Estimating Tetrachloroethene Sorption Coefficients Based on Soil Properties in Organic-Poor Soils

Abstract

In the context of contaminated site remediation, the fate of chlorinated solvents in the subsurface and subsequent groundwater contamination is influenced by soil properties governing sorption. The solid–water distribution coefficient (K_d) is a key parameter for modeling contaminant distribution and transport, essential for risk assessment and remediation planning. This study evaluated tetrachloroethene sorption isotherms in 34 low-organic-carbon soils from the Czech Republic, assessing the influence of soil properties on K_d. Soil samples exhibited variability in organic carbon content (˂0.05–0.81%), with clay ranging from 0% to 64.9%, silt 5.1% to 71.2%, and sand 5.2% to 88.9%, specific surface area (0.41–64.39 m² g⁻¹), particle density (2.05–4.09 g cm⁻³), and porosity (43.5–67.3%). Batch experiments were conducted using standard procedures, with K_d values ranging from 0.379 to 2.272 L kg⁻¹. Statistical analysis grouped the soils into three textural classes: sandy, clayey fine, and silty loam. The findings reveal that organic carbon content and specific surface area are the primary predictors of K_d, while clay and sand also play a significant role in shaping sorption behavior. Multivariate regression models explained 63.6% to 98.5% of K_d variability with high accuracy, as indicated by low root means square error (0.070–0.329) and mean absolute percentage error (3.8–28.8%) values. These models offer reliable predictions of sorption behavior, providing valuable tools for risk assessment and remediation strategies.

1. Introduction

The fate of nonpolar hydrophobic organic compounds, such as chlorinated solvents and aromatic hydrocarbons, in subsurface environments is predominantly controlled by their sorptive behavior [1]. Accurately characterizing this behavior is essential for predicting the transport, transformation, and ultimate fate of these compounds within the subsurface, which is crucial for conducting rigorous risk assessments and developing effective remediation strategies [2]. The extent to which a compound associates with solid phases at equilibrium is quantified by the solid–water distribution coefficient (K_d), which represents the ratio of the compound’s equilibrium concentration in the solid phase to its concentration in the aqueous phase [3]. K_d is a critical parameter that directly influences the modeling of volatile organic compounds’ (VOCs) transport in soil and groundwater [4].

Given the inherent complexity of soil as a geosorbent, practical constraints often necessitate limiting the assessment of sorption characteristics to fundamental parameters that can provide reasonable estimates of contaminant behavior. Early studies have highlighted the critical role of the quantity and nature of organic matter in soil in influencing sorption [5,6,7], leading to the normalization of sorption coefficients to organic carbon (OC) content [8,9]. However, the assumption that OC has uniform sorption properties has been challenged by observations such as the nonlinear shape of sorption isotherms [10,11] or multiphasic desorption kinetics [12]. The K_d values can be influenced by various factors, including clay mineral content and type [13,14,15,16], moisture levels [17,18,19], particle size distribution [20], porosity [21,22], the specific surface area (SSA) of the soil [23], and the presence of salts in soil solutions [24].

For nonpolar hydrophobic organic compounds, the K_d value is often estimated in practice [25] using the fraction of organic carbon content (f_OC) and OC-normalized K_d (K_OC, L kg⁻¹) applying the equation K_d = K_OC × f_OC [3]. This approach allows for efficient predictions, particularly in cases where detailed site-specific data are unavailable [26]. It is especially useful for rapid assessments, as it bypasses the complex and resource-intensive processes involved in fully characterizing contaminated areas. However, empirically estimated K_d values are often lower than the experimentally determined ones; and this approach is more accurate for soils with high OC content, where the correlation between OC content and sorption behavior is strong [27]. Conversely, for soils with low OC content, predictions based on K_OC are less reliable [28]. This reduced reliability stems from the increased influence of other soil properties, such as clay content, whose mineral surfaces play a significant role in physical sorption, which is neglected in these models. As a result, these models are less applicable to low-organic-carbon soils. This inaccuracy can lead to underestimating total contaminant levels in the subsurface, potentially resulting in an underassessment of associated risks [29,30]. Direct experimental measurements of K_d values are therefore essential for these soils to manage subsurface contamination precisely [31,32,33,34]. Nevertheless, determining K_d experimentally presents significant challenges due to the volatility of contaminants, their susceptibility to degradation, and competitive interactions among solutes [35]. Therefore, developing a robust and accurate K_d prediction methodology for soils with low OC content based on a wider range of soil characteristics would significantly enhance the precision of risk assessments and improve the effectiveness of remediation efforts [36,37,38].

