Benzene at ambient temperature is a colorless and transparent fluid characterized by a density of approximately 880 kg/m³. The saturated vapor pressure of liquid benzene demonstrates variation across different temperatures (Figure 1). Prolonged or high levels of exposure to liquid benzene can adversely affect health. A leakage resulting in the inhalation of benzene vapor can lead to symptoms such as headache, dizziness, drowsiness, causing severe neurological and liver damage, and being potentially fatal. Therefore, this paper aims to investigate the phenomenon of benzene leakage by developing a prediction model for the concentration and diffusion of heavy gas leakage.

The standard concentrations of Acute Exposure Guideline Levels (AEGLs), established by the US National Advisory Committee (NAC), were utilized to determine hazardous distances. AEGLs apply to the adverse effects associated with short-duration and sudden-onset chemical leakages (Zhao and Chen, 2014). AEGLs are categorized into three levels: AEGL-1, AEGL-2 and AEGL-3. Each level corresponds to a specific level of acute toxicity. Under these standards, AEGL-1, AEGL-2 and AEGL-3 thresholds, corresponding to the 10-min liquid benzene leakage, are 420 mg/m³, 6,500 mg/m³ and 31,000 mg/m³, respectively. The concentration limits associated with specific injury symptoms are outlined in Table 1.

This study examined an accident scenario involving a liquid benzene storage tank located within a chemical park. The tank, characterized by its horizontal orientation and a capacity of 135 m³, was maintained under ambient temperature and pressure conditions. The tank suffered a rupture due to the impact of an external object, forming a circular breach approximately 0.5 m above the ground, encircled by a 35 m radius cofferdam. Additionally, the internal and external factors that influence tank leakage are crucial to the study of gas leakage diffusion. Zhu et al. (2009) and Sun and Guo (2010) have discussed the significant effects of wind speed and atmospheric stability on gas diffusion. A summary of the current status of domestic and international research on leakage diffusion has been provided, and it has been demonstrated that leakage aperture, temperature and wind speed were important factors affecting gas diffusion (Zhou et al., 2012). Furthermore, Wang et al. (2023) constructed a liquid ammonia leakage prediction model based on environmental factors such as atmospheric stability, wind speed, and leakage aperture. Therefore, a range of values was selected for four factors: leakage aperture, wind speed, temperature, and atmospheric stability. These values are presented in Supplementary Table S2. The apertures considered were 100 mm 150 mm and 200 mm; wind speed ranged from 1 m/s to 6 m/s in 1 m/s increments. Temperatures were set at 20°C, 25°C, 30°C, 40°C and 50°C. Atmospheric stabilities were categorized as unstable, neutral and stable. The duration of leakage was set at 10 min. In total, 270 different scenarios were simulated, with the fundamental parameters of the leakage tank detailed in Supplementary Table S3.

The leakage rate of liquid benzene after a leakage is calculated using the Bernoulli Eq. 1 (Fu, 2008): Q L = C d A ρ 2 P − P 0 ρ + 2 g h   (1) where Q L represents the rate of liquid leakage, kg/s. C d , the liquid leakage coefficient, is taken as 0.65. A denotes the area of rupture, m². ρ signifies the density of the liquid, kg/m³. P and P 0 are the internal and ambient pressures, respectively, Pa. g represents the gravity acceleration at 9.81 m/s². h indicates the height of the liquid level above the rupture, m. Given that liquid benzene was stored at ambient conditions, where both the storage and ambient temperatures remained below its boiling point, flash and heat evaporation processes were precluded. This scenario led to the formation of a liquid pool on the ground. The subsequent evaporation of this pool was primarily driven by the air movement over its surface, and the mass evaporation rate is thus calculated as: Q v = α p M R T 0 u 2 − n 2 + n r 4 + n 2 + n (2) where Q v denotes the mass evaporation rate, kg/s. α and n represent the atmospheric stability coefficients. p specifies the vapor pressure at the surface of the liquid, Pa. M is the molar mass of the chemical, kg/mol. R stands for the gas constant, J/(mol·k). T 0 indicates the ambient temperature, K. u refers to the ambient wind speed, m/s. r is the radius of the liquid pool, m. The rate of mass evaporation varied dynamically with the radius of the liquid pool. In cases of the continuous leakage, the dynamics radius of the liquid pool, r t , as a function of time t , adhered to the following Eq. 3 (Nielsen et al., 1995). Ultimately, a CFD-based dynamic diffusion model of liquid benzene leakage has been developed. This model calculated the radius of the liquid pool and the corresponding evaporation rate per second throughout the 10-min leakage period under various environmental conditions. r t = t 9 π ρ 32 g Q L 3 3 4 (3)

(1) Multi-layer perceptron (MLP)

The Multi-Layer Perceptron (MLP), a form of feed-forward neural network, encompasses two main processes: forward and back propagation (Ehteram et al., 2022). During forward propagation, the input data is processed through the layers of network, guided by weights and biases, to generate the predicted output of the model layer by layer. Conversely, back propagation adjusts these parameters via gradient descent by computing the gradient of the loss function with respect to the weights and biases, thus refining predictions to more closely match the true values.

