Using Machine Learning to Predict Oil–Mineral Aggregates Formation

Abstract

The formation of oil–mineral aggregates (OMAs) is essential for understanding the behavior of oil spills in estuaries and coastal waters. We utilized statistical methods (screening design) to identify the most influential variables (seven factors in total) during OMA formation. Time was the most important factor, followed by temperature and oil/clay ratio. Moreover, machine learning was applied to predict the OMA median diameter (D₅₀). Among the three tested algorithms, the Random Forest (RF) algorithm showed the highest accuracy, with a training R² of 0.99 and testing R² of 0.93. An open-source software tool that integrates the RF algorithm was developed, allowing users to easily estimate the OMA D₅₀ based on input variables. The valuable results and the practical tool we have developed enhance the understanding and management of environmental impacts associated with oil spills.

1. Introduction

Oil spill incidents persist as one of the most critical contributors to marine environmental pollution [1]. These spills usually have long-term negative impacts on the marine environment and ecology [2]. When an oil spill accident happens in coastal and estuarine waters, the dispersed oil droplets may interact with suspended sediment particles and form oil–mineral aggregates (OMAs) [3,4,5,6,7,8]. In general, the density of oil is lower than that of water, while the density of sediment is higher. Therefore, the density of OMAs may be lower, higher, or equal to that of water, depending on the properties and formation of oil droplets and sediment particles. Hence, the movement of OMAs in the water column can be very different due to relative density to the local water; it may float to the water surface, sink to the bottom, or move with water. The transport of OMAs is important for oil spill modeling [9].

The initial conceptualization of potential interactions between oil and mineral particles in an aqueous medium was proposed by Poirier and Thiel (1941) [7]. They suggested that kaolinite, a type of clay mineral, was particularly effective in promoting oil sedimentation [7]. However, the phenomenon of flocculation between oil and mineral particles in natural environments was not observed until the cleanup operations following the Exxon Valdez oil spill in Prince William Sound, Alaska, in 1989 [10]. The term “clay–oil flocculation” was subsequently used to describe this occurrence [10,11]. Scientists then theorized that this mechanism could facilitate the removal of spilled oil from water columns, even in low-energy environments [3,10,11,12]. This hypothesis was corroborated by subsequent oil spills, including those in Tampa Bay, Florida (1993), and the Sea Empress spill in Wales (1996) [5]. The term “oil–mineral aggregates (OMAs)” was later adopted to describe these interactions, as it became evident that not only clay-sized minerals (<2 µm) contributed to the formation of OMAs [4,13].

The process of OMA formation is a crucial natural mechanism that facilitates oil transportation between environmental compartments, thereby promoting oil dispersion [3,12,13]. Previous studies reported that OMA formation is influenced by a multitude of factors; for example, Gong et al. (2014) suggested that the properties of the oil (e.g., type, droplet size, and concentration), the properties of the mineral particles (e.g., size, shape, density, concentration, and organic matter content), and ambient conditions (e.g., temperature, salinity, and mixing energy) [14]. Despite extensive research into OMA formation under various conditions, the formation mechanisms remain controversial [15]. For example, regarding the impact of salinity on OMA formation, some studies have suggested that low salinity levels (0–5 ppt) have a strong influence, while no significant effect was observed with increasing salinity [16,17,18,19]. However, Guyomarch et al. (1999) reported the opposite result, with increasing salinity from 10 to 50 ppt having a profound effect on OMA formation [20].

It is worthwhile noting that different OMA formation studies employed varying laboratory operations, leading to significant variance and uncertainty in the reported data. Unfortunately, few studies have attempted to replicate experimental runs to quantify experimental error [17,21,22], resulting in less reliable data [23]. The complexity inherent in the OMA formation system is evident [14]. However, there appears to be an absence of systematic research aimed at identifying key influencing factors through statistical design and analysis approaches [15]. The potential for interaction effects between various factors, such as the effect of temperature over time, is an important aspect of the OMA formation process. This is largely unexplored and represents a critical area for further research.

Meanwhile, recent developments in big data processing, enhanced computing capabilities, and machine learning algorithms have significantly impacted scientific research and industrial operations [24,25,26]. Machine learning techniques are gaining prominence across various research domains, including those related to oil spills. For instance, Cao et al. (2022) utilized machine learning to examine the influence of salinity and chemical dispersants on the biodegradation of spilled oil. They quantitatively predicted the strength of the relationship among dispersant use, salinity, cell count, and other variables [24]. Given the capacity of machine learning to process extensive datasets and its predictive accuracy, there is growing interest in its application in forecasting OMA formation, which we focus on in the present study.

