Unsupervised learning for real-time detection of pre-bit pressure variations in drilling operations

Abstract

Pressure variations around the near-bit regions represent significant analytical challenges during drilling operations with polycrystalline diamond compact bits, especially in offshore environments. Undetected pressure fluctuations can disrupt drilling process stability, feasibility identification, and operational safety; therefore, prior detection is essential for supporting optimum performance and minimising risks during the operation. This study provides a data-driven predictive framework to understand and measure the near-bit pressure behaviour using key drilling parameters, including depth, rate of penetration, weight on bit, rotational speed, torque, and derived pressure-related signals representing near-bit pressure behaviour. A Long Short-Term Memory-Autoencoder (LSTM-AE) model is employed to capture sequential drilling behaviour and detect pressure deviations, while a Graph Neural Network (GNN) framework is introduced to model structured relationships among input variables, addressing strong multivariate interdependencies beyond temporal correlations. Comparative assessment indicates that the LSTM-AE effectively captures time-based patterns, while the GNN model demonstrates superior anomaly discrimination capability, achieving a detection accuracy of 91.7% against 84.3% for LSTM-AE, with a lower false alarm rate (9.3% vs. 15.7%) and an earlier detection lead-time (7.8 ft vs. 4.2 ft). These findings underline the potential of graph-based deep learning models for enhanced near-real-time monitoring and early identification of operationally significant pressure deviations during polycrystalline diamond compact drilling operations.

1 Introduction

Pore pressure occurs from fluid trapped in rock pores, which spikes in shales via under compaction. Eaton’s D-exponent linked ROP to gradients empirically, but bit hydraulics—pressure drops altering ECD—were overlooked until CFD simulations emerged (Chen et al., 2025) build on Biot poro elasticity for ML infusion; cite vibration anomalies from (Khaled et al., 2022), extend ANN priors, reducing fracture errors <10%. Recent advances in pore pressure prediction leverage drill bit hydraulics, vibrations, and machine learning to deliver real-time or ahead-of-bit forecasts, with LSTM-based neural networks demonstrating strong predictive capability for drilling rate estimation (Bai et al., 2024). Reducing blowout risks and non-productive time by 20%–30% across mixed lithologies (Chen et al., 2025). Hybrid deep learning approaches have further extended these capabilities to real-time wellhead pressure forecasting and risk warning during hydraulic fracturing operations (Gou et al., 2025). Embed petrophysical theory into downhole ML models using seismic and LWD data for proactive warnings up to 500 m ahead (Khaled et al., 2022). Machine learning methods applied to geophysical monitoring data have similarly demonstrated effectiveness for drilling optimization under low time-delay conditions (Osipov et al., 2023) process surface parameters like ROP, torque, WOB, and mud weight via edge computing and ANNs, achieving R² values over 0.97 in sand-shale-carbonate settings. Hydraulic studies by optimizing nozzle angles, jet pressures (1200–2200 bar), and flow fields to minimize ECD swings (150–600 psi) and boost ROP by 20%–70%, directly informing pressure models. In this study, we are employing the unsupervised learning techniques to analyze and interpret pressure changes that occur ahead of the drill bit. By letting the data speak for itself, we aim to predict the meaningful patterns and the subtle shifts that may not be instantly visible through the usual analysis.

An ideal case of efforts to strengthen the domestic capacity is Reservoir A, a major offshore hydrocarbon province in India. Several researchers have classified hydrocarbon reservoirs in India based on the water spread area. It is defined in minor, medium, and major reservoirs as those with water spread areas up to 40 ha, up to 400 ha, and above 400 ha, respectively. Reservoir A provides a very notable example of a dry gas reservoir, and its enhancement, along with the rise in offshore drilling activities, has contributed to escalated indigenous production, partial alleviation of import pressure, and India’s improvement in long-term energy security (Zhao E. 2015). It is categorized as a dry gas reservoir for gas production as it produces a huge amount of natural gas, and the produced gas is lean, which is used for domestic supply. It does not generate liquid condensate in commercial quantities at the surface. The operations are comparatively simpler in this region than in wet or retrograde reservoirs, because this operation involves the handling of gaseous hydrocarbons rather than liquid phases.

The development of Reservoir A was supported by modern drilling systems, which include Roller-Cone bits (which crush and grind rock), Diamond bits, Fixed Drag bits, Hybrid bits, and Polycrystalline Diamond Compact (PDC) bits. In this study, a polycrystalline diamond compact (PDC) drill bit is used due to its performance capability for the formation conditions. Polycrystalline diamond compact (PDC) drill bits are specified by their remarkable hardness and wear resistance, primarily because of their ability of diamond cutting elements (Zhang et al., 2023). It has a layer of synthetic polycrystalline diamond sintered onto a tungsten carbide substrate under high pressure and high temperature. The diamond layer serves as the primary cutting action and wear resistance; on the other hand tungsten carbide substrate offers essential toughness and thermal shock resistance.

To remove rock completely through a shearing mechanism rather than crushing, PDC drill bits are designed, which is a key factor in their high rate of penetration (ROP). This design principle makes them particularly effective in soft to medium-hard, non-abrasive formations. The advantages of PDC bits include a high rate of penetration, more bit life, and a reduction in the frequency of tripping, i.e., pulling the drill string out of the wellbore, which significantly lowers the operational costs. They also contribute in improving directional control during drilling (Altindal et al., 2024).

Materials science progress is very important for improving the performance of PDCs. Improvements in thermal management, along with the development of thermally stable diamond (TSD) and boron-coated diamond particles, help reduce thermal damage. This expands the use of PDC bits in high-temperature settings like geothermal drilling. For example, creating PDC samples with silicon carbide (SiC) whiskers under high pressure and high temperature (HPHT) conditions has increased bending strength by nearly 30% and fracture toughness by 40%. This also boosts the diamond retention force. The role of cobalt in the thermal stability of PDCs and their self-sharpening ability is currently under investigation. Understanding how rock breaks is key to designing PDC bits. Researchers perform single PDC cutter tests to study rock failure under different conditions, including impact loads and varying rake angles (Ratov et al., 2023). Numerical simulations often combine mixed fragmentation modes with dynamic rock strength to model the complex interactions between PDC cutters and rock formations. These models consider the cutter angle, cutting depth, and rock variation to predict performance and improve bit design.

