1 Introduction

Methyl tert-Butyl Ether (MTBE) is one of the common oxygenates used as an anti-knock agent to supplant environmentally unsafe tetraethyl lead (TEL) in gasoline since 1979 in the US [1,2,3]. Following the global ban of TEL by year 2000s, the use of MTBE as a cheap alternative fuel additive became widespread worldwide. MTBE is released into groundwater aquifer and surface water through leaks from underground storage tanks and through a direct spill of MTBE-containing gasoline. The prevalence of MTBE in water resources portends significant challenges to the safety of drinking water [4,5,6]. This problem is worsened because of MTBE’s uniquely low Henry’s constant, high water solubility and its inherently poor in situ anaerobic biodegradability [1, 7]. The ingestion of MTBE via consumption of contaminated water or any other route has severe health consequences. For instance, eye and skin irritancy in human have been linked genotoxically with the long exposure to MTBE [5, 8, 9]. Also, MTBE has been reported to induce mutagenic breakages of DNA strands and modification of oxidative base pair [10]. In lower animals, MTBE causes depression and disruption of the nervous system [11]. In fact, the US Environmental Protection Agency (USEPA) and the International Agency of Research on Cancer (IARC) classified MTBE as a potential human carcinogen [12, 13].

Due to the various environmental and health implications of MTBE environmental contamination, different treatment and remediation strategies have been developed for its removal. Common examples of the technique employed include; adsorption, air stripping, bio-remediation and advanced oxidation processes (AOPs) [2, 14,15,16,17]. In recent years, the AOPs have emerged as an effective strategy for the treatment of MTBE. The AOPs involve the production of the hydroxyl radicals (•OH) of extreme oxidation potential that disrupt the structure and the bonds of the target analyte (organic compound) and eventually mineralizes it into harmless products mainly carbon dioxide and water [18]. This oxidation process can be initiated by photolysis (O3/UV) [19], (UV/H2O2) [20], Fenton process [8] and photocatalysis [21]. The other remediation techniques mentioned above have been reported to have certain limitation(s) when it comes to MTBE. For instance, adsorption has the advantage of generating little or no harmful by-products, but its performance in removing MTBE is limited by the fact that the saturated adsorbents are not regenerable [16, 22, 23]. Also, air stripping is cheap to operate and has been successfully applied to remediate many VOCs. However, the inherently low Henry’s Law constant of MTBE heightens the air–water ratio and residence time thereby reducing the air stripper’s efficiency [2]. Lastly, the bioremediation is a slow process that takes months which renders it less effective in the treatment of MTBE.

It is important to point out that photocatalytic oxidation has a high reaction rate which is suitable for better treatment of MTBE. Several important studies have been undertaken towards photocatalytic decomposition of MTBE using TiO2/UV [24,25,26,27,28,29,30]. It is remarkable to highlight that these referenced studies revealed that a host of reaction conditions (such as catalyst dose, solution pH, initial pollutant concentration, irradiation UV wavelength and treatment time) influence the efficiency of MTBE degradation through the photocatalytic process. Practically, investigating all the various environmental conditions is uneconomical, time-consuming and laborious. In the same token, empirical modeling is quite challenging due to the multifactorial and complex nonlinear nature of the problem. Consequently, researchers tend to select subjectively parameters’ values (especially initial MTBE concentrations) to work with based on their available reactor systems (batch, slurry, commercial reactor or self-designed system), their analytical instrument capability and sensitivity (injection system and GC detector type), and/or prior experimental experience [24, 25, 27, 31, 32]. As a result, a wide range of differing optimal experimental conditions is reported which makes systematic studies of optimal photocatalysis conditions very challenging [2]. Therefore, the development of a computational model that can examine the effect of the above-mentioned factors becomes highly necessary towards reducing the experimental burdens encountered while finding optimal conditions for the degradation of MTBE using TiO2 as a photocatalyst.