The objective of this investigation is to study the formation of OMA under various conditions, identify the significant factors and interaction effects, and assess the potential for using machine learning algorithms to predict OMA formation. Based on the study by Gong et al. (2014) [14], in this study, seven factors, namely salinity, temperature, time, oil/clay ratio, agitation speed, clay type, and the presence/absence of dispersants were selected for evaluation, and the median OMA diameter was used as the response variable. The influence of varying periods affects oil droplet dynamics, consequently impacting OMA size. The use of dispersants modifies oil viscosity and interfacial tension, influencing OMA stability. Variations in clay concentrations were implemented, along with different salinity levels, to replicate marine and river plume environments and simulate natural turbidity. A screening design statistical approach was adopted to design the experiment and identify the most influential factors and interactions. Furthermore, a dataset was created by integrating data from this study and the existing literature [16,18,27,28,29,30,31,32], which was then utilized to train three machine learning algorithms: Random Forest (RF), Gradient Boosting Regression (GBR), and Adaptive Boost Regression (AdaBoost). The predictive value of each model was evaluated, and the stability and generalizability of the optimal model were assessed. Lastly, an application software was developed to enable the prediction of the median OMA diameter by inputting OMA formation conditions. The findings of this study offer valuable insights into the mechanisms underlying OMA formation, facilitating the development of more accurate models to simulate the fate and transport of spilled oil in estuarine and coastal environments.

2. Materials and Methods

2.1. Materials

In this investigation, crude oil characterized by a density of 799.2 kg/m³ and a viscosity of 61.1 cSt was employed. The mineral components selected were kaolinite and montmorillonite; both are readily available in various natural environments, including soils and sediments. Their widespread availability and cost-effectiveness make them suitable for oil spill remediation through OMA formation [33]. Depending on the experimental conditions, kaolinite (2788.9 kg/m³ of density) or montmorillonite (2172.5 kg/m³ of density) was utilized. Additionally, a chemical dispersant, JAFIRST™001 (Xinluo Industrial Co., Ltd., Shanghai, China), was applied at a dispersant-to-oil ratio (DOR) of 1:10, adhering to the predefined experimental parameters. Previous studies have indicated that this specific DOR ratio enhances OMA formation [34].

2.2. OMA Formation Experiments

The experimental design was implemented using the Screening Design feature in Minitab 19 software, with the level settings detailed in

Table 1. Level settings for the seven studied factors for oil–mineral aggregate formation experiments.

Factor	Level
Temperature (°C)	0	15	30
Salinity (ppt)	0	17	34
Time (hour)	4	6	8
Agitation (rpm)	100	130	160
Mixing ratio (oil/clay, w/w)	1:2	1:1	2:1
Clay type	Kaolinite	Montmorillonite
Presence of dispersant	Yes	No

. A temperature of 0 °C was selected to simulate the winter conditions in most coastal areas. Temperatures of 15 °C and 30 °C were chosen to represent summer conditions in various coastal environments globally. The former is characteristic of temperate coastal regions, including Northern Europe, southern Australia, and the northeastern United States [35]. The latter represents tropical and subtropical areas, such as the Gulf of Mexico, the Caribbean, northern Australia, and Southeast Asia [35]. Regarding salinity, 0 ppt was used to simulate river water, while 17 ppt was selected to represent coastal regions influenced by riverine input or estuarine conditions. A salinity of 34 ppt was chosen to simulate subtropical and tropical coastal waters. Previous studies have shown that mixing durations of 4 and 6 h effectively form OMAs, thus these durations were used [30,36,37], along with an 8-h interval to examine the impact of extended mixing time. Agitation speeds of 100, 130, and 160 revolutions per minute (rpm), corresponding to shear rates of approximately 15, 18, and 20 s−¹ [38], were selected based on their demonstrated efficacy in OMA formation in prior research [16,31,36]. Oil-to-clay ratios of 1:2, 1:1, and 2:1, identified as influential in oil trapping efficiency, were also tested [31,39].

Each experimental run was duplicated to minimize experimental errors, with detailed runs provided in Supplementary Materials Table S1. For each experiment, 100 mL of aqueous solution with the desired salinity level was prepared. Then, 40 mg of crude oil and 20–80 mg of clay (depending on clay type and oil/clay ratio) were added to a 250 mL Erlenmeyer flask containing the solution. The sample-containing flask was agitated using a temperature-controllable shaker (see Figure S1 in Supplementary Materials) to form OMAs. Samples were collected hourly, and the OMA structures were analyzed using inverted microscopy (see Figure S2 in Supplementary Materials). The OMA size (area and perimeter) was measured using Image processing software (ImageJ 1.53k.exe).