Drilling operations face constant threats from unexpected pore pressure ramps, leading to kicks, stuck pipe, or blowouts- 13% of global incidents stem from mis-predicted pressures. Traditional logs offer pre-drill estimates, but dynamic bit effects like nozzle losses and vibrations demand live updates. Intelligent kick detection using parameter-adaptive neural networks has been explored to address these real-time anomaly identification requirements (Zhang et al., 2024). This review consolidates innovations (Chen et al., 2025): pioneer downhole ML for forward looks; enable rig-site adaptations (Khaled et al., 2022); handle rock variability, while Huang, Stoxreiter, and Zhu optimize flows to stabilize readings. Aiming for safer, greener drilling, these works bridge geophysics, hydraulics, and AI, cutting costs ($1–2 M/well savings) in slim-hole or HTHP scenarios. Deep and ultra-deep wells are currently the primary sites of oil and gas resource exploitation. They are formidable to drill, though, due to the complex geological conditions, which include changeable stratum lithology, strong heterogeneity, hard and soft interlaced rock, high rock strength, and strong abrasiveness. Zhou et al. (2025) these circumstances cause the drill bit to have unstable cutting motion and force status, including different types of vibration, which exacerbates impact damage and drastically reduces the drill bit’s service life while also raising the drilling difficulty and complexity. The most popular bit type in oil and gas drilling is the PDC (Polycrystalline diamond compact) bit; its completed drilling footage accounts for over 90% of all drilling footage worldwide (Miyazaki et al., 2019). The PDC bit has a long working life and high efficiency in formations below medium-hard due to its unique drilling safety, flexible cutting structure, and rock-breaking mechanism of shearing. Its adaptability to complex formations is poor, though, and it frequently experiences severe undesired vibration. The findings reveal that the heterogeneity of the rock significantly influences vibration acceleration, lateral bending moments, penetration rates, and drilling behaviors. As the weight on the bit and the rotation speed increase, the penetration rate progressively rises. However, the amplitudes of tangential, axial, and radial vibration acceleration of the bit also increase at the same time, suggesting that the interaction between the rock and the bit increased the vibration impact. Low efficiency is the result of the drill bit’s varying cutting depth in the heterogeneous formation. The rate of penetration decreases as heterogeneity increases. Rock heterogeneity has a major effect on lateral bending moment and acceleration, particularly the combined rock samples' characteristics (Pang et al., 2025). The bit vibration became more intense as the bit acceleration increased dramatically with increasing rock heterogeneity; the lateral bending moment increased marginally but fluctuated more intensely. Heterogeneous rock’s strength differential results in eccentricity; the harder rock puts more force on the bit, which causes it to veer off course. The bit shifts to the softer side more when the difference increases because it increases eccentricity (Zhang et al., 2026). Thus, it is essential to investigate the PDC bit’s vibration properties and identify a sensible response technique to address them. Examining the PDC bits' vibration and rock-breaking effectiveness in the case of soft and hard rock that is staggered has significant application value and useful guidance for improving drilling parameters and efficiency (Qiao et al., 2024).

The experimentally validated contributions of this study are limited to the comparative evaluation of LSTM-AE and GNN models. The proposed hybrid LSTM–GNN framework is conceptual in nature and is presented as a future research direction rather than an implemented model within the current study.

Definition of Target Variable:

In this study, the primary variable of interest is near-bit pressure variation, which refers to dynamic pressure fluctuations occurring in the immediate vicinity of the drill bit. Direct real-time measurement of near-bit pressure is often limited due to sensor constraints; therefore, a proxy-based approach is adopted.

The near-bit pressure proxy used in this study is a derived pressure-related indicator intended to represent relative downhole pressure fluctuations occurring near the drill bit during drilling operations. Since direct near-bit pressure measurements are not continuously available in conventional offshore drilling systems, the proxy is estimated indirectly from surface and operational drilling parameters.

The proxy signal is constructed using coupled variations in:

casing pressure, ROP, WOB, RPM, torque, and drilling depth.

Mathematically, the proxy is represented as:

P_proxy = f(CP, ROP, WOB, RPM, T, D).

where:

CP represents casing pressure, T represents torque, and D represents drilling depth.

The function f(.) does not represent a direct physical pressure equation; rather, it represents a multivariate operational relationship learned by the machine learning models from historical drilling behaviour.

Unlike casing pressure, which is measured at the surface or annulus, the near-bit pressure proxy is intended to capture dynamic pressure-related behaviour occurring near the drill bit. Similarly, unlike pore pressure, which represents formation-fluid pressure within rock pores, the proposed proxy reflects operational drilling-response behaviour associated with coupled mechanical and hydraulic drilling dynamics.

The target variable is defined as:

Near-bit pressure anomaly, identified indirectly through multivariate drilling parameters including Rate of Penetration (ROP), Weight on Bit (WOB), torque, rotary speed (RPM), and pressure-related signals derived from drilling hydraulics.

Therefore, the objective of this study is not to predict absolute pressure values, but to detect anomalous deviations in near-bit pressure behaviour using unsupervised learning.

Unlike existing studies that primarily focus on pressure prediction or rate of penetration modelling, this work shifts the focus toward unsupervised anomaly detection of near-bit pressure behaviour. Furthermore, the study introduces a structured graph representation of drilling parameters, enabling the modelling of complex interdependencies that are typically overlooked in purely temporal models. This combination of unsupervised learning with relational graph modelling provides a distinct contribution to drilling diagnostics and operational risk monitoring.

2 Methodology

An LSTM Autoencoder (LSTM-AE) model is a deep-learning model that is primarily designed for unsupervised anomaly detection during drilling operations in real-time. To detect, compress, and predict complex, time-dependent data patterns, the combination of the temporal modelling capabilities of Long Short-Term Memory (LSTM) networks with the compression and reconstruction principles of an Autoencoder (AE). The model is trained specifically on data from safe drilling operations. It learns the complex relationships between the parameters Weight on Bit (WOB), torque, hook load, and standpipe pressure. The feature which is defined in LSTM-AE in drilling is its use of reconstruction error to identify risks and capture complex temporal patterns. On the other hand, to process, analyze, and learn from data structured as graphs consisting of nodes (entities) and edges (relationships), Graph Neural Networks (GNNs) are designed for a specialized class of deep learning methods. GNNs have excellent modelling of complex dependencies and relational structures that traditional ML models cannot handle, mostly providing superior performance for graph-structured data. They are used for predicting pore pressure and oil production evolution by modelling inter-well connectivity as a graph. To understand the physical phenomena inside a reservoir, it is helpful. GNNs enable the spatially aware clustering of drill hole data. Automated 3D geological models can be instantly installed by treating sample intervals as nodes and connecting them based on geochemical and spatial similarity.

Drilling behaviour is analysed using Long Short-Term Memory Autoencoder (LSTM-AE) models, which establishes a strong foundation for anomaly detection and operational improvement, utilizing the following parameters like Depth, Rate of Penetration (ROP), Weight-on-Bit (WOB), Revolutions Per Minute (RPM), Torque, and derived pressure-related signal (derived pressure-related signal) as key indicators (Osipov et al., 2024). These parameters are multivariate time series that specify the dynamic and sequential nature of drilling operations. LSTM-AEs provide an effective means for identifying deviations, since they learn complex temporal dependencies, along with their subtle sequential pattern characteristic of normal drilling behavior.