So far, in pursuit of this goal, only a few studies have attempted to model photolytic AOP conditions using computational intelligent approaches. Few important examples include the development of an artificial neural network (ANN) model for the evaluation of MTBE concentration degradation using UV/H2O2 by Salari et al. [33]. Also, Vaferi et al. [34] used ANN to model the photolytic treatment of MTBE and related aromatic hydrocarbons. Meanwhile, a computational approach called support vector regression (SVR) has been shown to have better prediction capability than ANN and adaptive neuro-fuzzy inference system (ANFIS) for some problems [35]. In this contribution, we investigated the influence of TiO2 as a photocatalyst on the treatment of MTBE under various experimental conditions using the SVR model. TiO2 is a well-studied photocatalyst for the treatment of organic contaminants [19]. However, to the best of our knowledge, modeling the performance of TiO2 on MTBE under various experimental conditions has not been undertaken. The proposed model was developed using as inputs, 5 important factors which include; solution pH, TiO2 dose, initial MTBE concentration, UV wavelength and contact time. The proposed model exhibits a high correlation coefficient and low maximum absolute error of 98.3% and 0.02, respectively, which clearly indicates the reliability of the model. More importantly, the optimum experimental conditions for degradation efficiency of MTBE using TiO2 was established.

2 Description of the proposed support vector regression

2.1 Brief descriptions of SVM theory

The conceptual framework of Support Vector Machine (SVM) was founded by Vapnik [36]. Since its introduction, there have been increasing interests in the use of SVM across diverse fields of studies [37,38,39,40,41,42]. Originally, SVM was developed for classification tasks but was later extended to regression problems [43]. SVM used for classification is referred to as support vector classification (SVC) while SVM used for regression task is termed support vector regression (SVR) [36]. SVR was developed on the basis of structural risk minimization, which makes it to have improved generalization ability compared to the artificial neural network and partial least squares that are based on empirical risk minimization [36]. In SVR, the input data is mapped into higher dimensional feature space by using a kernel function that allows the linear and non-linear problems to be solved by a linear regression function.

Assuming we have training dataset defined by where χ denotes the space of the input patterns, for example, . In SVR, the main goal is to find a function f (x) that does not have more than ε deviation from the real value of targets (yi) for all the training data and such function should be as flat as possible [19, 44]. Simple case of a linear function is described by

(1)

where \(\langle . ,. \rangle\) is the dot product in χ, y (x) is the target variable, (x) is the input vector which consists of the design variables, w is the weight vector and b is the intercept vector. In order for the function to be flat as stated, w is required to be small, which necessitates the minimization of Euclidean norm i.e. \(\left| {\text{w}} \right|^{2}\).

This can be stated as convex optimization problem and the condition is given below:

$$\begin{aligned} & {\text{minimize}}\quad \frac{1}{2} \left| {\left| {\text{w}} \right|} \right|^{2} \\ & \quad {\text{subject to}}\left\{ {\begin{array}{*{20}l} {{\text{y}}_{\text{i}} {-} w ,x - b \le \varepsilon } \hfill \\ {w ,x + b - {\text{y}}_{\text{i}} \le \varepsilon } \hfill \\ \end{array} } \right. \\ \end{aligned}$$
(2)

The above holds if function f exists whereby all pairs of (xi, yi) are approximated with a precision, ε. In reality, some errors are introduced that violate the above condition. To deal with this, slacked variables \(\xi_{\text{i}} {\text{and }}\xi_{\text{i}}^{*}\) were introduced to take care of the impractical constraints of the optimization problem as shown below [45]

$$\begin{aligned} & {\text{minimize}}\quad \frac{1}{2} \left| {\left| w \right|} \right|^{2} + {\text{C}}\mathop \sum \limits_{{{\text{i}} = 1}}^{\text{l}} \left( {\xi_{\text{i}} + \xi_{\text{i}}^{*} } \right) \\ & \quad {\text{subject}}\;{\text{to}}\;\left\{ {\begin{array}{*{20}l} {{\text{y}}_{\text{i}} {-} w ,x - b \le \varepsilon + \xi_{\text{i}} } \hfill \\ {w ,x + b - {\text{y}}_{\text{i}} \le \varepsilon + \xi_{\text{i}}^{ *} } \hfill \\ {\xi_{\text{i}} \xi_{\text{i}}^{ *} \ge 0} \hfill \\ \end{array} } \right. \\ \end{aligned}$$
(3)

where C is a non-negative constant, referred to as box constraint. It controls data points that lie beyond the ε-insensitive loss margin and also useful in preventing overfitting [46]. Small values of C lead to flat functions while higher values may result in overfitting problem.

