A Deep Shale Gas Reservoir Rock Brittleness Index Prediction Method Based on a CNN-BiGRU-Attention Hybrid Model

Abstract

Hydraulic fracturing is a key technology for the commercial exploitation of deep shale gas reservoirs, and accurate prediction of rock-mechanical parameters is essential for optimizing these operations. Conventional approaches primarily rely on empirical formulas based on longitudinal and transverse wave velocities; however, obtaining transverse wave data is challenging, and these formulas often lack accuracy. Conventional machine learning algorithms also exhibit limited predictive performance and generalization due to the intrinsic heterogeneity of rock-mechanical data. Therefore, to address the extreme heterogeneity and complex nonlinear logging responses inherent in deep shale gas reservoirs in the Zigong (ZG) block, this study proposes a geology-tailored deep learning framework, CNN-BiGRU-AT. Unlike generic machine learning applications, this architecture is specifically designed to decode complex stratigraphic signals: the convolutional neural network (CNN) module extracts multi-scale spatial features to capture abrupt lithological transitions; the bidirectional gated recurrent units (BiGRUs) analyzes the continuous depth-sequential dependencies of overlying and underlying strata; and the attention mechanism (AT) dynamically regulates the weight allocation of critical input geophysical parameters, thereby delivering a geophysically informative and highly robust predictive performance. This paper employs the CNN-BiGRU-AT model to predict the Brittleness index (BI), using the ZG block as an example. The results demonstrate that the coefficient of determination (R²) for the brittleness index on the test dataset achieved 0.969, representing a 12% improvement over conventional models. The high accuracy of this model satisfies the precision requirements for predicting rock-mechanical parameters, thereby offering reliable theoretical support for optimizing hydraulic fracturing operations in deep shale gas reservoirs.

1. Introduction

In recent years, the depletion of conventional hydrocarbons has shifted global exploration toward unconventional shale gas. Characterized by its clean, low-carbon profile and vast reserves, shale gas—especially from deep reservoirs, which account for more than 60% of total resources—has emerged as the main frontier for production growth. However, the high vertical stress and pronounced heterogeneity inherent in deep formations pose significant challenges to hydraulic fracturing, often resulting in unidirectional fracture propagation and poor volumetric stimulation. Consequently, the accurate characterization of the Brittleness index (BI) is no longer merely a mechanical exercise but a prerequisite for optimizing reservoir development strategies [1].

While shallow and medium-depth shale reservoirs are characterized by low reservoir pressure, high porosity, short development cycles, and low single-well production, deep shale resources represent the strategic successor domain for growth in shale gas production. However, during hydraulic fracturing, the considerable burial depth and elevated vertical stress levels pose substantial challenges to fracture initiation and propagation. Furthermore, fractures tend to propagate unidirectionally along the direction of maximum principal stress, which limits the natural development of complex fracture networks. Consequently, natural fractures are difficult to activate, ultimately resulting in poor stimulated reservoir volume performance. Rock mechanical parameters are fundamental factors controlling the effectiveness of hydraulic fracturing in deep shale formations. In current engineering practice, the Brittleness index (BI) is typically determined through uniaxial and triaxial compression tests, X-ray diffraction, and empirical formulas. However, traditional laboratory experimental methods are inherently time-consuming and costly. Moreover, empirical formula-based approaches, which are primarily developed from longitudinal and transverse wave velocities, face significant challenges in data acquisition, suffer from low predictive precision, and require a high level of professional expertise [2]. In recent years, the rapid evolution of big data theory and technology has facilitated the widespread adoption of machine learning in petroleum engineering. Primarily, scholars have investigated various machine learning architectures and intelligent algorithms to enhance nonlinear mapping capabilities, thereby improving the precision of rock-mechanical parameter prediction. These methodologies encompass traditional feedforward neural networks, such as the Backpropagation (BP) model, as well as Long Short-Term Memory (LSTM) networks and emerging artificial intelligence algorithms, such as XGBoost. On the other hand, by incorporating a broad spectrum of geological and engineering feature parameters, including drilling, completion, seismic, well-logging, fracturing, and production data, these algorithms can effectively uncover latent patterns and inherent correlations embedded in the datasets. Brittleness evaluation is of great significance for assessing shale reservoir fracability, designing fracturing intervals, and improving fracturing stimulation effects. Cao et al. adopted digital rock physics experiments to calibrate the influence degree of different mineral components on the overall brittleness characteristics of rocks, quantitatively analyzed the variation relationship of rock elastic parameters with mineral component content, and used the brittleness index based on elastic parameters to establish the differential influence relationship of different mineral components on shale brittleness, thus proposing a brittleness evaluation method based on the adaptive change in the contribution degree of mineral components [3]. He et al. adopted four ensemble learning algorithms to address the nonlinear interdependence between logging responses and mechanical brittleness. Comparative analysis indicates that the ensemble model achieved the highest test-set prediction accuracy. This provides a cost-effective alternative to laboratory methods and demonstrates the feasibility of data-driven approaches in brittleness evaluation. Yapei et al. introduced a novel Principal Component Analysis (PCA)-Back Propagation Neural Network BPNN method for predicting the brittleness index using five logging parameters, namely natural gamma (GR), formation density (DEN), P-wave sonic (DTC), neutron porosity (CNL), and spontaneous potential (SP) [4]. Principal component analysis was applied to extract three principal components from these five logging datasets. The resulting PCA-BPNN prediction model, developed from these principal components, demonstrated superior predictive accuracy. Zhang et al. introduced a novel hybrid model, the Sparrow Search Algorithm-Extreme Learning Machine (SSA-ELM), to predict the shale brittleness index [5]. To evaluate the model’s effectiveness, twelve alternative machine learning algorithms were selected as benchmarks for comparison. The superiority of the proposed framework was subsequently verified by integrating conventional logging data with X-ray diffraction-derived brittleness indices. Shi et al. proposed several practical data-driven methods for predicting the Brittleness index based on backpropagation artificial neural networks (BP-ANN), extreme learning machines (ELM), and linear regression [6]. These models were developed by integrating conventional logging data with Brittleness index values calculated through laboratory mineral composition analysis. A comparative analysis revealed that artificial intelligence models achieved significantly better performance in predicting the Brittleness index than simple regression-based methods.