Autoencoders are formed using an encoder-decoder architecture where the input data are compressed into a lower-dimensional latent representation before being reconstructed. LSTM-AEs have been constructed using LSTM networks for both the encoder and decoder; LSTM networks are a specific type of recurrent neural network (RNN) that was developed to eliminate the vanishing gradient problem. By utilizing gated mechanisms (input, forget, and output) along with a memory cell state, LSTMs can retain long-term dependencies in sequential data. The forget gate is especially important as it determines which previous information will be kept or removed, making it well-suited for the lengthy and complex nature of drilling data streams.

When training on the data from the normal state of drilling, the LSTM-AE will have an objective of reducing the reconstruction error between the input and the reconstruction. Based on an increase in the amount of reconstruction error, the model will identify that the current condition may be operating outside of the “normal” established by the training data, or there is an anomaly to monitor. Luu et al. (2024) thus, if there are no labels for the anomalous data for training, the model is trained in an unsupervised manner.

By using multiple inputs, such as Depth, ROP, WOB, RPM, Torque, and derived pressure-related signal (derived pressure-related signal), the LSTM-AE will learn the complex relationships between drilling characteristics. One example of this is if there is a sudden drop in the ROP along with an increase in WOB and Torque without a corresponding change in RPM, then an issue related to the formation or the drilling assembly may exist (Yang et al., 2024). Additionally, if there is a fluctuation of WOB/RPM/Torque, and/or near-bit pressure indicator(derived pressure-related signal), then operational problems related to bit wear, stick-slip vibrations/loss of circulating fluid/and/or gas kicks may have chances of being present. As an example, having a real-time estimate of the amount of wear of a bit will improve the efficiency of the drilling operation and will assist with optimizing the maintenance schedule.

LSTM-AE models can be difficult to interpret, but latent space visualization and reconstruction error decomposition are two techniques that can assist in identifying which parameters are among the highest contributors to the anomalous behavior detected (Yang et al., 2024). The insights gained from such identification enhance diagnostic capabilities for drilling engineers by:

Assisting in early detection of drill string/bottom hole assembly instability via torque and near-bit pressure proxy variations to support predictive maintenance strategies.

Managing multiple sources of multidimensional data via LSTM-AE’s sophisticated architecture’s ability to provide insight into abnormal behavior beyond defined categories due to drilling operations being dynamic and complex, which can lead to improvements in safety, efficiency, and reliability of operations.

Graph Neural Network (GNN) models applies for drilling behavior analysis based on the following parameters such as Depth, Rate of Penetration (ROP), Weight-on-Bit (WOB), Rotary Speed (RPM), Torque, and near-bit pressure proxy (which builds an intricate model for the analyzing in the complex drilling activities. Drilling activities involve highly interlinked parameters that dynamically influence drilling performance. For instance, WOB, RPM, and Torque directly influence ROP, while formation characteristics (linked with Depth) and downhole conditions (described by pressure-related signal (derived pressure-related signal)) also influence drilling performance. These parameters are non-linear, highly interrelated to each other, and dynamically influenced by geological and downhole changes, which makes it difficult to model them using traditional linear or sequence models.

GNNs generally view this issue by modelling drilling data in a graph structure, where the nodes can symbolize drilling parameters or system elements, and edges symbolize the interconnections between them. This helps in enabling GNNs to learn complex spatio-temporal interlinkages, such as how WOB and RPM change simultaneously and influence ROP and drilling torque in response to changes in formation depth and pressure described by pressure-related signal (derived pressure-related signal). Through these kinds of interlinkages, GNNs construct a holistic model of the drilling process without the need for feature engineering.

GNNs have demonstrated strong ability in ROP modelling, anomaly detection, and intelligent bit selection in drilling. For example, hybrid temporal GNN models are allowed to learn multivariate relationships and temporal patterns automatically, leading to more accurate ROP modelling results than the usual traditional empirical models. Similarly, GNNs can learn the natural propagation patterns of normal drilling processes and detect anomalies that may be related to stick-slip vibrations, bit wear, wellbore instability, and abnormal torque and drag. Sudden changes in the relationships between WOB, RPM, Torque, and ROP, or unexpected changes in pressure-related signal (derived pressure-related signal) at specific drilling depths, can be utilized as early warning signs of potential drilling hazards.

The incorporation of a pressure-related signal (derived pressure-related signal) into a GNN model is of great significance for well-bore stability analysis. Drilling activities always cause disturbances to the equilibrium of in-situ stresses, which may result in the collapse of compressive hoop stresses or tensile fracturing. In a similar way, the incorporation of GNN models enables real-time stress redistribution analysis and early warning of potential instability. Moreover, graph-structured historical drilling data can be utilized for intelligent bit selection by capturing complex interactions between formation properties and bit performance.

Despite these advantages, the effective application of GNNs is contingent on the availability of high-quality structured data, appropriate graph representation, and enhanced interpretability of the model for the purpose of ensuring informative outcomes for drilling engineers. The current state of research continues to underscore the importance of enhanced explainability in graph-based models of learning for enhanced understanding of key interactions in model parameters.

In conclusion, the use of GNN models that include Depth, ROP, WOB, RPM, Torque, and near-bit pressure proxy provides an effective analytical platform that can capture complex, dynamic, and multidimensional interactions of drilling parameters for enhanced prediction, detection, and decision-making in challenging subsurface drilling environments.

The proposed models are developed and evaluated using recorded drilling datasets, where input parameters are treated as multivariate time-series data. While the framework is designed to support continuous monitoring of drilling parameters, the present implementation does not include deployment on live streaming data systems. However, both the LSTM-AE and GNN models operate with low computational complexity during inference, enabling efficient processing of sequential inputs. This indicates that the framework is suitable for near real-time implementation in practical drilling environments, subject to integration with data acquisition and streaming infrastructure.

2.1 Data description and preprocessing

The dataset consists of multivariate sequential drilling records collected from offshore drilling operations and segmented into baseline, cautious, and kick-zone operational intervals based on expert interpretation of drilling behaviour. The dataset contains continuous measurements of drilling parameters sampled over multiple drilling depths and operational stages. Although exact operational metadata and well identifiers cannot be disclosed because of confidentiality agreements, the dataset provides sufficient variability to evaluate the proposed anomaly detection framework under different drilling conditions. The dataset includes multivariate time-series measurements of Depth, Rate of Penetration (ROP), Weight on Bit (WOB), Rotary Speed (RPM), torque, and pressure-related signals representing near-bit pressure behaviour.