In this study, we propose novel sorption models for predicting K_d of tetrachloroethene (PCE) in low-OC soils. PCE was selected as the model contaminant due to its widespread occurrence and persistence in subsurface environments. This research was guided by four primary objectives: (1) to collect a statistically representative set of fully characterized low-OC soil samples; (2) to measure and analyze PCE sorption isotherms for these samples; (3) to perform detailed statistical analyses to identify the key soil properties influencing sorption behavior; and (4) to develop and validate new advanced predictive sorption models. In addition to the previous models, we involved soil parameters that are practical for routine environmental assessments and are proven to significantly contribute to the sorption. By integrating a comprehensive suite of soil property measurements into the evaluation, this study provides novel insights into the mechanisms governing sorption of hydrophobic pollutants in low-OC soils. Despite their simple implementation, which facilitates application by the wider professional community, these models enhance the precision of risk assessments and support effective remediation strategies for contaminated sites.

2. Materials and Methods

2.1. Chemicals

A list of all chemicals used is in Text S1 of the Supporting Information (SI).

2.2. Soil Samples

Soil samples were collected from 23 sites in the Czech Republic, targeting various soil horizons and aquifer materials during excavation. Sampling depths ranged from 30 cm to 4 m as part of a geological survey. The collected soil samples were homogenized, dried at 105 °C for 24 h, and subsequently sieved through a 2 mm mesh.

The particle size distribution was determined using two methods: mechanical sieving and sedimentation analysis. These methods were used to quantify the fractions of gravel, sand, silt, and clay. Based on these results, the soils were classified into different soil groups. The dry bulk density (ρ_b) and the soil particle density (ρ_s) were measured using the core method and the pycnometer method, respectively. Porosity (ε) was then calculated using the equation ε = (1 − ρ_b/ρ_s) × 100. The SSA of the soils was determined using the BET method with a Coulter SA 3100 (Beckman Coulter Life Sciences, Indianapolis, IN, USA).

The OC content was determined in samples pretreated with concentrated orthophosphoric acid to remove carbonates, using the dry combustion method on a LiquiTOC II (Elementar Analysensysteme GmbH, Langenselbold, Germany). The chemical composition of the soil samples was analyzed by X-ray fluorescence (XRF) with a wavelength-dispersive XRF spectrometer, ARL 9400 XP (Thermo ARL, Ecublens, Switzerland). The mineralogical composition of the soil samples was analyzed using X-ray diffraction (XRD) with a Bruker AXS D8 θ-θ powder diffractometer (Bruker, Ettlingen, Germany). Further details are provided in Text S2.

2.3. Sorption Experiments

Sorption experiments were conducted using a batch equilibrium technique based on established methods [39,40]. Each soil sample (10 ± 0.1 g, dry mass) was placed into 40 mL borosilicate glass tubes (28 × 95 mm) equipped with PTFE septa. To each tube, 5 mL of 1 M CaCl₂ solution and 30 mL of distilled water were added, maintaining a soil-to-solution ratio of 1:3.5 (w/v). An aliquot of the standard PCE solution in methanol (1000 mg L⁻¹) was then injected below the water level to achieve relative concentrations (C_w/S) of 0.015, 0.06, 0.25, 0.42, 0.831, and 1.35. These six points were used to construct the sorption isotherm. Duplicates of each sample were prepared and analyzed under the same experimental conditions. Following spiking, the tubes were shaken on a Laboratory Shaking Machine LT 2 (Kavalierglass, Sazava, Czech Republic) at a temperature range of 20 to 25 °C. The samples were allowed to equilibrate for 24 to 48 h before phase separation, which was achieved by centrifugation at 800 rpm for 3 min using a Jouan C3i Multifunction Centrifuge (Juan GmbH, Berlin, Germany). The extraction method followed EN ISO 10301. PCE concentration was measured using gas chromatography; further experimental parameters and details of the analysis method are provided in Texts S3 and S4.

2.4. Statistical Analysis and Development of K_d Prediction Models

Statistical analyses, including both univariate and multivariate approaches, were performed to identify the soil properties influencing PCE sorption and to develop an accurate sorption model for estimating K_d. The data analysis involved Pearson’s correlation to identify significant variables from the dataset, including a broad set of measured soil parameters. Principal Component Analysis (PCA) reduces the complexity by summarizing the data into a few principal components (PCs) that capture the most variance. PCA helps in visualizing and highlighting the most significant relationships between K_d and other soil properties, making the data easier to interpret and understand. Agglomerative Hierarchical Clustering (AHC) was employed to group soil samples into homogeneous clusters based on similar soil properties. Since soil data often do not meet the normality assumptions required for parametric tests, the Kruskal–Wallis test was used to compare statistically significant differences in soil properties across multiple sample groups without assuming normality. In combination with PCA, AHC, and the Kruskal–Wallis test, Linear Discriminant Analysis (LDA) was applied to identify linear combinations of soil properties that best separate the soil samples and classify them into different categories based on their properties. PCA and LDA also address potential collinearity among soil properties, improving model robustness. Finally, K_d prediction models were developed using linear regression. Linear regressions were performed between individual soil properties and K_d values to identify univariate linear model with the highest coefficients of determination. Subsequently, a multivariate linear regression method was used to construct a multivariate model for the prediction of K_d values using the significant soil properties. Model precision was evaluated using the coefficient of determination (R²) interpreted as the proportion of the variability of the dependent variable explained by the model, the root mean square error (RMSE) such as prediction errors and the mean absolute percentage error (MAPE) [41]. Further details are provided in Text S5.

