Machine Learning Models to Predict Early Breakthrough of Recalcitrant Organic Micropollutants in Granular Activated Carbon Adsorbers

Abstract

Granular activated carbon (GAC) adsorption is frequently used to remove recalcitrant organic micropollutants (MPs) from water. The overarching aim of this research was to develop machine learning (ML) models to predict GAC performance from adsorbent, adsorbate, and background water matrix properties. For model calibration, MP breakthrough curves were compiled and analyzed to determine the bed volumes of water that can be treated until MP breakthrough reaches ten percent of the influent MP concentration (BV10). Over 400 data points were split into training, validation, and testing sets. Seventeen variables describing MP, background water matrix, and GAC properties were explored in ML models to predict log₁₀-transformed BV10 values. Using the ML models on the testing set, predicted BV10 values exhibited mean absolute errors of ~0.12 log units and were highly correlated with experimentally determined values (R² ≥ 0.88). The top three drivers influencing BV10 predictions were the air-hexadecane partition coefficient and hydrogen bond acidity (Abraham parameters L and A) of the MPs and the dissolved organic carbon concentration of the GAC influent water. The model can be used to rapidly estimate the GAC bed life, select effective GAC products for a given treatment scenario, and explore the suitability of GAC treatment for remediating emerging MPs.

Graphical Abstract

INTRODUCTION

Granular activated carbon (GAC) adsorption is the best available technology for the control of many organic micropollutants (MPs) that are regulated by the United States Environmental Protection Agency (USEPA) as well as for MPs of emerging concern. A crucial step in full-scale GAC adsorber design is assessing the breakthrough behavior of targeted MPs through bench- and pilot-scale column studies. Frequently, mathematical models are used in conjunction with such data collection efforts to predict the full-scale GAC performance. One approach relies on mechanistic models such as the pore-surface-diffusion-model (PSDM)^1–3 to scale up results from bench-scale tests such as rapid small-scale column tests (RSSCTs).⁴ However, obtaining experimental results from RSSCTs for scale-up or collecting data from pilot-scale experiments to estimate the full-scale GAC performance is costly and time-consuming. To overcome this limitation, Kennedy et al. (2015)⁵ developed a data-driven model (eq 1) to predict the bed volumes of water that can be treated until MP breakthrough reached ten percent of the influent MP concentration (BV10). The multiple linear regression (MLR) model linked BV10 to adsorbate and background water matrix characteristics as follows:

$$\text{ln}\mathit{\text{BV}}\mathit{10}=(11.2\pm 0.2)+(-0.242\pm 0.052){\mathit{\text{DOC}}}_{\mathit{0}}+(0.138\pm 0.041)\text{log}D+(-0.305\pm 0.093)S+(0.157\pm 0.069)V$$ (1)

where DOC₀ is the dissolved organic carbon (DOC) concentration in the GAC influent water, log D is the pH-dependent octanol–water partition coefficient of the MP, and S and V are Abraham solvation parameters representing polarity/polarizability and McGowan molecular volume of the MP, respectively. However, the model overestimated BV10 by a factor of >4 when applied to a wastewater-impacted drinking water source.⁵ Furthermore, when the model was applied in a separate groundwater study, it tended to underestimate BV10, and the error tended to increase as MP adsorbability increased.⁶

While machine learning (ML) models have been developed to predict partition coefficients (log K_d) describing batch adsorption equilibria between MPs and carbonaceous adsorbents,^7–9 to date, there is no model to accurately predict the performance of full- or pilot-scale packed bed GAC adsorbers from commonly available MP, GAC, and water matrix properties. Thus, developing design and cost information for full-scale GAC adsorbers remains challenging without the use of physical column experiments. This limitation can prevent utilities from the timely implementation of effective facility upgrades in response to the myriad of MPs of emerging concern, such as per- and polyfluoroalkyl substances (PFASs), that are posing public health threats.^10–13

The overarching aim of this research was to develop predictive ML models through training and validation with available data generated in GAC column studies. ML can be used to exploit the nonlinear, complex relationships between input parameters and a target response, here BV10. The goal of this work was to develop predictive models that rely on readily obtainable input parameters describing MP, GAC, and background water matrix characteristics. This study explored multiple linear regression (MLR) and tree-based ensemble ML methods, including random forest (RF) and gradient boosting machine (GBM). The models served to achieve two objectives: (1) to estimate BV10 and (2) to identify the most influential factors (MP, GAC, and background water matrix properties) that impact BV10 by conducting a global sensitivity analysis (GSA).