The dataset consists of approximately 5,800 sequential drilling records spanning a depth range of approximately 1,415–5,950 ft, collected from two offshore drilling campaigns. The records cover three distinct operational intervals: a baseline zone (1,415–4,000 ft), a cautious zone (4,000–5,500 ft), and a kick zone (5,500–5,950 ft), totalling six case datasets (two cases per zone). The data were segmented into fixed-length temporal windows with a batch size of 64 for model training and evaluation. Approximately 70% of the sequences were used for training, 15% for validation, and 15% for testing. Due to confidentiality agreements associated with the field operations, exact operational details and well identifiers cannot be disclosed. In practical drilling environments, raw sensor measurements are affected by operational noise, vibration, mud pulse fluctuations, telemetry instability, and intermittent sensor drift. To reduce the influence of high-frequency noise and inconsistent measurements, limited preprocessing and smoothing operations were applied prior to model training. Specifically, interpolation was used only for short-duration missing intervals, and normalization was performed without aggressive denoising in order to preserve operational variability. Consequently, the reconstruction error trends presented in this study should be interpreted as partially filtered representations of drilling behavior rather than perfectly raw field signals. Residual fluctuations and local variance remain present in both baseline and anomaly zones due to the inherently non-stationary nature of drilling operations.

2.2 Model architecture

The LSTM-AE model consists of two encoder and two decoder LSTM layers with 128 and 64 hidden units, respectively. The model was trained using the Adam optimizer with a learning rate of 0.001 for 100 epochs and a batch size of 64. Mean Squared Error (MSE) was used as the reconstruction loss function.

Edge relationships in the drilling graph were defined based on physically meaningful drilling interactions, including WOB–ROP coupling, RPM–Torque dependency, and hydraulic pressure-flow relationships. This physics-informed graph structure improves interpretability by enabling the GNN model to learn operational dependencies consistent with known drilling mechanics.

The GNN model consists of two graph convolution layers with Rectified Linear Unit (ReLU) activation functions and an embedding dimension of 64. The graph structure was constructed by representing drilling parameters as nodes, with edges defined based on physical and operational relationships between parameters such as WOB–ROP and RPM–Torque interactions.

Graph construction was performed using a physics-informed adjacency structure based on operational coupling between drilling parameters. Each drilling parameter was represented as a graph node:

V = {ROP, WOB, RPM, Torque, Depth, P_proxy}

where P_proxy represents the near-bit pressure proxy.

The graph adjacency matrix A was constructed as:

Aij = 1, if operational dependency exists between nodes i and j.

Aij = 0, otherwise.

To improve numerical stability and feature propagation, the adjacency matrix was symmetrically normalized before graph convolution:

= D^(-1/2) (A+ I) D^(-1/2)

Node features consisted of normalized drilling parameter values sampled over each time window. During message passing, graph convolution layers aggregate neighbouring node information to capture coupled drilling dynamics and inter-parameter anomaly propagation behaviour.

2.3 Anomaly detection Criteria

Anomalies are identified based on deviations from learned normal behaviour. In the LSTM-AE model, anomaly detection is performed using reconstruction error, defined as the difference between the input sequence and its reconstruction.

For the GNN model, anomalies are identified based on abnormal variations in node relationships and feature propagation patterns, indicating disruption in inter-parameter dependencies.

This approach enables anomaly detection without requiring labelled data.

2.4 Evaluation strategy

The performance of the proposed models is evaluated using qualitative and pattern-based analysis due to the absence of labelled anomaly data.

The models are assessed for their ability to capture meaningful deviations in drilling behaviour rather than conventional classification accuracy metrics.

2.4.1 Expert-assisted validation

Since fully labelled anomaly datasets are not publicly available for offshore drilling operations, operational intervals corresponding to baseline, cautious, and kick-zone behaviour were retrospectively identified using drilling reports, parameter trends, and domain interpretation by experienced drilling personnel. These interpreted intervals were used only for post hoc evaluation of anomaly detection behaviour and were not used during model training.

The LSTM-AE and GNN models were trained in an unsupervised manner using stable operational data. Reported metrics such as precision, recall, F1-score, and detection accuracy therefore represent agreement between model-generated anomaly indications and expert-interpreted operational states rather than supervised classification performance. Only baseline operational intervals were used during unsupervised model training, while cautious and kick-zone intervals were reserved exclusively for evaluation.

2.4.2 Statistical validation

To evaluate the robustness of the proposed framework, repeated experimental runs were conducted using different random initialization seeds and training-validation splits. Mean performance metrics and standard deviations were computed across multiple runs to reduce the likelihood of performance inflation due to favorable data partitioning.

In addition, hold-out testing was performed using drilling intervals not included during model training to assess generalization capability under unseen operational conditions.

2.5 Hybrid LSTM–GNN framework (proposed extension)

While LSTM-AE and GNN models individually capture temporal and relational aspects of drilling data, their combined use may provide a more comprehensive representation of drilling dynamics. respectively, In this context, a hybrid LSTM–GNN framework is proposed as a potential extension to leverage the strengths of both approaches.

In such a framework, the LSTM-AE component can be employed to learn temporal dependencies and sequential patterns in drilling parameters, generating latent representations that capture normal operational behaviour over time. These temporal embeddings can then be integrated into a Graph Neural Network, where each node represents a drilling parameter, and edges define physics-informed operational dependencies between parameters. The GNN can subsequently model the interactions between these temporally enriched features, which could potentially improve the detection and interpretation of anomalies.

Alternatively, a parallel architecture can be adopted, where LSTM-AE and GNN operate simultaneously on the same input data, and their outputs are combined using a fusion mechanism (e.g., weighted aggregation or attention-based fusion). This may allow the model to jointly consider temporal evolution and relational dependencies when identifying pressure variations.

The integration of temporal and relational learning is particularly relevant in drilling environments, where changes in one parameter influence others over time in a coupled manner. Therefore, a hybrid LSTM–GNN framework may potentially improve anomaly detection accuracy, enhance interpretability, and provide more reliable insights into near-bit pressure behaviour.

Although the present study focuses on a comparative evaluation of LSTM-AE and GNN models, the proposed hybrid framework represents a promising direction for future work and practical deployment.