3. Results and Discussion

3.1. Characterization of the Soil Properties

Table 1. Summary of soil properties.

No.	Site of Origin	Samp. Depth (m)	Soil Texture	Distribution of Soil Particles ≤ 2 mm			ρs	ρb	ε	Elemental Composition			SSA
				Clay	Silt	Sand				OC	Si	Al
				(%)	(%)	(%)	(g cm−3)	(g cm−3)	(%)	(%)	(%)	(%)	(m2 g−1)
1	Chotikov	4.30	loamy sand	10.3	5.1	84.6	2.54	1.38	45.8	0.12	37.67	6.52	17.62
2	Vestec	2.00	silt loam	2.0	58.0	40.0	2.69	1.15	57.3	0.23	33.44	10.98	10.27
3	Vestec	<0.50	silt loam	6.1	71.2	22.7	2.54	1.20	52.8	0.42	34.27	10.63
4	Liberec	3.50	loam	25.0	29.2	45.8	2.58	1.21	53.0	0.12	35.08	9.24	13.64
5	Liberec	3.00	sandy loam	11.3	17.7	71.0	2.53	1.25	50.5	0.07	34.20	10.71	10.52
6	Kladno	3.00	sandy clay loam	21.8	27.3	50.9	2.43	1.00	59.1	0.25	40.65	5.30
7	Kladno	2.50	clay loam	32.0	47.4	20.6	2.48	1.11	55.3	0.81	35.18	8.62
8	Kladno	3.50	silt loam	20.2	65.7	14.1	2.39	1.25	47.5	0.58	36.78	8.63
9	Svetla n. S.	0.30	sand	2.8	8.3	88.9	2.62	1.11	57.6	0.15	33.34	8.48	0.41
10	Kladno	0.60	clay loam	28.6	40.2	31.2	2.52	1.00	60.3	0.65	40.65	5.57	40.81
11	N. Bydzov		silty clay	50.0	44.8	5.2	2.54	1.29	49.3	0.06	31.97	13.95
12	N. Bydzov		silty clay	44.3	45.7	10.0	2.59	1.20	53.7	0.28	33.28	9.29	6.89
13	Litvinov		silty clay loam	35.8	51.9	12.3	2.53	1.43	43.5	0.10	33.81	10.28	1.56
14	Jihlava	1.30	sandy clay loam	31.3	21.2	47.5	2.40	1.21	49.6	0.20	35.68	9.89	26.79
15	Jihlava	5.00	loam	16.9	38.9	44.2	2.50	1.23	50.9	0.32	27.92	14.01	36.96
16	Jihlava	1.20	sandy loam	18.4	21.4	60.2	2.56	1.05	59.0	0.50	28.60	13.82
17	Slany	0.30	clay	43.2	27.3	29.5	2.53	1.14	55.1	0.31	33.29	12.00	46.02
18	Struharov	1.90	loamy sand	< 0.1	17.3	82.7	2.45	1.25	49.0	0.07	29.73	11.75	10.24
19	Jihlava	1.50	clay loam	32.3	40.8	26.9	2.54	1.15	54.7	0.14	30.36	7.14	41.91
20	Jihlava	7.50	sandy loam	15.0	22.0	63.0	2.45	1.08	55.8	<0.05	30.39	6.11	18.46
21	Jihlava	10	silt loam	11.8	52.7	35.5	2.41	1.05	56.6	0.24	25.23	13.38	21.24
22	Struharov	2.00	loamy sand	3.5	18.6	77.9	2.51	1.25	50.1	0.11	28.56	13.14
23	Jihlava	1.20	silt loam	13.3	61.4	25.3	2.61	1.11	57.5	0.16	28.14	14.26
24	Chomutov		clay	64.9	27.9	7.2	2.05	0.80	61.0	0.50	33.25	13.51
25	Chomutov		clay	64.9	14.7	20.4	2.46	1.00	59.4	0.30	33.60	13.72	64.39
26	Slany		clay	43.2	27.3	29.5	2.56	1.25	51.2	0.37	33.62	11.28	46.65
27	Chomutov		clay	44.8	23.9	31.3	2.54	1.18	53.6	0.46	33.84	11.43
28	Jihlava	0.80	loam	15.7	33.7	50.6	2.42	1.08	55.5	0.25	29.08	12.27
29	Holesov	1.20	silty clay loam	30.0	65.0	5.0	4.09	1.34	67.3	0.26	35.94	8.99	28.35
30	Holesov	0.50	silt loam	10.3	61.9	27.8	2.32	1.21	47.6	0.81	35.80	7.99	13.95
31	Holesov	0.60	silty clay loam	31.0	63.0	6.0	2.49	1.40	43.8	0.31	35.70	9.27	16.53
32	Holesov	6.50	sandy loam	15.5	24.2	60.3	2.43	1.33	45.2	0.10	35.62	7.86
33	Holesov	3.00	silty clay	40.0	40.0	20.0	2.45	1.25	49.2	0.22	34.20	11.86	35.81
34	Holesov	6.00	sandy loam	11.7	35.1	53.2	2.60	1.25	51.8	<0.05	36.94	7.28