While previous studies have explored empirical formulas and conventional machine learning models for brittleness evaluation, these approaches exhibit specific limitations in highly heterogeneous deep shale gas reservoirs. First, traditional empirical approaches, primarily based on longitudinal and transverse wave velocities, face significant challenges in data acquisition and suffer from low predictive precision. Second, although conventional data-driven algorithms have been introduced to enhance non-linear mapping capabilities, their direct application often overlooks the inherent geological background [7]. They serve as generic models that fail to dynamically decode complex stratigraphic signals. Specifically, as major fields enter mature development stages, traditional data-driven modeling approaches encounter a dual limitation: the insufficient scale and quality of samples fail to satisfy the stringent data-completeness requirements of deep learning, and under such data-sparse conditions, conventional algorithms struggle to capture the complex non-linear mappings between heterogeneous geological settings and geomechanical responses.

To comprehensively enhance the predictive accuracy of the BI in highly heterogeneous deep shale formations, this study develops a geologically guided CNN-BiGRU-AT framework grounded in multi-source data fusion. First, CNN is employed to capture ‘spatial-scale’ features; unlike standard regression, its convolutional kernels can identify abrupt lithological transitions and local sharp variations in logging curves, which are typical of deep shale heterogeneity. Second, while deep shale data often face ‘small-sample’ constraints in specific blocks, the BiGRU layers mitigate this by learning bidirectional depth-sequential dependencies. By processing information from both overlying and underlying strata, the model maximizes the extraction of trend information from limited data points, enhancing generalization. Finally, the AT is integrated to dynamically reweight the input geophysical features. This addresses the non-linear response of different logging parameters to rock brittleness, ensuring that the model prioritizes the most physically relevant signals under complex stratigraphic conditions. By coupling well-logging suites with rigorous laboratory experimental data, the proposed model leverages a hierarchical architecture to capture not only localized spatial anomalies in rock facies but also long-range, depth-sequential geomechanical trends.

2. Geological Background

The Sichuan Basin serves as a strategic hub for shale gas exploration and development in China, hosting several national demonstration zones that are predominantly dedicated to exploiting shallow-to-medium-depth resources. As shown in Figure 1, recent exploration has revealed that deep shale gas possesses significant extraction potential, with geological resources estimated at approximately 24.28 × 10¹² m³. Unique regional geological settings primarily govern such enrichment characteristics [8]. The Sichuan Basin spans approximately 380–430 km from east to west and 310–330 kilometres from north to south, covering an area of roughly 40,000 km².

The study focuses on the ZG block in the Sichuan Basin. The ZG block is situated within the low-fold structural belt in the southwestern Sichuan Basin, spanning the administrative regions of Zigong and Yibin. The topography is characterized by hilly terrain, with a mining concession covering 2458 km². It represents a significant shale gas development block in the southern Sichuan region [9].

3. Data Preprocessing

Four representative wells (ZG1–ZG4) in the study area were selected for analysis. All samples were collected from the deep shale reservoirs of the Wufeng–Longmaxi Formation, with burial depths ranging from 3850 m to 4193 m. To ensure the model’s reliability, a standardized well-logging sampling interval of 0.125 m was used, yielding 5812 valid data points. Of these, Well ZG1 provided 2737 samples for model training, while Well ZG2 provided 1265 samples for model testing. To further verify the spatial generalization capability of the proposed model, 857 and 953 independent samples were reserved from Wells ZG3 and ZG4, respectively, for independent validation (

Table 1. Summary of dataset distribution and stratigraphic coverage.