METHODS

To develop information for model calibration and validation, a database of BV10 values was compiled from MP breakthrough curves published in the peer-reviewed literature, research reports, and engineering reports. These data sets, which included results from RSSCTs as well as pilot- and full-scale adsorbers, were analyzed with the PSDM to construct a database of experimentally determined BV10 values. Three modeling approaches to predict BV10—MLR, RF, and GBM—were compared by developing predictive models in R.¹⁴ An overview of the workflow from database curation to model deployment is summarized in Figure S1 of the Supporting Information (SI).

Database Development.

A database of 413 breakthrough curves from 17 studies was developed. The database included 43 MPs from 6 compound classes, 16 GAC products prepared from 3 base materials, and 38 water matrices from 5 matrix types (Figure 1). About one-third of the breakthrough curves were obtained from pilot- and full-scale studies, while the remainder originated from RSSCTs (Figure 1). Sources for bench-, pilot-, and full-scale data collected from the peer-reviewed literature, MS and PhD theses, and technical reports can be found in Table S1. The model BIOWIN2¹⁵ was used to determine whether a MP is recalcitrant; MPs were considered recalcitrant and included in the database if their fast biodegradation probability value was < 0.5 (Text S1). Only column studies that exhibited well-defined breakthrough curves and that included sufficient information about GAC and background water characteristics, as well as operating conditions, were included. Breakthrough data with high method reporting limits for the determination of MP concentrations or high noise (i.e., no clearly identifiable breakthrough curve) were excluded. BV10 values were obtained either directly from the data source if breakthrough data had been described by the PSDM or by analyzing breakthrough data digitized from published figures using WebPlotDigitizer.¹⁶ Digitized data were described with the PSDM, and model fits were interpolated to obtain BV10 values. For RSSCT data, BV10 values were subsequently scaled up using the equations shown in Text S2. Separate scale-up equations were applied to BV10 values from RSSCTs obtained with constant diffusivity (CD) and proportional diffusivity (PD) designs.^17,18 Details pertaining to data analysis of differing column scales, PSDM fits, and extracted BV10 values are summarized in Text S2 and associated Figures and Tables.

Figure 1.

Data distribution by (a) MP compound class, (b) background water matrix, (c) GAC type, and (d) adsorber scale and design. Data distribution summary is based on 413 breakthrough curves. PD-RSSCT: RSSCT data obtained with proportional diffusivity design,¹⁸ CD-RSSCT: RSSCT data obtained with constant diffusivity design.¹⁷

Predictor and Response Variables.

For model development, 17 input variables from four categories, MP properties, water quality, GAC characteristics, and adsorber scale and design, were selected as candidate features. Abraham solvation parameters (Text S3), which represent solute–solvent interactions,¹⁹ are commonly employed to model sorption processes involving organic MPs.^7–9,20 Six Abraham solvation parameters (L, V, A, B, S, E) were taken from the UFZ-LSER database.²¹ The net charge of an MP at a given solution pH (charge, Text S3) and the MP concentration in the GAC influent (C0) served as additional input variables. Three water quality parameters [pH, DOC concentration (DOC), and UV254 absorbance (UV254)] were included as model inputs. Apart from DOC, UV254 was included to describe the dissolved organic matter (DOM) character. For GAC characteristics, the BET surface area (BET), pH_pzc (pzc), and micropore ratio (mp_ratio = micropore volume/total pore volume) were included. GAC properties (Text S4) were obtained from other sources when only the GAC product could be identified for a given data set. For adsorber scale and design, empty bed contact time (EBCT) and 2 dummy variables to represent RSSCT data sets obtained with proportional diffusivity (PD)¹⁸ and constant diffusivity (CD)¹⁷ designs, respectively, were included. The 2 dummy variables were created to account for the three column types—pilot/full scale, PD-RSSCT, and CD-RSSCT—recognizing that scaled up PD- and CD-RSSCT data do not perfectly predict full- or pilot-scale GAC performance.⁴ Additional details for all input variables are summarized in Table S2. The response variable, which is also called the target for ML models, was the log₁₀ transformed BV10 [log(BV10)] value for each data point (RSSCT data points were scaled up as described above).

Model Development.