2.3. Machine Learning Model

The present study employed three tree-based machine learning algorithms, namely RF, GBR, and AdaBoost, to predict the median diameter of OMAs. These algorithms were selected due to their capacity to model the nonlinear relationships between input features and response variables. Additionally, their robustness against outliers and noise in data made them suitable choices for this analysis. A more detailed description of these algorithms is provided in the study by Yu et al. (2023) [26]. The models were developed using Scikit-learn libraries in the Anaconda3 environment based on Python 3.9 [40]. The input dataset was subjected to a nested cross-validation (CV) procedure, wherein the inner and outer loops comprised 5 folds. The outer loop was employed to obtain a less biased estimation of model performance, while the inner loop was used for model tuning, specifically the optimization of hyperparameters. In the hyperparameter tuning stage, a grid-search method was implemented to determine the optimal values of “max_depth” and “n_estimator.” The range for “n_estimator” was set within the 1 to 100 range, incremented by 5, while “max_depth” was evaluated between 5 and 100. After determining optimal hyperparameters, they were integrated into the model’s framework. The specific nested CV procedure is presented in Figure 1. The nested CV procedure was initiated by a random shuffling of the dataset (random state = 40) prior to its division into five equally sized folds. Within each outer loop iteration, a single fold was reserved for the final testing set; the remaining data was subjected to the inner loop. This inner loop was characterized by a 5-fold CV serving the purpose of hyperparameter tuning and model selection. The model’s overall efficacy was determined by computing the mean performance metric across all iterations in the outer loop. Finally, the best estimator was saved and used for further analysis.

2.4. Model Evaluation

Assessment of the models’ predictive accuracy was conducted using the coefficient of determination (R²), root means square error (RMSE), and 95% confidence interval (CI) [41]. A model is considered more accurate if it exhibits a higher R², and lower RMSE and 95% CI values. The calculation of these metrics is based on the following equations:

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

(1)

$$RMSE=\sqrt{\frac{1}{N}\left({{\displaystyle \sum }}_{i=1}^N{\left(y_i-\widehat{y_i}\right)}^2\right)}$$

(2)

$$95\% CI=\overline{y} \pm 1.96 \left(\frac{\sigma }{\sqrt{N}}\right)$$

(3)

where $N$ denotes the sample size; $\widehat{y_i}$ and $y_i$ denote the predicted and actual values of the $i^{th}$ sample, respectively; $\overline{y}$ is the mean of the actual values; $\sigma$ denotes the standard deviation.

Upon the establishment of models through the nested CV procedure for the three distinct algorithms, the optimal model was selected based on its superior performance, as evidenced by the highest R², lowest RMSE, and lowest 95% CI. Prior to deploying this selected model, a further evaluation was performed by applying varied test/train splits to examine the stability and generalizability of the model. The proportions of the original dataset assigned to the training set started at 10% and increased by 10% at each iteration, reaching 90% of the original dataset. Simultaneously, the portion of the original dataset allocated to the testing set, initially comprising 90%, was reduced by 10% with each iteration, ultimately constituting only 10% of the original dataset [42,43]. Importantly, to prevent any potential bias or order effects, the dataset underwent a random shuffling procedure (random state = 40) before the division of data. This ensures a randomized allocation of data instances, supporting the reliability and validity of the subsequent model evaluations.

2.5. Machine Learning Quantification of Feature Importance

In this study, two approaches were adopted to assess the significance of each feature. The first approach was the conventional feature importance, involving the calculation of the Gini importance derived from the Gini index. The Gini index served as the metric for assessing the purity of nodes within decision trees, where a higher Gini index corresponded to lower purity. The Gini decrease was quantified as the difference between the totaled Gini indexes of divided nodes and the Gini index of each individual node. The Gini importance, measured on a scale from 0 to 1, was derived by proportionally weighing the Gini decrease relative to the frequency of the node’s occurrence in all trees. A greater Gini importance value indicated a more substantial impact of the factor. This analysis utilized the feature importance tools available in the Scikit-learn libraries.

In addition to the conventional feature importance, permutation feature importance was utilized. This method quantifies the influence of each feature on the model’s performance by measuring the decrease in performance subsequent to a random permutation of the feature’s values. If the model’s performance decreased significantly when a feature’s values were shuffled, the feature was considered important. This measure provided an additional layer of robustness to the evaluation of feature significance, accounting for the impact of each feature on the model’s predictive accuracy.

This study further assessed the influence of each feature on the predictive model using a technique known as partial dependence plots (PDPs). These plots provide a graphical representation of the marginal effect of a feature on the predicted outcome of a machine-learning model, holding all other features constant. This method offers valuable insights into the nature and strength of the relationship between each feature and the predicted outcome, facilitating an understanding of the model’s behavior beyond the insights provided by feature importance metrics alone. By observing how the predictions vary with changes in a feature’s values, potential nonlinearities and interactions with other features can be identified, contributing to a more comprehensive understanding of the model’s inner workings. In this study, for the PDPs, the presence or absence of dispersants was indicated by values 0 or 1 respectively. The other factors utilized 100 values, evenly spaced between the maximum and minimum values.

2.6. Machine Learning-Based Software

This section introduces the machine learning-based software developed for predicting the median diameter of OMAs. The software utilizes machine learning algorithms selected based on their superior performance, characterized by the highest R² values and lowest RMSE and 95% CI values. The operational workflow of the software comprises three main components:

• Input parameters: The software requires the following input data to perform predictions:
  • Time: Duration of the experiment (min)
  • Clay type: Density of the clay used (g/cm³)
  • Oil type: Density of the oil used (g/cm³)
  • Dispersant: A binary input indicating the presence (Yes) or absence (No) of dispersants
  • Oil concentration: Concentration of oil in the mixture (mg/L)
  • Clay concentration: Concentration of clay in the mixture (mg/L)
  • Salinity: Salinity of the mixture (ppt)
  • Shaking rate: Agitation speed (rpm)
  • Temperature: Ambient temperature during the experiment (°C)
• Process: The software applies the selected machine-learning algorithm to the input data. This algorithm has been optimized for accuracy and reliability in predicting the median diameter of OMAs based on the input parameters.
• Output: The primary output of the software is the predicted median diameter of OMAs (µm). This aids in understanding the behavior of OMAs under different experimental condition.

