OPTIMIZATION OF WEIGHT OF SLUDGE REMOVED FROM WASTE AUTOMOTIVE ENGINE OIL USING RESPONSE SURFACE METHODOLOGY
Abstract- In this study, a mathematical model has been developed to predict the weight of sludge removal from waste engine oil (WEO). The experiments have been conducted in laboratory using full factorial design in the design of experiments (DOE).The weight of sludge removal has been predicted by developing a second order polynomial model. The model was developed by using response surface method (RSM). To check the validity of the model, 95% confidence level was applied in the analysis of variance technique. The effect of oil to solvent ratio, temperature and time on weight of sludge removal from WEO was analysed in detail. The efficiency and ability of the model was checked by comparing the predicted and experimental response values. The result shows that empirical models derived from response surface approach can be used to describe the weight of sludge removal from the WEO.
Keywords- Response surface methodology (RSM), Full factorial design, weight of sludge removal, Waste engine oil (WEO)
INTRODUCTION
Therefore in this study an attempt has been made to study the effect of oil to solvent ratio, time and temperature on weight of sludge removal from waste automotive engine oil. An empirical model was obtained using RSM. Weight of sludge removal was considered as response and oil to solvent ratio, time and temperature were the input factors.
MATERIALS AND METHODS
Raw material
Waste automotive engine oil (WEO) is taken as the raw material for the present study. The sample was collected from Maruti Suzuki Service Center, Sambalpur, Odisha. The sample was stored at normal atmospheric temperature and pressure for fifteen days to settle the suspended particle under gravity.
1-Butanol of analytical grade was used as a solvent for the present experimentation.
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Eggshell was collected, dried in sunlight for ten days. The dried egg shell was powdered using mortar. The powdered egg shell was sieved, and the particles which pass through the 20-?m mesh were used in the experiments. The egg shell was used as sorbent.
Response surface methodology (RSM)
Response surface methodology (RSM) is practical, economical and relatively easy to use. RSM is a collection of mathematical and statistical techniques that are useful for the modelling and analysis of problems in which output or response is influenced by several input-variables and objective is to find the correlation between the response and the input variables. It comprises: designing a set of experiments, determining a mathematical model and determining the optimal value of the response to better understanding of the overall system behaviour 20. A second order polynomial model was proposed to represent the relationship between weight of sludge removed and independent variables. The performance of the model depends on a large number of factors that can act and interact in a complex manner. In the present work, the input variables are oil to solvent ratio (O/S), Time (t), and Temperature (T) and the output (response) is weight of sludge removed (WS). A response surface model is usually expressed as:
y= ?? + i=1K?ixi+ i=1k?ixi2+ i=1ki=1k?ijxixj+ ? for i ? j (1)
where ?0, ?i (i = 1, 2, . . . , k) and ?ij (i = 1, 2, . . . , k, j = 1, 2, . . . , k) are the unknown as regression coefficients to be estimated by using the method of least squares. In this equations ? are experimentally random errors and x1, x2………. xk are the input variables that influence the response y, k is the number of input factors. The method of least square is used to estimate the coefficients of the second order model. The response surface analysis is then done in terms of the fitted surface. The degree of significance of the model was tested by analysis of variance (ANOVA) using the software MINITAB-17.
Design of experiments (DOE)
A full factorial design is used with three design factors of each of three levels to describe the response of weight of sludge removed and to estimate the parameters in the second order model. Overall 33 = 27 experiments were carried out.
Table 1. Important factors and their levels for sludge removal
Sl. No. Factor Notation Unit Levels
1 Oil/solvent O/S ml/ml 1:1 1:2 1:3
2 Temperature T ?60 80 100
3 Time t hr 2 3 4
Experimental Procedure
The WEO was filtered to remove immiscible solid particles like sand and metal chips. For filtration purpose a Buchner funnel was fixed to a filtering funnel with a rubber stopper and a vacuum pump was connected to the filtering funnel. Filter paper was used as a filtering medium. To carry out experiments, three litres of waste engine oil was filtered. The WEO was heated to 120°C for an hour to remove the water content. 2.0 gm of potassium hydroxide (KOH) was added carefully to 100 ml 1-Butanol solvent. The mixture was strongly mixed until all the KOH dissolved into the solvent. Then, the 1-Butanol-KOH solution was mixed with WEO to a ratio of 1:1-1:3 continuously with a stirring speed of 350 rpm for 15 min. Then the mixture was heated to a temperature of 60°C-100°C for 1-3 hours. After that it was allowed to settle for 24 hours at room temperature. The sludge layer was removed by filtration and dried at 105°C till constant weight. The solvent was extracted from the oil-solvent mixture by vacuum distillation at 5mm Hg and 120°C.
RESULTS AND DISCUSSION
Development of sludge removal model
By using the full factorial design, a total of 27 experiments are conducted and regression coefficients are calculated. The full models for weight of sludge removal (WS) can be expressed in terms coded values of the independent variables in equation (2).
