1 Introduction

The hydrocarbon business faces enormous hurdles in meeting our technologically evolved world’s increasing energy demand. Low-hanging food has been acquired in the past and now the focus is to address heterogeneous thin sand reservoirs embedded within strong pore pressure variations. Conventional technology limitations have prevented the industry from fully characterizing and utilizing such challenging, undiscovered resource potential. It has been stressed that an integrated machine learning (ML) methodology has the ability to address these difficulties. This method could aid in the more efficient and effective analysis of complex geological data like the case here. The ML approach has yielded results within reasonable time and cost limits, making it a viable implementation-ready option. The reservoir under study is complex shale-sand thin potential units embedded under challenging pressure variations. The study’s main goal is to focus on field development targets that are both economically and efficiently feasible to highlight thin heterogeneous potential layers while addressing a safe trajectory after precisely modeling pressure.

Petrophysical properties of rock formations inferred from well logs are porosity, permeability, saturation, mechanical properties of rock, pore pressure, and mineralogy (Khan et al. 2022; Munir et al. 2023; Xi et al. 2023; Babu et al. 2022). The elastic properties extracted through reflected seismic data display the main subsurface features and key rock properties. This petro-elastic relationship links petrophysical and elastic properties, allowing a better understanding of how reservoir qualities fluctuate geographically and vertically within a geological formation. Furthermore, the petro-elastic connection aids in fluid saturation changes, reservoir modeling, well planning, reservoir management, and other similar processes, making it a significant approach in the exploration and production sector (Hussain et al. 2023a; Ahmed et al. 2022; Shakir et al. 2022).

Conventional deterministic reservoir characterization and modeling methods sometimes fail to capture the underlying heterogeneity of thin reservoirs, resulting in inaccurate reservoir performance predictions. Stochastic inversion is a powerful tool for defining and modeling thin heterogeneous gas-bearing sand reservoirs by optimizing the coarser seismic resolution from 2 ms to a finer 0.1 ms. A geostatistical technique that generates several realizations of the reservoir model using available information about the reservoir, such as well log data and seismic data. Each realization represents a conceivable configuration of the reservoir attributes, and the ensemble of realizations depicts the reservoir uncertainty statistically. It has been used successfully worldwide to characterize and model a wide range of thin, heterogeneous gas-bearing sand reservoirs. It has been demonstrated to improve reservoir performance estimates’ accuracy (Khan et al. 2023; Hussain et al. 2023a). Likewise, Amjad et al. (2022) used PNN to model the only pore pressure in the Upper Indus Basin. Conventional approaches often require substantial, high-quality datasets, including a comprehensive suite of accurate petrophysical and elastic well logs. Therefore, these methods may demand excessive time and involve huge economics, and data intensity may come with uncertainty in the results. The presented study yields a comprehensive integrated approach by integrating high-resolution elastic and petrophysical properties obtained through stochastic inversion with ML to produce the geological align results by addressing the above-mentioned issues with optimized results.

ML approaches provide a wide range of tools for reservoir characterization, allowing significant insights to be extracted from complicated and multidimensional data. In recent years, ML has swiftly taken control of the technology landscape (Radwan et al. 2022; Ali et al. 2023). Every industry has used complex algorithms to complement and improve on already existing procedures. Similarly, ML in geoscience employs advanced computer algorithms to assist geoscientists in comprehending the relationships between huge amounts of geophysical or geological data or information and the subtle underlying geological conditions at the reservoir level (Gorain & Takur, 2015; Rajabi et al. 2021; Yang et al. 2024; Amjad et al. 2023a). The volumetrics of shale (VSHL) and effective porosity (PHIE) are estimated using probabilistic neural networking (PNN) deep learning (DL) techniques across the field. The PNN approximation is an artificial intelligence-based technique that works on non-linear patterns to analyze variability more precisely in reservoir facies (Ashraf et al. 2021; Akram et al. 2024).

