Response surface methodology-based model for prediction of NO and NO_{2} concentrations in nonthermal plasma-treated diesel exhaust
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Abstract
Nonthermal plasma (NTP) technique for diesel exhaust emission control has been in the interest of the researchers from the last two decades, and it almost became a laboratory-proven technique for its efficiency over conventional techniques. A prior prediction of effectiveness of the process may lead to overcome the constraints in bringing this technique to real-time applications of diesel exhaust pollution control. In this present study, an attempt is made to find out the most dominating parameters and to predict the sum of NO and NO_{2} concentrations in NTP-treated diesel exhaust with respect to variations in operating parameter values using response surface methodology (RSM). Experiments have been conducted following 3^{N} full factorial design and collected the data by varying voltage, flow rate, temperature, discharge gap and initial (NO + NO_{2}) concentrations. The regression coefficients of the RSM-based mathematical model have been obtained by training it using these experimental data. The root-mean-square error (RMSE) is 4.7 ppm during the training. When this model is tested for a data other than that given during training (test data), the RMSE is 5.6 ppm. Further, the results are also compared with the model derived using the only available method in the literature, i.e., dimensional analysis, and found to be performing better.
Keywords
Air quality Diesel exhaust Nonthermal plasma NO_{X} removal Prediction of NO_{X} Response surface methodology1 Introduction
Diesel exhaust emission control has become a challenge for the researchers, as the emission standards are becoming more stringent throughout the world. On the other hand, demand for diesel engines is increasing continuously. Thus, there is a need to look for a technology to substitute the existing conventional catalytic-based filtering systems.
Even though NTP treatment for diesel exhaust pollution control has been proven to be an efficient technique, the studies are still at the laboratory level. To bring it into real-time applications, prior prediction of pollutant concentrations with the treatment would be helpful. If the NO_{X} concentrations are accurately predicted through modeling, it facilitates to estimate the pollutant removal efficiencies for those parametric variations, which cannot be performed in the laboratory due to experimental limitations [1]. Experimental studies were conducted by the researchers throughout the world to know the effects of various operating parameters such as applied voltage [2, 3], flow rate [4], temperature [5], residence time [6], reactor configurations [7] and electrode configurations [8]. While there is sufficient literature available regarding the chemical kinetics of the treatment, there is no much work done to quantify the effects of different parameters on the NO_{X} removal from the exhaust. Further, this modeling also helps the researchers to plan for the real-time applications through providing the knowledge of the relation between different parameter values and NO_{X} removal.
The multi-criteria decision-making method was used to evaluate diesel exhaust emission characteristics by Hoseinpour et al. [9], while gasoline fumigation was added to reduce pollutant emissions under different operating conditions. A plant-specific multi-year and multi-parameter coal power stack emission model has been proposed by Walvekar and Gurjar [10] using the emission factor-based approach. However, very few studies have been carried out to predict the NO_{X} (NO + NO_{2}) concentrations in the diesel exhaust after the NTP treatment based on the parameter values.
In most of the studies [1, 11, 12], dimensional analysis has been used for this purpose by relating the NO_{X} concentration with two or three other operating parameters of the NTP process. The disadvantage of the models derived using this method is that the root-mean-square error (RMSE) between experimental and predicted values of NO_{X} concentrations would be more for an experimental data other than that by which the model is trained. The reason for this is the less experimental data requirement for the training of the model. It can be observed that the RMSE for the test data is 9.58 ppm in a study by the authors of this present study (Allamsetty and Mohapatro [13, 14]).
Deriving a mathematical model and training it with more number of experimental data with a wide range of parameter values can be helpful in accurately predicting the pollutant concentrations for the test data also. Thus, in this present study, an effort has been made to predict the sum of NO and NO_{2} concentrations in diesel exhaust with NTP treatment using RSM.
RSM has been used to model various types of parameters such as surface roughness and temperature of turning operation [15, 16], kerf width of laser machining [17], bending strength of aluminum alloys [18]. It has also been used in [19, 20, 21, 22] to predict the pollutant concentrations in the emissions from a diesel engine based on various control parameters such as engine speed, compression ratio, brake power and injection parameters.
In this present study, the sum of NO and NO_{2} concentrations (NO + NO_{2}) has been predicted using RSM-based predictive model, with respect to the changes in parameters voltage (V), flow rate (Fr), temperature (T), discharge gap (Dg), initial sum of NO and NO_{2} concentrations (NO + NO_{2})_{i}. The effect of each parameter on the response has been analyzed numerically to know the dominant parameters. Values of the regression coefficients of the model have been derived, and analysis of variance has been performed on the model. Then, the model has been used to predict the values of (NO + NO_{2}) and compared them with their corresponding experimental values for the test data. The model has also been compared with the model derived using dimensional analysis with respect to its performance during the testing.
