). Other procedures also have been employed, such as geostatistics (Di et al. 2021; Grana et al. 2022), dual-porosity theory (Zhou et al. 2021; Li et al. 2022), elastic parameters and rock physics template (Ahmad et al. 2022; Abe et al. 2022), and intelligence methods (Chenin and Bedle 2022; Ibrahim et al. 2022).

Petroleum engineers and geologists desperately need to discriminate lithology and fluid content accurately and fast by employing available data and considering all conditions as much as possible in different conditions. Previous studies have used either very expensive and time-consuming methods or have high uncertainty. Furthermore, the preceding rock physics studies did not pay attention to using multiple PRT to reduce uncertainty and increase accuracy in a short period and building rock physics modeling to organize and classify information for providing a quick look for discrimination. This study attempts to deal with the mentioned problems and improve the distinguishing lithology and fluid in hydrocarbon reservoirs. For this purpose, multiple rock physics templates and modeling were used simultaneously to evaluate their performance and cover all needed aspects. One of the great advantages of this study is that all results are validated through different information, tools, and scales; however, the preceding research used merely a few data to confirm. As a novel insight, this research uses rock physics modeling to engage geological features such as aspect ratio (AR) for pore fluid discrimination to transfer scattering data to organize with similar properties and validate with various parameters because one of the main goals of this study is to investigate rock physics patterns as much as possible. The research takes a further step and evaluates non-modeling data through PRT to discover events in the study area and compare them with modeling data.

Geological setting

The study area in southwestern Iran (Fig. 1) is in the Khuzestan province near the Abadan plain. A subsection of the Alpine–Himalayan belt, the area is considered part of the Mesopotamian Basin, next to the Dezful Embayment in the Zagros fold-and-thrust Belt (ZFTB). In general, the ZFTB has comprised several hydrocarbon reservoir formations, mainly carbonate, and different ages ranging from Triassic to Tertiary (Kordi 2019).

Fig. 1
figure 1

Location map of the zone of interest

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Two main elements have helped form these formations: different faults of this basin and distinct stages of Zagros folding dating back to early Cretaceous–late Tertiary. In particular, the surveyed region has been formed by the superimposition of late Tertiary folding due to Zagros Orogens. Being an Upper Cretaceous (Santonian) carbonate formation, the target region approximately has a maximum thickness of 100 m on average (AbdollahieFard et al. 2019). Stratigraphic studies of the carbonate formation show different fossils, namely Benthic, Rotalia, and Planktic foraminifera (Afghah 2016). Two shallow and deep facies exist in the carbonate formation, extending toward the northwest and southeast. However, this study is performed on the deep facies considered pelagic sediments (e.g., the inner neritic zone). The stratigraphic column of the study area can be seen in Fig. 2.

Fig. 2
figure 2

Sequence stratigraphy of the study area (Alavi 2004)

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Regarding the geological structure, the study region is an anticline covered by alluvium sediments and is classified into shallow relief (Mehrabi et al. 2020). The anticline is an elongated structure with low-slope ridges and a west–northwest–east–southeast orientation. In this structure, the northeastern ridges’ slope is higher than the southeastern ones. From a lithological point of view, this carbonate formation comprises wackestone, packstone, gray packstone, porous, and partly dolomitic. Also, PVT experiments indicate that this formation is occupied with crude oil whose API gravity is almost 23. Other petrophysical properties, such as porosity, average water saturation, and shale percent, are reported to be 18.2, 20, and 8.5%, respectively.

Materials and methodology

This study aimed to diagnose the lithology and fluids type of a carbonate reservoir zone in the west part of Iran. A set of raw data obtained by well-logging operations was used. The raw data, being in LAS format, included these logs: density (RHOB), corrected gamma-ray (CGR), later log deep (LLD), porosity, P-wave velocity (VP), S-wave velocity (VS), water saturation (SW), oil saturation (SO), and volumes logs including the volume of shale, limestone(calcite), and dolomite. Due to the availability of each of the log data, none of them were empirically estimated. The preceding logs accessibility and their units are presented in Table 1. It should be noted that P-impedance and S-impedance were, respectively, calculated by multiplying P-wave velocity and S-wave velocity by density.