Accurate pore pressure modeling is critical for successful reservoir development and management. Traditional pore pressure modeling methods like Eaton’s and Bowers’ rely on empirical correlations between pore pressure and reservoir parameters like depth and resistivity. However, these conventional approaches frequently fail to reflect the complicated link between pore pressure and shale-sand layer parameters in complex geological stratigraphic layering. DL models can be trained on enormous pore pressure and reservoir property data datasets to discover the non-linear intricate geological relationship between these factors. DL models, once trained successfully, can accurately predict pore pressure in complex geological scenarios for smooth drilling operations that are challenging in this area. PNN also provides significant probabilistic results, not just predictions, allowing us to quantify uncertainties and make more informed decisions.

Fig. 1
figure 1

The research area is located in the Central Indus Basin with rectangular projecting structural elements and the highlighted study area with red block (modified after Talib et al. 2022)

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Integrating stochastic with a DL approach has proven to be a promising tool for defining thin heterogeneous gas-bearing sand reservoirs and modeling pore pressure in challenging geological settings. To further enhance the characterization of thin-bed reservoirs, the study employed stochastic seismic inversion, which introduces high resolution within post-stack seismic data to resolve thin gas-bearing sand layers iteratively. This technique addresses the limitations of traditional deterministic inversion by incorporating statistical information and geological knowledge, improving the resolution and reliability of results. By combining PNN and stochastic inversion, the study aims to provide a comprehensive and robust approach to reservoir characterization. DL models can learn the intricate link between reservoir parameters and deliver accurate pore pressure estimates even in the presence of high uncertainty by using seismic and well data. However, it is critical to carefully choose the suitable DL model and train it on a large and representative dataset of pore pressure and reservoir parameter data.

2 Study area geological and stratigraphic description

The zone of study exists inside the graben of Panno-Aqil, bordered by the Highs of Jacobabad–Khairpur and Mari–Kandhkot of the Central Indus Basin (CIB), Pakistan (Fig. 1) (Saif-Ur-Rehman et al. 2016). The configuration of the structures within the area was influenced by tectonic proceedings, including the uplifting of Late Cretaceous formations and their erosion, Wrench faulting in the strata of Late Paleocene, and lastly, the uplifting of Late Tertiary to recent lithologies (Kadri 1995). The research area has been divided into horst-graben structures by a paleo-extension phase coupled with recent wrench faults. The Lower Goru Formation, chiefly comprised of intermixed sand-shale deposits, yields maximum production from the thin heterogeneous sand layers in the area (Tounkara et al. 2023; Ehsan et al. 2023).

As the Indian plate journeyed through the middle Jurassic period, fracturing commenced in the blocks of the upper brittle crust (period 1) due to extensional convectional currents. In the late-Paleozoic and early Mesozoic periods, it seems that the crust’s initial rifted portion stopped extending (signified via Hiatus in the late Jurassic period). The rocks resulting from rift deformation were left over after the collapse of the Indus basin. Episode 2 depicted the early Cretaceous sediment deposition on the migrant crust. Finally, during episode 3, i.e., the Indus Basin’s Mesozoic sedimentation, the crust of the rifted continent subsided (late Cretaceous). This episode is obvious via the rising elevation and the decreasing level of erosion (Zaigham and Mallick 2000).

An enormous portion of the CIB gas fields is produced from the reservoir sands of Lower Goru, which have major source rocks comprising the shales of Sembar and Lower Goru (Abbasi et al. 2016; Ullah et al. 2023; Ehsan and Gu 2020). The seal is provided in the research area by the inter-bedded Lower Goru shales and the transgressive Upper Goru marine shales (Ali et al. 2022). The study area is separated by fault blocks alongside wrench faulting, hence having a particular significance (MonaLisa et al., 2023). Precisely, degradation regarding reservoir characteristics northward, fault sealing, and accurate structural dips comprise the aspects that add complications to the trapping mechanism of the reservoir (Fig. 2).