3. Results and Discussions

3.1. Statistical Analysis

3.1.1. Significance Analysis of the Formation Factors

Based on previous studies [16,17,28,30,32,36,39], the formation of OMAs is mainly controlled by temperature, salinity, time, agitation speed, clay type, oil/clay weight ratio, and the presence or absence of dispersants. However, the level of their impact on the median diameter (D₅₀) of OMAs has not been thoroughly investigated and compared. In this study, a statistical method, screening design, was used to estimate the significance of these factors. A representative image of OMAs captured through inverted microscopy is presented in Figure 2, while the detailed experimental design and raw data are available in the Supplementary Materials (Table S1). A paired t-test carried out in Minitab produced a p-value of 0.329, higher than the 0.05 significance level. This implies no significant statistical variance between the means of the OMA D₅₀ in the two experimental setups. Consequently, this analysis suggests that measurement inaccuracies and human errors did not significantly influence the study’s outcomes. Analysis of variance (ANOVA) was employed to assess the impact of various factors on OMA D₅₀, with results summarized in

Table 2. Analysis of variance in the median diameter (D₅₀) of oil-mineral aggregates.

	p-Value	F-Value
Time	0.000	22.48
Temperature	0.014	6.96
Oil/clay ratio	0.023	5.77
Clay type	0.069	3.58
Time × Oil/clay ratio	0.004	9.64
Time × Temperature	0.020	6.17
Temperature × Oil/clay ratio	0.041	4.62

and Equation (3). The analysis identified time as the most influential factor on OMA median diameter, as indicated by a p-value significantly less than 0.05 and the highest F-value of 22.48. The temperature and oil/clay ratio were also identified as significant influencers of D₅₀, with p-values of 0.014 and 0.023, respectively. However, the effect of clay type was only marginally significant (0.05 < p-value = 0.069 < 0.1) in affecting D_50.

A regression model was developed to capture the relationship between the identified significant factors, involving their interaction effects and response variable (OMA median diameter), as shown in Equation (4). The model coefficients were estimated using the least squares method. The equation is as follows:

$$D_{50}=-32.9+0.109x_1+14.21x_2+3.42x_3+0.435x_4-0.1807x_1{x}_2+0.01251x_1{x}_4-0.1356x_2{x}_4$$

(4)

where $x_1$, $x_2$, $x_3$, and $x_4$ denote temperature (°C), time (hours), clay type (kaolinite and montmorillonite denoted as −1 and +1, respectively), and oil/clay ratio (1:2, 1:1, and 2:1 denoted as 25, 50, and 75, respectively).

A quantitative analysis of the impact of identified factors (time, temperature, oil/clay ratio, and clay type) on D₅₀ was conducted via Equation (4) and illustrated in Figure 3. Figure 3a demonstrates a direct correlation between extended mixing times and increased D₅₀. It was observed that increasing the duration from 4 to 8 h increased D₅₀ from 19 µm to 38 µm, implying that longer mixing periods promote the formation of larger OMAs. This finding is consistent with previous studies [31,44]. Sun et al. (2014) explored the effect of time on OMA size. They reported an increase with extended duration, potentially due to the incorporation or coalescence of small oil droplets into or onto the OMA structure [31]. In contrast, Ji et al. (2021) noted a decrease in OMA D₅₀ with increasing mixing time, proposing that this could be attributed to the continuous fragmentation of OMAs into smaller aggregates [28]. Additionally, Zhao et al. (2014) discovered that for many light to moderately viscous oils, equilibrium in oil droplet size distribution is usually attained within a relatively short timeframe, often less than several tens of minutes [45]. This finding implies that oil viscosity plays a critical role in determining the final size distribution of OMAs. Beyond viscosity, oil-water interfacial tension presents a more substantial barrier to droplet breakage, as demonstrated by a sharp decline in the breakage rate of oil droplets with increasing interfacial tension [46]. This resistance could significantly impact OMA formation and sizing during extended mixing periods. These opposing findings, along with the influence of oil’s physical properties, underscore the complexity of the factors affecting OMA formation. This emphasizes the necessity for further research to reveal the precise impact of mixing time on OMA formation.