Well	Usage	Depth Range (m)	Interval (m)	Sample Count
ZG1	Training set	3850–4192	0.125	2737
ZG2	Testing set	3910–4068	0.125	1265
ZG3	Validation set	3880–3987	0.125	857
ZG4	Validation set	3990–4109	0.125	953

). The model inputs variables include the bulk modulus ($K$), shear modulus ($G$), compressional sonic slowness (DTC), shear sonic slowness (DTS), Poisson’s ratio ($v$), and Young’s modulus ($E$), resistivity ($R$) (Figure 2 and Figure 3); the model output is the BI, which is obtained from laboratory testing. The selection of the seven input features is based on their fundamental physical relationships with rock brittleness and established practices in petrophysical modeling. Specifically, elastic parameters ($K$, $G$, $v$, $E$) and acoustic velocities (DTC, DTS) are direct indicators of rock stiffness and deformation characteristics, which are the primary mechanical components of BI. $R$ is included as it reflects lithological variations and fluid content, providing additional geological context for the machine learning model to distinguish between brittle and ductile intervals. These logging parameters exhibit strong non-linear correlations with laboratory-derived geomechanical properties in deep shale formations. Specifically, the input parameters primarily represent “dynamic” geomechanical responses derived from continuous well-logging suites. In stark contrast, the target variable is the BI, which is entirely decoupled from these logging data. The BI is a “static” mechanical indicator obtained solely through independent laboratory testing on drilled core samples. These two datasets are completely segregated in terms of spatial measurement scales, physical triggering mechanisms, and mathematical calculations, so there is absolutely no cross-utilization of baseline parameters. Statistical analyses of the training and testing datasets are summarized in

Table 2. Statistical analysis of the training data.

Features	$\mathit{K}$ (MPa)	DTC ($\mathbf{\mu }\mathbf{s}/\mathbf{m}$)	DTS ($\mathbf{\mu }\mathbf{s}/\mathbf{m}$)	$\mathit{v}$	$\mathit{R}$ ($\mathbf{\Omega }·\mathbf{m}$)	$\mathit{G}$ (MPa)	$\mathit{E}$ (MPa)	BI (%)
Mean	26.2067	75.6565	139.5028	0.3041	11.4311	12.818	41.8685	42.5695
Standard deviation	2.6799	4.2747	10.042	0.0069	3.0925	1.899	4.6281	9.1662
Minimum	21.5488	61.631	110.815	0.2923	6.475	8.397	22.2946	24.472
Maximum	38.3568	86.625	171.113	0.3138	37.602	20.099	51.2166	73.065
Range	16.8081	24.994	60.298	0.0215	49.672	25.6733	28.922	48.593

and

Table 3. Statistical analysis of the testing data.

Features	$\mathit{K}$ (MPa)	DTC ($\mathbf{\mu }\mathbf{s}/\mathbf{m}$)	DTS ($\mathbf{\mu }\mathbf{s}/\mathbf{m}$)	$\mathit{v}$	$\mathit{R}$ ($\mathbf{\Omega }·\mathbf{m}$)	$\mathit{G}$ (MPa)	$\mathit{E}$ (MPa)	BI (%)
Mean	26.0888	74.7886	135.3859	0.305	11.7361	13.4674	34.458	39.2384
Standard deviation	2.6527	4.1067	5.1227	0.0025	2.5621	2.0727	6.5453	11.0994
Minimum	23.7021	63.213	113.904	0.2994	8.115	11.5367	29.84	23.365
Maximum	36.5133	79.063	146.17	0.3119	40.531	18.9430	48.3376	71.171
Range	12.8112	15.85	32.266	0.0125	32.416	7.4063	18.4976	47.806

.

To ensure modeling accuracy and reliability, the well-logging data were rigorously preprocessed to mitigate systematic errors and environmental noise. The workflow consisted of four key steps:

Depth correction was performed to eliminate systematic discrepancies between core and logging depths, ensuring precise vertical alignment between the two datasets.

Standardization: To eliminate the influence of dimensions and numerical disparities among input features, a Z-score standardization method was applied to all logging data before feeding them into the CNN-BiGRU-AT model [10,11]. The transformation is defined as:

$$x^{\prime }={\displaystyle \frac{x-\mathrm{\mu }}{\sigma }}$$

(1)

where $x$ is the original feature value, $\mathrm{\mu }$ is the mean of the feature, and $\sigma$ is the standard deviation. This method ensures that each input variable contributes equally to the model’s gradient updates and prevents the loss function from being dominated by high-magnitude features, thereby accelerating model convergence and improving predictive stability.

Data cleansing: A critical process for enhancing dataset quality through systematic review and validation of records, correcting data errors, and handling outliers. The primary objectives include removing redundant records, rectifying data inconsistencies, and managing outliers. In this study, outlier detection was performed using scatter plot visualization, followed by mean imputation to correct anomalous values [12].