Fig. 2
figure 2

Generalized stratigraphy of the research area along the CIB’s petroleum system (Ahmed et al. 2022)

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The Cretaceous Lower Goru Formation deposition occurred in a shallow marine and deltaic environment during low-stand sea level. The sediments are detached as medium to coarse-grained above the distal sediments, i.e., shale and siltstone of the previous high-stand-system tract (Berger et al. 2009). The Lower Goru Formation’s sands demonstrate features similar to the sands of the Indian shield bordering toward the neighborhood (Ahmad et al. 2004). The comprehensive stratigraphic chart of the research area is depicted in Fig. 2. Several big and enormous producing fields, such as Mari, Miano, and Sawan, have been explored in this north–south oriented clastic play fairway (Dar et al. 2023; Yasin et al. 2019).

3 Data set and methodology

The present study utilized 3D post-stack time migration seismic data from the Kadanwari field. The exploratory wells of Kadanwari-18 (K-18), Kadanwari-19 (K-19), and Gorwar-01(G-01) lie within 3D seismic data. The well data contains the main logs of Gamma Ray (GR), Spontaneous Potential (SP), Caliper (CALI), Deep Resistivity (LLD), Shallow Resistivity (LLS), Micro-Spherical Focused Log (MSFL), Sonic (DT), Shear Sonic (SDT), Bulk Density (RHOB), and Neutron Porosity (NPHI) that were utilized for intended purpose. The other important information in the wellbore includes the formation tops and mineralogical information. The wells fully penetrated the E-Sand interval and produced gas from the Lower Goru Formation reservoir E-Sand interval. The location and the production (un-economical gas) for G-01 were available only, therefore it was kept as a blind well. Figure 3 explains that the workflow commences by performing petrophysical analysis at well logs after data QC. Well logs provide comprehensive subsurface details via attributes including petrophysical properties (VSHL, PHIE, Sw), Elastic properties (P-impedance, S-impedance, Vp/Vs ratio, etc.), and pore pressure at specific locations, while seismic data offers a broader, albeit lower resolution, perspective. Petrophysics commenced with a data quality check and used the GR log to identify the lithology of the reservoir rocks, which contributes to the calculation of shale volume. The porosity of the reservoir rocks is estimated using neutron porosity and bulk density logs, which compensate for shale content. The water saturation of reservoir rocks is evaluated using the Archie equation and by incorporating the LLD log and the reservoir water’s resistivity.

Due to data limitations and especially the unavailability of direct pore-pressure measurements in the wells due to data confidentiality issues, pore-pressure has been modeled using the established Eaton 1975 method (Amjad et al. 2022). A careful selection of relevant variables from both datasets (well and seismic) is crucial for subsequent analysis. Establishing a well-to-seismic tie aligns specific horizons in well log data with seismic key reflections, enabling correlation. Particular zones have been interpreted on the seismic to understand subsurface geometries and specific seismic attributes and characteristics against these zones that would help to understand subsurface geology. The structural interpretation of the Kadanwari field showed a feasible host-graben structure regarding the trapping of hydrocarbons (Ali et al. 2023; Manzoor et al. 2023; Ahmed et al. 2022; Khan et al. 2024).

The missing low frequencies in the seismic data are utilized from well data and interpolated through interpreted horizons in the form low-frequency model (LFM) for the seismic inversion process. Likewise, for the high-resolution geological information, a variogram analysis of seismic data aids in understanding spatial continuity, which is incorporated into a stochastic inversion process to generate high-resolution acoustic properties in the form of a geological stochastic inversion model (GEOSI) (Khan et al. 2023; Durrani et al. 2022; Hussain et al. 2023a). These properties further refine/fine-tune the prediction of petrophysical and reservoir properties. ML specifically PNN algorithms were trained using well log data to learn the relationship between well log parameters and seismic attributes extracted after stochastic inversion. These trained algorithms were applied to seismic data to predict petrophysical, elastic, and pore-pressure properties. A comprehensive correlation analysis between predicted/modeled and actual well log data was performed to validate these predictions. Ultimately, the broad and novice workflow culminates in comprehensive predictions of subsurface characteristics, providing valuable insights for exploration and development.