2 Experimental details
2.1 Experimental setup
Exhaust composition before treatment
(NO + NO_{2})_{i} (ppm) | NO (ppm) | NO_{2} (ppm) | CO (ppm) | O_{2} (%) | CO_{2} (%) |
---|---|---|---|---|---|
200 | 294 | 6 | 240 | 14.5 | 6.3 |
250 | 236 | 14 | 344 | 13.9 | 6.8 |
300 | 280 | 20 | 448 | 13.2 | 7.5 |
The high voltage applied to the plasma reactor during the NTP treatment has been generated and varied using a high-voltage AC test set (0–30 kV, 50 Hz, Make: Rectifiers & Electronics). This high voltage has been measured using a voltage divider (2000:1 ± 5%, Make: IWATSU, Model: HV-P60A, DC to 50 MHz, within − 3 dB) and a digital storage oscilloscope (Make: RIGOL, Model: DS 1074: 70 MHz).
The inner and outer diameters of the reactor are 15 mm and 17 mm, respectively. A layer of aluminum foil is wrapped to form the ground electrode over the reactor, between inlet and outlets, for a length of 280 mm. This can be described as the effective discharge length. The reactor is made up of borosilicate glass, which acts as the dielectric barrier when the high voltage is applied. The parameter Dg has been varied during the experiments by changing the diameter of the high-voltage electrode. The inner diameter of the reactor is maintained constant at 15 mm. Thus, when the electrode diameters are changed among 3 mm, 4 mm and 5 mm, they formed discharge gaps of 6 mm, 5.5 mm and 5 mm, respectively.
2.2 Design of experiments
The design of experiments (DoE) is a crucial aspect of RSM, which was formerly developed for the model fitting of physical experiments. Later, these strategies were also implemented for numerical experiments with an objective of selecting the input data points where the response needs to be experimentally found out.
Operating parameters and their levels
Operating parameters | Levels | ||
---|---|---|---|
− 1 | 0 | + 1 | |
Voltage (kV) | 16 | 21 | 26 |
Flow rate (lpm) | 4 | 10 | 16 |
Temperature (°C) | 25 | 50 | 75 |
Discharge gap (mm) | 5 | 5.5 | 6 |
Initial sum of NO and NO_{2} concentration (ppm) | 200 | 250 | 300 |
The NTP treatment primarily causes NO to NO_{2} conversion reactions leading to a decrement in NO concentration and an increment in NO_{2} concentration. If the applied high voltage keeps on increasing, the electric field gets intensified leading to the decrement in NO_{2} also. The possible chemical reactions those can take place in the reactor were given in a study by Saavedra et al. [24] with their rate constants. Major reaction pathways have been mentioned in a previous study of the authors [25]. The operating parameters have been varied in such a way to cover all the possible combinations with all the considered levels of each parameter, and corresponding (NO + NO_{2}) concentrations are noted down.
2.3 Experimental results
3 Model derivation
Estimated coefficients of quadratic RSM model
Term | Coefficient | SE coefficient | t-Stat |
---|---|---|---|
C | 382.8295 | 87.7362 | 4.3634 |
V | − 10.6173 | 1.5534 | − 6.8349 |
Fr | − 9.6690 | 1.0411 | − 9.2873 |
T | 0.7192 | 0.2554 | 2.8158 |
Dg | − 17.7552 | 28.8792 | − 0.6148 |
(NO + NO_{2}) | − 0.6918 | 0.1684 | − 4.1087 |
VFr | 0.5571 | 0.0151 | 36.9309 |
VT | − 0.0280 | 0.0036 | − 7.7217 |
VDg | 0.9144 | 0.1810 | 5.0517 |
V(NO + NO_{2}) | 0.0066 | 0.0018 | 3.6583 |
FrT | 0.0094 | 0.0030 | 3.1018 |
FrDg | − 0.0981 | 0.1508 | − 0.6506 |
Fr(NO + NO_{2}) | 0.0038 | 0.0015 | 2.5473 |
TDg | 0.0199 | 0.0362 | 0.5504 |
T(NO + NO_{2}) | − 0.0028 | 0.0004 | − 7.6256 |
Dg(NO + NO_{2}) | 0.0159 | 0.0181 | 0.8757 |
V ^{2} | − 0.1813 | 0.0256 | − 7.0805 |
Fr^{2} | 0.0516 | 0.0178 | 2.9022 |
T ^{2} | 0.0002 | 0.0010 | 0.1649 |
Dg^{2} | 0.6444 | 2.5600 | 0.2517 |
(NO + NO_{2})^{2} | 0.0030 | 0.0003 | 11.8548 |
The SE coefficient is an estimate of the standard deviation of the sampling distribution of the corresponding parameter. In other words, it is the ratio of standard deviation and the square root of the sample size. A lower value of SE coefficient indicates a more precise estimation. The t-stat is the ratio of the coefficient to its standard error. It is used to test the null hypothesis that the corresponding coefficient is zero against the alternative that it has some value other than zero, given the other predictors in the model. From the t-stat values obtained, it can be said that the coefficient values are well estimated. The values of both R^{2} and adjusted R^{2} of the model have been found to be 0.993, which indicate that this model is closely fitted with the experimental data. The RMSE is found to be 4.7 ppm. Further, the F value for the model has been found to be 1660 with respect to the constant model, which indicates a significant regression relationship between the response parameter and the operating parameters. The p value is 1.76e^{−229}, which indicates a strong significance of the model. According to these results, it can be said that the model is well derived and suitable to be used for prediction of the response parameter, i.e., (NO + NO_{2}).