(2) Decision tree (DT)

The Decision Tree (DT), a tree-based methodology, can effectively capture nonlinear relationships and clearly illustrate the decision-making process of each feature within a structured tree format. Nonetheless, the DT model exhibits a high sensitivity to noisy data, which can be mitigated by employing a Random Forest model, which mitigates the impact of noise (Yu et al., 2019).

(3) Random Forest (RF)

The Random Forest (RF) model enhances efficacy and robustness by integrating multiple DTs into a strong evaluator. It operates by having each decision tree independently predict on the input data, with the final prediction being derived through a method of weighted averaging or voting, as represented by the Eq. 4 Breiman (2001): g x = f x + f 1 x + f 2 x + ⋯ + f n x (4) where g x represents the aggregate prediction from each simple decision tree f x . In constructing each decision tree, the RF model mitigates noise and overfits by employing bootstrap sampling, which means drawing from the training set with replacement (Wu and Zhao, 2013).

(4) eXtreme gradient boosting (XGBoost)

The eXtreme Gradient Boosting (XGBoost) model represents an advanced implementation of gradient boosting algorithms and stands as a noteworthy component in the EL models, playing a pivotal role in ensemble learning (EL) models due to its efficacy in capturing complex and nonlinear interactions (Chen and Guestrin, 2016). The core of the XGBoost model is a gradient boosting framework that sequentially constructs an ensemble of weak learners, typically decision trees, to minimize a differentiable loss function. What sets XGBoost apart is its efficient handling of sparse data and missing values, an aspect crucial for robustness in real-world data applications. It incorporates a sparsity-aware algorithm for handling missing data and employs a weighted quantile sketch for efficient approximate tree learning. To enhance generalization and mitigate overfitting, the XGBoost model integrates specific regularization mechanisms, including L1 (Lasso regression) and L2 (Ridge regression) penalties. These regularization terms add a penalization component to the objective function, effectively controlling the complexity of the model. The main formulas for the XGBoost model are as follows Eqs 5–7: O b j e c t i v e Θ = ∑ i = 1 n y i , y ^ i + ∑ k = 1 K Ω f k (5) l y i , y ^ i = y i − y ^ i 2 (6) Ω f k = γ T k + 1 2 α ∑ j = 1 T k w k j + 1 2 λ ∑ j = 1 T k w k j 2 (7)

In formula (5), the first term, ∑ i = 1 n y i , y ^ i aggregates the losses computed over all n samples, where l y i , y ^ i measures the discrepancy between the predicted y ^ i and the actual y i values, which is defined here as the square of the residuals. The second term, ∑ k = 1 K Ω f k , is the sum of regularization terms for K weak learners, typically decision trees, to control the complexity of the model. The term γ T k adds a penalty proportional to the number of leaf nodes T k in the tree k , with γ serving as a non-negative regularization parameter. This term restricts tree growth and aids in mitigating overfitting by penalizing excessive complexity. The expression 1 2 α ∑ j = 1 T k w k j denotes the L1 regularization (Lasso), which imposes a penalty on the absolute values of the leaf weights w k j . This promotes sparsity in the leaf weights, potentially reducing some to zero, thereby facilitating feature selection within the trees. Meanwhile, 1 2 λ ∑ j = 1 T k w k j 2 signifies the L2 regularization on the leaf weights w k j of the tree, with λ serving as the regularization coefficient.

(5) Light Gradient Boosting Machine (LightGBM)

The Light Gradient Boosting Machine (LightGBM) model, also an ML algorithm based on gradient boosting trees (Zhu J. Y. et al., 2023), employs an innovative histogram-based learning method that not only reduces computational complexity but also significantly enhances training efficiency on large datasets (Gao et al., 2020). By iteratively learning from gradient boosting trees, the LightGBM model consistently improves model performance, exhibiting robust generalization capabilities and effectiveness, particularly in addressing regression problems (Li Z. et al., 2021; Wei et al., 2021).

The typical workflow for applying ML models encompasses several critical steps (Bruha, 2000): data collection, data preprocessing, feature correlation analysis, parameter tuning, model training and validation.