Fig. 3
figure 3

The adopted methodology for facies analysis and pore pressure prediction is demonstrated by combining ML and high-resolution acoustic properties extracted through stochastic seismic inversion. The high-resolution acoustic properties are trained with the best ML algorithm at the well location using multiple input features such as log suits raw curves and petrophysical interpreted curves. Following successful training and testing, the performance is evaluated at the blind wells before populating the corresponding characteristics for the entire cube

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A precise approach is stochastic seismic inversion employing 3D PSTM and well data to model high-frequency attributes (Fig. 4). Well log data is not only employed in petrophysics, but it also aids in the development of a low-frequency model that is integrated into stochastic seismic inversion (SSI). The variogram analysis captures the spatial variation of acoustic impedance. A prior model with a sampling interval for finer resolution greater than the acquired seismic sample interval of 2 ms. It is populated from LFM by injecting high frequencies generated after a high-resolution prior model for the respective property (acoustic impedance) via a variogram analysis. The prior model aided in the development of high-resolution seismic property volumes. These property volumes are then used in the PNN to establish a precise petro-elastic relationship. The PNN has been utilized to simulate this relationship across the volume that comprehensively models reservoir properties.

Fig. 4
figure 4

a Variogram analysis helps to capture the property variations, b 1D Analysis of seismic and synthetic seismic depicting their correlation, c High-resolution posterior model of P-impedance showing along an arbitrary section resulting after stochastic inversion

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The PNN method has been used to model S-impedance, shale volume, porosity, and pore pressure across the volume of a thin heterogeneous, gas-bearing sand reservoir. The petrophysical results include VSHL, PHIE, pore pressure, and raw log curves as input features for training PNN at well locations. The data was divided into training and testing, with 80% of the data utilized for training and 20% for testing. The high-resolution stochastic seismic inversion results have been employed while simulating the reservoir properties via the PNN approach across the volume.

A PNN architecture incorporated high-resolution stochastic seismic inversion results that were trained on multiple input attributes and resulted in high-resolution S-impedance, VSHL, PHIE, and pore pressure. The backpropagation technique was used to train the PNN on the training set. The PNN hyperparameters were tweaked to obtain the optimum performance. On the testing set, the trained PNN was evaluated. The trained PNN was used to forecast S-impedance, VSHL, PHIE, and pore pressure throughout the thin, heterogeneous gas-bearing sand reservoir. These quantities can be utilized to characterize the reservoir and make informed reservoir development decisions.

The model was trained using multi-point ensemble learning. Using data from only two wells was challenging because there is the possibility that it may not adequately capture the full variability of the subsurface conditions. The reliability of predictions might be compromised due to the limited data points. To tackle this and to ensure the reliability of predictions across the lateral extent of the field. The cross-validation approach was employed during training and evaluating the PNN model to assess the model’s generalizability. To further judge the model predictions, the third well was kept blind from which we got the high r2 score (above 90%) with low training loss i.e., mean square error (mse) provided the model’s reliability. Figure 5 shows the model training and validation accuracy over 1000 epochs as well as the r2 score to account for the model learning rate and performance.

