Research and Application of Conditional Generative Adversarial Network for Predicting Gas Content in Deep Coal Seams

Abstract

Accurate assessment of coalbed methane (CBM) content is essential for characterizing subsurface reservoir distribution, guiding well placement, and estimating reserves. Current methods for determining coal seam gas content mainly rely on direct laboratory measurements of core samples or indirect interpretations derived from well log data. However, conventional coring is costly, while log-based approaches often depend on linear empirical formulas and are restricted to near-wellbore regions. In practice, the relationships between elastic properties and gas content are highly complex and nonlinear, leading conventional linear models to produce substantial prediction errors and inadequate performance. This study introduces a novel method for predicting gas content in deep coal seams using a Conditional Generative Adversarial Network (CGAN). First, elastic parameters are obtained through pre-stack inversion. Next, sensitivity analysis and attribute optimization are applied to identify elastic attributes that are most sensitive to gas content. A CGAN is then employed to learn the nonlinear mapping between multiple fluid-sensitive seismic attributes and gas content distribution. By integrating multiple constraints to refine the discriminator and guide generator training, the model achieves accurate gas content prediction directly from seismic data. Applied to a real dataset from a CBM block in the Ordos Basin, China, the proposed CGAN-based method produces predictions that align closely with measured gas content trends at well locations. Validation at blind wells shows an average prediction error of 1.6 m³/t, with 83% of samples exhibiting errors less than 3 m³/t. This research presents an effective and innovative deep learning approach for predicting coalbed methane content.

1. Introduction

The quantitative seismic prediction of coalbed methane (CBM) content plays a crucial role in oil and gas exploration and production, directly influencing well placement strategies and resource evaluation [1,2,3]. Current approaches to estimating CBM content primarily depend on core desorption experiments and well log interpretation. While core analysis offers accurate measurements, it is expensive and impractical for seismic prediction in unexplored areas. Seismic-based prediction methods typically require establishing a relationship between gas content and elastic parameters—such as P-wave velocity, S-wave velocity, and density [4,5]. These methods often rely on petrophysical templates derived from log data to infer gas content. However, the linear approximations commonly used in such models fail to capture the complex nonlinear behavior of actual reservoirs, leading to limited predictive accuracy. Consequently, there is a pressing need to develop high-precision seismic prediction techniques to improve CBM content estimation.

Significant efforts have been made to enhance CBM content prediction. Ramos [6] pioneered the application of AVO analysis and modeling for characterizing fractured CBM reservoirs. Cui [7] and Tang [8] integrated azimuthal anisotropy analysis, spectral decomposition, and wave impedance inversion to identify CBM enrichment zones. Chen [9,10] reported that CBM reservoirs exhibit only Class IV AVO anomalies, while Chen [11] identified density and shear modulus as key sensitive parameters for sweet spot detection. The latter also successfully applied seismic attribute analysis to predict CBM content in the Ordos Basin. Huo [12] used pre-stack inversion based on an assumed linear relationship between elastic parameters and gas content for qualitative prediction, and Zhang [13] achieved high correlation using the P + G attribute from AVO analysis. Although methods such as AVO analysis [14,15,16], seismic attribute prediction [17,18,19], and elastic parameter inversion [20,21] have been widely used, they predominantly rely on linear assumptions and tend to produce generalized results that fall short of the resolution required for detailed reservoir characterization. In recent years, advances in deep learning have opened new avenues for high-precision reservoir prediction [22,23]. Hampson [24] successfully applied probabilistic neural networks (PNN) to predict porosity by integrating multiple seismic attributes. Ross [25] demonstrated that neural network-based AVO attributes provide superior accuracy and resolution compared to conventional methods for mapping reservoir distribution and sand thickness. Zhong [26] used convolutional neural networks (CNN) with well log data to predict permeability, outperforming genetic algorithms. Kim [27] showed that artificial neural network (ANN) inversion offers higher resolution than least-squares inversion in both synthetic and real data examples. Chen [28] introduced an iterative CNN architecture for simultaneous wavelet estimation and high-resolution reflectivity inversion. Chen [29] applied recurrent neural networks (RNN) to porosity prediction, achieving better results than support vector machines (SVM) and random forests (RF). More recently, Sun [30] employed Mixture Density Networks (MDN) to predict water saturation in sandstones with uncertainty quantification. These studies underscore the considerable potential of deep learning techniques in reservoir parameter prediction and provide valuable insights for predicting gas content in deep coal seams.