MLR and tree-based ensemble learning methods were evaluated and compared. All model training and evaluation was performed in R, using packages such as caret, glmnet, ranger, and gbm.^22–25 Compared with more complex machine learning algorithms, MLR yields a model that is both easily interpretable and predictive. Details pertaining to model training for MLR can be found in Text S5. RF²⁶ and GBM²⁷ are two popular tree-based ensemble learning methods commonly used in environmental science and engineering disciplines. RF and GBM are expected to yield highly predictive models while selecting the most predictive variables, even under the presence of multicollinearity, as these algorithms do not rely on assumptions about data distribution or variable independence.²⁸ While both methods use an aggregate of decision trees, RF averages regression results of independent trees, while GBM performs regression with additive, sequential trees.²⁹ Details about ensemble tree model development are presented in Text S6.

Data-Preprocessing and Data Splitting.

Data normalization/scaling can be important on a case-by-case basis and is especially relevant in algorithms that require Euclidean Distance²⁹ such as the MLR model. For MLR model development, data were normalized as described in Text S5. Data were not normalized/scaled prior to tuning of tree-based models.³⁰

Prior to the application of MLR or ensemble learning methods, the database was divided into training and testing sets at a split ratio of 9:1. A diversity of data within the testing set was ensured to cover different types of compound classes, water matrices, and GAC products. The training set (n = 371) was used to train the models, and the testing set (n = 42) was set aside to evaluate the trained models. The training set was also divided into separate folds during the model training process to create several validation sets so that the model performance could be evaluated via cross-validation (CV). During the data splitting process, a point selection approach, where individual BV10 data were taken from different column studies, was adopted over a group selection approach, where each GAC column study would constitute a group.⁷ The point selection approach was used to achieve well-balanced training and testing sets from the standpoint of diversity in MP, GAC, and background water matrix characteristics.

Model Training and Evaluation.

Training processes for MLR and ensemble learning methods differ, but they both require hyperparameter tuning through grid-search. For MLR, the model was developed with all 17 input variables using ordinary least-squares (Text S5). For ensemble learning methods (GBM and RF), hyperparameter tuning was performed with all candidate variables in the models. Subsequently, we calculated the permutation variable importance for both the tuned GBM and RF models and verified that none of the variables had zero importance (Texts S6–S7), thus justifying the use of all selected input parameters.

After completing model development, we compared the three modeling approaches by calculating the 10-fold CV error for the MLR, RF, and GBM models using the training set. Root-mean-square error (RMSE) and mean absolute error (MAE) were calculated for the CV error evaluation of log(BV10). The coefficient of determination $\left(R^2=1-\frac{\text{Sum}\text{of}\text{squares}\text{of}\text{residuals}}{\text{Total}\text{sum}\text{of}\text{squares}}\right)$ was calculated in addition to RMSE and MAE for the testing set. For the testing error evaluation, in addition to evaluating the models developed in this study, we also evaluated the MLR model developed by Kennedy et al. (2015)⁵ by computing its prediction error for an appropriate subset of the testing set.

A previous study⁷ evaluated the potential of data-leakage by comparing the validation error to the testing error, and we adopted the same approach in this paper.

GBM Model Interpretation and Global Sensitivity Analysis (GSA).

The permutation importance for all variables was calculated for the GBM model. To compute the permutation importance of a variable, we calculated the percent change in error when the variable was permuted from the original value in the training set (details in Text S7). Furthermore, a GSA was conducted by developing individual conditional expectations (ICEs) and partial dependence plots (PDPs) for individual variables, where each variable was varied over its full training set range.^31–35 To compute ICEs of a variable, we varied the selected variable and computed the corresponding predicted values of log(BV10) for each instance in the training data set (details in Text S8). We then plotted the centered ICEs (c-ICEs) of selected variables, and the centering procedure can be found in Text S8. For each variable, the average of the c-ICEs was plotted as a partial dependence plot (PDP) using the centered-scale.

RESULTS AND DISCUSSION

Comparison of Model Performance.

In this study, MLR, RF, and GBM models were constructed to predict BV10, the bed volumes of water that can be treated until the MP reaches 10% breakthrough in the GAC adsorber effluent. The MLR model (eq 2, Text S5) can be explicitly expressed while the RF and GBM models cannot. Additionally, confidence intervals for each of the coefficients in the MLR model can be found in Text S5.

$$\text{log}\mathit{\text{BV}}\mathit{10}=-0.072\mathit{\text{DOC}}-0.17\mathit{\text{UV}}\mathit{254}+0.049\mathit{\text{pH}}+0.19pzc-0.035m{p}_{\text{ratio}}+0.012BET-0.035C_0-0.38L-0.48A-0.55S+0.43V+0.85E+0.32B-0.24\mathit{\text{charge}}-0.10\mathit{\text{PD}}+0.047\mathit{\text{CD}}+4.2$$ (2)