This study generated various accident scenario hypotheses using the CFD model, with the CFD simulation data serving as the training datasets. For the accident scenario outlined in section 2.1.3, the CFD model was employed to simulate 270 different working conditions. This simulation generated concentration data at various downwind distances at 10-s intervals, culminating in a total of 515,160 datasets. The variables included in the analysis were time, leakage aperture, wind speed, temperature, atmospheric stability and downwind distance, with the concentration outcome (C1) serving as the target variable. These variables were normalized using Z-Score standardization. Atmospheric stability, a categorical variable, was converted into a numerical format using One-Hot encoding. Pearson correlation coefficient, designed by the letter ‘ P c ’, was employed to quantify the linear relationships between the variables. The correlation coefficient between each pair of variables was calculated using the following formula (8) (Shaik et al., 2024). To assess the model performance, a subset featuring specific conditions—200 mm leakage aperture, 6 m/s wind speed, 50°C temperature, and stable atmospheric stability—was selected for validation. The remaining data was divided into an 80% training set and a 20% testing set. Moreover, Bayesian optimization and 10-fold cross-validation were applied for parameter tuning and model training. Table 2 displays the hyperparameter range domains for each model and the optimization results achieved by the algorithm. P c = ∑ i = 1 n x i − x ¯ y i − y ¯ ∑ i = 1 n x i − x ¯ 2 ∑ i = 1 n y i − y ¯ 2 (8) where P c is the correlation coefficient. x i and y i denote the values of the two variables. x ¯ and y ¯ represent the means of the two variables. n signifies the number of samples.

To assess prediction accuracy for diffusion concentration within the ML algorithms, this study employed four principal metrics: the root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²) and index of agreement (IOA). The formulas are as follows Eqs 9–12 (Shaik et al., 2022; Shaik et al., 2023; Shaik et al., 2024): R M S E = 1 n ∑ i = 1 n P i − M i 2 (9) M A E = 100 % n ∑ i = 1 n P i − M i M i (10) R 2 = 1 − ∑ i = 1 n M i − P i 2 ∑ i = 1 n M i − M i ¯ 2 (11) I O A = 1 − ∑ i = 1 n M i − P i 2 ∑ i = 1 n ( P i − P i ¯ + | M i − M i ¯ 2 (12) where P i represents the value predicted by the ML model. M i denotes the value simulated by the CFD model. P i ¯ and M i ¯ correspond to the mean of ML predicted values and CFD simulated values, respectively, with n signifying the sample size.

Before providing accurate sample data for ML models, it is necessary to validate the reliability of the CFD model in simulating the diffusion of heavy gas leakage. The purpose of this study is to validate the efficacy of the PHOENICS software in simulating heavy gas leakage, specifically through the application of the renowned Burro series experiments. These experiments took place in a circular water tank, measuring 58 m in diameter and 1 m in depth, where the liquefied natural gas (LNG) was released at a temperature of −164°C (Koopman et al., 1982). The significant temperature difference between the released LNG and surrounding environment facilitated the rapid vaporization of LNG, resulting in the formation of a cold and heavy gas cloud, approximately 1.5 times heavier than air (Yu et al., 2018). Methane concentrations were measured using sensors located at distances of 58 m, 140 m, 400 m and 800 m downwind from the release point. The initial conditions of the Burro series experiments are comprehensively outlined in Supplementary Table S4.

(1) Physical model and governing equations

In this study, the computational domain was defined as 1,000 m × 300 m × 50 m. To enhance grid structure efficiency and minimize computational time, the domain was segmented into 200 × 100 × 25 using a gradient grid. The mesh independence analysis ensured that the CFD data remained consistent as the mesh size varied, as detailed in the Supplementary Text S1. Figure 2 illustrates the configuration of the detailed domain and grid setup within the CFD model. These modeling parameters were meticulously chosen to accurately simulate the heavy gas leakage scenario, laying a robust groundwork for subsequent analysis.

In this study, the Core module of the PHOENICS 6.0 software was used as the simulation platform. The turbulence model chosen was the widely used standard k-ε model within PHOENICS, with the specific equations given by Eqs 13, 14: ∂ ρ k ∂ t + ∂ ρ u j k ∂ x j = ∂ ∂ x j μ + μ t σ k ∂ k ∂ x j + P k − ρ ε (13) ∂ ρ ε ∂ t + ∂ ρ u j ε ∂ x j = ∂ ∂ x j μ + μ t σ ε ∂ ε ∂ x j + C 1 ε ε k P k − C 2 ε ρ ε 2 k (14) where μ t denotes the turbulent viscosity, kg/(m·s). u j indicates the velocity component in the j -direction, m/s, and x j corresponds to the spatial coordinate in that direction, m. μ is the molecular viscosity, kg/(m·s). σ k and σ ε are the Prandtl numbers associated with turbulence kinetic energy k and dissipation rate ε , respectively, with their values set at σ k = 1.0 and σ ε = 1.3. P k is the turbulence kinetic energy production term generated by the mean velocity gradient, m²/s³. C 1 ε and C 2 ε represent empirical constants taken as 1.44 and 1.92, respectively.