The impact of temperature on OMA D₅₀ is presented in Figure 3b. The findings suggest that increasing the temperature from 0 °C to 30 °C leads to a gradual reduction in OMA D₅₀, indicating that higher temperature conditions favor the formation of smaller OMAs. This observed phenomenon can be linked to the reduction in oil viscosity as temperature rises, which consequently facilitates the dispersion of oil into small droplets [47]. Additionally, the increase in temperature typically leads to a decrease in oil–water surface tension, further promoting the formation and dispersion of smaller oil droplets [48]. This simultaneous decrease in viscosity and surface tension at higher temperatures plays a crucial role in enhancing the dispersibility and spread of oil in aqueous environments. As a result, the OMA D₅₀ exhibits a decline in correspondence with increasing temperature.

Increasing the oil/clay ratio from 1:2 to 2:1 decreased the size of OMAs, as shown in Figure 3c. This outcome can be attributed to the reduction in available minerals to coalesce on oil droplet surfaces, resulting in the formation of smaller OMAs. Nevertheless, this finding deviates from the conclusions drawn in previous studies [34,49,50], which reported a positive correlation between the OMA size and the oil/clay ratio. They hypothesized that, at high mineral concentrations (low oil/clay ratio), the mineral surface could provide adequate penetration to break down the OMAs into smaller droplets [34,49,50].

Based on the data shown in Figure 3d, the median diameter of OMA was greater when using montmorillonite (32 µm) compared to kaolinite (26 µm). This finding indicates that montmorillonite, due to its higher hydrophobicity, is more efficient at interacting with the oil, resulting in larger OMAs. This observation aligns with prior research indicating that enhancing mineral hydrophobicity can lead to an increase in the size of OMAs, ranging from a few to tens of micrometers [22,49,51]. Regarding cation exchange capacity (CEC) and mineral surface properties, montmorillonite demonstrates a higher CEC than kaolinite [52]. This characteristic significantly enhances montmorillonite’s ability to adsorb many organic compounds, including petroleum hydrocarbons, a feature that significantly contributes to its efficacy in OMA formation [53]. The high CEC of montmorillonite also promotes its inherent adhesion properties [54] and facilitates the formation of stronger bonds with oil droplets, further aiding in the formation of OMAs. Additionally, montmorillonite’s high surface charge allows it to absorb oil droplets, accelerating OMA formation [53]. Furthermore, montmorillonite is characterized by a greater tendency to swell in aqueous environments relative to kaolinite [52,55]. This swelling behavior not only enhances the penetration of non-polar hydrocarbon molecules into the interlayer spaces of the clay mineral but also significantly contributes to its adhesion properties. As montmorillonite swells, the increase in the volume of its interlayer spaces allows for more extensive physical contact and intermolecular interactions with the hydrocarbon molecules [56]. This enhanced contact improves the adhesion between the clay particles and oil droplets, increasing the clay’s ability to absorb oil. Consequently, this improved adhesion due to swelling plays a pivotal role in the formation of larger OMAs. These properties of montmorillonite, including its higher surface charge, CEC, and swelling capacity, play a pivotal role in its effectiveness in OMA formation and the resultant increase in aggregate size [53].

3.1.2. Interaction Effects

This study extended beyond assessing the individual influences of factors by also examining the two-factor interaction effects. Significant interactions, as presented in Table 2, involved combinations of time, oil/clay ratio, and temperature. The influence of these interactions on the D₅₀ of OMA was quantified by Equation (4). For each combination of factor levels, the response value (D₅₀) was computed, with the mean value utilized for analysis. The resulting data are presented in Figure 4. Although the model incorporates interaction terms, it retains linearity concerning its parameters. This linear characteristic stems from the inherent linear properties of statistical modeling within an ANOVA framework, where “linear” suggests a direct relation to the model’s coefficients rather than the predictors. Consequently, a linear relationship between the factor and response is shown in Figure 4.

The statistical analysis presented in Table 2 revealed that the impact of time on D₅₀ was significantly influenced by the oil/clay ratio, as evidenced by the low p-value (0.004) for the interaction between time and the oil/clay ratio. This finding is further supported by the graphical representation in Figure 4a, showing that an increase in the mixing time from 4 h to 8 h did not significantly enhance D₅₀ (~24 µm) at an oil/clay ratio of 2:1. Conversely, a substantial increment in D₅₀ was observed (ranging from ~20 µm to 48 µm) with oil/clay ratios of 1:1 or 1:2. This suggests a significant dependency of the time effect on the oil/clay ratio. Specifically, a higher proportion of clay in the OMA formation system appears to amplify the effect of extended time, resulting in larger OMAs.

Additionally, the impact of time on OMA D₅₀ was significantly influenced by temperature, as indicated by a p-value of 0.02 (Table 2) and demonstrated in Figure 4b. At 0 °C, extending the formation time from 4 to 8 h significantly raised D₅₀ from 20 µm to 47 µm, while at higher temperatures of 15 °C and 30 °C, the increases in D₅₀ were less pronounced. This finding implies that longer formation times at lower temperatures are conducive to forming larger OMAs, whereas the effect of formation time on D₅₀ diminishes with increasing temperature.