Table 1 The well-logging data used in this survey with their standard units are available
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The workflow of this study was comprised of two main sections: (1) lithology and (2) saturation, which would be clarified further below.

Lithology

Quick-look identification

Intending to quickly know what kind of rock types there exists in the reservoir targets’ zone, the log data of VP, VS, and RHOB were imported into RokDoc software, cross-plotted, and compared with two empirical rock physics models, Greenberg and Castagna (1992) and Gardner et al. (1974). The former combines P-wave and S-wave velocities, and the latter connects RHOB to P-wave velocity for lithological discrimination. These two models developed through the laboratory evaluations of distinct rock types greatly assist petrophysicists. The reason for using the empirical models was that both seismic data (body waves) and the intrinsic rock data of density had been individually involved in the models, reflecting any lithology changes.

Rock physics templates

Rock physics models and templates were introduced by Ødegaard and Avseth (2004) as a magical methodology for forecasting lithology and fluids. These charts, known as cross-plots, have been used frequently to connect seismic variables with non-seismic to visually detect any irregularities in the reservoirs (Gelinsky 2020). Herein, two cross-plots were selected and plotted, including VP/VS versus CGR and RHOB versus CGR. Then, an in-depth analysis was made on them to find a direct relationship between the intrinsic rock data (of RHOB and CGR) and the seismic parameters (of VP and VS) for lithological distinguishment because multifarious clustering options have been introduced to differentiate shale from limestone, sandstone, and dolomite using the cross-plots (Avseth and Mukerji 2002).

Well-logging analysis

The gamma-ray logs, formation density, and neutron porosity were then used and interpreted to validate the lithology differentiations. Being highly impacted by rock characteristics and slightly impacted by fluid characteristics, the logs are the finest for lithological delineations (Zhou et al. 2018).

Saturation distinguishment

Saturation is one of the most critical data for many reservoir engineering calculations (Yang and Wei 2017). P-wave velocity (VP) is useful, practical petrophysical data for pore fluids detection. There exists adequate evidence that VS (S-wave velocity) is highly likely to help identify the fluid type (Avseth et al. 2010). Combining S-wave and P-wave velocities might help engineers with fluid-type discrimination (Pang et al. 2019). Acoustic impedance (AI), also called P-impedance, is an effective technique for distinguishing among pore fluids. The cross-plotting approach has drawn too much attention to calculating fluid saturation (Mavko et al. 2020). Herein, AI–VP/VS cross-plot, introduced by Ødegaard and Avseth (2004), was opted for and used as a fluid diagnostic tool. In addition to the two parameters of velocity ratio (VP/VS) and P-impedance (AI), resistivity log (LLD) variations were also investigated for the zone of interest to infer information about the presence of water or hydrocarbons. To better organize the velocity ratio data, VP and VS velocities were modified using the multiporosity model of Xu and Payne (2009). Building Xu and Payne (2009) in this case study involves several steps as follows (Fig. 3):

  1. (a)

    Mixing different lithologies by Reuss–Voigt–Hill (RVH) average equations to build a solid rock matrix (SRM).

  2. (b)

    Adding pore type to SRM through pore aspect ratio (AR) from sedimentology analysis utilizing differential effective medium (DEM) theory and Kuster and Toksöz's (1974) model to make dry rock module (DRM).

  3. (c)

    Mixing fluids using Wood equation (1955).

  4. (d)

    Adding the mixed fluid to DRM using the Gassmann equation (1951) to build fluid-saturated rock (FSR).

Fig. 3
figure 3

Workflow for building rock physics model (Xu and Payne 2009) in the study area

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The mixing law of the Reuss–Voigt–Hill was initially used for mixing the minerals present in the solid matrix because each component has a different elastic characteristic that must be taken into account when mixing, so that the rock physics model can be built within the boundaries according to its performance characteristics (Avseth et al. 2010). Clay pores (e.g., micron-sized pores filled with bound water) were next inserted into the solid matrix by applying the effective differential medium (DEM) model (Xu and Payne 2009). To consider the pores’ diameter when estimating VP, VS, and density, the theory of Kuster and Toksöz (1974) was also employed. To do so, the parameter of pore aspect ratio, whose values were provided from the sedimentological information of the study zone (see Table 2), was applied based on the previous theory.

