Chapter-5 Fixed Bed studies 5. Introduction Fixed bed experiments were carried out for removal of MB dye using PTMF, PTMFAC,ASD and A.niger as adsorbents. With each of the adsorbent, effect of change in bed height, MB concentration and dye solution flow rate were investigated. The performance of fixed bed in the form of breakthrough curves were obtained and tested using different kinetic models like Thomas, Adam-Bohart, Yoon-Nelson and Bed depth Service time(bdst). Adsorption capacity (mg/g) was found from the models. The constants obtained from the models can be utilized for designing the industrial scale fixed bed. The best fit model which fitted the experimental condition were determined by the computed R 2 value. The experiments of three different bed height, cm (.352 g), 5 cm(.899 g ), 2 cm( 2.464 g) respectively were operated at influent MB concentration of 5 mg/l and flow rate of 5.7mL/ min at ph of 6.Also, experiments with three different MB concentration (5, and 5 mg/l) were performed at 2 cm bed height, 5.7 ml/ min flow rate and ph of 6. 5.2 Column Studies Adsorption of methylene blue is presented in the form of breakthrough curves (i.e. C t /C o Vs t) 5.2. The effect of initial concentration on breakthrough curve From the Fig-5.2 it is found that the breakthrough time decreased with increasing influent MB concentration. At lower influent MB concentrations, breakthrough were dispersed and breakthrough occurred slower. As influent concentration increased, sharper breakthrough were
obtained. This result demonstrated that the change of concentration gradient effected the saturation rate and breakthrough time. (Han et al.,27). This can be explained by the fact that more adsorption site are being covered with increase in MB concentration. The larger the influent concentration, the steeper the slope of the breakthrough curve and the smaller the breakthrough time. These results established that change of concentration gradient effected the saturation rate and breakthrough time or in other words, the diffusion process was concentration dependent. As the influent concentration increased, MB loading rate also increased, causing the driving force for mass transfer to increase, which resulted in decrease of adsorption zone length. Similar trend was observed in the case of Congo red dye onto rice husk. (Han et al., 27) Fig-5. Breakthrough curves for MB biosorption onto A.niger biomass at different initial concentrations (bed height = 2 cm, flow rate = 5.7mL/min, ph=6)
5.2.. Evaluation of breakthrough curve for different concentration using linearized Thomas model Thomas model was applied to the experimental data with respect to influent concentration of MB. A linear regression analysis was used on each set of data to determine the Thomas model parameters of q and K Th. The determined coefficients and the R 2 were also obtained using linear regression analysis according Eq. (2.34 ). The results are listed in Table- 5.. Fig-5.2 Linearized form of Thomas model for MB biosorption onto A.niger at different initial concentrations (bed height = 2 cm, flow rate = 5.7mL/min, ph=6) Table-5. Thomas model parameters at different initial MB concentrations using linear regression (bed height =2cm, flow rate = 5.7mL/min, ph=6) Sl.no Initial dye q o (mg/g) K Th R 2 concentration (mg/l) ( ml/ mg.min) 5 25.45.978 2 42.6.99.9795 3 5 57.73.983
From Table-5. the following conclusion can be drawn, ) q o increased and K Th decreased with initial concentration of MB. The reason for increase in q o is that, the driving force for biosorption is the concentration difference between the dye on the biosorbent and the dye in the solution. Thus the high driving force due to the higher MB concentration resulted in better column performance.(han et al.,29) Whereas the K Th decreased due to due to the fact that the rate of mass transfer in the column turned slowly for higher concentration of MB, which was result in lengthening the contact time between solute and adsorbent. Similar trend was observed in the case of MB dye uptake by modified wheat straw (Zhang et al.,2). 2) R 2 values are greater than.978, indicating that for Thomas model, experimental and predicted data were very close. 3) From Fig-5.2, value of slope of the straight line decreased with increasing MB concentration. 5.2.2 The effect of different bed height on the curve breakthrough curve Thomas model was applied to the experimental data with respect to different bed height. A linear regression analysis was used on each set of data to determine the Thomas model parameters of q and K Th. The determined coefficients and the R 2 were also obtained using linear regression analysis according Eq. (2. 34). The results were listed in Table- 5.2.