Note: Clay, Silt, Sand mean clay, silt, sand particles content in samples (w/w%). ρ_s, ρ_b, ε is soil particle density, dry bulk density and porosity. Si and Al mean elemental silicon and aluminum content in samples (w/w%).

presents a summary of soil properties for 34 soil samples collected from various sites and depths in the Czech Republic. The main criteria for selecting sample sites were based on expected soil composition from geological map surveys with a special focus on sites with high clay content and low organic matter, site history and accessibility for sampling equipment. Preference was given to areas with minimal agricultural or industrial activity to reduce the risk of contamination from external sources. The surface soil layer was excluded from sampling due to the vegetation cover and expected higher OC content. Most of the collected samples originated from the unsaturated zone. Each sample is defined by its site of origin, sampling depth, soil texture, and a comprehensive set of physical and chemical properties. Clay content varied widely, from as low as 0% to as high as 64.9%, while silt ranged from 5.1% to 71.2%, and sand from 5.2% to 88.9% (w/w). The relative percentages of sand, silt, and clay were used to classify the samples according to the international soil texture classification standard; this system delineates 12 distinct textural classes. These were broadly categorized into two main groups: (i) fine-grained soils, comprising clay, silt loam, and silty clay loam; (ii) and coarse-grained soils, primarily consisting of sand, sandy loam, and loamy sand.

The soil samples exhibit a range of particle densities (2.05–4.09 g cm⁻³), indicating diverse mineral composition, relatively low bulk densities (0.80–1.43 g cm⁻³), and high porosity (43.5–67.3%), indicating soils with favorable characteristics for sorption processes. OC levels were generally low across the samples, ranging from ˂0.05% to 0.81% by mass. The samples were collected from both topsoil (˂1.20 m) and deeper soil layers, where higher OC content was expected in the topsoil. However, no significant correlation was observed between depth and OC content, with most samples showing OC concentrations consistent with those typically found in deeper soil layers (corresponding to a fraction of organic carbon (f_OC) ˂ 0.005) [3]. The only exceptions were samples 8, 10, 7, and 30, where the f_OC values ranged from 0.006 to 0.008. The range of SSA values varied considerably (0.41–64.39 m² g⁻¹), indicating differences in the sorption capacity of the soils. Additionally, the observed SSA values were generally lower than those typically associated with highly effective sorbents [42]. The elemental composition, particularly Si and Al content, suggests the presence of various clay minerals and metal oxides, which can contribute to sorption through mechanisms such as cation bridging and surface complexation, thereby impacting overall soil properties and potential interactions with contaminants [43,44].

XRD analysis revealed that the soils predominantly comprised quartz, clinochrysotile, muscovite, and various feldspars (including albite, orthoclase, microcline), and zeolites, along with clay minerals such as kaolinite and montmorillonite (Table S1). Fine-grained soils demonstrated a higher abundance of phyllosilicates, particularly clay minerals (kaolinite, montmorillonite, and illite) and muscovite, which are known for their high sorption capacities due to large specific surface areas and cation exchange properties. In contrast, these sorption-active minerals were often absent in coarse-grained soils, suggesting potentially lower sorption capacities in these samples. This mineral distribution pattern aligned with the particle size distribution results, reinforcing the textural classification of the samples.

Before the experiments, all soil samples were analyzed for PCE content. The results indicated that PCE concentrations were below the detection limit, confirming the absence of the compound in all samples.

3.2. Comparison of Measured and Estimated Linear K_d Values of Soil Samples

The distribution of PCE between the solid and liquid phases was characterized using adsorption isotherms.

Table 2. Measured and estimated linear sorption coefficients K_d.