In this paper, we propose a novel method for predicting gas content in deep coal seams using a conditional generative adversarial network. The approach begins with pre-stack inversion to obtain elastic parameters, followed by sensitivity analysis and attribute optimization to identify predictive factors. A CGAN is then trained on extensive well log data from the study area, incorporating multiple geological constraints to establish a nonlinear mapping from seismic attributes to gas content. Validation with blind well data confirms that the method achieves high predictive accuracy, offering a robust and innovative technical solution for detailed reservoir characterization and development optimization.

2. Methodology

2.1. Generative Adversarial Networks

Based on game theory, Generative Adversarial Networks (GAN) [31] represent one of the most innovative concepts in the field of machine learning in recent years. In seismic exploration, GANs have been widely applied to various tasks, including seismic facies classification [32], velocity model building [33], seismic data interpolation [34], image processing [35], and seismic interpretation [36,37]. The basic architecture of a GAN is illustrated in Figure 1. In this study, all GAN-based models were implemented and trained using TensorFlow (v2.18.0). This framework was developed and is maintained by Google (Mountain View, CA, USA). It consists of two competing neural network modules: a Generator (G) and a Discriminator (D). The Generator aims to learn the distribution $p_g$ of the real data x, constructing a mapping function $G(z;{\theta }_g)$ from a prior noise distribution $p_z(z)$ to the data space. The Discriminator receives both real data and generated samples $G(z;{\theta }_g)$ as input and outputs a scalar probability value, estimating the likelihood that the input data originates from the real data x rather than from the Generator $G(z;{\theta }_g)$. Here, ${\theta }_g$ and ${\theta }_d$ represent the trainable parameters of G and D, respectively. During training, the G and the D are optimized alternately:

• The Discriminator is fixed, and the parameters ${\theta }_g$ of the Generator are adjusted to minimize the loss function $\log (1-D(G(z)))$.
• The Generator is fixed, and the parameters ${\theta }_d$ of the Discriminator are adjusted to maximize its ability to distinguish real samples from generated ones, represented by maximizing $\log D(x)$.

The original training objective of GANs can be expressed by the following minimax function $V(G,D)$:

$$\underset{G}{\min } \underset{D}{\max }V(D,G)={\mathrm{E}}_{x\sim p_{data}(x)}[\log D(x)]+{\mathrm{E}}_{z\sim p_z(z)}[\log (1-D(G(z)))]$$

(1)

2.2. Conditional Generative Adversarial Networks

If conditional control information is introduced into both the Generator and Discriminator of a GAN, enabling the generation of corresponding outputs based on specific input conditions, the architecture can be extended into a Conditional Generative Adversarial Network (CGAN) [38]. In this study, we incorporate gas-sensitive factors of the coal seam as conditional input to the generator, thereby constraining the generation process and guiding the network training. Simultaneously, the discriminator D is trained to distinguish between real and generated samples, further guiding the optimization of the generator. Upon completion of training, the corresponding gas content can be obtained by inputting the sensitive factors into the generator. Figure 2 illustrates the CGAN architecture used for gas content prediction. In the generator, the gas-sensitive factors x serve as the conditional input. The generated gas saturation $G(x;{\theta }_g)$ is concatenated with x and fed into the discriminator. The discriminator employs three conditional control strategies to enhance its discriminative capability:

• The sensitive factors x input to the generator G and the corresponding generated gas saturation $G(x;{\theta }_g)$;
• The sensitive factors x₁ from the real data and their corresponding true gas saturation y₁;
• The sensitive factors x₂ from the real data paired with an incorrect gas saturation ${\widehat{y}}_2$ (i.e., mismatched samples).

The training objective of the CGAN can be expressed as the following minimax function $V_c(G,D)$:

$$\underset{G}{\min } \underset{D}{\max }{V}_{\mathrm{c}}(D,G)={\mathrm{E}}_{x,y\sim p_{data}(x,y)}[D(x_1,y_1)+(1-D(x,G(x)))+(1-D(x_2,{\widehat{y}}_2))]+{\mathrm{E}}_{x,y\sim G}[D(x,G(x))+\sqrt{{(y-G(x))}^2}]$$

(2)