(2) Physical Properties

In the Properties section, set the ambient temperature to 35.4°C and the atmospheric pressure to 101,325 Pa. The Inverse Linear option was selected for the density setting to configure the density of the methane-air mixture, thereby accurately simulating the settling process of heavy gas, incorporating the impact of gravity was vital. Additionally, activate the gravity option Density Difference and set the gravitational acceleration to −9.81 m/s² in the Z direction.

(3) Boundary condition settings

The inlet boundary conditions of the model utilized the Wind property to define wind speed and direction. The index method ensured an accurate representation of the vertical gradient change in wind speed (Li and Tian, 2011). Given that the Burro series experiments were conducted in an open area without obvious obstacles, the effective roughness height in this study was set at 0.0002 m, and the wind profile index was chosen as 0.16.

(4) Inlet settings

A series of Inlet objects were selected to simulate the evaporation rates from the liquid pool. The leakage scenario was simplified to model the complete evaporation of LNG from a 58 m diameter liquid pool. The evaporation rate was approximated as the leakage rate, with the Mass Flow of the Inlet object set to 24.2 m³/min. Additionally, the solver variable C1 was added into the Models section, assigning a value of 1.0. The results of C1 were extracted after the completion of simulation and converted to the concentration of methane (CH₄) using calculation formula (15): C C H 4 = C 1 × ρ a × 10 6 (15) where C C H 4 represents the concentration of CH₄, mg/m³.

The Burro nine experiment was selected to evaluate the accuracy of the CFD model in simulating the diffusion of heavy gas leakage. Figure 3 illustrates the concentration distribution of the gas cloud at T = 80 s for the Burro nine experiment across two planes. Figure 3A shows the Y-Z plane at a distance of 140 m downwind, where the observed gas cloud extended approximately 60 m to the left and 28 m to the right. Conversely, the CFD simulation showed an extension of about 48 m on both sides, revealing a minor discrepancy between the simulated and observed spreads. This discrepancy is likely due to a deviation between the actual and simulated wind directions, as well as the uneven terrain at 140 m. This uneven terrain could account for the slightly elevated height of the gas cloud on the northern side compared to the southern side. Figure 3B illustrates to the X-Y plane at a height of Z = 1 m, where the simulated range of CFD is slightly narrower than the actual observed diffusion range. The violent phase change reaction occurring near the leakage source affected the concentration sensor at 57 m, resulting in a discontinuity in the 5% concentration contour. Zhang et al. (2015) used the FEM3 and CFD models to validate the Burro nine experiment, simulating the gas cloud extent on the Y-Z plane at a downwind distance of 140 m to be 53 m and 75 m, respectively. The farthest distances by the CFD model for volume concentrations of 5%, 2%, and 1% on the X-Y plane were about 190 m, 368 m, and 500 m. Figures 3A,B demonstrate that the gas cloud extent simulated by the CFD model adopted in this paper is reasonable. Additionally, the simulated diffusion ranges being narrower than observed could also be attributed to the instability of the wind speed. Despite these differences, the overall diffusion ranges of the gas cloud were consistent with the actual experimental results, accurately reflecting the diffusion dynamics of the heavy gas leakage.

It specifically depicts the methane concentration over time at a distance of 140 m downwind in Figure 4A, with the observed peak concentration reaching 9.6%. The CFD simulation peaking at 9.62%, resulted in a minimal relative error of 0.2%. While at a distance of 400 m downwind, the observed maximum concentration was 3.96%, compared to the CFD simulation’s maximum value of 3.23%, leading to a relative error of 18.43% (Figure 4B). Sun and Guo (2010) used the DEGADIS model to validate the Burro nine experiment, and the relative errors of the simulation concentrations at downwind distances of 140 m and 400 m were 44.7% and 16.49%, respectively. Sun et al. (2013) simulated the maximum concentrations at different downwind distances of the Burro eight experiment using the Fluent software, with an average relative error of 19.62%. This demonstrates that the CFD model utilized in this study effectively enhanced the precision of concentration prediction, maintaining relative errors within permissible limits. Therefore, the CFD model is considered to accurately capture the trends of the observed methane concentrations, although temporal variations are present. Such variations may arise from the inconsistent evaporation rates of LNG leakage and the dynamics size of the evaporating liquid pool, which, if assumed constant in the model, will introduce validation uncertainties. Figures 4C,D reveal that the simulated heights of the air clouds with varying concentrations at a distance of 400 m downwind slightly exceeded the actual measurements, yet their lateral extents remained broadly consistent. The overall trend alignment and acceptable error margins confirm the CFD simulation’s efficacy for subsequent research.