4 Results and discussion
4.1 Surface plots
The trend followed by the response parameter, i.e., (NO + NO_{2}), with respect to the increase or decrease in the operating parameters can be observed in these plots. The apparent decrement in the (NO + NO_{2}) with the variation in V from 16 to 26 kV can be noticed in every subfigure of Fig. 3. It can be seen from Fig. 3a that the effect of V is less when the Fr is 16 lpm. The effect of the second parameter on the response can be observed in the remaining plots also and can be compared with each other. For example, from Fig. 3a, b, it can be noticed that the effect of Dg, when it is varied from its lower level to upper level, is lesser compared to that of Fr. Similarly, a decrement in (NO + NO_{2}) with an increase in T and with a decrease in Dg and (NO + NO_{2})_{i} can be observed from Fig. 3b, c and d, respectively.
4.2 Analysis of variance
Analysis of variance for the quadratic RSM model
Source | SS | DF | MS | F value | P value |
---|---|---|---|---|---|
V | 220,101.4 | 1.0 | 220,101.4 | 9951.1 | 2.2E−186 |
Fr | 91,027.0 | 1.0 | 91,027.0 | 4115.5 | 2.8E−145 |
T | 11,567.2 | 1.0 | 11,567.2 | 523.0 | 2.8E−60 |
Dg | 6343.1 | 1.0 | 6343.1 | 286.8 | 7.4E−42 |
(NO + NO_{2}) | 367,234.0 | 1.0 | 367,234.0 | 16,603.3 | 1.2E−210 |
VFr | 30,166.9 | 1.0 | 30,166.9 | 1363.9 | 9.4E−97 |
VT | 1318.8 | 1.0 | 1318.8 | 59.6 | 3.9E−13 |
VDg | 564.4 | 1.0 | 564.4 | 25.5 | 9.1E−07 |
V(NO + NO_{2}) | 296.0 | 1.0 | 296.0 | 13.4 | 3.2E−04 |
FrT | 212.8 | 1.0 | 212.8 | 9.6 | 2.2E−03 |
FrDg | 9.4 | 1.0 | 9.4 | 0.4 | 5.2E−01 |
Fr(NO + NO_{2}) | 143.5 | 1.0 | 143.5 | 6.5 | 1.2E−02 |
TDg | 6.7 | 1.0 | 6.7 | 0.3 | 5.8E−01 |
T(NO + NO_{2}) | 1286.2 | 1.0 | 1286.2 | 58.1 | 7.0E−13 |
Dg(NO + NO_{2}) | 17.0 | 1.0 | 17.0 | 0.8 | 3.8E−01 |
V ^{2} | 1108.9 | 1.0 | 1108.9 | 50.1 | 1.9E−11 |
Fr^{2} | 186.3 | 1.0 | 186.3 | 8.4 | 4.1E−03 |
T ^{2} | 0.6 | 1.0 | 0.6 | 0.0 | 8.7E−01 |
Dg^{2} | 1.4 | 1.0 | 1.4 | 0.1 | 8.0E−01 |
(NO + NO_{2})^{2} | 3108.4 | 1.0 | 3108.4 | 140.5 | 1.9E−25 |
e | 4910.2 | 222.0 | 22.1 | 1.0 | 5.0E−01 |
The calculated F values mentioned in the table for most of the terms of the model are greater in magnitude than the critical value of F, i.e., 3.88. If the F value of any term is lesser than the critical value of F of the model, then the P value increases and indicates the insignificance of that particular term. This has happened for few of the interaction and square terms of the model. The P values are comparatively higher for the interaction terms involved with the parameter Dg, i.e., FrDg, TDg and (NO + NO_{2})_{i}Dg, and square terms, i.e., T^{2} and Dg^{2}. However, the P values of linear terms along with the term associated with Dg are much lesser than 0.05, indicating that those terms are statistically significant at the 95% confidence level. In other words, it can be said that the changes in response values are associated with changes in parameter values and their inclusion in the model is meaningful.