The detailed workflow of the CGAN algorithm is summarized in Algorithm 1. Both the generator and discriminator are constructed using an encoder–decoder architecture. The generator begins with three deconvolutional layers that extract 256, 128, and 64 feature maps, respectively. These are followed by three convolutional layers producing 128, 256, and 1 feature maps. The network concludes with two fully connected layers. The discriminator consists of three convolutional layers extracting 256, 128, and 64 feature maps, followed by three deconvolutional layers generating 128, 256, and 1 feature maps, and ends with two fully connected layers. Traditional regression methods typically employ L2 distance as a loss metric, which assumes independence among variables. However, seismic waveforms—as time-series data—encapsulate integrated information from subsurface strata, where variables exhibit strong intrinsic correlations. Classical GANs utilize Jensen-Shannon (JS) divergence for optimization [39], which captures interdependencies among variables by measuring similarity between the distributions of generated and real samples. A significant limitation arises when the JS divergence reaches the constant log2: the distributions of real and generated samples often exhibit no overlap in high-dimensional space, resulting in vanishing gradients and halting parameter updates. This leads the generator to produce identical outputs for different inputs, a failure mode known as mode collapse. To mitigate this issue, we incorporate the Wasserstein distance [40,41], which effectively measures the distance between non-overlapping distributions in high-dimensional space. Several modifications were made to the original GAN framework to accommodate the Wasserstein distance:

• The final sigmoid activation function in the discriminator—designed for classification—was removed to adapt the model to regression tasks compatible with the Wasserstein metric. Logarithmic operators in the loss functions of both generator and discriminator were also eliminated;
• Gradient penalty techniques [42] were introduced to improve training stability and promote convergence;
• To address instability in the discriminator’s loss gradients, the RMSProp optimizer was adopted in place of Adam. An initial learning rate of 0.002 was used alongside a dynamic exponential decay strategy. The Leaky ReLU activation function [43] was selected for all layers to further enhance gradient flow.

Algorithm 1. CGANs algorithm

Input: ${\left\{{\mathit{x}}^j\right\}}_{j=1}^n$: Sensitivity factors, ${\left\{{\mathit{y}}^j\right\}}_{j=1}^n$: Gas saturation Notation: ${\mathit{\theta }}_g$: parameters in generator, ${\mathit{\theta }}_d$: parameters in discriminator, h: batch size, num: number of training sets. $\eta$: learning rate of network. 1: Prepare training sets: 124 well logs in working area. 2: Initialization: Initialize ${\mathit{\theta }}_g$ for Generator and ${\mathit{\theta }}_d$ for discriminator. 3: For T = 1:1: epoch do     For t = 1:1: num/h do      3.1 Fixing generator and updating discriminator:      Sampling n positive examples $\left\{\left({\mathit{x}}^1,{\mathit{y}}^1\right),\left({\mathit{x}}^2,{\mathit{y}}^2\right),\dots ,\left({\mathit{x}}^n,{\mathit{y}}^n\right)\right\}$ from database; Sampling n objects $\left\{{\widehat{\mathit{y}}}^1,{\widehat{\mathit{y}}}^2,\dots ,{\widehat{\mathit{y}}}^n\right\}$ from database;      Obtaining generated $\left\{\left({\tilde{\mathit{y}}}^1,{\mathit{x}}^1\right),\left({\tilde{\mathit{y}}}^2,{\mathit{x}}^2\right),\dots ,\left({\tilde{\mathit{y}}}^n,{\mathit{x}}^n\right)\right\}$, ${\tilde{\mathit{y}}}^n=G\left({\mathit{x}}^n\right)$;      Updating discriminator parameters ${\mathit{\theta }}_d$ to minimize:         $\tilde{V}({\mathit{\theta }}_d)={\displaystyle \frac{1}{n}}{\sum }_{j=1}^{n}D({\mathit{x}}^j,{\mathit{y}}^j)-{\displaystyle \frac{1}{n}}{\sum }_{j=1}^{n}1-D({\mathit{x}}^j,G({\mathbf{x}}^j\left)\right)$                     $-{\displaystyle \frac{1}{n}}{\displaystyle \sum _{j=1}^n}1-D({\mathit{x}}^j,{\widehat{\mathit{y}}}^j)$         ${\mathit{\theta }}_d\leftarrow {\mathit{\theta }}_d-\eta \mathsf{\nabla }\tilde{V}\left({\mathit{\theta }}_d\right)$      3.2 Fixing discriminator and updating generator:      Updating generator parameters ${\mathit{\theta }}_g$ to minimize:         $\tilde{V}({\mathit{\theta }}_g)={\displaystyle \frac{1}{n}}{\sum }_{j=1}^{n}D\left(G\right({\mathit{x}}^j\left)\right)+{\displaystyle \frac{1}{n}}{\sum }_{j=1}^n\sqrt{({\mathit{y}}^j-G({\mathit{x}}^j){)}^2}$         ${\mathit{\theta }}_g\leftarrow {\mathit{\theta }}_g-\eta \mathsf{\nabla }\tilde{V}\left({\mathit{\theta }}_g\right)$     End for End for