WS = -10.6 + 5.04 O/S + 0.642T – 10.57 t – 0.453 O/S*O/S – 0.00327 T*T
+ 0.950 t*t – 0.0775 O/S*T + 0.465 O/S*t+ 0.0506 T*t (2)
Analysis of variance (ANOVA)
Analysis of variance (ANOVA) and the F-ratio test have been performed to check the adequacy of the model as well as the significance of the individual model coefficients. The ANOVA was carried out on the model for a confidence level of 95%. The results of ANOVA tables for weight of sludge removal are listed in Table (2, 3). Table 2 represents the ANOVA table for the second order model propose for weight of sludge removal given in equation (2). It can be appreciated that the P-value is less than 0.05 which means that the model is significant at 95% confidence level. Furthermore, the significance of each coefficient in the full model was examined by T values and P values and the results are listed in Table 3. The larger values of T-test and smaller values of “P” indicate that the corresponding coefficient is highly significant 21. Hence the result given in Table 3 suggest the influence of (O/S) 2, T*T, O/S*t and are non significant and are therefore can be removed from full model to further improve the model.
Regression Equation
% sludge = -9.1 + 3.23 O/S + 0.642 T – 10.57 t – 0.00327 T*T + 0.950 t*t
– 0.0775 O/S*T + 0.465 O/S*t + 0.0506 T*t (3)
Table 2. ANOVA for weight of sludge removed (Full Model)
Source DF Adj SS Adj MS F-Value P-Value
Model 9 201.898 22.4332 4.56 0.004
Linear 3 141.253 47.0845 9.57 0.001
O/S 1 44.746 44.7458 9.09 0.008
T 1 96.281 96.2809 19.57 0.000
t 1 0.227 0.2267 0.05 0.033
Square 3 16.918 5.6395 1.15 0.359
(O/S)2 1 1.233 1.2331 0.25 0.623
T*T 1 10.270 10.2704 2.09 0.167
t*t 1 5.415 5.4150 1.10 0.309
2-Way Interaction 3 43.727 14.5755 2.96 0.062
O/S*T 1 28.830 28.8300 5.86 0.027
O/S*t 1 2.595 2.5947 0.53 0.478
T*t 1 12.302 12.3019 2.50 0.132
Error 18 83.651 4.9206
Total 26 285.549
Table-3 Estimated regression coefficient for weight of sludge removed of WEO (Full Model)
Term Effect Coef SE Coef T-Value P-Value VIF
Constant 7.48 1.13 6.62 0.000
O/S -3.153 -1.577 0.523 -3.02 0.008 1.00
T 4.626 2.313 0.523 4.42 0.000 1.00
T 0.224 0.112 0.523 0.21 0.033 1.00
(O/S)2 -0.907 -0.453 0.906 -0.50 0.623 1.00 (NS)
T*T -2.617 -1.308 0.906 -1.44 0.167 1.00
t*t 1.900 0.950 0.906 1.05 0.309 1.00
O/S*T -3.100 -1.550 0.640 -2.42 0.027 1.00
O/S*t 0.930 0.465 0.640 0.73 0.478 1.00
T*t 2.025 1.012 0.640 1.58 0.132 1.00
Table 4. ANOVA for weight of sludge removed (Reduced model)
Source DF Adj SS Adj MS F-Value P-Value
Model 8 200.665 25.0832 5.32 0.002
Linear 3 141.253 47.0845 9.98 0.000
O/S 1 44.746 44.7458 9.49 0.006
T 1 96.281 96.2809 20.42 0.000
T 1 0.227 0.2267 0.05 0.009
Square 2 15.685 7.8427 1.66 0.217
T*T 1 10.270 10.2704 2.18 0.157
t*t 1 5.415 5.4150 1.15 0.298
2-Way Interaction 3 43.727 14.5755 3.09 0.053
O/S*T 1 28.830 28.8300 6.11 0.024
O/S*t 1 2.595 2.5947 0.55 0.468
T*t 1 12.302 12.3019 2.61 0.124
Error 16 84.884 4.7158
Total 26 285.549
Table-5 Estimated regression coefficient for weight of sludge removed of WEO (Reduced Model)
Term Effect Coef SE Coef T-Value P-Value VIF
Constant 7.179 0.935 7.68 0.000
O/S -3.153 -1.577 0.512 -3.08 0.006 1.00
T 4.626 2.313 0.512 4.52 0.000 1.00
T 0.224 0.112 0.512 0.22 0.009 1.00
T*T -2.617 -1.308 0.887 -1.48 0.157 1.00
t*t 1.900 0.950 0.887 1.07 0.298 1.00
O/S*T -3.100 -1.550 0.627 -2.47 0.024 1.00
O/S*t 0.930 0.465 0.627 0.74 0.468 1.00
T*t 2.025 1.013 0.627 1.62 0.124 1.00
ANOVA was performed on the reduced model and the results are presented in Table (4, 5) and found that the model is highly significant. Thus Eq. (3) represents the coded form of final empirical model for weight of sludge removed from waste automotive engine oil.
Fig. 1: Normal probability plot of the residuals (Response is % sludge removed)
Fig. 2: Residual versus order of the data (Response is % sludge removed)
Fig. 4: Residuals versus the fitted values (Response is % sludge removed)