4. Methodology

4.1. Convolutional Neural Network (CNN)

In this study, the CNN is adapted from its conventional role in image processing to serve as a one-dimensional spatial feature extractor tailored for well-logging sequences in the depth domain. The convolutional layers apply sliding-window filters directly across logging parameters aligned by depth [13,14]. These input parameters include compressional and shear sonic slowness and elastic moduli. This mathematical operation isolates localized spatial anomalies and captures abrupt lithological boundaries. By applying kernels of varying sizes, the CNN functions as a multiscale geological filter. It effectively smooths out environmental logging noise while preserving the localized, high-frequency facies variations critical to brittleness transitions in deep shale reservoirs.

The convolutional layer is as follows:

$$C{\mathrm{on}}_k=\alpha (W{t}_k\otimes X+B{i}_k)$$

(2)

where $C{\mathrm{on}}_{\mathrm{k}}$ is the $k$-th feature map of the convolutional output; $\alpha$ is an activation function; $W{t}_k$ is the weight matrix of the $k$-th convolution kernel in the current convolution layer; $B{i}_k$ denotes the offset of the $k$-th convolution kernel within the current convolutional layer; $\otimes$ denotes the symbol for the convolution operation; $k$ denotes the number of convolution kernels. The architecture of the CNN is illustrated in Figure 4.

A pooling layer subsequently processes the feature maps extracted by the convolutional layer to reduce spatial dimensionality while retaining essential information. Equation (3) defines the pooling operation:

$$P_i={\mathrm{pool}(\mathrm{C}}_i)$$

(3)

where $C_i$ represents the $i\text{-}th$ feature map input to the pooling layer (the output of the preceding convolutional layer), and $P_i$ denotes the corresponding output feature map after the down-sampling operation. Specifically, this study employs max-pooling, which selects the maximum value within a sliding window to capture the most prominent local features and enhance the model’s translational invariance.

4.2. Bidirectional Gated Recurrent Unit (BiGRU)

While the CNN excels at extracting localized features, the BiGRU is integrated to analyze the broader, depth-wise sequential trends inherent in well-logging data. This architecture processes the logging parameters bidirectionally, allowing the network to simultaneously evaluate the geomechanical characteristics of both the overlying and underlying formations [15]. By using streamlined gating mechanisms, the BiGRU identifies and retains the essential stratigraphic signatures that govern rock mechanical behavior [16]. Consequently, the BiGRU facilitates a more holistic understanding of stratigraphic dependencies than traditional unidirectional models. The architecture of the BiGRU is illustrated in Figure 5.

4.3. Attention Mechanism (AT)

Rock brittleness is driven by a complex, nonlinear interplay among distinct geophysical parameters. These parameters do not contribute equally across different depth intervals. To avoid the standard opaque limitations of generic modeling, the attention mechanism is integrated to provide a physics-constrained weighting paradigm. Instead of treating all extracted features uniformly, this mechanism dynamically evaluates the relevance of various logging inputs. For example, it assigns higher attention scores to critical mechanical indicators, such as shear modulus and Poisson’s ratio, when predicting failure characteristics. By computing a weighted sum, the model adaptively isolates the core geomechanical factors governing rock brittleness at any given depth [17,18]. This process suppresses redundant signals and significantly enhances both the predictive accuracy and the physical interpretability of the BI profile. As illustrated in Figure 6, by flexibly allocating these weights, the mechanism substantially improves the model’s capability to handle lengthy sequences and complex tasks.

The definition of attention is given by Equation (3)

$$\mathrm{Attention}(Q,K,V)=\mathrm{soft}\max ({\displaystyle \frac{Q{K}^T}{\sqrt{d_k}}})V$$

(4)

Here, $Q$, $V$, and $K$ denote the query, value, and key matrices, respectively, while represents the vector dimension of $Q$, $K$, and $V$.

4.4. Polar Lights Optimizer (PLO)

The PLO algorithm employs two primary mechanisms to navigate complex optimization landscapes: gyration motion and the aurora oval walk [19,20]. The gyration motion mathematically models velocity decay to facilitate detailed local exploitation, progressively improving convergence accuracy throughout the iterative process. Simultaneously, the aurora oval walk utilizes the swarm centroid to guide stochastic tracking, enabling extensive global exploration with an adaptive step size. By integrating these components with dynamic step adjustments, the algorithm effectively avoids getting trapped in local optima. This framework achieves a dynamic mathematical balance by extensively exploring potential regions during the early search phase. It progressively shifts toward highly precise local exploitation as iterations continue, thereby significantly augmenting overall performance and convergence accuracy [21,22].

$$A_0=\mathrm{Levy}(d)\times (X_{avg}(j)-X(i,j))+LB+r_1\times (UB-LB)/2$$

(5)

$$X_{\mathrm{avg}}={\displaystyle \frac{1}{N}}\times {\displaystyle \sum _{i=1}^{N}X(i)}$$