No.	Kd (L kg−1) Estimated	Linear Regression					No.	Kd (L kg−1) Estimated	Linear Regression
		Kd (L kg−1) Measured			R2	Sum of Sq.			Kd (L kg−1) Measured			R2	Sum of Sq.
1	0.44	0.49	±	0.04	0.991	62	18	0.25	0.47	±	0.07	0.946	382
2	0.84	1.08	±	0.11	0.963	994	19	0.51	0.92	±	0.29	0.92	420
3	1.52	1.33	±	0.20	0.954	1044	20	0.18	0.63	±	0.32	0.97	363
4	0.44	0.83	±	0.09	0.99	179	21	0.87	0.66	±	0.17	0.899	1262
5	0.25	0.61	±	0.10	0.971	135	22	0.40	0.56	±	0.26	0.973	247
6	0.91	0.90	±	0.08	0.887	1455	23	0.58	0.67	±	0.06	0.944	710
7	2.94	0.98	±	0.11	0.946	1261	24	1.82	2.27	±	0.18	0.983	937
8	2.11	0.80	±	0.07	0.957	994	25	1.09	1.83	±	0.32	0.921	4601
9	0.54	0.38	±	0.06	0.89	251	26	1.34	1.44	±	0.19	0.929	2203
10	2.36	1.55	±	0.99	0.877	899	27	1.67	1.26	±	0.19	0.976	788
11	0.22	0.40	±	0.03	0.993	35	28	0.91	1.15	±	0.16	0.958	1056
12	1.02	0.71	±	0.14	0.879	1777	29	0.94	0.76	±	0.10	0.941	924
13	0.36	0.44	±	0.04	0.96	241	30	2.94	1.53	±	0.12	0.961	1722
14	0.73	0.87	±	0.11	0.96	779	31	1.13	0.88	±	0.11	0.912	1781
15	1.16	0.67	±	0.15	0.973	755	32	0.36	0.49	±	0.02	0.997	22
16	1.82	0.84	±	0.22	0.955	834	33	0.80	0.89	±	0.07	0.984	310
17	1.13	1.02	±	0.10	0.981	170	34	0.18	0.79	±	0.07	0.982	289

provides the comparison of measured and estimated linear K_d values for all samples, along with their respective coefficients of determination (R²) and least squares values. The linear sorption model (K_d = K_OC × f_OC) was employed to estimate the K_d values in soil samples [45,46]. The measured K_d values for PCE ranged from 0.38 to 2.27 L kg⁻¹ across different soil samples. Lower K_d values were observed in sand-dominated samples, while higher values were associated with clay-rich materials. These findings are consistent with previously reported K_d values for PCE in similar studies [47], highlighting the influence of soil composition on sorption behavior. Although the PCE sorption isotherms were slightly non-linear, a common occurrence in soils with low OC content (<1%) and high clay content, the differences in sum of squares and R² were minimal. The measured K_d values were generally higher than their corresponding estimated values. This trend suggests that empirical sorption models may underestimate K_d values [48,49]. This indicates that factors other than OC, such as clay content or SSA, might also significantly influence sorption in these soils. A paired sample t-test showed no significant difference between them (t(33) = 1.056, p = 0.299) [50]. While this indicates that the linear predictive model maintains reliability in estimating K_d values, the result from MAPE (45.6) suggests that empirically estimated K_d values may underestimate the sorptive behavior of soils.

3.3. Statistical Data Analysis

Table 3. Descriptive statistics of input data.

Variable	Number of Samples	Mean	Standard Deviation	Variance	Minimum	Median	Maximum
Kd (L kg−1)	34	0.92	0.43	0.18	0.38	0.84	2.27
OC (%)	34	0.28	0.21	0.04	0.05	0.25	0.81
Clay (%)	34	24.9	17.2	296.8	0.0	21.0	64.9
Silt (%)	34	36.8	18.1	326.7	5.1	34.4	71.2
Sand (%)	34	38.3	24.5	598.7	5.0	31.2	88.9
Si (%)	34	33.41	3.51	12.32	25.23	33.71	40.65
Al (%)	34	10.27	2.65	7.05	5.30	10.46	14.26
ρs (g cm−3)	34	2.54	0.29	0.09	2.05	2.53	4.09
ρb (g cm−3)	34	1.18	0.13	0.02	0.80	1.21	1.43
ε (%)	34	53.2	5.4	29.1	43.5	53.3	67.3
SSA (m2 g−1)	21	24.2	17.1	289.9	0.4	19.9	64.4

presents the descriptive statistics of the input data used for the multivariate analysis. The measured K_d values were generally low, with an overall mean of 0.92 ± 0.46 L kg⁻¹, indicating limited sorption capacity for PCE in these low-organic-carbon soils. The generally narrow range of K_d values (0.38–2.27 L kg⁻¹) suggests a degree of uniformity in sorption behavior among the studied soil samples. The working hypothesis suggested that the observed variations in K_d values were primarily attributable to differences in soil physicochemical properties. This assumption forms the basis for subsequent multivariate analysis to elucidate the specific soil characteristics influencing PCE sorption in these low-organic-carbon environments.

Correlations between soil properties and K_d values were examined to identify the key components governing PCE sorption in soils. Pearson’s correlation tests were conducted, with the null hypothesis evaluated against a stated significance level (α = 0.05). The most relevant properties were OC content, SSA, clay and sand content (Figure 1). Calculated p-values below the significance level (α = 0.05) confirmed the statistical significance of these correlations. Higher values of Pearson’s coefficients for SSA and clay content (0.679 and 0.510, respectively) indicate enhanced PCE sorption in soils with smaller particle sizes and consequently higher surface areas. K_d values showed a positive correlation with OC content (0.614), despite OC levels being <1%. Sand content demonstrated a moderate negative correlation with K_d values (−0.424), indicating reduced PCE sorption capacity in sandy soils. Other soil properties displayed non-significant correlations. Additionally, low Pearson’s correlations were observed between Al content and clay/silt particles (Al/Clay = 0.225; Al/Silt = 0.0173), as well as between Si content and sand particles (Si/Sand = −0.136), indicating no significant relationship between these elemental compositions and particle size distributions.