The quadratic optimization problem above can be solved by constructing the Lagrangian (L) from (3) as shown below

$$\begin{aligned} L = \frac{1}{2}\left| {\left| \omega \right|} \right|^{2} + C\sum\nolimits_{i = 1}^{l} {(\xi_{i} + \xi_{i}^{*} )} - \sum\nolimits_{i = 1}^{l} { \propto_{i} (\xi + \xi_{i} - y_{i} + (w,x_{i} ) + b)} \hfill \\ - \mathop \sum \limits_{{{\text{i}} = 1}}^{\text{l}} \propto_{\text{i}}^{ *} \left( {\xi + \xi_{\text{i}}^{ *} + {\text{y}}_{\text{i}} - (w,x_{i} } \right) - {\text{b}}) - \mathop \sum \limits_{{{\text{i}} = 1}}^{\text{l}} \left( {\eta_{\text{i}} \xi_{\text{i}} + \eta_{\text{i}}^{ *} \xi_{\text{i}}^{ *} } \right). \hfill \\ \end{aligned}$$
(4)

where ɳi*, ɳi, \(\propto\)i and \(\propto\)i* are the Lagrange multipliers which are non-negative real numbers

By taking the partial derivatives of the variable L with respect to these variables (\(\xi\)i, \(\xi\)i*, b, \(\omega\)) in (4), and then setting the results to zero for optimality condition, we obtained dual optimization problem in (5). More details of the derivation is contained in the references [47,48,49].

$$\begin{aligned} & {\text{maximize }}\left\{ {\begin{array}{*{20}l} {\frac{1}{2}\mathop \sum \limits_{i = 1}^{l} \left( { \propto_{i} - \propto_{i}^{ *} } \right)\left( { \propto_{j} - \propto_{j}^{ *} } \right)\left( {x_{i} ,x_{j} } \right)} \hfill \\ { - \varepsilon \mathop \sum \limits_{i = 1}^{l} \left( { \propto_{i} + \propto_{i}^{ *} } \right) + \mathop \sum \limits_{i = 1}^{l} y_{i} \left( { \propto_{i} - \propto_{i}^{ *} } \right)} \hfill \\ \end{array} } \right. \\ & \quad \quad \quad \quad \quad \quad {\text{subject to }}\mathop \sum \limits_{{{\text{i}} = 1}}^{\text{l}} \left( { \propto_{\text{i}} - \propto_{\text{i}}^{ *} } \right) = 0 {\text{and }} \propto_{\text{i}} , \propto_{\text{i}}^{ *} \in \left[ {0,{\text{C}}} \right] \\ \end{aligned}$$
(5)

From the above derivatives, the value of

$$\varvec{w} = \mathop \sum \limits_{i = 1}^{l} \left( { \propto_{i}^{ *} - \propto_{i} } \right)\left( {x_{i} } \right)$$
(6)

It follows that the objective function y(x) can be expressed as shown in (7) as

$$\varvec{y}\left( \varvec{x} \right) = \mathop \sum \limits_{i = 1}^{l} \left( { \propto_{i}^{ *} - \propto_{i} } \right)x_{i} ,x + b$$
(7)

The b value is evaluated from the Karuysh–Kuhn–Tucker (KKT) conditions [49]. The above treatment is for linear problems. However, it can be extended to nonlinear function by simply transforming the training patterns xi into some feature space, then apply Eq. 7 to the transformed xi patterns. This leads to a new expression for the weight and the objective function

$$w = \mathop \sum \limits_{i = 1}^{l} \left( { \propto_{i}^{ *} - \propto_{i} } \right)\varphi \left( {\text{x}} \right)$$
(8)

The actual objective function then takes the form of

$$\varvec{f}\left( \varvec{x} \right) = \mathop \sum \limits_{i = 1}^{l} \left( { \propto_{i}^{ *} - \propto_{i} } \right)x_{i} ,x + b$$
(9)

where \({\mathbf{K}}\left( {{\mathbf{x}}_{{\mathbf{i}}} ,{\mathbf{x}}} \right)\) is the kernel parameter that transforms non-linear function into higher dimensional space.