We compared the performance of each model through (1) 10-fold cross-validation (CV) of the training set and (2) prediction of the testing set, as shown in Table 1. First, CV error was used to compare prediction accuracy across different algorithms as it is more robust than the testing error. In CV, the GBM model had the lowest RMSE (0.15) and MAE (0.11, Table 1), followed by those of the RF and MLR models. To put the log-unit based error values into perspective, for a BV10 value of 10,000, an RMSE value of 0.15 corresponds to a range of 7,100 to 14,100 bed volumes. Both ensemble tree models outperformed the baseline MLR model; CV RMSE decreased from 0.33 for the MLR model to 0.19 and 0.15 for the RF and GBM models, respectively (Table 1). Testing errors confirmed CV error trends: the GBM model had the lowest RMSE (0.15) and MAE (0.12) (Table 1), followed by the RF and MLR models for predicting the testing set.

Table 1.

Summary of 10-Fold Cross Validation (CV) and Testing Errors Obtained with the MLR, RF, and GBM Models for log(BV10)^a

Model name	RMSE	MAE	IQR RMSE	IQR MAE
10-fold cross validation (CV) errors for log(BV10)
MLR model	0.33	0.28	0.29–0.36	0.25–0.30
RF model	0.19	0.14	0.17–0.19	0.12–0.15
GBM model	0.15	0.11	0.14–0.17	0.10–0.13
Testing errors for log(BV10)
MLR model	0.30	0.22	N/A	N/A
RF model	0.16	0.12	N/A	N/A
GBM model	0.15	0.12	N/A	N/A
Testing errors for a subset of bituminous coal-based GACs (Calgon F400 and Norit 1240) for log(BV10)
MLR Model	0.27	0.20	N/A	N/A
Kennedy et al. (2015)5 MLR model	0.54	0.36	N/A	N/A

^a10-fold CV error metrics (RMSE and MAE) calculated based on training data and testing error (RMSE, MAE, and R²) metrics calculated based on testing data. Testing errors for the MLR model of Kennedy et al. (2015)⁵ are shown in the last row. IQR refers to the interquartile range of the 10-fold CV errors. Observed BV10 values in the database ranged from ~800 to 100,000 bed volumes, corresponding to 2.9 to 5 log units.

We compared testing RMSE and MAE values to the respective interquartile ranges (IQRs) of CV error values to determine if hyperparameter tuning was performed appropriately from the standpoint of overfitting and data leakage (Table 1). Overall, testing errors were either within the IQR (GBM) or slightly below the 25th percentile value of CV errors (MLR, RF, Table 1), meaning the models did not overfit the training data and our data splitting approach did not result in data leakage.⁷

To further analyze the effectiveness of the MLR model developed in this study, we evaluated the prediction accuracy of a prior MLR model.⁵ For this comparison, we included only a subset of our testing set data obtained with bituminous coal-based GACs (Calgon F400 and Norit 1240), for which the prior model was developed. The earlier MLR model⁵ had an RMSE of 0.54 (Table 1), which is twice that of the MLR model developed in this study. By including more data than the previous MLR model (n = 371 compared to n = 26) as well as additional input parameters that describe water quality, MP properties, and GAC characteristics, the MLR model developed in this study is more effective and more broadly applicable than the previously developed MLR model.

For each model, we evaluated prediction performance on the testing set across different compound classes, background water matrix types, and BV10 values (Figure 2). The MLR model (Figure 2a) more effectively predicted treatment scenarios with BV10 values > 15,000 than those with BV10 values ≤ 15,000. Compared to the MLR model, the ensemble tree models (GBM, RF) effectively predicted the GAC performance across the entire range of BV10 values (Figure 2b and 2c). Additionally, the ensemble tree models performed well across different types of water, including treated wastewater (Figure 2b and 2c), overcoming a challenge faced by an earlier MLR model,⁵ which overestimated GAC performance by a factor of 4.2 for wastewater-impacted source water. The prediction performance on the same testing set across different types of GAC products (Figure S2) also indicates that the ensemble tree models apply to various GAC types.

Figure 2.

Parity plots comparing predicted and observed BV10 values in the testing set (42 data points) for (a) MLR, (b) RF, and (c) GBM models. Error metrics shown are those for log(BV10).

Overall, the two ensemble tree models outperformed the MLR models developed in this and an earlier⁵ study both in terms of CV and testing error (Table 1). Tree-based ensemble learning methods yielded highly predictive models even under multicollinearity among predictors (Text S5). The GBM had smaller CV errors than the RF model, and the GBM model is hence explored further in the following sections.