Upon the leakage of benzene, its high boiling point resulted in the formation of a liquid pool on the ground. The evaporation of the liquid pool was facilitated by the airflow over the pool surface, with both the radius of the pool and the evaporation rate changing dynamically. Before exploring the impacts of various factors on the diffusion distances of benzene, this study initially analyzed the influences of four factors on the dynamic changes of the radius and evaporation rate of the liquid pool. The results are presented in Figure 5, which displays the dynamic changes of the liquid pool radius and evaporation rate under different wind speeds, temperatures, leakage apertures and atmospheric stabilities, labelled A-L respectively.

An increase in wind speed from 1 m/s to 6 m/s extended the duration required for the liquid pool to achieve its maximum radius from 145 s to 163 s, currently elevating the evaporation rate from 7.36 kg/s to 31.88 kg/s (Figures 5A,B). This indicates that higher wind speeds not only delay the attainment of the maximum radius of the liquid pool but also substantially enhance the evaporation rate. Such an increase accelerates the volatility and diffusion rate of benzene, thereby enlarging the potential hazardous ranges. Furthermore, a temperature increase from 20°C to 50°C similarly impacted these dynamics, lengthening the time to reach the maximum radius from 144 s to 163 s, while elevating the evaporation rate from 6.03 kg/s to 31.88 kg/s (Figures 5C,D). The rise in temperature not only accelerated the evaporation rate but also slowed down the growth rate of the radius of the liquid pool, prolonging the time to reach its maximum. Variations in the leakage aperture slightly adjusted the time for the liquid pool to achieve its maximum radius from 159 s to 163 s. The evaporation rate attained a consistent peak of 31.88 kg/s at different apertures (Figures 5E,F), indicating a minimal effect of the leakage aperture on the growth of the radius and evaporation rate. Under disparate conditions of atmospheric stability, the radius reached its zenith between 163 s and 165 s, with the lowest evaporation rate under unstable conditions at 31.88 kg/s, and slightly higher under stable and neutral conditions at 33.62 kg/s and 33 kg/s, respectively (Figures 5G,H). Atmospheric stability exerts a minor influence on liquid pool expansion and evaporation rate, as indicated by the coefficients α and n in formula (2). Subsequent research will investigate the effects of these factors on the distribution of concentrations and hazardous distances, providing scientific support for effective risk management and emergency preparedness.

A comprehensive analysis indicated that temperature was the primary factor influencing the growth of the evaporation rate. The impact of wind speed on the radius growth was negligible but significantly enhanced evaporation rate. The impact of leakage aperture and atmospheric stability was insignificant. Related studies (Galeev et al., 2013; Hu et al., 2024) have also emphasized the important role of environmental factors in chemical leakage accidents, in particular the significant effect of wind speed and temperature on the consequences of leakage.

To explore the dynamic characteristics of concentration distribution, a specific scenario was chosen for detailed analysis: liquid benzene leakage under stable atmospheric conditions, featuring a 200 mm aperture, a wind speed of 6 m/s and a temperature of 50°C. This study methodically examined the changes in concentration distribution within the hazardous distances for various AEGLs at 150 s, 300 s, 450 s, and 600 s. Figure 6 illustrates the concentration distribution at different times, where A-D, E-H, and I-N correspond to AEGL-1, AEGL-2, and AEGL-3 distances, respectively.

Initially, at 150 s, the hazardous range of AEGL-1 was predominantly near the leakage source (Figure 6A). By 600 s, the concentration range had spread to 2780.20 m, revealing a significant downwind stretch while the lateral enlargement of the plume remained comparatively limited (Figure 6D). Compared to AEGL-1, the diffusion rate and the hazardous range of AEGL-2 were markedly reduced. Notably, at 300 and 390 s, the maximum AEGL-2 distance exhibited minimal change, suggesting a plateau in the diffusion speed and expansion range once a certain concentration was reached (Figure 6F). Beyond 300 s, both the downwind distance and plume width remained relatively stable, leading to a more homogeneous distribution of concentration (Figures 6G,H). The diffusion speed and range of AEGL-3 showed an even more pronounced reduction (Figure 6I–L). By 270 s, the hazardous range reached a steady state at 74.27 m, highlighting the restricted diffusion range for high-concentration benzene over a brief period. The lateral expansion of the plume was notably constrained, primarily due to the dominance of wind speed over turbulent mixing, facilitating predominantly downwind diffusion. Consequently, wind speed emerges as a critical determinant in the plume diffusion process, determining the velocity of downwind diffusion (Gong et al., 2023). Meanwhile, initial release conditions, such as leakage rate and temperature, along with local turbulence, play collective roles in shaping the plume width and diffusion uniformity.