Fig. 5
figure 5

The figure illustrates the training and validation performance of the PNN model. The left panel displays the model’s accuracy in correctly classifying data points over successive training epochs. Both training and validation accuracies are presented to assess the model’s learning progress and potential overfitting. The right panel depicts the corresponding loss curves, quantifying the model’s error during the training and validation phases. The high training and validation accuracy and low training and validation loss mark the high performance of the model

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The major PNN parameters tuned are the number of neurons in each layer, the learning rate, the weight decay, and the momentum. The number of neurons in each layer determines the complexity of the PNN. A greater number of neurons results in a more complicated PNN capable of learning more intricate associations between inputs and outputs. A more sophisticated PNN, on the other hand, is more prone to overfitting. The learning rate determines how fast the PNN learns. A greater learning rate will cause PNN to learn faster but also cause PNN to overfit. Weight decay is a regularization method that can aid in the prevention of overfitting. It operates by punishing the PNN for having too many weights. Momentum is a technique that can assist the PNN find a better solution faster. It works by updating the weights based on prior gradients. These parameters can be optimized using a variety of methods, including grid search, random search, and Bayesian optimization. However, Bayesian optimization is the most effective in this case. The backpropagation is a training algorithm for artificial neural networks. It operates by computing the gradient of the loss function with respect to the network weights. Following that, the gradients are used to update the weights in order to lower the loss function.

PNN is chosen over other DL methods for thin sand evaluation as it is a non-linear method that can learn complicated correlations between inputs and outputs. This is critical for evaluating thin sand since the interactions between seismic data and reservoir parameters can be quite complex. Convolutional neural networks (CNNs) and recurrent neural networks (RNNs) are two more DL approaches commonly employed for image classification and natural language processing. These approaches are of limited use for thin heterogeneous sand evaluation because they do not explicitly model the non-linear correlations between the inputs and outputs. It has the best capability of fast learning complex correlations between inputs and outputs, is relatively simple to implement and train, and is computationally efficient. In several investigations, PNN has been demonstrated to help evaluate thin sand.

4 Result and discussions

The petrophysical results clarified the reservoir zones by assessing the properties, including the porosities, saturation, lithologies, etc., for detailed reservoir facies characterization (Magoba and Opuwari 2020). Figure 6 delineates the reservoir E-Sand potential zones of K-18 and K-19 with an average thickness of about 15 m.

Fig. 6
figure 6

Petrophysical interpretation highlighting the potential of E-Sand of wells: a K-18, b K-19. It shows input log in the correlation track, measure depth in the depth track, resistivity curves in the resistivity track, porosity logs in porosity tracks, VSHL and sandstones volumes in the volumetric track with PHIE in the porosities track and Sw in the saturation track

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The key estimated properties of E-Sand are summarized in Table 1. The properties delineated the capability of the potential facies presence throughout the field.

Table 1 Key petrophysical properties within E-Sand
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One of the main advantages of the petrophysics results is their usage in the PNN algorithm in relation to elastic properties to approximate the producing facies regarding their reliable elastic and petrophysical responses incorporating heterogeneities (Rathore et al. 2023; Avseth et al. 2009; Dvorkin et al. 2014). The identified potential sands are clearly distinguished on the cross plot of elastic properties in accordance with petrophysical attributes at well locations (K-18 and K-19) (Fig. 7a). The lithofacies are identified using petrophysical cut-off values, i.e., Shale (VSHL > 0.3), Wet sand (VSHL ≤ 0.3, Sw ≥ 0.45), and Gas sand (VSHL ≤ 0.3, Sw ≤ 0.45). The potential sands bear a specific range of low P-impedance < 9000 m/s*g/cc and a Vp/Vs ratio < 1.6 that is distinguished from the remaining shale and gas sands. The polygon-enclosed sand facies are projected in the well cross-section to build a comprehensive petro-elastic relationship, i.e., low P-impedance, Vp/Vs ratio, VSHL, Sw, and high PHIE (Fig. 7).