Fig-5.3 Breakthrough curves for MB biosorption onto A.niger at different bed height(c =5 mg/ L, flow rate = 5.7mL/min, ph=6) From the Fig-5.3, it was seen that as bed height increased, MB had more time to contact with A.niger that resulted in higher removal efficiency of MB. So the higher bed column resulted in a decrease in the solute concentration in the effluent at the same operational time. The slope of the breakthrough curve decreased with increasing bed height, which resulted in broadened mass transfer zone. Higher uptake was observed at the highest bed height due to an increase in the surface area of the biosorbent, which provided more binding sites for the sorption( Vijayaraghavan et al.,24; Han et al.,29). when the bed height was reduced, axial dispersion phenomena predominated in the mass transfer and reduced the diffusion of the solute, and
therefore the solute had not enough time to diffuse into the whole of the adsorbent mass(i.a.w.tan et al.,28). 5.2.2. Evaluation of breakthrough curve for different bed height using linearized Thomas model Fig-5.4 Linearised form of Thomas model for methylene blue biosorption onto A.niger biomass at different bed height(concentration= 5 mg/l, flow rate = 5.7mL/min, ph=6) Table-5.2 Thomas model parameters at different bed height of A.niger using linear regression (C = 5 mg/l, flow rate = 5.7mL/min, ph=6) Sl.no Bed height q o (mg/g) K Th R 2 (cm) ( ml/ mg.min) 2 25.45.978 2 5 24.26 37.9838 3 22.5 5.9763
5.2.3 Estimation of breakthrough curves using non-linear regression analysis In order to describe the fixed-bed column behavior and to scale it up for industrial applications, four models, Thomas, Adams Bohart, Yoon Nelson and BDST were used to fit the experimental data in the column. Although linear least-square regressive analysis is often used to obtain the model parameters ( Han et al., 26), non-linear regressive analysis is also adopted to determine the relative parameters (Kumar & Sivanesan, 27) for change in initial concentration and bed height. 5.2.3. Thomas model The column data were fitted to the Thomas model to determine the Thomas rate constant (K Th ) and maximum solid-phase concentration (q ). The determined coefficients and relative constants were obtained using non-linear regression analysis according to Eq. (2.33) for varying inlet MB concentration and bed height and the results are listed in Table-5.3. Table-5.3 Thomas model parameters at different conditions using non-linear regression analysis for biosorption of MB onto A.niger (Flow rate=5.7ml/min, ph-6) Co(mg/L) Z(cm) K Th (ml/min.mg) q o (mg/g) R 2 SS 5 2 377 24.246.9935.2449 2.9942 39.563.98924.2797 5 2.762 49.767.98965.2575 5 6644 2.982.3563 5 5 359 23.377.9932.2448 From Table-5.3 the following inference can be drawn As the influent concentration increased the value of K Th decreased and q o values increased. Similar trend was observed as the bed height was increased. These observations were analogous to the findings given in section 5.7.. and 5.7.2.