3 Model evaluation and result

3.1 Baseline drilling

It represents the initial or normal operations in which the drilling conditions are relatively stable (Figures 1, 2). As we drill deeper, the WOB, hook load, drill pipe length, and torque all go up. Around 60 ft/h, the rate of penetration is found to be stable. Figure 1A shows the rate of penetration fluctuates between 45 and 105 ft/h, ultimately stabilizing at a mean of 60 ft/h with negligible variance. Figure 1B shows the maintenance efficiency at greater depths; the weight on bit scales from 400 kN to 1200 kN. Figure 1C shows that internal casing pressure increases with depth from 1500 to 6000 psi, consistent with standard hydrostatic and lithostatic pressure gradients. Figure 1D shows that rotational resistance increases from 300 to 900 kNm, reflecting the higher mechanical effort required to rotate the drill string at depth. Figure 1E shows the values range from 1.6 to 2.5, which provides an estimate of rock hardness and pore pressure, indicating lesser variations in lithological properties. Figure 1F displays the signal intensity for parameters such as ROP and WOB, showing their relative influence within the Graph Neural Network model.

FIGURE 1

FIGURE 2

Figure 2A shows that the rate of penetration is sustained for the second dataset. Figure 2B, verifying the first dataset, shows that the WOB increases with depth, ranging between 450 and 1050 kN. Figure 2C shows that pressure readings show a steeper gradient compared to the first set, rising from 2500 to 10,000 psi. Figure 2D shows an upward trend from 330 to 770 kNm as depth increases. Figure 2E shows the values here are significantly higher (3.2–5.4) than those in Figure 1. This shift supports a transition into harder rock formation or a distinct change in the downhole drilling conditions. Figure 2F shows a visual representation of the raw signal magnitude across all measured drilling variables.

3.2 Cautious zone drilling

In the cautious drilling phase, the drilling operations are directed with increased vigilance due to challenging geological formations and potential technical issues, as illustrated in Figures 3, 4. The associated table data highlights a significantly reduced Weight on Bit (WOB) compared to the baseline, indicating a proactive approach to reducing risks. From Figures 3A, 4A, the ROP exhibits substantial fluctuations, ranging from 50 to 250 ft/h. In Case 2 (Figure 4), the ROP peaks at 240 ft/h at a depth of 5,450 ft, suggesting continuous adjustments based on real-time drilling conditions. This inherent variability reflects the less predictable nature of the drilling environment during this phase.

FIGURE 3

FIGURE 4

Figures 3B, 4B demonstrate, consistent with a cautious drilling strategy, that the WOB is generally lower, typically maintained within the range of 300 and 1,200 kN. The detailed cautious zone drilling parameters are presented in Table 1. The elevated percentage deviation indicates a more complex well path during the cautious drilling phase. Figure 3C illustrates that the casing pressure remains stable, fluctuating between 300 and 1,200 psi. Torque values range from 315 to 735 kNm in Case 1 (Figure 3D) and between 150 and 750 kNm in Case 2 (Figure 4D). Figures 3E, 4E reveal that while d-exponent values are similar to the baseline (1.2–2.5 and 1.1 to 2.5, respectively), the trends differ, potentially providing insights into pore pressure variations. Figures 3F, 4F reveal the raw signal power for the key parameters (ROP, RPM, WOB, DP, and torque) during this cautious phase, derived from GNN spatial attention.

3.3 Kick zone drilling

A kick occurs when formation fluids (oil, gas, or water) flow excessively into the wellbore because the hydrostatic pressure of the drilling mud is exceeded by the formation pressure. The data for this zone reveals a paradoxical relationship: the Weight on Bit (WOB) is kept very low, yet the Rate of Penetration (ROP) is extremely high. This phenomenon indicates the drill bit’s encounter with a very soft rock layer or a high-pressure zone. Furthermore, the percentage deviation is exceptionally high (ranging from 72% to 82%), suggesting a significant change in the well path or the use of a highly angled well design.

Figure 5A shows that ROP is high, fluctuating between 115 and 460 ft/h, and such a sudden increase may indicate abnormal pressure-related drilling behaviour potentially associated with kick conditions. Figure 5B shows that WOB is maintained between 300 and 1,200 kN, while Figure 5C shows that casing pressure is elevated between 2,500 and 10,000 psi. The corresponding kick zone drilling parameters are summarized in Table 2 which may be associated with abnormal formation-fluid interaction or pressure imbalance conditions. Figure 5D shows that torque values range from 300 to 1,200 kNm, and Figure 5E shows the values are lower here (0.9–2.5), where a decreasing corrected d-exponent may suggest a transition toward potentially overpressured formations, although similar behaviour may also arise from lithological variations and operational drilling adjustments. Figure 5F shows the raw signal power for drilling parameters during the kick event.

FIGURE 5

Figure 6A shows that ROP is even more aggressive, ranging from 250 to 1,000 ft/h, highlighting the extreme conditions of this specific kick zone. Figure 6B shows that, consistent with Case 1, WOB remains between 300 and 1,200 kN, and Figure 6C shows that pressure remains high, between 2,500 and 10,000 psi. Figure 6D shows that torque is significantly higher in this case, ranging from 600 to 2,400 kNm, while Figure 6E shows values are lower, ranging from 0.8 to 2.5. Figure 6F displays the GNN spatial attention raw signal power for the parameters.

FIGURE 6

3.4 Expert-assisted quantitative evaluation: LSTM-AE vs. GNN

The quantitative metrics reported in this section are derived using post hoc expert-assisted operational interpretation rather than supervised training labels. The LSTM-AE and GNN models were trained exclusively using unlabelled stable drilling data in an unsupervised manner.

For evaluation purposes only, drilling intervals corresponding to baseline, cautious, and kick-zone behaviour were retrospectively identified by experienced drilling personnel using drilling reports, operational logs, casing-pressure trends, ROP deviations, and drilling-event documentation. These interpreted operational intervals were used as reference regions to assess agreement between model-generated anomaly indications and operationally observed abnormal behaviour.

Therefore, the reported accuracy, precision, recall, F1-score, false alarm rate, and detection lead-time metrics should not be interpreted as conventional supervised classification performance, but rather as measures of agreement between unsupervised anomaly indications and expert-interpreted drilling events. The quantitative comparison and performance metrics are summarized in Tables 3–5.

The results in the above table confirm that the GNN model consistently outperforms LSTM-AE across all reported metrics. The most operationally significant advantage is the detection lead-time: the GNN flags abnormal drilling behaviour an average of 7.8 ft before the retrospectively interpreted operational anomaly onset, compared to 4.2 ft for LSTM-AE. This 3.6 ft advantage, while appearing modest, translates to several minutes of additional warning time at typical ROP values (60–450 ft/h), which is operationally meaningful for well control decisions. The reduction in false alarm rate from 15.7% (LSTM-AE) to 9.3% (GNN) further reduces the risk of alert fatigue in real-time drilling environments.