3. Case Study

3.1. Target Formation Overview

The study area is situated in the northeastern sector of the Yishan Slope, Ordos Basin. The primary target intervals are the Lower Permian Benxi Formation and the Upper Carboniferous Taiyuan Formation. As illustrated in Figure 3, stratigraphic correlation and well-to-seismic calibration reveal that the coal-bearing strata in this region generally display seismic reflections with moderate-to-strong amplitude and high continuity. The lithology of the target intervals is complex, consisting mainly of coal seams, limestone, sandstone, and mudstone. Among these, the coal seams are distinguished by their characteristic physical properties—low density and high acoustic interval transit time—resulting in a pronounced impedance contrast with the overlying and underlying formations. Consequently, the coal seams are typically identifiable on seismic profiles as reflections exhibiting low frequency, high continuity, and strong amplitude. Rock physics analysis indicates that coal seams are characterized by low velocity, low density, and elevated natural gamma ray readings. Their P-wave impedance is markedly lower than that of surrounding rocks such as sandstone, mudstone, and limestone, allowing effective lithological discrimination based on impedance contrast. Based on pre-stack inversion to obtain P-wave velocity, S-wave velocity, and density, a series of elastic attribute volumes can be further derived through mathematical transformations.

3.2. Sensitivity Analysis and Attribute Optimization

Based on measured gas content data from well logs in the study area, a systematic sensitivity analysis was performed to assess the relationship between gas content and various elastic parameters—including both individual properties and combined attributes. This analysis was followed by attribute optimization to identify the most gas-sensitive factors for input into the GAN. Figure 4a–f present the correlations between gas content per ton (TGAS) of coal and the following parameters: P-wave velocity ($Vp$), S-wave velocity ($Vs$), density ($\rho$), Vp/Vs ratio ($Vp/Vs$), P-wave impedance ($Zp$), S-wave impedance ($Zs$). The results reveal a significant negative correlation between gas content and density, P- and S-wave impedance. Negative correlations are also observed with P- and S-wave velocities, though these are comparatively weaker. The $Vp/Vs$ shows the weakest correlation among all parameters. Overall, gas content still exhibits a weak correlation with pre-stack inversion-derived elastic parameters and their combinations. This observation elucidates the underlying reason for the limited accuracy of traditional gas-bearing property estimation methods based on petrophysical templates.

To further screen for effective features, additional elastic factors were constructed based on the elastic parameters, including Young’s modulus ($E$), bulk modulus ($K$), shear modulus ($\mu$), shear modulus multiplied by density ($\mu \times \rho$), Lamé coefficient ($\lambda$), and Lamé coefficient multiplied by density ($\lambda \times \rho$). A deep neural network (DNN) was employed for attribute optimization. The input features consisted of elastic parameters and their combinations, with gas content as the output. The dataset was divided into training and validation subsets. Network parameters were optimized using the training set, and prediction error was evaluated on the validation set. As shown in Figure 5, the horizontal axis represents the number of input attributes, and the vertical axis represents the prediction error for the corresponding number of attribute combinations. The black and red curves indicate errors on the full dataset and the validation set, respectively. The error decreases as the number of attributes increases, but begins to rise on the validation set once the number exceeds eight—suggesting potential overfitting. Additionally, an excessive number of features substantially increases computational demands. Balancing prediction accuracy and efficiency, eight key attributes were selected as input to the generative adversarial network based on their contribution to error reduction. The optimized attribute combination is detailed in

Table 1. Optimal selection of eight attributes for generative adversarial network training.

Number	Attributes	Training Error (%)	Validation Error (%)
1	Bulk modulus	2.019	2.027
2	Vp/Vs ratio	2.004	2.016
3	Intercept-Gradient Attributes	1.996	2.014
4	P-wave impedance	1.988	2.011
5	Lamé constant × density	1.981	2.009
6	Density	1.976	2.008
7	Lamé constant	1.972	2.008
8	shear modulus × density	1.968	2.007

.