Examples of common kernel parameters include:

  • Gaussian or radial basis function (RBF): K (xi, xj) = exp(−γ.|xi, xj|2).

  • Linear; K (xi, xj) = (xi, xj)

  • Polynomial; K(xi, xj) = [γ. (xi, xj) + 1]d, γ > 0

In this study, we employed the radial basis function due to its ability to give excellent results.

3 Methodology

3.1 Sources and description of the data

The experimental data used in this study were collected from nine (9) different literature sources listed in Table 1 with their details. In the experiments, synthetic MTBE contaminated water was prepared from 97 to 99.9% pure MTBE and, treated with specific doses of anatase TiO2 in a batch [25, 28, 30] or slurry photocatalytic reactor system equipped with UV lamps [24, 29]. The pH of the contaminated water was adjusted using 0.1 N NaOH or 0.1 N HCl [26]. The degradation reaction was allowed to run for a specified time from zero to a maximum of 360 min (see Table 1). Initial and final MTBE concentrations in the solution were analyzed using gas chromatography (GC) equipped with either a flame ionization detector (FID) [28, 29, 50] or mass spectrometer (MS) [25, 27, 30]. During the analysis, samples are injected on to the GC via headspace [26, 28, 30, 31], purge and trap [24, 25] or solid-phase micro extraction (SPME) technique [27]. These sample injection methods are suitable for highly volatile water-soluble VOCs like MTBE. The degradation efficiency of the photocatalytic treatment was evaluated using the equation:

$$Degradation\; Efficiency \left( \% \right) = [(C_{o} - C_{f} )/ C_{o} ] \times 100\%$$
(10)

where Co and Cf are initial and final MTBE concentrations respectively.

Table 1 Sources and details of the experimental data used for building the SVR model
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3.2 Statistical analysis of the datasets

Table 2 shows the basic statistics of the five input variables used in building the SVR model. The wide differences in the values of the mean and median of all the independent variables suggest that the sample data are not normally distributed. The standard deviation, mean and the range values also give an indication of wide variations in the data of all the parameters. In particular, the standard deviation of initial MTBE concentration is notably more (by almost twice) than the mean value. This wide variation is due to the detection limits of the analytical instruments used in measuring the MTBE concentration. In other words, while GCMS is capable of accurately measuring MTBE concentration from a very low sub-ppb range up to low ppm range, reliable results are obtainable from GCFID only in the low ppb to ppm range [51]. Our data come from researches that used both types of GC detectors. Hence, the wide dispersions are expected. Nevertheless, normally distributed datasets have better prediction ability than otherwise [40]. We, therefore, normalized the datasets to manage the wide dispersion using the equation;

$$x_{new} = \frac{{x - x_{min} }}{{x_{max} - x_{min} }}$$
(11)
Table 2 Basic statistics of the independent variables and their correlations with degradation efficiency
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The relationships between each of the independent variables and the target were investigated by finding their Pearson product-moment correlation coefficients (r). The values of r show that the predictors with significant correlations have positive relationships with the target. In contrast, catalyst dose and contaminant initial concentration have a negative and non-significant relationship with the dependent variable. The implication of this observation is that these two parameters are possibly poor predictors of our output. In fact, traditional regression would likely exclude these parameters. Experimentally however, the solution pH and initial concentration indeed have a somewhat strong relationship with the degradation efficiency of the photo-catalysis. Moreover, one of the strengths of computational methods and SVR in particular is the ability to utilize hidden and nonlinear relationships (which tranditional statistics may overlook) to make accurate predictions [35].