Table 2 The aspect ratio for different lithologies in the studied zone
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Using the DEM model, two other micron-sized pores, e.g., water-wet and dry (non-bond-water), were inserted into the solid matrix system, aiming to calculate the bulk modulus of the dry solid matrix.

The residual water with the hydrocarbons of oil and gas was mixed using the suspension model of Wood (1955), and then, the VP value for the fluids was estimated (Avseth et al. 2010). After that, the fluids’ system was added to the dry rock system using the Gassmann equation. The objective was to measure the bulk modulus for the fluid-saturated rock system and observe how the fluid addition would influence the seismic properties. Considering pores’ average diameter was found to help particles with similar properties set together (Li and Zhang 2018). The intrinsic rock property of porosity has established a close relationship to the presence or absence of fluids in the reservoir rocks—a high porosity in a reservoir is bound to the company of a considerable amount of fluids (Qing et al. 2020). Thus, the porosity effect on fluids distribution within the zone of interest was separately examined in another AI–VP/VS cross-plot scaled with the porosity values. The cross-plot was also scaled with oil saturation (SO) and water saturation (SW) and analyzed to correlate the involved parameters to each other, attempting to recommend a local rock physics template. A new series of cross-plots were designed and closely investigated to verify the results obtained from the cross-plots. Avseth et al. (2010) suggested two cross-plots: VP/VS versus VS and VP versus VS. The higher sensitivity of P-wave velocity to fluid changes than S-wave velocity was the reason for choosing the cross-plots. The popular cross-plot of S-impedance (SI) versus P-impedance (AI) was also used to regard the non-seismic parameter of density in pore fluid prediction (Avseth et al. 2010). It should be emphasized that the verification was performed using the well-logging data, not the modeling one, and also by applying SO and SW simultaneously.

Results and discussion

Lithology discrimination results

Quick-look evaluation results

The compressional and shear wave velocities data were plotted versus each other and fitted with Greenberg and Castagna’s empirical model (1992) to guess the possible lithology in the study zone quickly. The results are shown in Fig. 4, in which X-axis represents VS and Y-axis represents VP.

Fig. 4
figure 4

The cross-plot of VP versus VS fitted with Greenberg and Castagna’s model (1992)

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The sandstone line crossed no point on the cross-plot and fell at the bottom of the data points, expressing that no sand existed in the zone. Many scatter points perfectly matched the two lines of limestone and dolomite, showing significant lithologies. Only a tiny amount of the data points was fitted with the shale line, indicating a low-shale formation. Therefore, three particular lithology types could be identified based on the cross-plot of Greenberg and Castagna (1992) and the seismic velocities of VP and VS. Nonetheless, limestone was quite recognizable as the dominant lithology. The lithology prediction could be justified based on the CGR scale (Fig. 4), a reliable indicator of rock mineralogy (Dong et al. 2016). The yellow, orange, and red points were identified as shale lithology due to being overlaid with Greenberg and Castagna’s shale line. The points being of CGR values above 20 API designate the presence of marl, shale, or minerals with high levels of potassium (K19) and thorium (Th90) because shaley formations commonly release more elevated amounts of gamma-ray than the rest of sedimentary rocks (Asquith et al. 2004). The dark, bright, and pale blue points, which were found to be of limestone and dolomite mineralogy, possess CGRs below 20 API. Generally, CGRs lower than 20 API are attributed to sandstone, limestone, and dolomite (Nazeer et al. 2016). However, because Greenberg and Castagna’s sand line did not cross any of the points, the CGRs herein merely corresponded to limestone and dolomite.

In the previous section, lithology discrimination was made only based on the amounts of seismic velocities. The experimental model of Gardner et al. (1974) was also utilized to ensure the already-made discrimination. Unlike Greenberg and Castagna’s model (1992), the parameter of formation density (RHOB), which is affected by both rock and fluid properties, is applied in this model for marking out the lithologies. The cross-plot of RHOB versus VP is presented in Fig. 5.