In the case of liquid benzene leakage, the hazardous consequences were evaluated using AEGLs distances. The mechanism of the change of AEGLs distances under the four main factors was analyzed by altering the environmental conditions, with the findings illustrated in Figure 7. Notably, the AEGL-1 and AEGL-2 distances increased significantly as temperature rose. The trend for the AEGL-3 distance was only exhibited at higher temperatures. This phenomenon may be attributed to the fact that an increase in temperature elevated the saturated vapor pressure of benzene, thereby expediting the evaporation rate and diffusion process (Yu et al., 2021). Furthermore, for AEGL-3, the concentration value (31,000 mg/m³) represented a high concentration that may be life-threatening following exposure. In this study, it was observed that the distances of AEGL-3 were only present under higher temperatures and were relatively short. This suggested that elevated temperatures may facilitate rapid evaporation of benzene, yet may also facilitate its rapid diffusion and dilution, resulting in rapidly declining concentrations at a distance from the leakage source (Zhou et al., 2024).

Wind speed significantly influenced the diffusion ranges of benzene, with wind speed increasing from 1 m/s to 6 m/s, the AEGL-1, AEGL-2, and AEGL-3 distances exhibiting different growth trends. The increase in diffusion distances was attributed to the turbulent mixing effect at higher wind speeds. However, the extent of this increase was limited, particularly as the AEGL-2 and AEGL-3 distances stabilized more quickly at higher wind speeds. The AEGL-3 distance initially rose with an increase in wind speed until it stabilized approximately 200 s. The maximum distance of 73.93 m was reached at a wind speed of 4 m/s, after which it slightly decreased with further increases in wind speed. Before reaching a steady state in concentration distribution, wind speed primarily served as a mechanism for transporting the cloud over longer distances within the same time frame. Upon reaching a steady state, wind speed facilitated dilution in addition to transportation (Zhou et al., 2021). An increase in wind speed not only enhanced the dilution effect but also accelerated the diffusion speed, thereby narrowing the hazardous range. The impacts of leakage aperture and atmospheric stability on the hazardous distance were minimal. An incremental rise in the AEGL-1 distance was observed with the enlargement of leakage aperture, whereas the AEGL-2 and AEGL-3 distances exhibited negligible changes. Furthermore, the AEGL-1, AEGL-2, and AEGL-3 distances showed no significant variance under different atmospheric stabilities, indicating that over longer periods, atmospheric stability exerted minimal influence on diffusion distances.

To evaluate the performance of the five ML models on CFD standard data, various evaluation metrics were calculated, as depicted in Figure 9. Figure 9A reveals that R² for the training set among these models varied from 0.962 to 0.999, and IOA varied from 0.990 to 0.999. Notably, R² and IOA of the XGBoost and LightGBM models were both 0.999, indicating nearly-perfect prediction accuracy. In terms of RMSE, the XGBoost model outperformed other models with a score of 181.669 mg/m³, closely followed by the LightGBM model, which scored 204.089 mg/m³. Additionally, these models also exhibited outstanding MAE, with the XGBoost model at 85.742 mg/m³ and the LightGBM model at 108.414 mg/m³, underscoring the exceptional predictive performance of the XGBoost model.

On the testing set, both the XGBoost and LightGBM models exhibited strong correlations with R² of 0.996 and 0.993, and IOA of 0.999 and 0.998, respectively (Figure 9B). In contrast, despite the MLP and RF models exhibiting high R² on the training set (0.962 and 0.964, respectively) and acceptable R² on the testing set (0.894 and 0.968), their higher RMSE and MAE suggested a significantly lower prediction accuracy compared to the XGBoost and LightGBM models. The DT model performed well on the training set, with RMSE of 1546.323 mg/m³. Nonetheless, its accuracy decreased on the testing set, with RMSE and MAE of 1483.873 mg/m³ and 686.351 mg/m³, respectively, and slightly lower R² and IOA. This analysis indicates that the MLP and DT models may not be optimal for low-dimensional sample data. However, ensemble models such as the XGBoost and LightGBM models can effectively mitigate the risks of overfitting by integrating multiple simple models, thereby ensuring improved accuracy of concentration prediction.

