Predicting PAHs removal from contaminated soil via subcritical water extraction using support vector regression

Mohammad Nazrul Islam; Jeong-Hun Park

doi:10.4491/eer.2024.122

Environ Eng Res > Volume 30(1); 2025 > Article

Islam and Park: Predicting PAHs removal from contaminated soil via subcritical water extraction using support vector regression

Short Communication

Environmental Engineering Research 2025; 30(1): 240122.

Published online: July 12, 2024

DOI: https://doi.org/10.4491/eer.2024.122

Predicting PAHs removal from contaminated soil via subcritical water extraction using support vector regression

Mohammad Nazrul Islam^1,², Jeong-Hun Park³

¹Department of Chemical and Biological Engineering, University of Idaho, Moscow, ID 83844, United States

²Department of Farm Structure and Environmental Engineering, Khulna Agricultural University, Khulna 9202, Bangladesh

³Department of Environment and Energy Engineering, Chonnam National University, Gwangju 61186, South Korea

^†Corresponding author: E-mail: parkjeo1@jnu.ac.kr, Tel: +82-62-530-1855

Received February 29, 2024 Revised July 10, 2024 Accepted July 11, 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Subcritical water extraction (SCWE) has been increasingly studied and applied in recent decades for the extraction of organic pollutants from contaminated soil. However, the efficacy of the SCWE technique for soil remediation depends not only on the operating parameters but also on the soil and pollutant properties. Models for predicting PAHs removal by the SCWE process are highly desirable for the process design and for facilitating a global understanding of the influence of each parameter for optimal remediation without numerous trials. In this study, a support vector regression (SVR) model was developed to predict PAHs removal from contaminated soil based on the SCWE operating parameters and soil and PAHs’ properties. Results revealed that the model exhibited a good predictability with the correlation coefficients of 0.99 and 0.93 for the training and testing datasets, respectively. The importance of input variables was in the following order: operating conditions > chemical properties > soil properties. The statistical analysis demonstrated the reliability and robustness of the developed model. Based on our findings, the SVR model is suitable for predicting the removal rate of PAHs by SCWE process.

Keywords: Contaminated soil, PAHs removal, Subcritical water extraction, Support vector regression

Graphical Abstract

Keywords: Contaminated soil, PAHs removal, Subcritical water extraction, Support vector regression

1. Introduction

Polycyclic aromatic hydrocarbons (PAHs) have emerged as a source of significant concern for more decades owing to their carcinogenic, mutagenic, and teratogenic potential [1–2]. Additionally, because of their high hydrophobicity, PAHs have a strong affinity to soil organic matter (SOM) and retained in the soil for extended period of time, which is one of their primary sinks [3–4]. Moreover, they typically exhibit low biodegradability, which results in a high environmental persistence. Particularly, Wild et al. [5] reported that the half-life of PAHs can be 5–9 years depending on their molecular weight (MW). Therefore, the remediation of PAHs-contaminated soils is significantly important owing to the extent of exposure and potential toxicity. Accordingly, the efficacy of several remediation approaches has been investigated either as a stand-alone approach or a combination of physical, biological, and thermal processes [4, 6–9]. Among various investigated approaches, the (hydro)thermal technique can efficiently and rapidly remove and/or degrade PAHs [10–11]. Over the last three decades, subcritical water has been employed as a solvent for the extraction of organic compounds from various solid matrix [12–13], and the first report on subcritical water extraction (SCWE) of organic pollutants from soil was published in 1994 [14]. Lagadec et al. [15] conducted the first pilot-scale study of SCWE-based treatment of PAH-contaminated soil.

Water exhibits distinct properties, such as reduced dielectric constant, surface tension, and viscosity, at subcritical conditions (temperature 100–374°C and pressure < 22.1 MPa) [16–17]. For example, at 250°C and 10 MPa, the dielectric constant of water is 27, which is similar to that of ethanol (24), indicating that subcritical water can act like an organic solvent and extract non-polar organic contaminants, such as PAHs, from the soil. Several previous studies have demonstrated the effectiveness of the hydrothermal, particularly subcritical water extraction (SCWE) process for remediating PAH-contaminated soils [15, 17–18]. However, most of these studies have not provided a comprehensive overview of an individual PAH or considered different soil properties. Typically, the extraction of PAHs from soil depends on the soil properties (e.g., soil texture and SOM), SCWE operating conditions (e.g., temperature, time, and solid–liquid ratio), and PAH properties (e.g., solubility and MW). Lagadec et al. [15] reported that the optimal SCWE temperature for all low- and high-MW PAHs is 275°C for 35 min. In addition, as reported in our previous study, PAHs removal is significantly influenced by water temperature and time, in which a comparatively lower temperature (e.g., 175–200°C) is required for low-MW PAHs (e.g., naphthalene and phenanthrene), whereas a higher temperature (e.g., 275–300°C) is required for high-MW PAHs (e.g., pyrene), and a higher temperature could reduce the extraction time [10]. This indicates that the values of parameters investigated may vary from one research or one molecule to another, making it difficult to achieve a global understanding of the influence of individual parameters. In addition, the optimal process condition is always obtained after several experimental trials, resulting in a high time and cost consumption. Furthermore, it is challenging and complex to investigate all the previously mentioned process parameters involved in PAHs extraction and the influence of various factors on the extraction of PAHs.