3.3 Computational methodology and SVR parameter optimization

We carried out the computational processing using MATLAB, version R2015b. Libsvm, a Matlab tool-box containing the necessary SVR function for the model development and simulation, was used. The data were normalized prior to data training to enhance computational efficiency. The 249 experimental data were divided randomly into two portions, namely; training and testing datasets. The training dataset (224 datapoints) was used to develop the SVR model, while the remaining were used as testing datasets to validate the performance of the model. We applied 10-fold test-set-cross validation for the model development. The prediction accuracy of the proposed SVR model depends on selecting the optimum values of the SVR turning parameters. In our case, the four (4) SVR model parameters that modulate support vector learning system include C, λ, k-option and ε. Each of the parameters was separately optimized. For example, for the optimization of C, the values of λ, ε and k-option were kept constant while C is varied. The values of the coefficient of correlation (CC) and the root mean square error (RMSE) were monitored during each computational run. The value of C (regularization parameter) that gives the highest coefficient of correlation and the lowest RMSE was taken as the optimized C value. The approach is repeated for other parameters and the final SVR optimized parameters are presented in Table 3 and Figures S1–S4.

Table 3 Optimized SVM parameters
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4 Results and discussions

4.1 Validation of the SVR model

Figures 1 and 2 are the correlation plots used to compare the values of SVR predicted degradation efficiency and their corresponding experimental values. The correlation coefficients (r) of the regression lines of fit (shown in the plots) are 0.9885 and 0.9828 for training and testing datasets respectively. A good model has the value of r closer to 1, whereas if the value of r is closer to 0, the model is poor. The proposed SVR model is therefore suitable for modeling the photocatalytic degradation of MTBE since the values of ‘r’ are close to unity. Moreover, since the regression line of fit is assumed linear, it is essential to examine the randomness of the error term in order to confirm the model’s validity. The residual plot of testing data (Fig. 3) shows that the data are well dispersed around the zero line and, has no particular pattern. These further affirms the validity of the SVR model.

Fig. 1
figure 1

Correlation plot between experimental and SVR predicted results for the photocatalytic degradation efficiency of MBTE in the presence of TiO2 as the photocatalyst (training data)

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Fig. 2
figure 2

Correlation plot between experimental and SVR predicted results for the photocatalytic degradation efficiency of MBTE in the presence of TiO2 as the photocatalyst (testing data)

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Fig. 3
figure 3

Distribution of residuals from the predicted values of MTBE photodegradation efficiency using testing dataset

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4.2 Evaluation of prediction capability of the proposed model

After establishing the validity of the model, we investigated its prediction capability in terms of accuracy. We compared the experimental testing data with the SVR predicted results from testing data to check the model’s accuracy. As shown in Fig. 4, the SVR model correctly predicts the pattern and points of the experimental data. This close match confirms the accuracy of the SVR model. Even though the model line deviates slightly from a few experimental points, the deviation still falls within acceptable experimental error. Still, the estimation of this error gives information about the reliability of the model. The statistical parameters used for the evaluation of the model’s prediction ability include the root mean square error, mean absolute error and the Pearson’s correlation coefficient. These indices are expressed mathematically in Eqs. (12–14). Table 4 shows the correlation coefficients and error estimates obtained during the training and testing phase of the model development. The RMSE obtained for both training and testing datasets are less than 6% and fall within the analytical QC acceptable criteria which could be up to 20% [52]. Similarly, the MAE values obtained are very small. These confirm the accuracy and reliability of the proposed SVR model.