In the field of environmental science, numerous studies (Li J. et al., 2021; Zang et al., 2021; Xu et al., 2022) have employed a range of ML algorithms to construct prediction models for air pollutant concentrations, with R² primarily falling within the range of 0.68–0.88. In comparison, our models demonstrated a significant improvement in prediction accuracy. Moreover, in the field of risk assessment of accident consequences, related studies (Ni et al., 2020; Wang et al., 2023) have demonstrated the performance of ML models based on CFD simulation data, where R² of the models was higher than 0.90. The ML models constructed on the basis of idealized CFD data in our study, in particular the XGBoost model, not only matched but even outperformed these performance ranges reported by these studies. These results demonstrated the effectiveness of the XGBoost model in terms of prediction accuracy, and illustrated the capacity of the model to process complex and high-dimensional data. The findings suggested the potential applicability of the model in the field of environmental sciences.

To further assess the accuracy of various models in predicting concentrations, a validation analysis was performed under a stable atmosphere scenario, characterized by a 200 mm leakage aperture, a wind speed of 6 m/s, and a temperature of 50°C. Concentrations at different distances were compared, with the results presented in Figure 10. This figure demonstrates that the MLP model was unable to accurately predict concentration distributions and trends at both near and distant distances, leading to unsatisfactory outcomes. Conversely, the other models showed improved accuracy in capturing the concentration trends. Notably, from distances of 10 m–500 m, the predictive curves of these models closely aligned with the actual concentration curves, demonstrating high consistency. At a distance of 50 m, all models except the MLP model produced predictions nearly identical to the actual concentrations, with the predictive and actual curves almost overlapping, indicating their robust performance in near-distance prediction. However, the accuracy of these predictions decreased as the distance increased. Beyond 1,000 m, the MLP, DT, and RF models exhibited considerable deviations and were unable to accurately capture the actual concentration distribution and trends, highlighting their limitations in distant-distance concentration prediction. In contrast, the predictive curves of the XGBoost and LightGBM models remained closely aligned with the actual curves, demonstrating their capacity to handle large-scale and complex data effectively. Nevertheless, Figure 10C clearly shows some deviations between the predictive curve of the LightGBM model and the actual concentration curve during abrupt increases. Although the LightGBM model exhibited a slightly stable trend aligning with the actual values in high concentration ranges (Figures 10A,B), the XGBoost model adapted more quickly to near-actual values in rapidly changing concentrations (Figures 10E,H). This indicated that the XGBoost model may provide more timely decision support in dynamic prediction scenarios. Considering their performance with respect to prediction latency and accuracy in high concentration intervals, the XGBoost model outperformed the LightGBM model, corroborating the findings discussed in Section 3.3.1. These results provide a scientific framework for model selection in particular scenarios.

In order to more closely match real-world measured data and to evaluate the generalizability of the model, noise is often introduced into the standard data to mimic real-world variations (Li X. et al., 2021). Therefore, Gaussian noise was incorporated into the CFD standard data and the mean and variance of the Gaussian noise were adjusted to generate datasets with different noise levels. The performance of each model on the training and testing data was evaluated with a noise scale of 0.5, and the results of this evaluation are depicted in Figure 11.

Figure 11 shows that the MLP model achieved RMSE and MAE of 3062.884 mg/m³ and 1430.555 mg/m³ on the training set, and 3078.269 mg/m³ and 1494.641 mg/m³ on the testing set, respectively. Although the DT and RF models performed slightly better in terms of RMSE and MAE, they still exhibited significant sensitivity to the presence of noise. In comparison, both the XGBoost and LightGBM models demonstrated exceptional performance across all evaluation metrics, with the lowest RMSE and MAE. RMSE for the XGBoost and LightGBM models on the training data were 1856.175 mg/m³ and 1831.244 mg/m³, respectively, while MAE were 778.301 mg/m³ and 785.941 mg/m³, respectively. R² was 0.973 for the XGBoost model and 0.974 for the LightGBM model, with both models achieving IOA of 0.993. The difference in performance between the two models was minimal, with the LightGBM model slightly outperforming in terms of predictive accuracy. On the testing data, RMSE for the XGBoost and LightGBM models were 2091.083 mg/m³ and 2162.072 mg/m³, with MAE were 918.705 mg/m³ and 41.887 mg/m³, respectively. R² was 0.963 and 0.961, and IOA was 0.991 and 0.990, respectively. Here, the performance of the XGBoost model was more pronounced. Overall, both models demonstrated high robustness in processing and predicting noisy data, which is vital for the effective operation of ML algorithms in diverse real-world situations. Nevertheless, the XGBoost model displayed an advantage in predictive accuracy and stability.