(6)

$$X_{\mathrm{new}}(i,j)=X(i,j)+r_2\times (W_1\times v_t+W_2\times A_0)$$

(7)

where $A_0$ represents the auroral elliptical walking trajectory, $\mathrm{Levy}(d)$ denotes the step size value of $\mathrm{L}\mathrm{é}\mathrm{vy}$ flight, $X_{\mathrm{avg}}$ is the centroid position of the high-energy particle swarm which indicates the current position of a high-energy particle, $UB$ and $LB$ represent the upper and lower bounds of the solution space, $r_1$ and $r_2$ are random numbers within [0, 1] simulating environmental disturbances, $X_{\mathrm{new}}(i,j)$ corresponds to the position of the energy particle, $v(t)$ is the particle velocity, and $W_1$ and $W_2$ are weighting coefficients.

The high-dimensional hyperparameter space and the intricate nonlinear mappings required within the hybrid framework are highly susceptible to local optima. This vulnerability becomes particularly acute under the conditions with sparse data typically encountered in mature deep shale reservoirs. The PLO algorithm is specifically employed to overcome this methodological bottleneck. Rather than relying on manual tuning, PLO maintains an optimal mathematical balance between global exploration and local exploitation. Within our framework, PLO efficiently and precisely adjusts critical network configurations. It automatically modifies convolutional kernel sizes to match local logging resolutions and optimizes BiGRU hidden units to scale the memory capacity for depositional continuity. This systematic optimization ensures robust convergence, strictly controls model complexity to prevent overfitting, and maximizes the spatial generalization capacity across wells used for blind testing.

4.5. Framework of the Hybrid Model

As illustrated in Figure 7, the proposed framework adopts a four-tier hierarchical architecture: Spatial local features are extracted from the data using a CNN; within the attention mechanism layer, a self-attention algorithm dynamically assigns weights to feature vectors, emphasising critical information; the BiGRU layer effectively captures the non-linear geological spatial dependencies and long-range temporal characteristics present in the logging data through its bidirectional gating mechanism; Finally, parameter estimation is achieved via a fully connected output layer. The innovation of this architecture manifests in three aspects: the synergy between CNN and attention mechanisms facilitates hierarchical feature extraction and importance-based screening; BiGRU compensates for CNN’s limitations in processing sequential contextual information by capturing the sequential characteristics and long-range dependencies inherent in logging data. PLO is employed to automatically search for and lock in the model’s critical hyperparameter combinations. This specifically involves optimizing grid structure parameters (such as the number and size of convolutional kernels in CNN layers to adapt to the local feature scale of logging curves, and the number of hidden layer neurons in BiGRU layers to regulate temporal memory capacity) alongside training strategy parameters (such as the initial learning rate determining the gradient descent step size) [23].

5. Experimental Results and Discussion

To comprehensively validate the proposed model’s superiority from multiple perspectives, several comparative experiments were designed. To ensure fairness in these comparisons, the key hyperparameters of each benchmark model were optimized using the PLO, guaranteeing that all models were evaluated under their optimal conditions (

Table 4. Search space and optimal values of hyperparameters based on the PLO algorithm.

Category	Optimized Hyperparameter	Search Space	Optimal Values
CNN	filters	[16, 128]	48
	kernel_size	[2, 8]	4
BiGRU	units	[32, 128]	64
Training strategy	learning rate	[0.001, 0.1]	0.001
PLO settings	Population	/	30
	Maximum Iterations	/	300
Objective function	fitness function	/	RMSE

).

5.1. Evaluation Metrics

To assess the predictive accuracy of the developed models, three standard metrics were employed: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the Coefficient of Determination (R²). MAE measures the average magnitude of the residuals, providing a direct reflection of error scale. RMSE further quantifies the deviation between predicted and observed values, penalizing larger errors more heavily. Meanwhile, R² indicates the degree of correlation between predicted and actual values. Among these, MAE and RMSE are loss-type metrics, while R² is a gain-type metric. That is, the larger the R², the smaller the MAE and RMSE, indicating better model fitting and more accurate predictions [24,25]. The definitions of these three metrics are as follows:

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|yi-\widehat{y}i\right|}$$

(8)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=0}^n{{\displaystyle (y_i-{\widehat{y}}_i)}}^2}}$$

(9)

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{(y_i-\widehat{y})}^2}}{{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}}}$$

(10)

In the formula, n denotes the number of data samples; $y_i$ and ${\widehat{y}}_i$ represent the actual value and model-predicted value of the brittleness index at time, respectively; $\overline{y}$ is the mean value of the actual values $y$.

5.2. CNN-BiGRU-Attention

The model demonstrated excellent performance in predicting the BI with a reasonable set of hyperparameters (

Table 5. Hyperparameter configuration of the proposed CNN-BiGRU-AT model.