Therefore, identifying the optimum conditions for maximum PAH-removal efficiency via an empirical approach to facilitate a global understanding of the influence of soil properties, chemical properties, and SCWE operating conditions could reduce the requirement of time, labor, and costs involved in this process, as well as to help designing an optimal hydrothermal extraction reaction. To the best of our knowledge, no effort has been devoted to predicting the PAH-removal efficiency of the SCWE process using machine learning approach. Given the complexity of three different categorical variables, including the chemical properties of pollutants, soil properties, and SCWE process variables involved in PAHs removal, a non-linear model could be ideal to maximize the predictive accuracy while avoiding overfitting. A support vector regression (SVR) was chosen for this study due to its ability to handle non-linear relationships, robustness to outliers, high generalization ability, flexibility with kernel functions, and proven effectiveness in similar environmental applications [19–20]. By comparing the performance of SVR with multiple linear regression (MLR), one can also evaluate the added value of employing a more complex, non-linear model over a linear approach. Both regression models have been extensively employed within the field of environmental science and engineering research [21–22]. Therefore, this study employed SVR and MLR approach to predict PAHs remediation efficiency which incorporates the effects of SCWE temperature, time, soil to water ratio, and the specific characteristics soil and PAHs.

2. Materials and Methods

2.1. Dataset Compilation

The experimental data were collected from past literature through keyword searches from various databases, such as Google Scholar and Web of Sciences. The keywords employed in this literature search include subcritical/superheated water extraction, PAHs, and soil/contaminated soil. Only studies that utilized lab-scale SCWE apparatus in continuous flow mode were considered. A total of 76 experimental data points were compiled from our previous study and literature [10, 15, 23–24]. The removal rates of PAHs range from 50 to 99% depending on the conditions and MW (Fig. S1). The comprehensive SCWE process for removing organic pollutants from contaminated soil is described elsewhere [10, 15, 25–26]. The data points for the SCWE operating parameters and their corresponding removal rate were extracted from the plots using the Plot Digitizer (https://apps.automeris.io/wpd/). The soil (e.g., SOM) and chemical properties of solubility in water at ambient temperature and MW were used as the input variables in developing the model, along with the SCWE operating parameters (temperature, extraction time, and soil–water ratio), whereas the removal rate was used as the output variable. The input variables chosen for this study were based on their substantial impact on removing organic pollutants from contaminated soil via SCWE process and cover the primary factors that affect the efficiency of the removal rate [10, 27–28]. Prior to finalizing the model variables, we also conducted statistical analyses to confirm their significance (see section 2.2). The solubility and MW of PAHs were obtained from the chemical database (https://pubchem.ncbi.nlm.nih.gov/). The PAH elimination rate was calculated using the Eq. (1):

(1)

RE (%) = \frac{Initial concentartion - residual concentartion after treatment}{Initial concentration} \times 100

2.2. Model Development and Evaluation

First, the compiled dataset was randomly divided into a training set (80% of the data) for developing the model and a testing set (the remaining 20%) for validating the developed model. In this study, MLR and SVR were used to drive a comprehensive predictive equation for PAHs removal using variables related to three key aspects of the SCWE process, including operating parameters, and soil (SOM) and chemical (MW and solubility in water at ambient temperature) properties. To evaluate the input variables, “all subset” regression, principal component analysis (PCA), and correlation analyses were employed, which aided the understanding of the key parameters that influence PAH removal. All the regression and statistical analyses were performed using R software (version 4.3.0).

During the both MLR and SVR process, five-fold cross validation was used with the training dataset, while the developed models were validated using the test dataset. In SVR, the cost, kernel function, and epsilon hyperparameters were tuned to obtain the minimal mean-squared error to predict the PAH removal efficiency. The prediction performance of the regression model was assessed using correlation coefficient (R²), root mean square error (RMSE), and the hat matrix (leverage approach). The R² and RMSE values were calculated using Eq. (2) and Eq. (3):

(2)

R^{2} = 1 - \frac{Σ_{i = 1}^{n} {({RE}^{predicted} - {RE}^{experimental})}^{2}}{Σ_{i = 1}^{n} {({RE}^{predicted} - {RE}^{average})}^{2}}

(3)