) The values of SS (less than.35) and R 2 greater than.98, suggests that the data fits very well to the Thomas model. 2) The breakthrough curve simulated by the Thomas model, as presented in Fig-5.5, 5.6, and 5.7 coincided well with the experimental data. Fig-5.5 Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/l according to the Thomas model for biosorption of MB onto A.niger Fig-5.6 Comparison of the experimental and predicted breakthrough curves obtained at mg/l according to the Thomas model for biosorption of MB onto A.niger
Fig-5.7 Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/l according to the Thomas model for biosorption of MB onto A.niger 5.2.3.2 Adam- Bohart model The Adams Bohart adsorption model was applied to experimental data for the description of the breakthrough curve. This approach was focused on the estimation of characteristic parameters, such as maximum adsorption capacity (N ) and kinetic constant (K AB ) from Adams Bohart model. After applying Eq. (2.37) to the experimental data and plotting breakthrough curves as shown in Fig-5.8, 5.9 and 5., the parameters were obtained and is listed in Table-5.3. It was seen from the tabulated values that as initial concentration was increased K AB values decreased and N values increased. The R 2 values were in the range of 2-.9, indicating that Adam Bohart model was not fitting to the data points very well. After applying Eq. (2.37 ) to the experimental data, the parameters were obtained for relative concentration region up to i.e up to 2% breakthrough curve for 5 mg/l and.3 i.e up to 3% breakthrough curve for and 5 mg/l respectively as shown in Fig -5., 5.2 and 5.4. It is clear from the Table-5.4 that
there is good agreement between experimental and predicted values(r 2 >.97), suggesting that Adam-Bohart model will be valid for limited range of condition used. Fig- 5.8 Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/l according to the Adam- Bohart model for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height = 2cm) Fig-5.9 Comparison of the experimental and predicted breakthrough curves obtained at mg/ L according to the Adam- Bohart model for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2cm)
Ct/C Fig-5. Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/ L according to the Adam- Bohart model for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2cm).9.7.5.3. Experimental predicted(2%) 2 3 4 5 6 t,min Fig-5. Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/ L according to the Adam- Bohart model at 2% concentration for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2cm)
Ct/C Ct/C.9.7.5.3 Experimental Predicted(3%). 5 5 2 25 3 35 4 45 t, min Fig-5.2 Comparison of the experimental and predicted breakthrough curves obtained at mg/l according to the Adam- Bohart model at 3% concentration for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2cm).9.7.5.3 Experimental predicted(3%). 5 5 2 25 3 35 4 t, min Fig-5.3 Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/l according to the Adam- Bohart model at 3% concentration for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2cm)
Table-5.4 Adam-Bohart model parameters at different conditions using non-linear regression analysis for biosorption of MB onto A.niger.( Flow rate = 5.7min/mL, bed height = 2cm) C o (mg/l) K AB (L/min.mg) N o (mg/l) R 2 SS 5.642 ( 567) 744 (96.2) 252 (.993).7 (.262).3437 243.4 973.864 (.563) 5.259 (.54) (454.94) 625.42 (63.84) (.9952).975 (.9734) (.4727).77 (.) (in brackets are values of various parameters at C t /C o = (for 5 mg/l ) &.3 (for,5 mg/l) 5.2.3.3 Yoon Nelson Model A simple theoretical model developed by Yoon Nelson was applied to investigate the breakthrough behavior of MB on A.niger. So the values of K YN (a rate constant) and τ (the time required for 5% MB breakthrough) could be obtained using non-linear regressive analysis from Eq.(2.38). The values of K YN and τ are listed in Table-5.5. From Table-5.5, the rate constant K YN increased and the 5% breakthrough time τ decreased with increasing both flow rate and MB inlet concentration. Fig- 5.4 Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/l according to the Yoon-Nelson model for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2 cm)
Fig-5.5 Comparison of the experimental and predicted breakthrough curves obtained at mg/l according to the Yoon-Nelson model for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2 cm) Fig-5.6 Comparison of the experimental and predicted breakthrough curves obtained at 5 mg/l according to the Yoon-Nelson model for biosorption of MB onto A.niger ( Flow rate=5.7min/ml, bed height =2 cm)
Table-5.5 Yoon Nelson model parameters at different conditions using non-linear regression analysis for biosorption of MB onto A.niger.( Flow rate=5.7min/ml, bed height =2 cm) Co(mg/L) Z(cm) K YN (min - ) τ (min) SS τ exp (min) 5 2.3226 455.5.27 28 2.3437 49.2.864 7 5 2.3779 356.7.77 4 The data in Table-5.5 also indicated that values τ from the calculation were significantly different compared to experimental results. Fig-5.4 to 5.6, is the comparison of the experimental curve and predicted curve according to Yoon Nelson model. The experimental breakthrough curves are not close to those predicted by the Yoon Nelson model. The values of SS are larger according to Table-5.5. So it was referred that the Yoon Nelson model cannot be used to predict the experimental data. 5.2.3.4 The Bed depth/service time analysis (BDST) model The BDST model is based on physically measuring the capacity of the bed at different breakthrough values. This simplified design model ignores the intraparticle mass transfer resistance and external film resistance such that the adsorbate is adsorbed onto the adsorbent surface directly. With these assumptions, the BDST model works well and provides useful modeling equations for the changes of the system parameters (Han et al., 27).A modified form of the equation that expresses the service time at breakthrough, t, as a fixed function of operation parameters is the BDST model (Goel et al.,25). ( ) (5.)