Module	Hyperparameter	Optimal Value
CNN	filters	48
	Kernel_size	4
	pooling strategy	1D Max Pooling
	layers	2
BiGRU	units	64
	layers	2
Regularization	dropout rate	0.2
AT	type	Scaled Dot-Product
Training	learning rate	0.001
	batch size	32
	epochs	200
	optimizer	Adam

). For BI prediction, the training set yielded an R² of 0.984, an MAE of 2.0832, and an RMSE of 3.1295. The test set demonstrated equally robust performance, achieving an R² of 0.969, an MAE of 6.3384, and an RMSE of 12.5206. The regression-fitting curves for both parameters showed strong consistency with actual observations in trend direction and fluctuation characteristics, accurately capturing the practical variation patterns of the BI (Figure 8).

To further investigate the error characteristics and assess potential model bias, a residual distribution analysis was conducted (Figure 9). The results show that the residuals for both the training set (Well ZG1) and the independent test set (Well ZG2) are symmetrically distributed and strictly centered around zero. The overall normal distribution of residuals demonstrates that the model maintains robust generalization capability despite the inherent geological variations between different wells (Figure 9).

To rigorously assess the model’s generalization capability and ensure reliable and stable evaluation, we adopted a hierarchical validation strategy. Specifically, a 10-fold cross-validation procedure was implemented exclusively using the data from Well ZG1 to optimize the model’s hyperparameters and provide an objective measure of internal stability [26]. The ZG1 dataset was randomly partitioned into 10 mutually exclusive folds; in each iteration, nine folds were combined for training and one was reserved for validation, ensuring that each data point from ZG1 served as the validation set exactly once. Once the optimal architecture was finalized, Well ZG2 was held out as an entirely independent blind test well to evaluate the model’s performance on truly unseen stratigraphic data. The mean performance metrics obtained from the 10-fold cross-validation are summarized in

Table 6. 10-fold cross-validation results.

Fold Number	R2	RMSE	MAE
Fold 1	0.956	14.3825	6.9725
Fold 2	0.962	13.1185	6.4578
Fold 3	0.949	14.8529	7.2145
Fold 4	0.97	11.8826	6.2276
Fold 5	0.958	13.8684	6.7751
Fold 6	0.967	12.9924	6.3955
Fold 7	0.953	14.4526	7.0023
Fold 8	0.961	13.2574	6.6245
Fold 9	0.958	13.9035	6.7812
Fold 10	0.969	12.0532	6.3497

.

Through 10-fold cross-validation, the model demonstrated outstanding performance metrics: an average R² of 0.96, RMSE of 13.4764, and an MAE of 6.68. The results indicate that the model maintains robust predictive performance across diverse data partitioning scenarios, fully validating its exceptional robustness and stability.

5.3. Other Model Predictions

To rigorously evaluate the predictive performance and robustness of the proposed CNN-BiGRU-AT model, several widely recognized machine learning algorithms—including XGBoost, SVM, CNN, and LightGBM—were selected as benchmarks. Additionally, a CNN-BiGRU hybrid model was constructed to validate the attention mechanism’s enhancement effect on the CNN-BiGRU architecture [27]. Based on these algorithms, we established separate predictive models for the brittleness index, with the predicted results shown in Figure 10 and Figure 11.

To comprehensively evaluate the feasibility and applicability of the proposed hybrid model, we designed and conducted systematic comparative experiments [28], as shown in

Table 7. Comparison of BI prediction experimental results across different models.

Model	R2		RMSE		MAE
	Training	Testing	Training	Testing	Training	Testing
CNN-BiGRU-AT	0.984	0.969	3.1295	12.5206	2.0832	6.3384
CNN-BiGRU	0.945	0.92	3.8526	15.5241	2.4221	7.6135
XGBoost	0.902	0.862	5.3218	25.1677	3.0204	10.8832
SVM	0.887	0.85	8.8521	28.1803	4.3575	13.452
CNN	0.908	0.879	5.0235	23.156	2.7856	9.5945
LightGBM	0.913	0.883	4.4835	21.0387	2.5964	8.3752

and Figure 12. After training and validating six models, R², RMSE, and MAE were computed. For the training set, the R² values for CNN-BiGRU-AT, CNN-BiGRU, XGBoost, SVM, CNN, and LightGBM were 0.984, 0.945, 0.913, 0.902, 0.887, and 0.908, respectively; For the test set, the R² values for CNN-BiGRU-AT, CNN-BiGRU, XGBoost, SVM, CNN, and LightGBM were 0.969, 0.92, 0.883, 0.862, 0.85, and 0.879, respectively. A high R² value during the training phase indicates that the model has adequately learned the intrinsic patterns present in the training dataset. Similarly, a high R² during testing indicates that the model has successfully extracted the essential features of the data, enabling it to generalise well to new, unseen samples and demonstrating strong generalisation [29].