Fig. 7
figure 7

Petro-elastic relationship developed after petrophysical interpretation highlighting E-Sands’ potential: a Cross plot between P-impedance and Vp/Vs ratio with reservoir facies on color axis. The gas-sand in red exhibits low P-impedance (6500–9000) with Vp/Vs ratio (1.48–1.64), b The highlighted box in the cross plot reflected the potential zones (gas-sand) on the well cross-section along with petrophysical logs

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The productivity of the E-Sand interval, identified through the petro-elastic relationship, is evaluated with the pore pressure valuation. The pore pressure is approximated using the Eaton method (Eaton 1975), a simple and comprehensive technique incorporating p-wave velocity. The pore pressure is calculated with the normal compaction trend line (NCTL) along with the overburden pressure. The high pore pressure is observed at the E-Sand interval, reaching up to 50 MPa, while the overburden is observed at around 80 MPa (Fig. 8). The auto-fit determines the trend of the pressure following the P-wave velocity.

One of the critical aspects is estimating the accurate reservoir characteristics away from the well location. Both linear and non-linear regressions were employed for the relationship among elastic and petrophysical properties (Lorenzen 2018). All these associations work well but have limited reliability due to the variability of reservoir properties, such as the E-Sand distribution in the Lower Indus Basin. The artificial intelligence technique, i.e., PNN, established on DL, is a non-linear interpolation technique, as explained in detail by Kirkwood et al. (2022). Therefore, its application reliability solves the complexities associated with reservoir sands intercalated with shales (Amjad et al. 2023b; Khan et al. 2023).

Fig. 8
figure 8

Pore pressure estimated at K-18 and K-19 delineates high pore pressure zones and overburden pressure

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Generally, the internal attributes are produced by mathematical transforms on seismic amplitudes, including amplitude-weighted cosine phase, trace envelope, amplitude-weighted frequency, instantaneous phase, etc., while inverted elastic properties are employed as external. The high-resolution stochastic P-impedance was employed in the PNN process as an external attribute for approximating high-resolution elastic properties, i.e., S-impedance, Vp/Vs ratio, etc., that was further employed for the improved petrophysical properties approximation, including PHIE, VSHL, and pore pressure.

As shear wave (S-wave) was present in both the training wells K-18, 19. So, S-impedance was obtained by multiplying S-wave with the available density log and later these S-impedance logs were used to train the seismic trace at the well location via PNN as shown in Fig. 9. Figure 9 delineates a good approximation of S-impedance with consistent trends between actual (black) and modeled (red) logs. The cross plot is drawn, which shows a cross-correlation of 0.96 among the logs (actual vs. modeled). These statistics help in the accuracy determination at well locations that will be populated throughout the field for the corresponding property estimation (S-impedance). The Vp/Vs ratio is obtained by the division of P-impedance over S-impedance, while their low values are critical for assessing gas fluids within pores (Jain et al. 2012).

Fig. 9
figure 9

S-impedance prediction utilizing high-resolution P-impedance as an input employing PNN for both wells with high cross-correlation ranging up to 94.6% between measured (black) and modeled (red) S-impedance

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Fig. 10
figure 10

Arbitrary section view depicting high-resolution P-impedance, S-impedance, and Vp/Vs ratio passing through wells K-18, K-19, and G-01wells along the E-Sand interval matching at the wells. Low ranges of respective elastic attributes depict the potential zones

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The arbitrary lines, including the stochastically derived posterior mean (50 stochastic realizations) of P-impedance along with the PNN approximated s-impedance and Vp/Vs ratio, are depicted in Fig. 10. The low-value range of P-impedance (around 8000 m/s), S-impedance (around 6000 m/s*g/cc), and Vp/Vs ratio < 1.6 illuminated the thin reservoir sands of the E-Sand layer. Their cumulative analysis comprehensively differentiates producing sand facies (Hussain et al. 2023a). The wells are colored with their respective logs to show a reliable match of wells with predicted volumes.

Fig. 11
figure 11

E-Sand horizon slice of P-impedance and Vp/Vs ratio. Low ranges of elastic attributes depict the producing wells, whereas a relatively high value of these attributes in non-producing zones reflects the high ranges

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The mapping of key elastic reservoir properties, focusing on the bottom part, depicted that K-18 and K-19 are placed in a good location with low values of P-impedance (< 8000 m/s*g/cc) and Vp/Vs ratio (< 1.6) (Fig. 11). The G-01 is tested to assess the efficiency of the predicted properties without being incorporated into the process. The G-01 is a limited gas producer, while a good zone is present just toward its southern side with low values of elastic attributes, so the well can be beneficial if deviated accordingly.