RMSE = \sqrt{\frac{Σ_{i = 1}^{n} {({RE}^{experimental} - {RE}^{predicted})}^{2}}{N}}

where N is the total number of sample data points. The leverage value (h) has been widely used to visually characterize the applicability domain (AD) [29–30], with the hat matrix calculated from the model variables as follows Eq. (4):

(4)

h = \frac{1}{n} + \frac{{(X_{i} - X)}^{2}}{Σ_{i = 1}^{n} {(X_{i} - X)}^{2}}

where X_i is the variable value of the ith object and X is the variable average. The outliers of the model predictions (Y-outliers, standardized residuals greater than two standard deviation unit) and the influential or problematic variables (X-outliers, defined by the critical hat values) were visualized using the William’s plot (the standardized residuals of RE mapped against the leverage value). The critical leverage threshold (h* cut-off value) is often fixed at 3(p+1)/n, where n is the number of observations in the dataset and p is the number of variables in the model. The data predicted for high leverage compounds (h > h*) was considered extrapolated by the model.

3. Results and Discussion

3.1. Model Performance of MLR and SVR

In this study, the MLR and SVR analysis were conducted based on three categorical variables, including SCWE operating conditions (temperature, time, and soil/water ratio), soil properties (SOM), and chemical properties (solubility and MW). Fig. 1 (a) shows that dataset compiled for this study was from diverse ranges with the range of Tanimoto similarity indices 0.1–0.3 (dark blue in Fig. 1 (a) indicates strong similarity). Among input variables, they exhibited a very low correlation to each other, except solubility (Fig. 1 (b)), indicating that all input variables uniquely contributed to the model. Prior to the model development, selection of highly linked variables is crucial to better determine the predictive performance of the developed model. Therefore, feature engineering was conducted to filter out the less significant variables. During the hierarchical cluster analysis, solubility and MW were found within the same cluster corresponding to the same empirical category (Fig. 1 (c)). However, MW was more important than solubility (Fig. S2). Similarly, the subset regression analysis demonstrated that the solubility had a minor impact on the model prediction performance (Table S1). Therefore, the solubility was determined as the redundant variable and removed from the dataset.

The prediction performances of the developed models, based on both training and validation, are reported in Table 1. Fig. 2 shows the MLR model’s performance with the relative importance of input variables. The correlation coefficient values for the training and testing datasets of the MLR model were 0.87 and 0.78, respectively. Although the training dataset produced a good prediction accuracy, the performance of the testing dataset for the prediction of the PAHs removal was not satisfactorily high. The subset regression and correlation analysis revealed that the removal rate of PAHs from contaminated soil is highly dependent on the SCWE operating conditions and MW. Although the MLR with only SCWE operating variables (including temperature, time, and soil-water ratio) was statistically significant (p<0.001), the inclusion of the MW of PAHs and SOM increased the reliability of the model. A simplified MLR model based on the selected parameters, including β coefficient values, is expressed in Eq. (5).

(5)

\begin{array}{l} RE (%) = 102.71 - 4.261 \times SOM (%) + 0.303 \times Temp . (° C) + \\ 0.478 \times Time (min) - 51.89 \times \\ Soil / Water ratio - 0.302 \times MW (g / mol) \end{array}

Fig. 3 shows the prediction results of the SVR model. Although MLR models produced acceptable results, the tuned SVR model performed well with R² value 0.99 and 0.93 for training and testing datasets, respectively. After tuning, optimum cost and epsilon values for the best performance were 8 and 0.01, which is indicated (darker blue region) in Fig. 3 (a). Based on the leverage approach, the AD assessment results also revealed that the SVR model exhibited a remarkable prediction coverage of more than 98% (Fig. 3 (c)). The identified minimal outliers in the training and testing datasets indicated the accuracy of the proposed SVR model for predicting the PAHs removal rate by the SCWE technique.

3.2. Variable Importance Analysis

The relative importance analysis performed using the “relative importance” package revealed that the SCWE operating conditions were the most influential factors, accounting for 60% of the relevance of the factors for the prediction of the PAHs removal, followed by MW (25%) and SOM (15%) (Fig. S2). Further, PCA was performed to understand the roles of the input parameters in explaining the variance in the dataset. As shown in Fig. 1 (d), the first and second principal components (PCs) explained approximately 44% and 20% of the total variance, respectively, whereas the first three PCs accounted for more than 85% of the variance (Table S2 and Fig. S3). The first PC was loaded for temperature, SOM, and MW, whereas PC2 was responsible for loading SCWE time and soil–water ratio. This indicated the significance of all the categorical variables in the dataset.