Variable Contributions via Permutation Importance and GSA.

To assess which variables are the most influential predictors of BV10 and how certain parameters affect BV10 prediction in the GBM, two approaches were taken for model interpretation: (1) permutation importance was calculated to rank variables (Figure 3); and (2) a GSA was conducted and visualized in the forms of PDPs and c-ICEs (a decomposed form of PDPs, Figure 4) to evaluate partial dependency and interaction effects of selected variables.

Figure 3.

Permutation importance ranking of variables for the GBM model. Percent mean-squared error (MSE) increase indicates the permutation importance score of each variable; the larger the value, the more important the variable in the model.

Figure 4.

Centered individual contribution expectations (c-ICEs) and partial dependence plots (PDPs, red lines) for the GBM model. Evaluated parameters: (a) L, (b) A, (c) DOC (all data, left; 0.1–4 mg/L DOC, right), and (d) UV254. In (a), blue lines/dots represent the c-ICEs/predictions for data entries with BET ≥ 800 m²/g and DOC ≤ 4 mg/L and pink lines/dots represent those of the remaining data set. In (b) and (d), individual black lines/dots represent the c-ICEs/predictions for all data entries. In (c), blue lines/dots represent the c-ICEs/predictions for data entries with charge ≤ −0.1 and pink lines/dots represent those of the remaining data set.

Predictor Influence.

We identified the most influential predictors of BV10 from each category—MP properties, water quality, and GAC characteristics—based on their permutation importance in the GBM model (Figure 3).

Among the 17 predictors, the most important was Abraham solvation parameter L, the logarithm of the hexadecane-air partition coefficient of each MP (Figure 3), which is linked to nonspecific dispersion interactions between an MP, the solvent, and the sorbent.^19,36 In addition, Abraham solvation parameter A, which represents the hydrogen bond acidity of a MP, was the third-most important predictor in the GBM (Figure 3).

DOC, a measure of the DOM concentration in the GAC influent water, was the second most important predictor across all categories. It is well-known that DOM concentration has a strong negative effect on MP removal in GAC adsorbers.^5,37 Furthermore, UV254 absorbance (UV254), which is a response to aromatic and unsaturated functional groups in DOM,³⁸ ranked fourth (Figure 3), highlighting that both DOM concentration and character impact MP removal in GAC adsorbers.

Predictors of intermediate influence included MP charge, binary variable PD, solution pH, Abraham parameters V and E, and initial MP concentration C0 (Figure 3). GAC characteristics exhibited comparatively lower importance with pzc being the most important (Figure 3). The fact that GAC characteristics were less important than MP and background water matrix characteristics may be the result of the selected data having been collected with GAC products of high quality such that differences in GAC performance were smaller among GACs than among MPs of very different characteristics and background water matrices with widely differing DOM content and character. Inclusion of the binary variable PD suggests that model predictions for scaled up PD-RSSCT data differed from those for pilot-/full-scale data and scaled up CD-RSSCT data.

Effect of MP Properties.

We used centered individual contribution expectations (c-ICEs) and partial dependence plots (PDPs) to evaluate the marginal effect of MP properties on BV10 predictions. MP properties were represented by Abraham solvation parameters (L, V, S, A, B, E) as well as net ionic charge at a given pH. Abraham parameter L, which is linked to the strength of van der Waals interactions an MP can undergo,³⁶ had the largest effect on BV10 predictions (Figure 4a). This finding is consistent with the interpretation of models developed to predict MP adsorption capacities derived from batch isotherm experiments.^8,20 Values of L ranged from 1.4 to 26, and log(BV10) increased on average by ~0.45 over this range, with the majority of the increase in log(BV10) occurring in the data-dense region of 1 < L < 6 (Figure 4a). The c-ICEs for individual scenarios varied widely, and dependence of log(BV10) on L was lowest for data sets with BET < 800 m²/g and DOC > 4 mg/L (Figure 4a). The latter finding suggests that DOM fouling effects may be severe when GAC with a low BET surface area is exposed to water with high DOM concentrations such that MP removal is poor and the effect of increasing L is masked.

Apart from L, Abraham solvation parameter A, which represents the H-bond acidity of an MP, had a strong effect on BV10 predictions (Figures 3 and 4b). A values ranged from 0 to 1.55, and in the PDP, log(BV10) decreased by ~0.6 over this range (Figure 4b). The magnitude of A is strongly correlated with the charge of the most positive H-atom in an organic compound.³⁹ Thus, PDP results for the GBM model suggest that a strong H-bond donating capacity adversely impacts MP adsorbability when all other properties are held constant. In our study, adsorbates with large A values included iopromide, sucralose, erythromycin, and bisphenol A.