As shown in

Table 8. Comprehensive comparison of BI prediction models.

Model	R2	MAE	RMSE	Complexity	Training Time	Inference Time
CNN-BiGRU-AT	0.969	6.3384	12.5206	high	200 epochs, ~1.5 h	~0.45 s
CNN-BiGRU	0.92	7.6135	15.5241	moderate	200 epochs, ~1.2 h	~0.38 s
LightGBM	0.883	8.3752	21.0387	low	~12 min	~0.04 s
XGBoost	0.862	10.8832	25.1677	low	~10 min	~0.07 s
CNN	0.85	9.5945	23.156	moderate	200 epochs, ~1.0 h	~0.21 s
SVM	0.879	13.452	28.1803	low	~5 min	~0.12 s

, in addition to accuracy metrics (R², MAE, RMSE), we evaluated the models’ computational complexity and efficiency. The CNN-BiGRU-AT model, while more complex than other approaches, provides superior predictive accuracy and stability across wells. Simpler models, such as SVM and XGBoost, require significantly less computational resources but exhibit lower predictive performance. The proposed hybrid framework exhibits relatively high computational complexity, requiring approximately 1.5 h to complete 200 training epochs. This training overhead is significantly larger than that of traditional machine learning algorithms such as XGBoost (~10 min) or LightGBM (~12 min). However, in the context of deep shale gas engineering, this trade-off is highly justified.

First, model training is inherently an offline, one-time expenditure. Given that drilling campaigns and core acquisition operations often span several months, a 1.5 h computational investment before field deployment is practically negligible. Second, and most critically for industrial applications, the CNN-BiGRU-AT model’s online inference time is extremely efficient, averaging approximately 0.45 s to generate a continuous brittleness profile for a well-logging sequence. This rapid execution speed fully satisfies the low-latency constraints required for real-time, on-site logging interpretation and dynamic fracturing decision-making.

Finally, the substantial gain in predictive accuracy firmly validates the added architectural complexity. While simpler models like LightGBM require less computational overhead, their predictive accuracy (R² = 0.883) is insufficient for resolving the extreme vertical heterogeneity of deep shale. In contrast, the CNN-BiGRU-AT model achieves a commanding R² of 0.969. In highly cost deep shale gas development, this enhanced precision translates directly into optimized perforation cluster placement and a tangible reduction in ineffective stimulation stages. Therefore, the superior geomechanical resolution provided by the hybrid model far outweighs its initial training cost, making it a highly robust and viable tool for practical deployment.

5.4. Performance Comparison of CNN-BiGRU-AT with Different Optimization Algorithms

As illustrated in Figure 13 and Figure 14, among the three intelligent optimization algorithms (Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Cuckoo Search (CS)), the CNN-BiGRU-AT model optimized by the CS algorithm achieved the best predictive performance for the BI, yielding an R² of 0.915, an RMSE of 13.9171, and an MAE of 8.2752. Although the performances of GA and PSO were slightly inferior, their R² values consistently exceeded 0.8.

The CNN-BiGRU-AT model optimized by the PLO algorithm demonstrates a substantial improvement in brittleness index predictive performance; specifically, the R² value improves by 0.054 compared to the CS-optimized version. Furthermore, the PLO algorithm exhibits superior convergence efficiency, requiring only 72 iterations to identify the global optimal hyperparameter configuration for the CNN-BiGRU-AT model. Compared with PSO (197 iterations), GA (163 iterations), and CS (125 iterations), the iteration counts are reduced by 63.5%, 55.8%, and 42.4%, respectively, indicating a significant advancement in optimization efficiency.

5.5. Validation of the Results

In the analysis of continuous well-logging data, the dense sampling interval (0.125 m in this study) inevitably leads to strong geophysical similarity between adjacent data points along the vertical trajectory, known as depth-wise autocorrelation. While this inherent correlation provides the exact physical foundation for the BiGRU module to extract stratigraphic sequential dependencies, it simultaneously introduces a potential pitfall for objective model evaluation. If a conventional random split strategy is employed to partition the dataset, test samples are highly likely to be spatially adjacent to the training samples. This proximity triggers “data leakage,” leading to an artificially inflated prediction accuracy that masks the risk of poor generalization when the model encounters entirely new geological environments.

To further evaluate the model’s practical generalization capability, following the successful application of the CNN-BiGRU-AT hybrid model to achieve high-precision predictions for wells ZG1 and ZG2 within the study area, the model was deployed to forecast two additional experimental wells (ZG3 and ZG4) that had not been utilized in the modeling process. The brittleness indices for wells ZG3 and ZG4 were predicted using the proposed hybrid model (CNN-BiGRU-AT). Results demonstrate that, compared to single models, the proposed hybrid model exhibits outstanding stability and reliability, with coefficient of determination (R²) values consistently exceeding 0.9 (Figure 15 and Figure 16). This fully validates the CNN-BiGRU-AT model’s capability to efficiently and accurately predict the brittleness index within the target study area.