Fig. 5
figure 5

The cross-plot of RHOB versus VP for the study area is based on Gardner’s model

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The lithology results of this chart were in good agreement with those of Greenberg and Castagna. Similarly, a few data points were overlaid with Gardner’s shale line, restating that a small amount existed. The best line fitted on the data was limestone, followed by dolomite as the second-best. Observing such behavior dictated that the reservoir zone of interest mainly comprised dolomite and limestone. The shaley points were of higher RHOB and placed in the range of more P-wave velocity, whereas the trend was the opposite for dolomite and limestone points, possessing lower VP and RHOB. It was probably because of the higher porosity of this area, meaning that they could accommodate more fluid than the shaley area (Crain 2013).

Rock physics templates findings

The shear and compressional transient time values can be utilized for quick-look lithology discrimination based on the P-wave to S-wave velocity ratio (VP/VS) (Avseth and Mukerji 2002). The ratio of VP/VS was hence plotted versus CGR values (Fig. 5) to differentiate the target zone in terms of lithology. Crain’s thumb rules say that VP/VS for shale is higher than 1.90, and the figure for limestone is between 1.80 and 1.95. Dolomite will also be of VP/VS 1.65 to 180. It, for sandstone, will range from 1.55 to 1.65. Using the VP/VS and CGR values recommended in Crain’s petrophysical handbook (Crain 2013) for different lithologies, the reservoir area was subdivided into three zones, shale, dolomite, and limestone as follows. Looking at Fig. 6, CGR values higher than 20 API and VP/VS more than 1.90 show a few shaley points highlighted by a black oval. This implies that the target zone contains a small amount of shale. CGRs below 20 API may also indicate limestone, dolomite, or sandstone since there is no exact amount of CGR in the literature to discriminate these three lithologies.

Fig. 6
figure 6

The cross-plot of VP/VS against CGR for the study area

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We looked at the values of VP/VS as a good lithological indicator based on Crain’s rules of thumb. Almost two-thirds of the points had VP/VS 1.80–1.90, and about one-third had VP/VS 1.65–1.80, which were inferred to be limestone (red oval) and dolomite (yellow oval), respectively. However, there were no points VP/VS less than 1.65, indicating sandstone. These results, being in good agreement with Greenberg and Castagna’s or Gardner’s cross-plots, reassure that limestone is the primary lithology of the target zone, whereas sandstone had no contribution whatsoever.

The cross-plot of density (RHOB) with the corrected gamma-ray (CGR) was also generated to more accurately delineate the various lithologies of the area of interest. Choosing this specific cross-plot was to involve RHOB for better lithology identification. Plotting RHOB versus CGR in well AB indicated four clusters (Fig. 7). The first cluster, highlighted with a black oval, contains the points with CGRs higher than 20 API and densities higher than almost 2.63 g/cm3. This cluster was named shale because shales have high gamma ray and high rigidity—the more the rock rigidity, the higher its density. The lithology for the region where CGR is lower than 15 API cannot be shale, thanks to the low amount of gamma-ray. Plus, since it has already been found that the study region is not made of any sand, this area (CGR < 15 API) should be merely composed of dolomite and limestone. The lithology for where density ranged from 2.55 to 2.7 g/cm3 was guessed to be dolomite (yellow oval) because the bulk density of dolomite is more than that of limestone.

Fig. 7
figure 7

The cross-plot of RHOB against CGR for the study area

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And for where density was below 2.55 g/cm3, the lithology was selected to be limestone (red oval). Different fluids in the target zone might justify the tangible difference in the density values. The part with lower densities might be occupied with hydrocarbon, and the position with higher densities could be filled with water. The green points had CGRs 15–20 and were determined to be intercalation of shale and limestone (blue oval). When two different depositional environments are in close spatial proximity, they are likely to migrate preferably across the contact and streak through each other. It is to be pointed out that all lithologies change completely gradually in the study area, and there are no certain borders among them. This is due to the similar properties of calcite and dolomite (Wei et al. 2020), which make up a large percentage of the lithologies.