Other Abraham parameters (V, E, B, S) exhibited lower permutation importance than L and A (Figure 3) even though subsets of these parameters were found to be important for the prediction of MP adsorption capacities derived from batch isotherm experiments.^7,8,20 The Abraham parameter L was not used in many prior studies, in which case the importance of van der Waals interactions was primarily associated with Abraham parameter V. Interestingly, A was the most important Abraham parameter (with V a close second) for predicting the Freundlich isotherm capacity parameter (K_F) in a model⁸ that included chemical adsorbent characteristics. In contrast, A was not important in models that did not consider chemical adsorbent characteristics;^7,20 in the latter models, Abraham parameters S and/or B became important. Thus, it is possible that parameters S, and/or B in earlier models^7,20 embodied specific adsorbate/adsorbent interactions that were captured by the incorporation of chemical adsorbent descriptors, such as pzc in our study or carbon content, H/C, and O/C in another study.⁸ Parameter pzc implicitly considers the oxygen content of GAC because GACs with lower pH_pzc values generally have higher oxygen contents⁴⁰ and thus interact more strongly with water, which decreases MP adsorbability.⁴¹

Our models included pH, MP charge, and pzc to account for possible electrostatic interactions. The variable importance ranking (Figure 3) captured a quantifiable permutation importance of charge on the log(BV10) predictions. Previously developed models^5,7 were limited to describing hydrophobic interactions between neutral MPs and the GAC surface or required separate models to predict the adsorption capacities of (1) anionic and polar MPs and (2) cationic MPs.⁸ In contrast, the combination of adsorbate, adsorbent, and background water matrix characteristics permitted the development of a ML model that effectively predicted the log(BV10) of MPs with a range of charges (−1 to +1).

Variable importance ranking (Figure 3) further suggested that C0, the MP concentration in the GAC influent, is of lower importance, which has been confirmed by data obtained from GAC adsorbers treating MPs in the presence of DOM; in such systems, initial MP concentration does not impact early breakthrough of MPs in the GAC effluent when breakthrough curves are plotted on a normalized basis; i.e., C_effluent/C_influent as a function of bed volumes of water treated.^37,42,43

Effect of Water Quality.

Both DOC and UV254 are important parameters that affect the GAC performance. For DOC, the majority of available data covered a concentration range of 0.1–4 mg/L, and BV10 predictions decreased by up to ~ 0.25 log units (~44% on a linear scale) in this region (Figure 4c, insert). It is important to note that we held UV254, as well as all other model parameters, constant at the value of a given data point to assess the marginal effect of DOC. We assessed the combined effect of varying DOC and UV254 in the local sensitivity analysis discussed below. The partial dependence of BV10 on DOC was stratified by MP charge (Figure 4c)—log(BV10) decreased more strongly for MPs with charge ≤ −0.1 as DOC increased than for MPs with charge > −0.1, especially in the data-rich region (Figure 4c, insert). Note that a charge of −0.1 was assigned to an ionizable MP that was partially dissociated; i.e., 10% as anions with a charge of −1 and 90% in the neutral form. The stronger negative effect of DOC on MPs with a net charge of ≤ −0.1 can be explained by repulsive electrostatic interactions between adsorbed, negatively charged DOM and negatively charged MPs. Over the entire range of DOC values, predicted BV10 decreased by ~0.6 log units on average; furthermore, when the same analysis was conducted for UV254, the average decrease in BV10 prediction was ~0.4 log units (Figure 4d) over the entire range of UV254 values (0.00–0.25 cm⁻¹). Therefore, the DOC variance accounted for a portion of the DOM impact on BV10 prediction while the UV254 variance accounted for another portion of the DOM impact. A possible strength of the GBM model is that it considers both DOC and UV254 and thus may be able to predict the effect of DOM on BV10 for a range of DOM concentrations and characteristics [i.e., water with different DOC concentrations and specific ultraviolet absorbance (SUVA) values]. ML models developed in prior studies^7,9 to predict batch MP adsorption capacities of carbonaceous adsorbents did not account for water quality parameters, and it is unclear whether the data sets included results from batch experiments conducted with DOM. Overall, variables describing DOM are of high importance to predict the performance of packed bed GAC adsorbers for MP removal, and our model results agree with empirical observations that have highlighted the adverse effect of DOM on MP adsorption by GAC.^5,37,44,45

Effect of GAC Characteristics.