4.3 Model validation
The second part of the validation process is testing the quadratic RSM model for an entirely new set of data which has not been used during training or while finding out the regression coefficients. Experiments have been conducted to obtain the test data of twelve sets with a random variation in the operating parameter values.
The operating parameter details of this test data set of twelve experiments are given in Table 4 along with the predicted values of NO + NO_{2} concentrations. In this table, experimental values of NO + NO_{2} concentrations are mentioned as (NO + NO_{2})_{e} and predicted values of NO + NO_{2} obtained using RSM model are mentioned as (NO + NO_{2})_{p_RSM}.
Test data with predicted (NO + NO_{2}) using quadratic RSM and dimensional analysis-based models and their errors
Experimental order | V (kV) | Fr (lpm) | T (°C) | Dg (mm) | (NO + NO_{2})_{i} (ppm) | (NO + NO_{2})_{e} (ppm) | (NO + NO_{2})_{p_RSM} (ppm) | E_{RSM} (ppm) | (NO + NO_{2})_{p_Dim} (ppm) | E_{Dim} (ppm) |
---|---|---|---|---|---|---|---|---|---|---|
1 | 25 | 8 | 25 | 5 | 250 | 146.7 | 152.5 | 5.8 | 154.8 | 8.1 |
2 | 18 | 4 | 50 | 5.5 | 300 | 260.7 | 254.7 | − 6 | 224.1 | − 36.6 |
3 | 24 | 12 | 75 | 6.5 | 200 | 141.4 | 148.2 | 6.8 | 107.1 | − 34.3 |
4 | 16 | 12 | 25 | 5 | 250 | 232.6 | 229.0 | − 3.6 | 264.5 | 31.9 |
5 | 20 | 8 | 75 | 6 | 300 | 251.1 | 243.3 | − 7.8 | 243.7 | − 7.4 |
6 | 21 | 6 | 50 | 5 | 200 | 138.7 | 132.9 | − 5.8 | 92.4 | − 46.3 |
7 | 17 | 10 | 100 | 5.5 | 250 | 210 | 208.7 | − 1.3 | 189.5 | − 20.5 |
8 | 23 | 14 | 50 | 6 | 300 | 262.1 | 262.8 | 0.7 | 275.9 | 13.8 |
9 | 19 | 4 | 25 | 6.5 | 200 | 177.9 | 169.4 | − 8.5 | 116.9 | − 61.0 |
10 | 23 | 16 | 50 | 6 | 250 | 209.7 | 216.8 | 7.1 | 198.7 | − 11.0 |
11 | 15 | 4 | 25 | 5 | 300 | 286.4 | 284.4 | − 2 | 288.8 | 4.4 |
12 | 20 | 18 | 75 | 6 | 200 | 187.2 | 192.5 | 5.3 | 137.8 | − 49.4 |
4.4 Comparison with dimensional analysis-based model
The predicted values of NO + NO_{2} concentrations obtained using the dimensional analysis-based model are mentioned as (NO + NO_{2})_{p_Dim} in Table 5. The error in these predicted values is mentioned as E_{Dim}. It can be observed from this column of Table 5 that for the experiments with order numbers 1, 5, 8, 10 and 12, the error is lesser compared to that of the remaining experiments. From this, it can be understood that the error is more when there is simultaneous variation in two or more operating parameters with respect to the data for which the model is trained.
5 Conclusion
A prior knowledge about the outcome of any experimental process would always be helpful in bringing the theory toward practical applications. In this present study, an attempt is made to predict the sum of NO and NO_{2} concentrations in diesel exhaust during the NTP treatment, with respect to changes in operating parameters, using RSM. The 3^{5} full factorial design has been adopted for conducting the experiments with three-level variations in the five operating parameters: Those are V, Fr, T, Dg and (NO + NO_{2})_{i}. From the main effect plots, it is noticed that the change in (NO + NO_{2})_{i} and V affects the (NO + NO_{2}) more than the other parameters.
Regression coefficients of the quadratic RSM model have been obtained by feeding it with the experimental data. The results of the chosen model have been analyzed using the surface plots, ANOVA and model validation. From the F values and P values obtained with ANOVA, the model can be described as significant at the 95% confidence level.
The predicted values are observed to be in good agreement with the corresponding experimental values. The RMSEs are found to be 4.7 ppm and 5.6 ppm for training data and test data, respectively. From all these results, this quadratic RSM model can be described as well suited for the prediction of (NO + NO_{2}) concentrations in diesel exhaust during NTP treatment.
Notes
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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