Previous studies (Ni et al., 2020; Wang et al., 2023) have typically constructed ML prediction models based on idealized data from CFD simulations. However, in real-world environments, real data frequently contain noise due to monitoring equipment failures and measurement errors. This study sought to assess the reliability of the predictive performance of ML models based on noisy data by adding noise to the data to reflect the real-world situation, and enhance the robustness and generalization of the models. The results demonstrated that the XGBoost model exhibited excellent predictive performance despite the presence of noise.

A comparative analysis of concentration predictions at various distances from the source was performed using noisy data, with the results illustrated in Figure 12. The analysis clearly indicated that as the downwind distance increases, the difference between the predictions of the models and the noise values also increased, indicating a higher level of uncertainty in the prediction. At near distances, the’ predictions of all models were closer to the actual values. However, at distant distances, the prediction curves become more volatile, with the MLP model’s predictions deviating significantly from the true values. The MLP model was ineffective in predicting noisy data. The DT and RF models, while providing predictions closer to the true values, did not accurately reflect the overall trends. Conversely, the XGBoost and LightGBM models demonstrated exceptional predictive performance, accurately capturing changes in concentration trends at both near and distant distances. This evidence reinforces the notion that ensemble models, especially the XGBoost and LightGBM models, exhibit strong generalization capabilities and robustness in both standard and noisy data, excelling in predicting concentration distributions and trends effectively. Overall, the inherent features of ensemble models, such as model averaging, robustness, and overfitting prevention, contribute to their effectiveness in making reliable predictions within noisy environments (Cong et al., 2023). These attributes render ensemble models indispensable tools for addressing the complexity and uncertainty inherent in real-world data.

In emergency rescue operations, accurately predicting the temporal distribution of hazardous chemical concentration over time and the corresponding hazardous distances for concentration limits is essential for devising the effective emergency response strategies. This study evaluated the efficiency of the XGBoost model in predicting the diffusion of liquid benzene leakage following a leakage from a tank with a 200 mm aperture under conditions of a 6 m/s wind speed, a 50°C temperature, and stable atmospheric conditions. The aim is to replicate an industrial scenario with specific environmental parameters. The comparison between CFD simulation results and hazardous distance predictions from the XGBoost model, as presented in Figure 13, underscores the exceptional ability of the model in accurately predicting benzene concentration levels and determining hazardous distances. Specifically, the XGBoost model demonstrates the capacity to accurately predict concentrations at different distances, whether near the leakage source or at distant distances. Notably, Figure 13A confirms the accuracy of the model in matching saturation concentrations, whereas Figures 13B,C indicate a minor temporal delay in the model’s predictions compared to the actual values, suggesting a negligible hysteresis effect without compromising overall accuracy. Moreover, the model demonstrated exceptional alignment with real-world distances for AEGL-1, AEGL-2, and AEGL-3, with minimal relative errors. Specifically, it predicted distances of 2705.1 m, 378.4 m, and 74.44 m against the true distances of 2780.2 m, 368.9 m, and 74.27 m, achieving relative errors of 2.70%, 2.58%, and 0.23%, respectively. Compared to the CFD model, the enhanced efficacy and speed exhibited by the XGBoost model indicate that ML algorithms may significantly improve the real-time emergency response capabilities, potentially reducing the risks these accidents pose to humans and the environment. In addition, the XGBoost model exhibited a markedly superior predictive efficiency compared to the CFD model, resulting in significant savings in computational costs. The model took only 0.218 s to output the prediction results when running on a computer with an AMD Ralon R7 6800H CPU and 32G of RAM, while the CFD model took about 3 h to complete a simulation on a computer with an 11th Gen Intel^® Core (TM) i5-11400H CPU and 8G of RAM for this leakage scenario. It should be noted that the simulation time may vary depending on the specific leakage scenario under consideration. Obviously, using ML algorithms can significantly improve the prediction efficiency and meet the current demand for dynamic, accurate and fast predictions in smart parks.

The precise prediction of hazardous distances is crucial for assessing the consequences of leakage accidents and for immediate emergency response measures. The investigation of XGBoost models that not only provide accurate predictions but also maintain prediction efficiency has enabled the fast provision of prediction ranges for emergency response. It is recommended that further development and integration of ML techniques for the prediction and management of hazardous situation be a priority in industrial safety and environmental protection strategies.