Sensitivity Analysis was done to evaluate model dependence on input parameters. Each feature was perturbed (±10%) while keeping others constant. The evaluation concluded that ROP, WOB, and near-bit pressure proxy showed the highest influence on model outputs, GNN captured inter-feature dependencies (WOB–RPM–Torque interactions) and LSTM-AE showed stronger sensitivity to temporal variations This implies that accurate sensing of key drilling parameters is critical for reliable predictions.

For Noise Robustness Analysis Gaussian noise (2%–10%) was added to simulate sensor inaccuracies. The analysis revealed that LSTM-AE performance degraded with increasing noise due to temporal distortion, GNN remained more stable due to relational learning and both models showed acceptable robustness within realistic noise limits (<5%). Both models are suitable for real-world deployment, with GNN showing higher resilience.

From the overall findings we can conclude that while LSTM-AE performance declined due to sequence disruption, GNN handled missing data better when graph structure remained intact.

3.5 Machine learning model outputs and analysis

This section presents the direct outputs of the LSTM-AE and GNN models, including reconstruction error behaviour, anomaly score distributions, feature importance analysis, and latent space structure. These outputs substantiate the comparative evaluation presented in Section 5.4 and provide interpretability of the model decisions.

3.5.1 Reconstruction error behaviour

The 2σ anomaly detection threshold was defined as: mean reconstruction error of the baseline zone +2 × standard deviation of the baseline zone. Any depth point where the reconstruction error exceeds this threshold is flagged as an anomaly. This unsupervised threshold is consistent with standard practice in reconstruction-error-based anomaly detection (Luu et al., 2024).

Although drilling data distributions may exhibit non-Gaussian characteristics due to operational variability and geological heterogeneity, the 2σ threshold was adopted as a practical unsupervised detection criterion for identifying statistically significant deviations from baseline reconstruction behaviour. The threshold provides a balance between sensitivity and false alarm generation and is commonly applied in reconstruction-error-based anomaly detection frameworks. Nevertheless, adaptive or distribution-aware thresholding strategies may further improve robustness under highly non-stationary drilling conditions and represent an important direction for future work.

Although the reconstruction error profiles demonstrate distinguishable anomaly trends, the observed behavior should not be interpreted as perfectly separable under real field conditions. The 2σ threshold was adopted as a practical unsupervised anomaly detection criterion for identifying statistically significant deviations from baseline reconstruction behaviour. The threshold was selected to provide a balance between sensitivity to abnormal pressure-related events and minimization of excessive false alarms during stable drilling intervals. In reconstruction-error-based anomaly detection, such statistical thresholding approaches are commonly used when labelled anomaly distributions are unavailable.

Drilling data are inherently noisy due to lithological variability, drill-string vibration, sensor uncertainty, mud circulation fluctuations, and operational parameter adjustments. The preprocessing procedures applied in this study, including interpolation and normalization, reduce part of the short-term signal instability and contribute to smoother reconstruction-error trajectories. Nevertheless, local fluctuations and intermittent overlap between normal and anomalous behavior remain observable, particularly within transitional drilling intervals such as the cautious zone. Therefore, the presented anomaly separations should be interpreted as indicative operational trends rather than perfectly isolated classes.

3.5.2 Anomaly score distribution

Baseline zone: Both models produce anomaly scores concentrated below 0.5, confirming that the models reliably learn normal behaviour without generating spurious alerts.

3.5.2.1 Cautious zone

LSTM-AE scores are broadly distributed between 0.4 and 1.2, indicating ambiguity at the normal–anomalous boundary. GNN scores cluster more distinctly between 0.7 and 1.4, showing sharper separation.

Kick zone: LSTM-AE scores range from 1.1 to 2.8. GNN scores range from 1.4 to 3.6, demonstrating stronger anomaly amplification and clearer separation from the normal distribution.

The bimodal separation between the GNN’s normal-zone and kick-zone anomaly score distributions is more pronounced than that of the LSTM-AE, which contributes to the lower false alarm rate and higher precision reported in Table 6.

3.5.3 Feature importance and GNN attention weights

The GNN model assigns attention weights to each parameter node during the message-passing aggregation step. These weights indicate the relative contribution of each drilling parameter to the anomaly score. Table 6 summarises the mean GNN attention weights per parameter across each drilling zone.

The attention weight analysis reveals that near-bit pressure proxy and ROP are the primary drivers of anomaly detection in the GNN model, which is consistent with domain knowledge: kick events are characterised by a sudden increase in ROP (formation fluid reducing effective rock hardness) and a corresponding rise in near-bit pressure proxy. Conversely, WOB and RPM receive lower attention in the kick zone as these are typically reduced by the driller in response to warning signs.

For the LSTM-AE, feature importance was assessed through reconstruction error decomposition: the contribution of each input feature to the total reconstruction MSE was computed by masking one feature at a time and recording the change in reconstruction error. The results show that near-bit pressure proxy contributes 34% of the reconstruction error increase in the kick zone, followed by ROP (28%), Torque (19%), WOB (10%), RPM (6%), and Depth (3%). This is consistent with the GNN attention weights and confirms that both models identify the same physically meaningful signals, with the GNN providing a more explicit relational representation.

3.5.4 Latent space analysis (LSTM-AE)

To assess the representational quality of the LSTM-AE encoder, the 16-dimensional latent space representations were projected into two dimensions using Principal Component Analysis (PCA). The projection reveals the following structure to quantitatively evaluate latent-space separability. Cluster validation metrics were additionally computed using the PCA-projected latent embeddings. The Silhouette Coefficient, Davies–Bouldin Index (DBI), and Calinski–Harabasz (CH) score were used to assess inter-cluster separation and intra-cluster compactness.

The positive Silhouette Coefficient indicates moderate-to-good cluster separability between baseline, cautious, and kick-zone operational states. The relatively low Davies–Bouldin Index further supports improved inter-cluster distinction with limited intra-cluster dispersion. However, partial overlap between baseline and cautious-zone embeddings confirms that transitional drilling conditions remain difficult to separate perfectly under unsupervised learning conditions.

Baseline cluster: Tight, compact cluster centred near the origin. The low intra-cluster variance confirms that the encoder has learned a consistent representation of normal drilling behaviour.

Cautious zone cluster: Partially overlapping with the baseline cluster but displaced along PC1, indicating that the model captures the gradual nature of the transition between normal and anomalous states.

Kick zone cluster: The kick-zone embeddings demonstrate comparatively stronger separation from baseline behaviour in the latent representation space, although partial overlap remains present near transitional operational states.

The degree of cluster separation supports the anomaly detection performance reported in Table 5. The partial overlap between baseline and cautious zone clusters explains the moderate false alarm rate of 15.7% for the LSTM-AE in transitional zones; the GNN’s relational learning reduces this ambiguity.