Observations from Figure 4a,b reveal that at shorter mixing times (4 h), variations in temperature or oil/clay ratio have a minimal impact on OMA D₅₀. This is possibly due to insufficient duration for the complete development of OMAs during the initial mixing stages. Consequently, the influences of temperature and oil/clay ratio on OMA formation are less noticeable in this early stage. However, as the mixing time extends, the gradual growth in OMA D₅₀ can be attributed to the continuous aggregation of free particles onto the oil droplets or the already formed OMAs [31].

3.2. Machine Learning Prediction

3.2.1. Algorithm Selection

In this study, we investigated the feasibility of employing machine learning algorithms for predicting OMA D₅₀, a topic that has received minimal attention to date. To accomplish this, we utilized three machine learning algorithms, namely RF, GBR, and Adaboost, to estimate OMA D₅₀. The dataset used in this study comprised the data generated in our work and previously published data [16,18,27,28,29,30,31,32], with the D₅₀ size distribution presented in Figure 5. It is evident from Figure 5 that most of the data fell within the 5–80 µm range, while data for OMA D₅₀ in the range of 80–300 µm were limited. The literature experimental conditions and the resulting OMA median diameter are provided in the supplemental Excel file described in the Data Availability Statement section.

The methodological strategy for model selection involved the application of nested CV, enabling the identification of the most effective model. This methodological approach effectively simulates the process of model training and subsequent evaluation on independent datasets, ultimately ensuring a more unbiased estimate of the model’s predictive performance. The R² scores derived from the nested CV process for each algorithm are presented in

Table 3. Average score and standard deviation of nested cross-validation (CV) for studied algorithms. The nested CV score is calculated as the average of the performance scores obtained from each of the outer “testing” folds.

Algorithm	Average R2	Standard Deviation
Random Forest (RF)	0.930	0.036
Gradient Boost Regression (GBR)	0.886	0.051
Adaptive Boosting (AdaBoost)	0.908	0.041

, providing a detailed comparative comparison. It should be emphasized that the nested CV score is derived from the mean of the performance scores yielded from each of the outer “testing” folds. Among the array of evaluated algorithms, the RF exhibited superior performance with an R² score of 0.930. This performance metric is notably higher than those achieved by the GBR (0.886) and AdaBoost (0.908) algorithms, highlighting the relative effectiveness of the RF approach in this specific setting. Furthermore, the standard deviation of the R² scores obtained from the nested CV serves as an indicator for model stability. The RF model demonstrated the lowest standard deviation of 0.036, implying a more consistent performance across data folds than the GBR (0.051) and AdaBoost (0.041). In essence, the RF’s performance was less influenced by the specific division of data into training and validation subsets. Consequently, the most efficient model derived from the RF algorithm was retained for subsequent analyses and predictions.

Following the identification of optimal models for each algorithm via nested cross-validation, the predictive capabilities of each model were assessed using the entire original dataset. The predicted results are presented in Figure 6. The RF algorithm presented the highest degree of predictive performance, achieving an R² score of 0.990 (Figure 6a), signifying that it accounted for 99.0% of the variation in the dependent variables. Additionally, the model’s RMSE was 5.050 (Figure 6a), illustrating high predictive accuracy with a relatively low average squared difference between the observed and predicted values. Lastly, the confidence interval (CI) for the RF model was 9.898 (Figure 6a), emphasizing the model’s precision in predicting outcomes within this range. Comparatively, the GBR and AdaBoost algorithms yield lower R² values of 0.976 and 0.979 (Figure 6b,c), respectively, implying slightly less variance explanation. Concurrently, both models generated higher RMSE values (GBR: 7.836; AdaBoost: 7.346; Figure 6b,c), implying slightly lower prediction accuracy than the RF model. Regarding CI, both the GBR and AdaBoost models have broader intervals (GBR: 15.359, AdaBoost: 14.341; Figure 6b,c) than the RF model, indicating less precision. Although all three models exhibit high predictive capabilities, the RF model demonstrates a marginally superior performance in terms of accuracy and precision. Therefore, considering the nested CV results and the predictive metrics from the entire dataset, the RF model appears to be the most suitable model for this specific application.

3.2.2. Sensitivity Analysis of Dataset Partitioning

The nested CV strategy produced an RF model with notable predictive capabilities, demonstrated by the highest average R² values of 0.930 ± 0.036 for unseen data and 0.990 for training data. Nonetheless, it was deemed critical to conduct a sensitivity analysis to assess the stability and reliability of this optimal model, as well as to ascertain the sufficiency and quality of the input dataset by employing various training/testing ratios [43,57].