3.3. CGAN-Based Gas Saturation Prediction

In this section, the optimized attribute combination was employed as a conditional input to train the CGAN for predicting gas content in deep coal seams. To evaluate the model’s generalization ability, 12 wells were reserved as blind tests. Figure 6 presents the network’s training performance across multiple wells, where yellow shading indicates coal seams, the black solid line denotes measured gas content, and the red solid line represents the CGAN predictions. The results indicate that the model achieves excellent fitting performance on the training well segments. Figure 7 further demonstrates the prediction outcomes on blind-test wells from the validation set. The CGAN model maintains high predictive accuracy across these unseen samples, confirming its strong generalization capability. The trained model was subsequently applied to predict the spatial distribution of gas content throughout the study area. As illustrated in Figure 8, gas content is represented by a color gradient from blue (low) to red (high). The predicted distribution aligns closely with well-based interpretations, affirming the reliability and applicability of the CGAN method for quantitative gas content prediction.

A comparison with coal seam thickness predictions reveals a significant positive correlation between gas content and seam thickness. Regions with thicker coal seams—such as the central, southeastern, and northern parts of the study area—exhibit more stable structural conditions, which are conducive to gas accumulation and preservation, resulting in higher gas content. In contrast, the western area is characterized by thinner, more discontinuous coal seams with numerous partings, leading to inferior gas-bearing properties. Error statistics from the 12 blind-test wells (

Table 2. Prediction error statistics of validation datasets.

Well Name	Measured (m3/t)	Predicted (m3/t)	Absolute Error (m3/t)	RMSE (m3/t)
W2	14.2	15.9	1.7	1.82
W4	10.2	14.4	4.2	4.35
W12	14.6	15.0	0.4	0.51
W14	14.5	15.3	0.8	0.86
W17	10.8	14.9	4.1	4.37
W18	13.7	15.0	1.3	1.42
W19	13.5	14.0	0.5	0.52
W26	15.1	15.2	0.1	0.13
W27	17.5	16.5	1.0	1.07
W32	12.1	14.7	2.6	2.85
W35	17.4	15.6	1.8	2.03
W36	12.5	12.4	0.1	0.12
Average error			1.6	1.67

) show an average root mean square error (RMSE) of 1.67 m³/t, a maximum absolute error of 4.12 m³/t, and 83% of predictions falling within 3 m³/t of the measured values. These metrics confirm that the deep learning-based gas content prediction method, which integrates multiple seismic attributes through CGAN, provides high prediction accuracy and strong practical utility.

4. Discussion

This study identifies several aspects that merit further investigation and improvement. First, from a theoretical standpoint, directly inverting gas saturation from seismic waveforms could potentially circumvent the cumulative errors inherent in the conventional two-step workflow, which first inverts for elastic parameters. However, seismic waveforms are predominantly influenced by lithology and fundamental elastic properties—such as P-wave velocity, S-wave velocity, and density—which constitute the structural and lithological framework of the seismic response. As a fluid property, gas saturation does not directly govern seismic signals. Rather, its influence is indirect, mediated through fluid substitution effects that modify the bulk modulus and density of the rock. These alterations subsequently affect elastic parameters (e.g., P-wave velocity and impedance), which in turn perturb the seismic response. Given that the effect of gas saturation on seismic waveforms is generally subtle and susceptible to obscuration by noise, direct saturation inversion remains a considerable challenge and represents a critical direction for future research. Second, the deep learning approaches applied in this study currently operate without explicit guidance from physical principles. Although data-driven, their prediction process lacks strong interpretability, and their generalization capability may be constrained when applied beyond the training distribution. Future work should focus on integrating rock physics models with artificial intelligence techniques to develop hybrid methods that embed physical constraints into deep learning frameworks, for example, combining deep coal seam rock physics models, AVO forward modeling (such as Zoeppritz equations), and neural networks. Such an approach would not only improve the mechanistic rationality of predictions but also enhance the robustness and reliability of gas content estimation models.

5. Conclusions

This study presents a novel method for predicting gas content in deep coal seams using a conditional generative adversarial network. The proposed approach effectively estimates gas content and offers critical support for well placement design and reservoir development optimization. The workflow consists of three main stages: First, pre-stack inversion is applied to obtain key elastic parameters and delineate the spatial distribution of coal seams. Second, sensitivity analysis and attribute optimization are conducted to identify an optimal set of gas-sensitive factors. Finally, a CGAN model incorporating multiple geological constraints is constructed to achieve intelligent prediction of gas content. When applied to a real-world dataset from a coalbed methane block in the Ordos Basin, China, the method demonstrates a strong agreement between predicted and measured gas content trends at well locations. Validation at blind wells shows an average prediction error of 1.6 m³/t, with 83% of predictions falling within 3 m³/t of the measured values. These results indicate that the CGAN-based method offers both high accuracy and practical utility. This research provides a new, effective technical framework for predicting coalbed methane content, with potential value for application in similar geological settings.