Similarly, using the elastic properties (P-impedance, S-impedance, and Vp/Vs ratio) in the PNN process, the petrophysical properties (PHIE and VSHL) along with pore pressure are trained at well locations, and the relationship is extended throughout the field. The variations in reservoir zones regarding key geological features played a vital role in field optimization. The 1D training at well locations and their cross plot for assessing accurate trends and cross-correlation valuation are depicted in Fig. 12a, b for effective porosity, 11 c, d, for VSHL, and 11 e, f for pore pressure. High cross-correlation values are achieved for the predictions of all petrophysical properties (above 0.90).

Fig. 12
figure 12

One dimension (1D) PNN-based prediction of petrophysical properties: a PHIE trend and range matching, b PHIE cross plot depicting 97.6% of cross-correlation, c VSHL trend and range matching, d VSHL cross plot illustrating 92.2%; e Pore pressure trend and range matching, f Pore pressure cross plot showing 93.1% cross-correlation. Modeled log curve in red is overlaid with measured logs in black

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The modeled petrophysical properties are displayed in section view through an arbitrary line (Fig. 13). The wells were colored with respective attributes to evaluate the approximated property displayed in the section. Overall, a reliable match is observed with the respective approximated property. The thin layering in the reservoir E-Sand level is prominent in the appraised attributes. The high porosity values (about 0.20) are observed at well locations, while high porosity wells are present throughout the section. Similarly, low VSHL (< 0.30) values indicate the presence of sands passing through well locations. The section presents the pore pressure with high values of approximately 50 MPa in the lower portion of the E-Sand interval. All three properties are assessed in collaboration to evaluate their variability and delineate the producing facies with low risk.

Fig. 13
figure 13

Arbitrary section view of effective porosity, shale volume, and pore pressure passing through wells K-18, K-19 and G-01 with the wells colored according to the respective properties

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The distribution of vital petrophysical properties, including PHIE and VSHL are assessed by mapping the E-Sand interval (Fig. 14). Decent porosity values are observed in the producing wells, including K-18 K-19, while good porosities up to 20% are present in the center of the field. Similarly, less shale volumetric is observed near the producing wells, and good sands are in the center and the eastern portion.

Fig. 14
figure 14

E-Sand horizon slice containing the arithmetic mean of porosity and shale volume focusing on the bottom part covering 20 ms thickness. Good porosity and low shale volume are present at the wells, while feasible locations are also demarcated in the field

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P-impedance helps in differentiating fluids due to its sensitivity to density and P-wave velocity, while S-impedance is more attuned to lithological changes as its shear component is non-sensitive towards fluids (Li et al. 2023; Sayers et al. 2015; Das and Chatterjee 2018; Akpan et al. 2020). However, a combined analysis of both properties provides in the form of Vp/Vs ratio a comprehensive understanding of the subsurface.

The analysis of P-impedance and S-impedance data reveals distinct spatial patterns with implications for reservoir characterization. The middle and right portions of Fig. 10 exhibit lower impedance values, suggesting potential hydrocarbon zones. This observation aligns with the P-impedance and Vp/Vs ranges identified in Fig. 7 as indicative of gas-sand facies.

Furthermore, Fig. 10 highlights a zone of low impedance values (CDP 259–370) coinciding with a potential hydrocarbon zone. This is corroborated by Fig. 10, where S-impedance exhibits variations reflecting lithological changes, potentially delineating sand-shale intervals. The integration of these parameters in Fig. 10 (Vp/Vs ratio) optimizes the analysis, clearly demarcating potential hydrocarbon zones. The presence of the G-01 dry well adjacent to a high-amplitude anomaly in this zone suggests a potential fault or pinch-out disrupting the hydrocarbon accumulation.