GAC characteristics had a lower permutation importance than MP and background water matrix characteristics (Figure 3). Among the included GAC characteristics, the point of zero charge, pH_pzc, (pzc) was ranked as the top predictor (Figure 3). Increasing pzc exhibited a complex, nonmonotonic effect on BV10 prediction (Figure S3) which indicates that increasing pzc does not always lead to larger BV10 values. For some cICEs, increasing pzc increased BV10 by more than 0.2 log units but in others, increasing pzc led to a decrease in BV10 by 0.3 log units (Figure S3).

Apart from pzc, the GAC surface area (BET) and micropore to total pore volume ratio (mp_ratio) were additional adsorbent descriptors. Nonmonotonic trends were also observed for BET and mp_ratio effects (Figure S4–S5). The BET effect is consistent with experimental studies that attempted to correlate specific throughput in RSSCTs⁴⁶ or activated carbon adsorption capacity⁴⁰ with BET, which resulted in poor correlations.

As mentioned above, pzc in combination with the MP charge and solution pH helps describe electrostatic interactions between ionizable MPs and the GAC surface. Furthermore, the mp_ratio provides readily available, albeit limited, information about the pore size distribution of GACs. Pore size distribution not only is important from a standpoint of MP adsorption capacity⁴⁰ but also from a standpoint of controlling GAC fouling by DOM.⁴¹ Together, the selected adsorbent descriptors accurately captured the MP removal efficacy of different GAC products when water containing a wide range of DOM concentrations was treated (Figure S2). Our approach differs from prior studies that included BET surface area and total pore volume of the adsorbent for the prediction of MP partition coefficients,⁷ or information about the BET surface area and elemental composition of the sorbent (percent C, H/C, O/C) to predict Freundlich isotherm parameters for a wide range of carbonaceous sorbents, including sorbents with substantially lower carbon (C) contents than those of GACs.⁸

Effect of EBCT.

We evaluated the importance of EBCT (range: 4.6 to 24 min), an important parameter for the design of GAC adsorbers. The effect of EBCT on the BV10 prediction was found to be less important than those of other variables (Figure 3), and the effect of EBCT was found to be ambiguous (Figure S6). These observations are consistent with previous studies that found EBCT has only small effects on GAC use rates for MP removal when EBCT was varied between 10 and 20 min.^5,42

Local Sensitivity Analysis (LSA).

To demonstrate how the GBM model can be used to predict changes in BV10 for scenarios with varying MP, water quality, and GAC characteristics, we conducted a local sensitivity analysis (LSA). LSA differs from GSA in that selected input variables were varied from a base case scenario to illustrate how the GBM model behaves in a more applied setting. For the purposes here, we explored how PFAS chain length, combined changes in DOC and UV254 for water with a constant SUVA value, and changes in GAC characteristics affect BV10. For the baseline prediction (simulation ID1), we selected a test data set that described PFOA removal from groundwater (pH = 7.56, DOC = 2.7 mg/L, UV254 = 0.0259 cm⁻¹); the GAC adsorber contained bituminous coal-based GAC (BET = 1132 m²/g, pzc = 7.4, mp_ratio = 0.87) and had an EBCT of 10 min.⁴⁷ First, we varied DOC from 0.1 to 11.4 mg/L to assess its effect on BV10 prediction while keeping SUVA constant at 0.96 L/mg-m (ID2–3). Second, we predicted BV10 values for the removal of perfluoroalkyl carboxylic acids (PFCAs) with chain lengths ranging from 4 (perfluorobutanoic acid, PFBA) to 10 (perfluorodecanoic acid, PFDA) by the same GAC in the same water matrix to assess how varying MP properties in a homologous series affects BV10 predictions (ID4–9). Third, we varied BET (from 575 to 1132 m²/g) and pzc (from 6.4 to 10), one parameter at a time, to evaluate their impact on BV10 predictions (ID10–13). Finally, we increased EBCT from 10 to 20 min (ID14). Resulting BV10 values from these simulations and the % changes in BV10 for ID2–14 relative to ID1 are summarized in Figure 5.

Figure 5.

Predicted BV10 values (left) and % change in predicted BV10 (right) for the GBM model scenarios. ID1: baseline scenario; ID 2–3: min and max DOC while keeping SUVA constant; ID 4–9: varying PFCA chain length from 4 (PFBA) to 10 (PFDA); ID 10–11 min and max pzc; ID 12 min BET; ID13: EBCT doubled. Observed BV10 value for ID1 was 16,600 bed volumes, and the predicted value was 24,000 bed volumes.