$$RMSE = \sqrt {\frac{1}{n}\left\{ {\mathop \sum \limits_{i}^{n} (D_{{e\left( {pr} \right)}} - D_{{e\left( {ex} \right)}} )^{2} } \right\}}$$
(12)
$$MAE = \frac{{\mathop \sum \nolimits_{i}^{n} \left| {(D_{{e\left( {pr} \right)}} - D_{{e\left( {ex} \right)}} } \right|}}{n}$$
(13)
$$r = \frac{{\mathop \sum \nolimits_{i}^{n} \left( {D_{{e\left( {ex} \right)}} - \overline{{D_{{e\left( {ex} \right)}} }} } \right)\left( {(D_{{e\left( {pr} \right)}} - (D_{{e\left( {pr} \right)}} } \right)}}{{\sqrt {\mathop \sum \nolimits_{i}^{n} \left( {D_{{e\left( {ex} \right)}} - \overline{{D_{{e\left( {ex} \right)}} }} } \right)^{2 } \left( {\left( {D_{{e\left( {pr} \right)}} - \left( {\overline{{D_{{e\left( {pr} \right)}} }} } \right)} \right)} \right)^{2} } }}$$
(14)

where n is the total number of the dataset. \(D_{{e\left( {ex} \right)}}\) and \(D_{{e\left( {pr} \right)}}\) refers to the experimental and the predicted values of degradation efficiency, respectively. While \(\overline{{D_{{e\left( {ex} \right)}} }}\) and \(\overline{{D_{{e\left( {pr} \right)}} }}\) refer to their respective mean.

Fig. 4
figure 4

Comparison of the experimental and SVR model prediction for degradation efficiency of MBTE in the prescience of TiO2

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Table 4 Estimation of model reliability using estimates of errors
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4.3 Effects of experimental input variables on MTBE degradation

As mentioned earlier, five experimental parameters were considered as independent variables in building the SVR model. These parameters influence MTBE photocatalysis differently. It is, therefore, imperative to study how they affect the photocatalytic process. We compared the SVR model with experimental data and used graphical representation to investigate their effects on MTBE photo degradation.

4.4 Effect of catalyst dosage

Figure 5 summarizes the influence of catalyst dosage on the degradation of MTBE in wastewater. The SVR model accurately captures the experimental observations. Although the model appears to slightly underestimate the observed data at dosages beyond 2.4 g/L, the difference is not significant and, probably, the model results are approximation of experimental/instrumental errors that could not be detected during the experiments. As shown in the figure, the optimum dosage is around 2.4 g/L. Lower dosages (< 2 g/L) are not enough for generation of sufficient hydroxyl radicals. In addition, dosages above the optimum do not result in any significant improvement in MTBE degradation. It is important to mention that both UV and catalyst must be present before photo-degradation can occur. This is because TiO2 does not adsorb MTBE significantly and MTBE is inert to UV radiation [30, 53,54,55,56]. The mechanism of photo-degradation is such that the photons of UV light generate energy greater than 3.2 eV which is enough to excite an electron (e−) in the valence band of TiO2 semiconductor, promoting it to the conduction band and leaving a positive hole behind. The e− in the conduction band rapidly reduces the adsorbed water on TiO2 surface into hydroxyl radicals while the positive hole oxidizes the water and converts to •OH radicals. Insufficient amount of the semiconductor photo-catalyst translates to short supply of •OH radicals and eventually results in poor degradation efficiency. Therefore, it is important to have a good dose of catalyst. Conversely, if the TiO2 is excessive, its surfaces bounce off UV radiation lowering the production of •OH radicals. Our SVR model gives a good estimation of these observations.

Fig. 5
figure 5

Effect of TiO2 dose on the photocatalytic degradation efficiency of MTBE

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4.5 Effect of contaminated solution pH

Figure 6 shows the effect of solution pH on MTBE mineralization. The SVR model gives a good approximation of the experimental observations, implying good performance of the model. From Fig. 6, the solution at pH 3 resulted in better MTBE degradation. Two important factors account for this; first, the solubility of MTBE in water is lowest at pH 3 (as our numerous laboratory experiments show). MTBE is thereby more readily available to •OH radicals for degradation at around pH 3 than at any other pH values. The second factor is due to the influence of interference from inorganic species present water. Anions such as carbonate form layer on TiO2 surfaces hindering the photocatalytic formation of •OH radicals and also interfering the reactivity of inefficiently produced •OH radicals with MTBE [32]. This phenomenon occurs mainly at higher pH values because, at acidic pH, the anions are unstable and therefore cannot compete well with the •OH radicals and MTBE. Extreme low pH values such as ≤ 1.0 lead to the dissolution of TiO2 [28] and reduced photocatalytic activity of the semiconductor.