Well-logging assessments

So far, well logs have been utilized to have a concise, precise view of formation characteristics at different depths of reservoirs. This study used the CGR, RHOB, and neutron well logs to justify the lithology identification. Looking at Fig. 8, which depicts the findings of the four preceding well logs, it can be viewed that the CGR values recorded versus depth laid in the range of nearly 3–34 API, being very low. The small area possessing CGR amounts of more than 20 API (2933–2940 m) confirmed the existence of a negligible quantity of shale in the survey zone. Although the shaley area constituted a minor part of the survey zone, a significant part of the zone, CGRs less than 20 API, accounted for a carbonate formation, either limestone, dolomite, or a combination of both (2940–3020 m). Such findings were verified by the position of the density and neutron logs, which is the most well-founded indicator of distinct lithologies. Limestone was the study zone’s primary lithology since the density log had generally laid to the right of the neutron. However, the trend was reversed in the first few meters of the zone, showing the presence of shale. As far as saturation is concerned, the less density, the further the oil saturation. At first, where density was so high (shaley zone), it was deduced that the shaley zone was filled with water. But then, where density decreased gradually, and neutron fell considerably, oil saturation experienced significant growth, reaching its maximum at a depth of 2963 m. The logs of density and neutron met each other. Beyond the depth, the former saw a progressive decrease, and the latter suffered from a significant increase, implying that oil saturation declined and water saturation inclined. In conclusion, limestone was the primary lithology, whereas there was a minor shale in the first part of the studied depth.

Fig. 8
figure 8

Well-logging data and lithology column for the study area

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Saturation results and sensitivity study of rock physics modeling data

As explained in the methodology section, Xu–Payne’s model (2009) was utilized to determine saturation in the interest zone. Involving geological factors, the rock physics model helps provide a more accurate estimate of the unknown data. The VP, VS, RHOB, and AI parameters were modeled using the preceding rock physics model in this connection. Before using the parameters, their compatibility with the real data points was investigated via the R-squared (R2) coefficient to assure reliability. R2 is a statistical goodness-of-fit index showing how well the modeled data match the real data in linear regression. R2 values, which generally lie between zero and one, are commonly reported percentages from zero to one hundred. In general, the higher R2, the better match for the model. As shown in Fig. 9, different values of R2 were obtained for the four parameters of VP, VS, RHOB, and AI.

Fig. 9
figure 9

Correlations between a VP versus VP. DEM with R2 = 0.88, b VS versus VS. DEM with R2 = 0.78, c RHOB versus RHOB.DEM with R2 = 0.96, and d AI versus AI. DEM with R2 = 0.93

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The proportions of R2 for RHOB and AI were the highest and quite similar, at almost 97% and 93%, respectively (Fig. 9c–d). This means there is only a slight difference of three-to-seven percent between the matched values and the observed data regarding density and acoustic impedance. Also, while R2 accounted for 88% of VP, this figure was slightly lower for VS, at 78% (Fig. 9a, b). In other words, there are higher differences between the modeling data and the raw data for this data set. The density estimation is so good because the total density (the density of the rock and fluid) has remained unchanged. The lithology column in Fig. 6 is predominantly carbonate, and the fluids are mostly oil. So lithological changes, including rock and fluid changes, should not have changed much. As for S-wave and P-wave velocities, the estimation of compressional wave velocity has been better than the shear one. This is because VP is more sensitive than VS to porous media contents like fluids (Assefa et al. 2003). Thus, impedance (AI) estimation, which is the product of the compression wave velocity by density, is acceptable.

Modeling data

Due to the high sensitivity of P-wave velocity (VP) and P-impedance (AI) to fluid changes (Pang et al. 2019), the cross-plot of AI–VP/VS color-coded with a deep resistivity log (LLD) was employed to characterize the zone of interest in terms of fluid content. To solve the problem of data scattering, the VP/VS was modified using the DEM model and used as VP/VS.DEM. As can be seen in Fig. 10a, there is a linear relationship between the modified velocity ratio and the acoustic impedance.