Since SSA data were only available for 21 samples, PCA was conducted separately on two datasets to ensure a thorough analysis: (i) the first set comprising 34 soil samples with 7 variables (six soil properties and K_d values), and (ii) a second set consisting of 21 soil samples with 9 variables, including SSA and porosity. Further details are provided in Text S5. The optimal number of PCs was determined by eigenvalues of the correlation matrix. In the first PCA analysis, PC1 and PC2 explained 63.77 % of the variance (PC1 38.83%; PC2 24.95%), both with eigenvalues higher than 1.7 (Table S2). Figure 2 presents a biplot combining loading and score plots, illustrating the contribution of original variables to the main components. Proximity between variables in the biplot indicates strong correlations. The PCA results revealed a strong positive correlation between K_d and OC, as well as moderate positive correlations between K_d and both clay and silt content. A negative correlation between K_d and sand content was indicated by an angle close to 180° between their vectors. Si and Al content showed minimal relevance in the PCA model. These findings suggest that OC, clay, and silt content are primary factors governing PCE sorption in the studied soils, while sand content negatively influences sorption, aligning with results from previous studies [45,51,52,53]. In the second PCA analysis, which included SSA and porosity, PC1 and PC2 explained 56.38% of the variance (PC1: 36.84%; PC2: 19.54%), both with eigenvalues higher than 1.7 (Table S3). The results highlighted the contributions of SSA and porosity to PCE sorption in soils. The corresponding biplot is displayed in Figure S1.

AHC was utilized to group samples based on their soil properties and measured K_d values resulting in a dendrogram (Figure S2) with three distinct clusters (green, red, and blue). The green cluster, containing 14 samples, is the most cohesive, while the red and blue clusters contain 6 and 14 samples, respectively. Most mergers occur at low dissimilarity levels (below 5000), but the three clusters remain distinct until around 6400 units, indicating strong between-cluster differences.

Combined with PCA, these analyses revealed a relationship between soil particle size distribution and K_d. The samples in this study were categorized into 10 classes according to the international soil texture classification standard. The soil texture triangle in Figure 3A depicts the relative proportions of sand, silt, and clay particles in the samples. Each soil texture class exhibits unique characteristics, such as water retention, permeability, and pore volume.

As the result of the AHC analysis, soil samples were grouped into three distinct classes of soils, primarily differentiated by their textural characteristics: Class 1 included fine- to coarser-grained soils with predominantly sand particles content (>50%), Class 2 comprised the finest soil types with lower sand particles content (˂50%), and Class 3 consisted of high or predominantly silt (>50%) and small sand particle content (˂50%) (Figure 3B). The resulting clusters showed strong agreement with the traditional sections in the soil textural triangle, validating the effectiveness of the clustering approach.

These findings are consistent with prior research that highlights the relationship between particle size distribution and sorption behavior. The observed classifications enhance the accuracy of sorption models by incorporating textural differences, which influence sorption capacity. This supports the broader understanding of how soil texture impacts the interactions between contaminants and soil particles [22].

The Kruskal–Wallis test was employed to assess the statistical significance of individual soil properties in influencing sample distribution across clusters. The results with Chi-squared (Chi²) values exceeding 5.991 (degrees of freedom (df) = 2) and p-values below 0.05 indicated statistically significant differences across the three clusters. Significant differences (p < α) were observed in OC, clay, silt, and sand content (

Table 4. Summary of Kruskal–Wallis test and corresponding p-values.

Variables	Chi-Squared Value	p-Value
OC	8.394	0.015
Clay	23.362	<0.001
Silt	19.061	<0.001
Sand	24.964	<0.001
Si	0.218	0.890
Al	0.976	0.614
ρs	0.435	0.813
ρb	0.500	0.829
ε	0.520	0.771
SSA	3.889	0.143

). These findings corroborated the initial assumptions derived from PCA and Pearson´s test. Mean values of significant soil properties for each cluster are summarized in Table S4.

LDA elucidated relationships within clusters based on significant soil properties: OC, clay, silt, and sand content (%). Soils in the first class, predominantly sandy, exhibited lower organic carbon content compared to soils in the second and third classes (

Table 5. Mean values of significant soil properties and descriptive statistics of K_d by class.