Beyond statistical accuracy, these continuous, high-precision BI profiles provide crucial support for reservoir characterization and hydraulic fracturing optimization in the Zigong block. In deep shale reservoirs characterized by pronounced vertical heterogeneity and elevated in situ stress, the mechanical contrast between adjacent strata directly dictates hydraulic fracture behavior. Formations with higher predicted BI are more prone to overcoming principal stress constraints, enabling natural fractures to activate and form complex, multi-directional fracture networks, thereby maximizing the stimulated reservoir volume. Conversely, intervals with lower BI tend to undergo plastic deformation, often resulting in unidirectional fracture propagation and significant energy dissipation.

Crucially, our CNN module’s ability to capture abrupt lithological transitions provides profound geological insights into vertical fracture containment. The sharp geomechanical boundaries between highly brittle shale and adjacent ductile mudstone layers frequently act as stress barriers. These barriers arrest the vertical growth of hydraulic fractures, ensuring that stimulation energy remains concentrated within the target payload.

Consequently, the predicted BI serves as a vital quantitative indicator that seamlessly integrates into the on-site decision-making workflow for “engineered completions”. Field engineers can utilize the real-time BI profiles generated from logging data to optimize stage and cluster spacing. Specifically, perforation clusters can be targeted and grouped in high-BI “sweet spots” to maximize fracture-initiation efficiency. At the same time, low-BI (ductile) isolation zones can be skipped to prevent energy dissipation. Furthermore, for ultra-high-BI sections, pumping strategies can be adjusted by using lower-viscosity slickwater and smaller-mesh proppants to activate micro-fractures; whereas in moderately brittle zones, hybrid fluids and larger proppants might be selected to ensure main fracture conductivity. Thus, the CNN-BiGRU-AT model demonstrates significant practical value by bridging machine learning and field geomechanics to reduce operational costs and enhance deep shale gas recovery.

6. Conclusions

This paper presents a hybrid model, CNN-BiGRU-AT, for predicting BI based on logging data. By synergistically integrating CNN, AT, and BiGRU, we have developed a more precise predictive model. Using the deep shale reservoirs in the ZG block as a case study, extensive comparative experiments and performance evaluations were conducted, leading to the following conclusions:

(1)

A robust, data-driven hybrid framework has been developed to predict the BI in complex deep shale reservoirs. Based on the Polar optimisation algorithm, the CNN-BiGRU-AT model is employed to forecast brittleness indices. The training and testing datasets for brittleness index prediction achieved R² values of 0.984 and 0.969, respectively, with MAE values of 2.0832 and 6.3384, respectively. This hybrid model leverages the CNN’s ability to learn convolutional kernels to precisely capture localized critical information within the logging-curve input parameters, effectively filtering out noise in deep shale reservoir data. The BiGRU component exhaustively captures the bidirectional sequential dependencies within geological parameters. Furthermore, integrating an AT dynamic adjusts the feature weights of input logs, highlighting the geophysical parameters that strongly correlate with rock-mechanical responses.

(2)

The proposed hybrid model successfully integrates the strengths of the PLO, CNN, BiGRU, and AT, demonstrating nice predictive efficacy and achieving optimal performance in brittleness index forecasting. Compared to other predictive models, it exhibits lower MAE and RMSE values, achieves a higher R² coefficient, and demonstrates nice predictive accuracy, offering considerable practical value. This methodology provides a practical, data-driven framework for characterising deep shale reservoirs, offering a valuable reference for future investigations into modelling complex geomechanical parameters.

(3)

Although the hybrid model exhibits excellent predictive performance, several inherent limitations must be objectively recognized to guide its practical field deployment. First, the model possesses an intrinsic dependence on the dataset. Its network weights and PLO-optimized hyperparameters are specifically tailored to the sedimentary environment, mineralogical characteristics, and high in situ stress field of the Longmaxi Formation in the ZG block. Regarding cross-region transferability, the pre-trained model cannot be directly applied to other shale basins. When deploying this framework in geological settings with varying conditions, the model must be retrained on local core data, or transfer learning techniques should be applied to adapt it to new geomechanical benchmarks. Second, the proposed model is inherently sensitive to the quality of logging data. Although the spatial filtering capability of CNN can effectively suppress minor environmental noise, the accuracy of BI prediction relies heavily on the fidelity of input acoustic logging and elastic parameter data. Under poor borehole wall conditions, logging instruments may record non-geological abnormal signals. If such physical artifacts are not strictly eliminated during data preprocessing, they will propagate through the neural network and substantially reduce the reliability of brittleness evaluation. Future research will focus on integrating highly robust outlier detection algorithms and transfer learning mechanisms to further improve the adaptability of the proposed framework across diverse and complex geological domains.