To facilitate this, a sensitivity analysis was undertaken by systematically adjusting the proportions of the original dataset allocated in the testing set in 10% increments, ranging from 10% to 90%. Conversely, the training set proportion was decremented from an initial 90% to 10% in similar 10% steps. [42,43]. The influence of the partitioning strategy was quantified using R² and RMSE. The corresponding outcomes are graphically represented in Figure 7a,b. As the proportion allocated to the training dataset increases, a corresponding enhancement occurs in the model’s performance for the training and testing datasets. Specifically, the R² for the training set increases from 0.878 to 0.986 as the training size increases from 10% to 90%. This increment suggests an enhanced ability of the model to account for the variance in the training data with an increasing data volume. In terms of the testing set performance, there is a substantial improvement in the R² values, transitioning from 0.583 to 0.967. This suggests an improved generalization capacity of the model. Moreover, it is particularly noteworthy that the performance on the testing set undergoes a more pronounced enhancement when the training set is increased beyond 50% of the total dataset. This emphasizes the significance of a sufficiently sized training dataset to ensure not only a good fit to the training data but also effective generalizability to unseen data. The observations underscore the necessity of partitioning the data, especially in contexts where model predictions are crucial. Concurrently, the training and testing RMSE witnesses a general decline, as shown in Figure 7b, further corroborating the superior fit of the model with enlarged training data. This phenomenon is consistent with previous investigations that an enlarged training set and, consequently, a diminished testing set can result in better model performance [58,59,60]. Additionally, a notable decrease in the testing RMSE to 7.72 occurs when the training size is 80%, representing the minimum across all evaluated sizes. However, increasing the training size to 90% results in a slight increase in RMSE, even though the R² remains high. This suggests an 80% training size might offer a good trade-off between training and testing performance.

The difference between training and testing R² and RMSE is represented as gray bars in Figure 7a,b. A notable decline in the R² difference, from 0.30 to 0.02, is observed as the proportion of data allocated for training increases from 10% to 90%. Typically, a narrowing between the training and testing performance metrics suggests a reduction in overfitting and an enhancement in the model’s ability to generalize [61]. In this study, it is evident that as the model is trained on a larger dataset, its ability to make accurate predictions for unseen data (testing set) increases, corroborating its robust stability and superior generalization attributes.

3.2.3. Feature Importance

Utilizing the current study and relevant literature, various factors were applied to estimate the D₅₀ of OMAs, including shaking rate, time, temperature, salinity, clay and oil concentrations, clay and oil types (density), and the presence or absence of dispersants. As clarified in Section 3.2.1 and Section 3.2.2, the RF algorithm was identified as the most appropriate method for predicting OMA D₅₀. Through its implementation, the significance of each factor was quantified using conventional and permutation feature importance analyses, as shown in Figure 8. The conventional feature importance results (Figure 8a) indicate that oil concentration, clay concentration, and clay type had the greatest influence on D₅₀, contributing to more than 90% of the outcome. This was consistent with the permutation feature results (Figure 8b), showing that the model’s performance decreased significantly when the oil concentration, clay concentration, and clay type were changed. Consequently, future studies on OMA formation should prioritize these three factors.

The conventional and permutation feature importance analysis methods agree on the most and least important variables for OMA median size, yet they diverge in ranking the intermediate variables. This divergence arises from their inherent methodological differences. The conventional method focuses on model-centric criteria and is well-suited for analyzing how the model processes different data features. This approach is useful for model optimization and understanding its algorithmic behavior. Conversely, the permutation method adopts an empirical approach and is more effective in assessing the real-world impact of feature variations on OMA size. This provides valuable insights for practical application.

Furthermore, the influence of individual factors on OMA D₅₀ prediction was investigated using PDPs, as shown in Figure 9. These plots illustrate the partial dependence of a single predictor variable on the predicted response of a machine learning model while controlling for the values of other predictor variables. A noteworthy observation was the decline in predicted OMA D₅₀ from approximately 25 µm to 11 µm with an increase in oil concentration from 200 mg/L to ~250 mg/L. Beyond this, a further rise in oil concentration did not markedly influence the OMA median size. Given the limited studies on this particular impact of oil concentration, additional investigations are required.

Regarding clay concentration, an uptrend was observed in OMA median size, peaking at ~800 mg/L. Further increments to 1200 mg/L showed a reduction in the median size, beyond which OMA D₅₀ largely remained invariant. This observation parallels findings from Guyomarch et al. (2002), who claimed a Gaussian distribution for average OMA size, with the peak at a clay concentration of 800 mg/L [34].

For clay type (density), as illustrated in Figure 9, there is a noticeable stratified reduction in OMA D₅₀ from approximately 50 µm to 15 µm with increasing clay density. This observation was consistent with prior research where OMAs formed by silica (density = 2.46 g/cm³) presented a larger median size compared to that by kaolinite (density = 2.63 g/cm³) [49]. Nonetheless, most prior studies have focused on properties like clay hydrophobicity and cation exchange capacity rather than clay density and its implications on the OMA size distribution [37,49,53].

Both agitation time and speed exhibited slight influences on OMA D₅₀, particularly at their lower values. As shown in Figure 9, OMA D₅₀ remained relatively consistent initially, followed by a minor decrease between 1.5 and 3 h. Subsequent to this, there was a gradual increase in OMA D₅₀, peaking at 6 h, beyond which it stabilized with prolonged agitation. This behavior is similar to earlier observations where OMAs form rapidly at the initial 3 h, followed by their breaking apart. With prolonged agitation, the reformation of OMAs was observed, potentially due to the increased presence of oil droplets on the water surface [28]. In relation to agitation speed, a reasonable increase in OMA median size was noted until reaching peaking at approximately 150 rpm. Beyond this point, OMA median size exhibited a reduction with increased agitation speed. This can be explained by acknowledging that an optimal agitation speed promotes OMA formation [31], whereas an overly aggressive agitation speed might lead to OMA breakage [22].