Figure 11 reinforces these findings by showcasing the spatial distribution of P-impedance and Vp/Vs ratios within the E-Sand horizon. The presence of favorable P-impedance and Vp/Vs ranges around wells K-18 and K-19, coupled with the absence of a hydrocarbon discovery at the nearby G-01 well, implies a potential hydrocarbon accumulation within the identified anomaly.

Figure 13, depicting petrophysical properties, supports this interpretation. The anomalous zone exhibits high porosity and low clay content, further enhancing its productivity. The absence of significant hydrocarbon presence at G-01, despite favorable petrophysical properties, underscores the complexity of reservoir prediction and the need for integrating multiple data types for a comprehensive evaluation.

Figure 13 highlights favorable petrophysical properties within the anomalous zone, characterized by porosity values exceeding 13% and low shale content. These observations align with the previously identified elastic property trends, strengthening the prospect of hydrocarbon accumulation. The spatial correlation between favorable petrophysical properties and the anomalous zone further supports its hydrocarbon potential.

Pore pressure was modeled using a PNN employing key elastic attributes (P-impedance, S-impedance, and Vp/Vs ratio) and petrophysical parameters as input features. The model learns the relationship between these attributes and pore pressure, enabling prediction. The image Fig. 13 displays noticeable lateral stratification with alternating high and low pressures adhering to the subsurface geological changes highlighting the potential risk zones in terms of pore pressure. Analyzing the pore pressure cross-section around the CDP 259–370 anomaly reveals elevated pore pressures. This zone requires careful drilling planning due to the potential risks associated with high pore pressure.

The utilization of P-impedance and S-impedance for seismic interpretation offers distinct advantages over traditional P-velocity and S-velocity and density parameters. The inherent uncertainty associated with density estimation has a more pronounced impact on the accuracy of P-velocity and S-velocity calculations compared to P-impedance and S-impedance. For this reason, quantitative seismic interpretation makes use of petrophysical attributes formulated in terms of P-impedance and S-impedance helps to distinguish between potential and non-potential zones comprehensively in complex zones. Consequently, quantitative seismic interpretation based on P-impedance and S-impedance attributes extracted by utilizing high signal-to-noise ratio seismic processed data provides a more robust foundation for delineating potential and non-potential zones, particularly in complex geological settings (Sayers et al. 2015).

While the availability of high-quality well data in the vicinity of wells mitigates uncertainties, these uncertainties tend to amplify with increasing distance from well control. To address this, acquiring additional high-quality datasets is recommended for future work. The application of advanced PNN-based predictions, demonstrating a strong correlation with measured attributes and successful validation at the blind well G-01, has significantly reduced the uncertainties associated with the PNN algorithm and data limitations, enhancing confidence in the results beyond the immediate well vicinity.

5 Conclusions

The research area’s heterogeneous properties, including varied thickness, porosity, shale volumetrics, and variation in elastic properties, are assessed using the limited data set. The band-limited post-stack seismic data is employed in stochastic processes, and improved P-impedances are achieved that are further incorporated into the PNN algorithms and approximate the missing component of post-stack seismic data, i.e., S-impedance, comprehensively. The high-resolution elastic properties are assessed for the identified facies valuation and mapped throughout the field for reservoir facies distribution. The low values of P-impedances, along with the low Vp/Vs ratio, constrain the producing facies while indicating suitable zones. The PNN approximated petrophysical properties and demarcated the varying porosities with the existence of highly valued locations. These locations are confirmed with less shale volumetrics in the map view, while high pore pressure zones exist in the lower portion of the E-Sand interval. Overall, integrating wells and seismic through stochastic inversion and PNN approximation delivers significant results that collectively assess complex, heterogeneous, and thin plausible zones robustly and effectively.