When the DOC concentration was varied (ID2–3), we observed the expected negative impact of DOC on BV10 predictions. In these simulations, the SUVA value was kept constant (0.96 L/mg-m) to avoid introducing effects associated with DOM character as expressed by SUVA. We observed that minimizing DOC (0.1 mg/L) led to a ~160% increase of BV10 while maximizing DOC (11.4 mg/L) led to a ~85% decrease of BV10 relative to the baseline condition (Figure 5).

By predicting BV10 values for PFCAs of different chain lengths (ID4–9), we were able to assess the impact of MP properties on the GAC performance. Relative to results for PFOA, BV10 for PFBA, the smallest among the evaluated PFCAs, exhibited the largest percent decrease (69%) while BV10 for PFDA, the largest among the considered PFCAs, exhibited the largest percent increase (26%, Figure 5). Furthermore, the order of BV10 for the other PFCAs in the homologous series was correctly predicted by the model; i.e., BV10 increased with increasing PFCA chain length.⁴⁷

We then varied carbon characteristics such as pzc and BET (ID10–13) to evaluate their effect on the BV10 values. For the lowest pzc (ID10) the model predicted a 4% decrease in BV10 while for the largest pzc (ID11), the GBM predicted an 11% increase in BV10. Minimizing BET (575 m²/g, Simulation ID12) led to a negative change of 31% in the BV10 prediction relative to the baseline. It is important to note, however, that increasing the BET surface area will not always lead to higher BV10 values (Figure S5). Overall, GAC properties did not drive BV10 prediction as much as MP and background water matrix properties.

Simulation ID14 showed that doubling EBCT from the baseline value of 10 to 20 min increased BV10 by 8% over the base case (Figure 5). This observation can be explained by the sharpening of breakthrough curves; i.e., breakthrough curves become steeper as EBCT increases.^48–50 In a pilot study, increasing EBCT from 3.6 to 10.3 min led to a ~30% increase in BV10 for PFCAs with 4–10 carbon atoms.⁵⁰ In a bench-scale GAC column study,⁴⁹ BV10 for PFOA almost doubled when EBCT increased from 3 to 6 min, but no further change was observed when EBCT was increased from 6 to 9 min. In RSSCTs, BV10 increased by a factor of >4 for some short-chain PFCAs when the simulated EBCT increased from 5 to 20 min in bench-scale GAC columns.⁴⁸ Together, these studies suggest that the bed volumes of water that can be treated by GAC to early breakthrough of some PFASs can be increased by increasing EBCT, but the magnitude of the effect is likely dependent on a combination of factors, including scale. The magnitude of change predicted by our GBM model is more consistent with that observed in a pilot-scale study⁵⁰ rather than the larger changes observed with RSSCTs.⁴⁸

Implications and Limitations.

The developed ensemble tree models, which have an average testing MAE of ~0.12 logunits (Table 1), equivalent to an average of −24% to +32% error on a linear BV10 scale, are more effective than previous BV10 estimation methods that were based on MLR models.⁵ The effectiveness of the model can be attributed to the comparatively large data set that was used to develop the model as well as the consideration of a wide range of adsorbent, adsorbate, and background water matrix characteristics that served as model inputs. Nonetheless, ML models are only as good as the training data used to construct them. Distributions of model input variables are discussed in Text S9. Additional data covering a wider range of MPs, initial MP concentrations, GAC products, and background water qualities can help improve the prediction accuracy and applicability domain. Specifically, data in data-sparse regions, such as higher DOC concentrations (DOC > 4 mg/L) along with documented UV254 values as well as data for GACs with a wider range of properties would enhance the robustness of the developed database and models.

A local sensitivity analysis demonstrated ways the model can be used to assess GAC characteristics, EBCTs, and possible pretreatment approaches that remove/alter DOM. While ML models, such as the one developed here, should not be used to design full-scale treatment processes directly, the model serves as an effective tool for designing pilot studies and for estimating preliminary operation and maintenance costs, which are largely determined by GAC use rates. A limitation is that the developed models are static; that is, they cannot adapt to sudden changes in influent water quality. However, results from a sensitivity analysis can be used to assess how changes in influent water quality affect BV10.

Finally, the described GBM model is available as a web-based application (https://shiny.stat.ncsu.edu/GACwebapp/) along with associated codes (https://github.com/furtman/GAC_BV10_estimation). License specifications pertaining to the codes and database, along with a user guide, are included in Text S9. Model predictions can be used to develop initial GAC adsorber designs and reduce costs associated with design and planning processes.