As illustrated in Figure 9, the effects of several parameters, namely the presence of dispersants, oil type (density), temperature, and salinity, on the median size of OMAs were evident. The role of dispersants in affecting OMA size has been a point of contention in existing literature [16,17,18,19,20,62]. In this analysis, OMA D₅₀ data were collected from multiple studies, each employing varied dispersant types and differing dispersant-to-oil ratios (DOR). This variability could be a primary reason for the RF model’s inability to accurately reflect the dispersant’s influence on the median OMA size. Similarly, salinity’s effect on OMA size has been inconsistent across different studies [22,29,63,64,65], potentially impacting the PDPs for salinity concerning OMA median diameter. The influence of oil type on OMA’s median size appeared negligible, supporting prior studies that suggest that the oil type does not significantly impact OMA size [18]. It was further observed that OMA sizes under colder conditions were marginally larger compared to those at higher temperatures. This observation resonates with previous findings [30] and can be attributed to the decrease in oil viscosity with a rise in temperature, enhancing the dispersion of oil into finer droplets. Consequently, the D₅₀ of OMA demonstrates a reduction with temperature increase.

The feature importance derived from the machine learning algorithm and the significant factors identified through statistical analysis underscores the importance of oil and clay concentrations (correlating closely with the oil/clay ratio) and clay type. However, there are subtle differences in the results concerning other factors when comparing the two methodologies. This variation may be attributed to differences in data sources and the investigation range.

3.3. Machine Learning-Based Prediction Software

As Section 3.2.1 and Section 3.2.2 demonstrated, the RF algorithm exhibits satisfactory predictive capability for OMA D₅₀, registering R² values of 0.93 for unseen data and 0.99 for training data. Based on these observations, a software application incorporating the RF algorithm was developed to optimize the predictive workflow. A visual representation of the software’s user interface is illustrated in Figure 10. This tool expedites the estimation of OMA D₅₀ by permitting users to input relevant formation process parameters. Available as an executable (.exe) file in the Data Availability Statement section. This open-source software can be easily downloaded on a user’s computer for convenient use.

4. Conclusions

This research utilized a screening design to methodically investigate the formation of oil–mineral aggregates (OMAs) and identify the most influential factors. Seven process variables were analyzed, including temperature, time, salinity, clay type, agitation speed, oil/clay weight ratio, and the presence or absence of dispersants. The findings indicated that time exerted the most significant influence on the median diameter of OMAs, with temperature and oil/clay ratio also important factors. Notably, the effect of time was heavily influenced by the specific temperature and oil/clay ratio. Extending the mixing time to 8 h, particularly at a low temperature of 0 °C and an oil/clay ratio of 1:2, resulted in a significantly larger OMA D₅₀ (approximately 50 µm).

Furthermore, this study evaluated the possibility of employing machine learning algorithms for OMA median diameter prediction for the first time. Three tree-based machine learning algorithms, including Random Forest (RF), Gradient Boosting Regression (GBR), and Adaboost, were assessed. The nested CV method was applied to identify the most effective model. RF demonstrated the most satisfactory performance predicting D₅₀, with high R² values (0.93 for unseen data and 0.99 for training data) and low RMSE values. The stability and generalizability of this optimal RF model were investigated using various test/train splitting. The results indicated that as the model is trained on a larger dataset, the RF model’s talent in making accurate predictions on previously unseen data (testing set) increases, corroborating its robust stability and superior generalizability.

The RF algorithm was employed to quantify the significance of each process factor. The outcomes from conventional and permutation feature importance analyses concurred, highlighting the concentration of oil and clay and clay type as the most important factors in predicting the median size of OMAs in this investigation. Furthermore, partial dependence plots (PDPs) were utilized to assess the influence of individual variables on OMA median size prediction. The observed trends for several factors, such as clay concentration and type and agitation time and speed, were consistent with existing literature. However, future research is needed to further examine the influence of these factors on OMA size prediction.

This research also led to the development of an open-source software application incorporating the RF algorithm. This tool, designed for user-friendly installation on personal computers, facilitates rapid predictions of OMA D₅₀ based on input formation process variables. Despite its utility, further research is needed to expand the dataset and refine the model for enhanced predictive accuracy.

Overall, this multi-disciplinary research successfully identified key factors and their interactions influencing the formation of OMAs. Furthermore, it innovatively incorporated machine learning algorithms for the prediction of OMA median diameter. The findings and the practical tools developed in this study demonstrate significant potential for future, more detailed investigations of OMAs, particularly regarding size distribution. These advancements are important in enhancing the accuracy of tracking the fate and trajectory of oil spills, contributing significantly to the field of environmental monitoring and remediation.