Fig. 6
figure 6

Effect of solution pH on the photocatalytic degradation efficiency of MTBE in the prescience TiO2

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4.6 Effect of treatment contact time

Treatment time affects the extent and kinetics of photocatalytic degradation of organic compounds. Figure 7 shows that the proposed SVR model correctly modeled the trend of the experimental data to a large extent. Importantly, the model indicates that the degradation kinetics progressed at three different rates. The reaction rate was fastest within the first 20 min, reaching a degradation efficiency rate of 2.32 percent per minutes on average. A previous study [32] showed that the production of the first intermediate product of MTBE oxidation, tert-Butyl formate (TBF), is peaked at 20 min of contact time. Typically, MTBE degrades to organic intermediates which are mainly tert-Butyl alcohol (TBA), TBF and acetone [25, 57, 58]. These products compete with MTBE for OH radicals and slow down MTBE degradation efficiency rate significantly to about 0.60 min−1. During this stage, the contaminant and its intermediates are photodegraded to final products, water, and CO2. After 100 min, the SVR model predicted a maximum MTBE degradation efficiency of about 98%. Then, during the last stage of the quasi-static reaction rate of ~ 0.00 min−1, the intermediates are mineralized completely [30]. This suggests that the treatment time of 2 h is optimum for complete mineralization of MTBE and intermediates.

Fig. 7
figure 7

Effect of reaction time on the photocatalytic degradation efficiency of MTBE in the prescience TiO2

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4.7 Effect of initial MTBE concentration

The type of GC detector used in analyses of MTBE concentrations before and after treatment limits the concentration range that researchers are able to investigate. Support vector machine (SVM) produces a global solution to problems like this. The effect of MTBE concentration on the efficiency of photo-degradation is shown in Fig. 8. From the figure, the SVR model gives an accurate estimation of the experimental observations. Under the same experimental conditions, MTBE initial concentration in water has an inverse relationship with degradation efficiency. Degradation rate, on the other hand, increases with increasing concentration [24] suggesting appreciable degradation even at high MTBE concentration. Accordingly, the proposed SVR model showed that while about 96% of up to 20 ppm MTBE can be photodegraded within 60 min, the degradation efficiency of ~70% is attainable within the same time when the initial MTBE concentration is high (≥ 100 ppm). It is therefore instructive to increase treatment time and/or catalyst dosage when the MTBE initial concentration is greater than 20 ppm. As discussed under the previous subsection, the contact time of 2 h could give optimal MTBE treatment.

Fig. 8
figure 8

Effect of initial MTBE concentration on the photocatalytic degradation efficiency of MTBE in the presence of TiO2

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5 Conclusion

In this study, photocatalytic degradation efficiency of Methyl tert-Butyl Ether (MTBE) in the presence of TiO2/UV as photocatalyst were accurately modeled using support vector regression model (SVR). The model was developed using as inputs the following parameters; TiO2 dose, initial MTBE concentration, UV wavelength and contact time. The developed SVR model successfully modeled the efficiencies of degrading MTBE using TiO2/UV and under various experimental conditions. The prediction performance of the SVR model was very high as measured by correlation coefficients of 98.85% and 98.28% for training and testing dataset, respectively. Furthermore, root means square errors were calculated as 5.07% and 5.54% for training and testing dataset, respectively. More importantly, the effects of experimental conditions such as catalyst dose, solution pH, initial pollutant concentration and treatment time indicate that excellent treatment of 0.5–100 ppm MTBE-contaminated water is achievable using 2.4 g/L catalyst dose with UV radiation and maintaining a solution pH 3 and treatment time of 2 h. These computationally determined optimal experimental conditions can be useful for upscaling of photocatalysis for industrial water treatment applications.