Fig. 10
figure 10

The cross-plots of VP/VS. DEM versus AI. DEM scaled by a deep resistivity and b porosity

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Low AI and VP/VS values are associated with high resistivity values and vice versa. To justify this trend, two possible theories are suggested, one of which will be rejected: it is due to (1) the existence of any fluid in the pore system and (2) the co-existence of two or more fluids. As for theory one, it is thought that a high-density rock without any fluid should be responsible for high resistivity. A rock system simultaneously has a higher resistivity, AI, and VP/VS than fluids. In Fig. 10a, where the resistivity is high, the other two (AI and VP/VS) are not high but low, meaning that theory No. 1 is incorrect. The pore system is occupied with different fluids of different densities (theory No. 2). Considering resistivity values, it can be deduced that when resistivity is high, and AI and VP/VS are low, a low-density, low-conductivity fluid like oil is filled into the pore system. Also, when AI and VP/VS are high and resistivity is low, a high-density, high-conductivity liquid like water should exist in the porous media. And a mix of water and oil occupies the pore system when resistivity, AI, and VP/VS are mean. This is because all the parameters are highly correlated; the more density, the more AI and VP/VS, and the less resistivity. In the following, the color bar of resistivity is substituted with that for porosity to verify theory No. 2 is accurate (Fig. 10b), where resistivity shows a high value in Fig. 10a and porosity has a high value in Fig. 10b, proving the presence of a tremendous amount of fluid.

On the contrary, high values of VP/VS and AI represent low porosity and resistivity, which is to say the rock is so dense that it might have no pores or its pore space is low. This area is more likely to be occupied with high density and conductivity fluid. It is now evident what type of fluids is filled into the zone of interest. When a porous medium’s porosity increases, its fluids’ volume increases. Consequently, the density and the seismic velocities decrease (Borgomano et al. 2019). The propagation of seismic waves in a porous medium depends very much on the elastic properties of the porous medium and its density. Therefore, the denser the rock, the higher the seismic velocities and acoustic impedance, and vice versa (Boxberg et al. 2015). AI–VP/VS was also plotted with known oil saturation (SO) and water saturation (SW) color bars (see Fig. 11) to prove the accuracy of what has been anticipated so far.

Fig. 11
figure 11

The cross-plots of VP/VS. DEM versus AI. DEM scaled by a water saturation and b oil saturation

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As expected, high oil saturation (Fig. 11b) or low water saturation (Fig. 11a) is seen at low values of AI and VP/VS exactly where resistivity (Fig. 10a) and porosity (Fig. 10b) are high, which conveys good coordination with the previous results. To conclude, when porosity and resistivity are high, or AI (density) and VP/VS are low, it is expected to have the most oil and the least water. VP and VS decrease in a region filled with oil because oil has a lower density than water and is sensitive to density. As a result of seismic velocities and density reduction, acoustic impedance also decreases. The concept of acoustic impedance is the acoustic resistance of a porous medium against the propagation of waves so that with an increase in density, this resistance increases and vice versa. Hence, acoustic impedance decreases due to the lower oil density than in water, where more oil is seen (Li and Peng 2017).

Non-modeling data

The previous section measured fluid distribution using modeling data, fluids resistivity, and rock porosity. It was proven that the less AI and VP/VS, the more porosity and fluids of high resistivities, like oil. This section aims to estimate fluid saturation using non-modeling (well-logging) data and the parameter of fluid density. It is related to both VP and VS. Considering this in mind, the velocity ratio of VP/VS was plotted versus VS at different saturations of oil and water (Fig. 12) to find a relationship among them.

Fig. 12
figure 12

The cross-plot of VP/VS against VS was scaled by different oil and water saturation values

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In this plot, SO ≥ 0.7 (oil zone) delineated by the little triangular black dots demonstrates low values of VS, and SW ≥ 0.8 (water zone) specified by the dark blue circular dots represents high values of VS. Stated alternatively, water saturation (Sw) experiences a gradual upward trend when P-wave velocity increases and oil saturation (SO) decreases steadily when P-wave velocity proceeds to increase. S-wave velocity (VS) is directly and inversely proportional to the square root of shear modulus (µ) and density (ρ). Also, oil density is much lower than water, and the shear modulus is constant. It is thus expected to see a lower VS for the oil zone than the water zone; however, this trend is entirely reversed in Fig. 12. This behavior may be related to the high volume of oil in the study area affecting seismic velocities. Lee (2003) reported that when oil saturation increased in a hydrocarbon region with relatively high and abnormal pressures, VS would reach its minimum value, whereas it should be maximum. Our results, which agree with previous studies, are shown in Fig. 13, color-coded with oil saturation. The highest oil saturation was seen when VS was minimum and vice versa.