3.5.5 Summary of ML model outputs

While conventional methods rely on threshold-based detection and are effective for clear deviations but may fail in complex, multivariate conditions. The proposed LSTM-AE captures temporal anomalies that precede observable threshold violations. The GNN model identifies relational inconsistencies between drilling parameters (e.g., WOB–RPM–Torque interactions).

3.5.6 Comparison with conventional drilling diagnostics

Conventional drilling diagnostics such as d-exponent analysis and threshold-based kick indicators are widely used because of their simplicity and ease of implementation. However, these approaches mainly rely on isolated parameter trends and may not adequately capture coupled multivariate drilling behaviour. In contrast, the proposed LSTM-AE and GNN models learn temporal and relational drilling patterns directly from operational data. Nevertheless, the present comparison remains qualitative because conventional diagnostic methods were not implemented on the same dataset for direct quantitative benchmarking. Future work should include field-scale benchmarking against established drilling monitoring systems.

4 Discussion

The experimental results obtained from the recorded offshore drilling dataset demonstrate that both LSTM-AE and GNN models are capable of identifying deviations associated with abnormal near-bit pressure behaviour. However, the two models exhibit different sensitivities to operational transitions and parameter interactions.

The LSTM-AE model captured gradual temporal deviations effectively, particularly during the transition from baseline to cautious drilling conditions, where reconstruction error increased progressively with depth. However, partial overlap between normal and transitional operational states contributed to moderate false-positive behaviour in cautious zones.

In contrast, the GNN model demonstrated stronger anomaly discrimination capability due to its ability to model inter-parameter relationships among ROP, WOB, RPM, torque, and pressure-related signals. The experimentally observed reduction in false alarm rate and earlier anomaly onset detection indicates that relational modelling improved sensitivity to coupled drilling behaviour changes within the recorded dataset.

The major strength of LSTM-AE is based on its capability to identify the long-term dependencies in the time series data. The vanishing gradient problem, which is a major issue in the traditional recurrent neural networks (RNNs), is overcome by the LSTM networks using their “gated” structures (input, forget, and output gates) and memory cell state. The “forget gate,” for example, plays a pivotal role in deciding what information should be retained or discarded from the past, making LSTMs ideal for handling the potentially large and complex data streams generated during the drilling process. The LSTM-AE, trained on data that represents normal drilling conditions in an unsupervised learning process, learns to optimize the reconstruction error between the input data and the reconstructed output. As a result, an increase in the reconstruction error indicates a departure from the normal behaviour, which could be an indication of an anomaly or a variation in the near-bit pressure. This makes the LSTM-AE an ideal tool for unsupervised anomaly detection, where it can identify the early warning signs of stuck pipe occurrences, which could otherwise result in major downtime and losses.

Although LSTM-AE performs very well in terms of temporal analysis, drilling parameters tend to have strong multivariate interdependencies that cannot be captured by mere time-correlations. GNN models are particularly well-equipped to handle this problem by modelling the relational structure of the input variables. In a GNN model, each drilling parameter (such as WOB, ROP, torque, differential pressure, and hook load) can be considered as a node, and the physical and operational relationships between these parameters are shown as edges. This graph representation enables GNN models to analyse how changes in one parameter affect other parameters, giving a more holistic view of drilling dynamics and, by extension, near-bit pressure behaviour.

GNNs can capture complex, non-linear relationships between multiple sensors that might be overlooked by traditional time-dependent models like LSTM-AE. For instance, a GNN can effectively model how variations in WOB and RPM jointly affect ROP and, consequently, near-bit pressure, considering the interplay with formation characteristics and drilling fluid properties. The ability of GNNs to aggregate information from a node’s neighbourhood through message passing enables them to learn from relational data, offering superior performance for graph-structured data. This relational understanding is crucial for predicting dynamic phenomena such as pore pressure and oil production evolution by modelling inter-well connectivity. It should be noted that the analysis presented is based on recorded drilling datasets; therefore, the results demonstrate the capability of the models for anomaly detection rather than validated real-time deployment performance.

The comparative analysis of LSTM-AE and GNN models highlights their complementary strengths in capturing temporal and relational aspects of drilling data. This observation suggests that a hybrid modelling approach, integrating both temporal sequence learning and inter-parameter relationship modelling, could potentially enhance anomaly detection performance. By combining these capabilities, such a framework would be better suited to capture the coupled dynamics inherent in drilling systems, where both time-dependent evolution and parameter interactions play a critical role in pressure behaviour.

5 Limitations

While LSTM-AE and GNN models offer promise for real-time drilling anomaly detection, they have key limitations. LSTM-AE excels at temporal dependencies but suffers from relational blindness, struggling to capture complex inter-parameter interactions like WOB’S non-linear effects on ROP, which impedes precise anomaly diagnosis. GNN’s mastery of relational structures falters in modelling long-term temporal sequences in dynamic drilling data without recurrent components (Berrocal et al., 2022). Both face challenges defining normal behavior amid shifting geology, equipment wear, and scarce labelled anomalies, leading to false positives or negatives. Interpretability remains poor, weakening engineer trust while high computational costs and vulnerability to sensor noise, missing data, and drift demand resource-intensive retraining, especially in offshore environments (Brenjkar and Delijani., 2022).

The application of Graph Neural Networks (GNNs) for analyzing drilling behavior comes with several challenges, mainly related to data quality and interpretability. Gan et al. (2023) GNNs perform well only when the input data is accurate and properly structured. In drilling applications, this means that the relationships between parameters must be correctly represented in graph form. If the data is incomplete, or poorly organized, the model’s predictions and analysis can become unreliable. Another major challenge is interpretability. Although GNNs are powerful in capturing complex, non-linear relationships, it is often difficult to clearly explain how the model arrives at a specific conclusion. This lack of transparency can limit their usefulness in real-time operations, where drilling engineers need quick and understandable insights to make decisions and diagnose problems (Kanfar et al., 2020). Therefore, improving the explainability of GNNs remains an important area of research. Liu et al. (2024).

While LSTM-AE models are effective at learning temporal patterns and detecting deviations from normal drilling operations, they also face issues with interpretability. These models are inherently complex, making their internal processes quite difficult to understand. Nakagawa et al. (2021) methods such as latent space visualization and reconstruction error analysis can provide some indication of which parameters contribute to anomalies, but they do not always offer a clear explanation of the root cause. For drilling engineers, simply detecting an anomaly is not enough; they also need to understand why it occurred to take the right corrective action. Boukredera et al. (2023) as a result, despite their strong detection capabilities, the practical application of LSTM-AE models is often limited due to the difficulty in making the output more transparent and interpretable. Additionally, the current study does not evaluate real-time deployment aspects such as data streaming, system latency, and edge-level implementation. These factors are critical for field-scale applications and require further investigation to enable seamless integration into operational drilling systems.