	OC (%)	Clay (%)	Silt (%)	Sand (%)	Kd (L kg−1)
Class	Mean	Mean	Mean	Mean	Mean	Std. Dev.	Variance	Min	Median	Max
1	0.17	14.22	22.87	62.92	0.69	0.21	0.05	0.38	0.65	1.15
2	0.34	41.78	39.99	18.21	1.10	0.53	0.28	0.40	0.95	2.27
3	0.41	10.61	61.81	27.58	1.01	0.36	0.13	0.66	0.94	1.53

). Class 2, which comprised the finest particles, exhibited the highest K_d values, while Class 1, consisting mainly of sandy soils, showed the lowest K_d. This trend aligns with the general principle that smaller particles tend to have higher sorption capacities due to their larger surface area and greater cation exchange capacity [54,55,56,57,58]. Figure 4 shows the correlation of initial variables with two factors. The first factor (F1) accounted for 70.72% of the variance and strongly correlated with sand and clay content; this indicates that these variables are important for distinguishing between groups. Factor 2 (F2) showed strong correlations with silt and clay content (Figure 4A). The score plot with confidence ellipses (Figure 4B) represents each observation on the factor axes, with observations classified based on highest probability of belonging. All observations fell within the 95% confidence ellipses. The confusion matrix summarized the classification of observations into three classes (14, 14, and 6 observations per class, respectively). These results indicate 100% accuracy in discrimination, demonstrating accurate sample discrimination based on four significant parameters (OC, clay, silt, and sand content).

3.4. Univariate and Multivariate Linear Regression

Firstly, the relationship between K_d and individual soil properties was assessed using univariate linear regression, with prediction models summarized in

Table 6. Linear regression for prediction of K_d and goodness-of-fit statistics.

Linear Regression Model	Units of x	Standard Error		Observations	R2	RMSE	MAPE
		Intercept	Slope
Kd(PCE) = 0.475 + 0.016 SSA	m2 g1	0.104	0.003	21	0.511	0.271	24.5
$K_{\mathrm{d}}\left(\mathrm{P}\mathrm{C}\mathrm{E}\right)=0.556+127.6$fOC	-	0.101	29.0	34	0.378	0.343	28.4
$K_{\mathrm{d}}\left(\mathrm{P}\mathrm{C}\mathrm{E}\right)=0.598+1.27$fClay	-	0.114	0.38	34	0.260	0.374	34.1
$K_{\mathrm{d}}\left(\mathrm{P}\mathrm{C}\mathrm{E}\right)=0.839+0.207$fSilt	-	0.094	0.23	34	0.008	0.433	39.3
$K_{\mathrm{d}}\left(\mathrm{P}\mathrm{C}\mathrm{E}\right)=1.199-0.74$fSand	-	0.127	0.28	34	0.180	0.394	34.4

Note: f_OC, f_Clay, f_Silt and f_Sand mean mass fraction of clay, silt, sand particles in samples.

. Each model was based on 34 observations, except for SSA, which had 21. Significant soil properties such as SSA, OC, clay, silt and sand content were further investigated. The correlation between K_d and SSA showed the highest Pearson’s correlation (0.679, with linear regression indicating statistically significant relationships between K_d and both SSA and OC. SSA accounted for 51.1% of the variability in K_d, while OC contributed 37.8% from Table 6. These results emphasize OC as a crucial factor in PCE sorption, even in soils with OC levels below 1%. SSA is strongly correlated with OC and inversely related to particle size. Despite achieving the best fit through univariate regression, the models exhibited low precision. Although clay and silt content are generally considered important for organic substance sorption, the regression analysis revealed that silt was not statistically significant, displaying the lowest coefficient of determination alongside the highest RMSE and MAPE values.

The second approach utilized multivariate analysis based on the AHC, Kruskal–Wallis, and LDA results. The models were developed by combining significant soil parameters: f_OC, f_Clay, f_Silt, f_Sand, and SSA. Multiple regression consistently achieved higher R² than univariate linear regression. As with the PCA analysis, multivariate models were applied to two separate datasets.

Table 7. Multivariate linear regression models for predicting K_d and corresponding goodness-of-fit statistics.

Class	Model
1	Kd(PCE) = 1.22 + 34.9fOC + 0.05fClay − 0.94fSand
2	Kd(PCE) = −0.74 + 131.5fOC + 2.87fClay + 1.01fSand
3	Kd(PCE) = 1.44 + 115.3fOC − 5.37fClay − 1.17fSand
	Standard Error				Observations		R2		RMSE		MAPE
	Intercept	X1	X2	X3
1	0.41	34.96	0.85	0.47	14		0.636		0.147		11.3
2	0.41	46.97	0.78	0.95	14		0.698		0.329		28.8
3	0.24	14.40	0.75	0.55	6		0.985		0.070		3.8

Note: X1, X2, X3 means standard error of slope for variable f_OC, f_Clay and f_Sand.

summarizes the models for each soil class from Figure 3B (sandy (1), clay particles (2), and silt particles (3)) without including SSA, while models incorporating SSA are presented in Table S5. Multicollinearity, especially among f_Sand, f_Silt, and f_Clay, was detected using tolerance (<3.0 × 10⁻⁶) and variance inflation factor (VIF) metrics (>3.4 × 10⁵). As a result, silt was excluded from the multivariate models to mitigate multicollinearity. The multivariate models for each class using f_OC, f_Clay and f_Sand provided better fits than single-variable regression. These models explained 63.6%, 69.8% and 98.5% of the variance in K_d for Classes 1, 2, and 3, respectively. The highest R² of 98.5% represents excellent fit but should be interpreted cautiously due to the small sample size in that class. Predictions deviated on average by 0.147, 0.329, and 0.07 units from measured K_d values, demonstrating high accuracy with low RMSE and MAPE values.