The relative contribution was calculated to assess the importance of input variables to the model fitting. As can be seen from Fig. 2 (b) and Fig. 3 (d), soil to water ratio is the most impactful variables on PAH removal prediction followed by extraction time, water temperature and MW, while SOM contributes a little. This is understandable, as higher temperature and lower soil–water ratio thus longer residence time would enhance solubility, internal and external diffusion, and mass transfer of PAHs, thus enhance the removal (remediation) efficiency.

3.3. Partial Dependence Plot Based on SVR Model

To provide further insight into the most impactful variables, one– and two–way partial dependence plots based on SVR model are presented in Fig. 4, which can also demonstrate how the prediction of PAH removal depends on the values of SCWE operating parameters and MW. As shown in Fig. 4 (a–d), all the model variables played an important role in establishing a range of suitable conditions for the removal of PAHs from the soil. For example, a removal effectiveness of more than 90% was projected when the temperature was close to 300ºC, and the extraction time was approximately 60 min (Fig. 4 (a) and 4 (b)). Obviously, the PAH removal efficiency increased as the water temperature increased, which is consistent with the findings of previous studies [10, 31]. In addition, the subcritical water temperature could enhance the solubility, distribution coefficient, and molecular diffusion coefficient of PAHs, which may affect the extraction efficiency. A comparatively longer extraction time (e.g., 70 min) is required when the operating temperature was held between 250ºC and 275ºC (Fig. 4 (e)). In relation to the soil–water ratio, the extraction efficiency of PAHs depends on internal mass transfer from solid to liquid phase, which is controlled by the water flow rate. The optimum soil–water ratio was observed between 0.2 and 0.5 at temperature 250–275ºC (Fig. 4 (f)). Furthermore, the removal efficiency significantly depended on the MW of PAHs. Low-MW PAHs exhibited the highest removal rate, whereas high-MW PAHs require either a longer extraction time or a higher temperature (Fig. 4 (d) and 4(g)).

4. Conclusions

It is well known that the SCWE method can remove PAHs from contaminated soil; however, the effectiveness of remediation is significantly affected by soil and chemical properties, as well as the operating conditions. Meanwhile, determining the best SCWE operating conditions, as well as significant parameters affecting the PAH removal rate, through simultaneous testing is difficult. To address this issue, this study developed an SVR model with three categorical variables, i.e., SCWE operating parameters (temperature, time, and soil–water ratio), soil properties (SOM), and chemical (MW) properties. This study presented the first application of machine learning for the prediction of PAHs treatment and removal by the SCWE process. The results of this study demonstrated the accuracy of the training and testing datasets of the developed SVR model for the prediction of PAH removal efficiency. The PCA and variable importance analysis results revealed that the SCWE operating condition was the most influential variable. Furthermore, the subclass variables within each main category reaffirmed the overall importance ranking of operating conditions, chemical and soil properties. Soil-water ratio, extraction time and temperature are paramount among input variables, while MW of PAHs and SOM are also critical parameters. Only a few observations that are considered outliers were identified based on the AD assessment. Furthermore, the R² and RMSE values demonstrated that the developed predictive model shows immense promise and could help with the process design and optimization of the SCWE method for the removal of PAHs from soils. Although the developed model is suitable for predicting the removal rate of PAHs by SCWE from this study, large amounts of data from more diverse experimental conditions are needed to improve its accuracy.

Supplementary Information

eer-2024-122-supplementary.pdf

Acknowledgments

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Notes

Conflict-of-Interest Statement

There are no conflicts to declare.

Author Contributions

M.N.I. (Assistant Professor) developed the conceptualization and methodology, conducted model development and wrote the manuscript. J.H.P. (Professor) did supervision, reviewing and editing the manuscript.

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Fig. 1

(a) Tanimoto similarity analysis of the dataset. Dark blue indicates close similarity among data points used in the model development, (b) Pearson correlation coefficients of any two variables, (c) Hierarchical analysis of the input variables to identify any redundant feature, and (d) PCA analysis of the dataset.

Fig. 2

(a) Predictive performance of MLR model, (b) Relative contribution of input variables to MLR model fitting.

Fig. 3

(a) Hyperparameters tuning in the SVR model, (b) Predictive performance of tuned SVR model, (c) Model assessment based on AD leverage approach, and (d) Relative contribution of input variables to the SVR model fitting.

Fig. 4

One-way (a d) and two-way (e f) partial dependency plot of input variables. (a) Effect of water temperature, (b) Effect of extraction time, (c) Effect of soil to water ratio, (d) Effect of molecular weight of PAHs, (e) Combined effect of temperature and time, (f) Combined effect of temperature and soil to water ratio, and (g) Combined effect of temperature and molecular weight.

Table 1

Summary of the model performance statistics

Model	Dataset	R²	RMSE	MAE
MLR	Training	0.87	9.72	7.64
	Test	0.78	13.16	11.02
SVR	Training	0.99	2.45	1.37
	Test	0.93	7.95	4.97