Furthermore, the reconstruction-error behavior observed in this study may appear more structured than field-scale real-time drilling streams because the analysis was conducted on recorded datasets after preprocessing and quality-control operations. In continuous field deployment, additional operational disturbances, streaming latency, telemetry loss, and sensor drift may introduce greater uncertainty into anomaly boundaries.

6 Conclusion and Scope of future work

LSTM-AE models are highly effective at extracting time-related dependencies and patterns from drilling data, which makes them ideal for detecting anomalies in drilling data. They are very good at learning what constitutes the expected behavior of drilling parameters and alerting when this behavior is no longer the case.

GNN models, on the other hand, are designed to detect complex, non-linear relationships and interdependencies between different drilling parameters. Li et al. (2021) this enables them to grasp how different inputs to the senses are intertwined in a “web of data” that can be crucial to comprehend the underlying causes of pressure variations (Bicciato et al., 2024).

While LSTM-AEs can implicitly learn some parameter interactions through their multi-variate input, they primarily focus on the temporal sequence and may not explicitly capture the complex, non-linear, and structural relationships between different sensors as effectively as GNNs.

Traditional GNNs might not inherently excel at long-term sequential pattern modelling unless they are integrated with recurrent components or tailored for spatio-temporal graphs. However, this can be addressed with hybrid models (e.g., CNN-GNN-LSTM) by combining their strengths. In offshore drilling, real-time monitoring and early anomaly detection are critical due to the high costs and significant safety risks associated with unexpected events like kicks, stuck pipes, or blowouts.

LSTM-AE models are highly valuable anomaly detection in offshore drilling. Through the continuous processing of incoming drilling data, the model can generate a reconstruction error. When this error crosses a statistically defined threshold, it detects an anomaly, such as an early sign of a stuck pipe or abnormal pressure variations. This unsupervised nature means it does not require labelled anomalous data, which is often scarce in drilling operations (Mohagheghian et al., 2024). The ability to detect subtle sequential patterns allows for early-stage identification of potential issues before they escalate into catastrophic events. For example, anomalous behavior in hook load, overpull, slack off, or torque can be identified in real-time, preventing costly situations.

GNNs can potentially offer a better insight into the root causes of pressure variation through the direct analysis of inter-parameter relationships between various drilling sensors and parameters. For example, if a near-bit pressure anomaly is identified, a GNN can potentially be used to identify the specific combination of WOB, RPM, torque, and formation properties that are driving this particular anomaly (Ghanitoos et al., 2024). This is particularly useful in complex geological environments that are often encountered in offshore deep and ultra-deep wells, where the formations are heterogeneous and have varying lithology. Through the integration of real-time data from multiple sensors, GNNs can potentially improve overall situational awareness in RTOC, thereby improving the timely identification and mitigation of anomalies. Nevertheless, it is important to recognize that the observed drilling parameter variations are not uniquely attributable to kick events alone. Similar signatures may also arise from formation heterogeneity, changes in rock strength, drilling optimization procedures, operational adjustments, or sensor uncertainties. Therefore, the anomaly patterns identified in this study should be interpreted as early warning indicators of abnormal drilling behaviour rather than definitive evidence of kick occurrence.

The most effective strategy for near-bit pressure variation prediction during PDC drilling in an offshore environment is likely to be a synergistic integration of both LSTM-AE and GNN models (Li et al., 2025). An LSTM-AE can potentially be used as a first-level anomaly detection tool to scan for temporal anomalies. Once an anomaly is identified, a GNN-based system can potentially be used to quickly scan the inter-parameter relationships, thereby offering more detailed insights into the specific causes of the pressure variation.

A future hybrid implementation integrating LSTM-AE and GNN models may potentially combine the strengths of temporal sequence learning and relational graph modelling. Such an approach could improve anomaly detection robustness, interpretability, and operational monitoring capability in complex offshore drilling environments. However, the hybrid framework proposed in this study remains conceptual and has not yet been experimentally implemented or validated.

Within the evaluated drilling dataset, the GNN framework consistently demonstrated stronger anomaly separation, lower reconstruction variance in baseline conditions, and earlier detection of pressure-related operational deviations compared to the LSTM-AE model. The latent-space analysis and reconstruction-error behavior indicate that relational parameter learning improves discrimination between stable and abnormal drilling states under complex multivariate conditions.

Furthermore, the complementary strengths of LSTM-AE and GNN models indicate strong potential for hybrid modelling approaches that integrate temporal and relational learning. Future work will focus on developing and validating such hybrid LSTM–GNN frameworks, enabling more robust and interpretable anomaly detection in complex drilling environments.

7 Equations

Annular velocity in ft/min =

Annular velocity equation (ft/min): This equation calculates the upward velocity of drilling fluid in the annulus, which is very important for removing cuttings effectively and for avoiding formation damage from the settled debris. Proper annular velocity ensures that the hole is effectively cleaned and that it stabilizes the borehole during the circulation.

DRS in rpm =

DRS equation (rpm): This equation connects the drill string’s rotation speed to the surface parameters and the bit size, helping in choosing the optimal RPM for the formation type. It also balances penetration rate with bit wear and the torsional vibrations in rotary drilling.

MFR in lpm =

MFR equation (lpm): This equation determines the mud flow rate based on pump performance and the fluid rheology. Accurate flow predictions supports hydraulic optimization, bit nozzle selection, and cuttings transport in different well conditions.

Surface hook load kN (W) =

Surface hookload equation (kN): This equation computes the hook load from the rig and line tension data, monitoring the total drill string weight. It reveals friction, drag, and connection integrity, ensuring safe tripping and drilling.

MD in ppg =

MD equation (ppg): This equation derives the mud density from vertical pressure to maintain the hydrostatic balance against formation pressures. This prevents kicks and lost circulation, helping to achieve precise equivalent circulating density management across well sections.

ROP (m/s) =

ROP equation (m/s): This equation predicts the penetration rate by including bit wear, collar shape, and safety margins, enabling realistic drilling forecasts. It directs adjustments in WOB and RPM to maximize footage while reducing connection times and bit trips.

WOB =

WOB equation (kN): This equation calculates the effective bit load taking into consideration buoyancy, inclination, friction, and safety factors in deviated wells. It advances optimal force transfer to improve ROP without risking excessive torque or loss of directional control.

PD equation (psi): This equation calculates the flow rate-induced pressure loss at the bit nozzle to improve hydraulic power at the formation face. Good pressure management further enhances cutting removal, cooling, and mechanical efficiency in PDC drilling.

Radial position equation (m): This equation models the force distribution and torque through cutter radial positioning during bit rotation. This analysis optimizes lateral stability, reduces whirl, and helps optimize cutting structure for better drilling dynamics.

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