Fig. 13
figure 13

The cross-plot of pore-pressure versus VS scaled by oil saturation

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The cross-plot of S-wave velocity (VS) against P-wave velocity (VP) was alternatively used for further confirmation. A linear behavior governs VS and VP, as shown in Fig. 14.

Fig. 14
figure 14

The cross-plot of VS against VP is scaled by different oil and water saturation values

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Again in this figure, higher oil saturation is achieved at lower values of the velocities. In contrast, as previously explained, water saturation is achieved at higher velocities values due to the high oil pore pressure. This graph signifies that where a more compressible, lighter fluid-like oil saturates porous media, it should be expected to have lower VP and VS and conversely for water, which is an almost incompressible and heavier fluid. The cross-plot of S-impedance (SI) versus P-impedance (PI) was finally investigated to consider the simultaneous impact of the velocities and density on pore fluids distribution. As presented in Fig. 14, the oil-saturated zone (SO ≥ 0.7) can be differentiated by a reduction in both acoustic impedances compared to the water-saturated zone (SW ≥ 0.8). Oil presence decreases AI and SI, and water presence increases AI and SI (Fig. 15). The oil’s lower density and bulk modulus cause a decrease in the total density and VP, leading to a considerable reduction in AI and SI. In agreement with other studies (Fawad et al. 2020), the results express that different P-wave and S-wave velocities inside a reservoir would reflect different fluid saturations.

Fig. 15
figure 15

The cross-plot of SI against AI was scaled by different oil and water saturation values

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Conclusions

The present investigation indicated that rock physics templates could yield a proper qualitative characterization of lithology in the area under study. Greenberg and Castagna’s (1992) and Gardner et al. (1974) empirical rock physics models helped identify lithologies quickly. It also confirmed that the cross-plots of VP/VS-CGR and RHOB-CGR could be used as an alternative tool to rapidly and effectively differentiate lithologies, since lithology classifications using those yielded broadly similar results to those derived from well logs. Limestone and dolomite constituted the primary lithology, and shale the minor lithology. On the contrary, the target zone was composed of no sand. The shale area had higher VP and RHOB than dolomite and limestone, perhaps due to less or no fluid. Regarding fluid distribution, it was discovered that as P-impedance (AI) and the velocity ratio (VP/VS) descended, porosity and fluid saturation with low conductivity (high resistivity) ascended. In other words, the pay zone was maximally occupied with oil when porosity and resistivity were maximum, or VP/VS and AI were minimum. These two seismic factors (VP/VS and AI) were thus found to be so powerful for reservoir fluids discrimination using the cross-plot analysis. This method could be applied more effectively when the theory of DEM corrected the velocity ratio of VP/VS. This theory provided conditions where most data points were positioned more regularly and a linear relationship governed by the cross-plot of AI and VP/VS. DEM. It was also understood that when oil pore pressure was relatively high, VS values would be minimum because a lower VS was seen in the zone of interest where oil volume was high, causing an abnormal pressure.

The methods and techniques used in this research have some limitations that can be improved in the next studies. This research was carried out in an area with moderate porosity; the utilized RPT and models do not work in areas with high porosity, tight sands, shaly and laminated sands, so it is suggested to conduct rock physics analysis in an area with the mentioned characteristics and try to build a local rock physics model for it that can help in the discrimination of fluids and lithology. Additionally, here, we successfully applied some RPT in new directions and insights to discriminate pore fluids and lithology with enough data, but in some areas, maybe there would not be enough data, especially some data such as pore aspect ratio; we suggest that first the required data be estimated based on the available data using artificial intelligence techniques, especially machine learning, and then the mathematical relationship between the parameters is discovered after the physical rock analysis.