Figure 5 compares predicted and measured K_d, providing insights into model errors for each soil class. Analyzing the residuals helps identify outliers or samples that the model does not accurately represent. Notably, all residuals fell within the 95% confidence interval, indicating generally accurate predictions with no significant outliers. In Class 1, larger residuals were detected by loam (No. 15, 28) and sandy loam samples (No. 32). Similarly, clay loam soil (No. 7) shows some small residuals in Class 2, likely due to its proximity to the boundaries of the neighboring classes. Loam soils with balanced clay, silt, and sand content suggest areas for potential model improvement and highlight the need for a larger sample set to confirm trends. Additionally, acceptable residuals were observed in samples with higher OC content compared to other samples within the same class, reflecting potential variability in the dataset. These models are applicable to soils with low organic carbon content (<1%, w/w).

When applying the models for Classes 1 to 3 to real soils, it is crucial to assess the accuracy of K_d predictions and their alignment with measured values. A paired sample t-test confirmed that differences were not statistically significant for Class 1 (t(13) = 0.09, p = 0.935), Class 2 (t(13) = −0.07, p = 0.942), and Class 3 (t(5) = 0.25, p = 0.80). Since p-values exceeded the significance level of α = 0.05, the null hypothesis (H0: No differences between measured and predicted K_d values) was not rejected. The necessity of maintaining separate models for each class is reinforced by a t-test for paired differences, which showed significant results when applying the same model to Classes 2 and 3, with p-values below 0.05. This indicates that using distinct models for each class is essential for accurate sorption description. Additionally, although SSA was found to influence sorption, the models developed without SSA remained reliable. This is a valuable finding, as excluding SSA reduces the need for an additional, often costly soil characterization method, making the predictive models more cost-effective without significantly compromising accuracy.

The commonly used prediction model for K_d value, based on the equation K_d = K_OC × f_OC (Karrickhoff, 1979), was compared to measured K_d values across soil classes. Karickhoff’s model showed high RMSE of 0.400, 0.646, and 0.801, and MAPE values of 45.5, 41.1 and 56.4 for Classes 1, 2, and 3, respectively. The newly developed model demonstrated significantly higher accuracy, clearly indicating that it outperforms Karickhoff’s model for soils with such low organic carbon content.

4. Conclusions

This research utilized an extensive database of low-organic-carbon soil samples from across the Czech Republic to develop reliable sorption models for predicting K_d of tetrachloroethene. Based on the data and analyses conducted, this work classified low-organic-carbon soils into three distinct texture-based classes: loam to sandy, clay, and silty loam, highlighting the significant role of soil texture and composition in modeling contaminant behavior. OC content and SSA were identified as the dominant predictors of K_d, with clay and sand content also contributing significantly to its variability. These findings reinforce the importance of texture-specific modeling for accurately predicting the behavior and transport of PCE in low-OC soils.

Multivariate linear regression models were developed and demonstrated improved predictive accuracy over univariate approaches, explaining substantial variance in K_d values. Statistical tests validated the need for separate models for each soil class, ensuring precise sorption predictions. These models are specifically designed for soils with low OC content (up to 1%) and may not be applicable to soils with higher OC content. Soils with higher OC content were not included in this study, and for such soils, older, simplified models based on f_OC are generally more appropriate.

Our research highlights that multivariate regression models are not only effective but also cost-efficient, using affordable inputs and eliminating the need for expensive soil characterization methods. They provide a practical tool for predicting the distribution and transport of contaminants in low-OC soils, supporting both environmental and health risk assessments, while also guiding effective remediation strategies and monitoring at contaminated sites.

While linear models facilitate comparisons across different soil types, they may not fully capture nonlinear sorption behavior, especially under extreme conditions. Nonlinear models could improve accuracy but introduce added complexity, making direct comparisons and evaluations more challenging. Our linear multivariate regression models strikes a balance by providing reliable predictions without this added complexity, making it suitable for a wide range of applications.

Future research could explore the application of these models to other contaminants and soil types, as well as their integration into large-scale environmental monitoring and risk management systems. By refining and expanding these models, we can improve our ability to predict contaminant behavior in diverse soil environments, contributing to enhanced environmental protection and public health outcomes.