Where, K a is rate constant in BDST model (L mg - min - ), A plot of time, t vs. bed depth, Z, should yield a straight line where N o and K, are the adsorption capacity and rate constant, respectively, which can be evaluated. Fig-5.7 Iso removal lines for, and breakthrough for different bed height for biosorption of MB onto A.niger. (C o =5 mg/l, flow rate = 5.7mL/min ) Table-5.6 The calculated constants of BDST model for biosorption of MB onto A.niger (Co =5ppm, flow rate = 5.7mL/min ) C t /C o K a (L mg - min - ) N o (mg/l) R 2.68 55.5.987.232 885.99966.567 9.3.9994 The lines of t Z at values of C t /C,, are shown in Fig-5.8, respectively. The related constants of BDST according to the slopes and intercepts of the lines along with uncertainties of the relative parameters are also listed in Table 5.6. The adsorption capacity of the bed per unit
bed volume, N, was calculated from the slope of BDST plot, assuming initial concentration, C, and linear velocity, v, as constant during the column operation. The rate constant, K a, calculated from the intercept of BDST plot, characterizes the rate of solute transfer from the fluid phase to the solid phase (Padmesh et al., 25). With the values of C t /C increasing, the values of N increased while K a decreased. The BDST model parameters can be helpful to scale up the process for other flow rates without further experimental run. 5.3 Fixed bed studies- PTMF The experiments of three different bed height 5cm, 8cm, cm respectively were operated at influent MB concentration of 5 mg/l and flow rate of 7.5 ml/ min at ph of 6. Also, experiments with three different MB concentration (5,,5 mg/l) were performed at 8 cm bed height, 7.5 ml/ min flow rate and ph of 6.The effect of flow rate (4.6, 7.5 and ml/min) experiments were studied at 8cm bed height, mg/l and ph of 6. 5.3. Effect of different bed depth on breakthrough curve Fig-5.8 Breakthrough curves for methylene blue adsorption onto PTMF at different bed height ( C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6)
From the Fig-5.8, it was seen that as bed height increased, MB had more time to contact with PTMF that resulted in higher removal efficiency of MB. So the higher bed column resulted in a decrease in the solute concentration in the effluent at the same time. The slope of the breakthrough curve decreased with increasing bed height, which resulted in broadened mass transfer zone. Higher uptake was observed at the highest bed height due to an increase in the surface area of the biosorbent, which provided more binding sites for the adsorption. The rice husk employed for MB dye removal also showed the similar trend.( Han et al.,29) 5.3.2 The effect of initial MB concentration on breakthrough curve Fig-5.9 Breakthrough curves for methylene blue adsorption onto PTMF at different initial concentrations ( bed height= 8cm, flow rate = 7.5 ml/min, ph=6) From the Fig-5.9, it is illustrated that breakthrough time decreased with increasing influent MB concentration. A decrease in inlet concentration gave an extended breakthrough curve, indicating a higher volume of solution could be treated.. As influent dye concentration increased, sharper breakthrough curves were obtained. The driving force for adsorption is the concentration
difference between the solute on the adsorbent and the solute in the solution. As high concentration differences provides a higher driving force, which favors the adsorption process. Further, at high initial dye concentrations, a sharper breakthrough curve indicated shortened mass transfer zone and higher adsorption rates. Therefore, when quick dye uptake is desired, which is often the case, operating with high initial dye concentrations appears to be favorable. The change of concentration gradient affected the saturation rate and breakthrough time or in other words, the diffusion process was concentration dependent. Similar findings were obtained for MB uptake by Peanut husk (J.Song et al.,2), phenoix tree leaf powder (Han et al., 29). 5.3.3 Effect of flow rate on Breakthrough curve Fig-5.2 Breakthrough curves for methylene blue adsorption onto PTMF at different flow rate (initial concentrations = mg/l, bed height= 8cm, ph=6) From Fig-5.2, breakthrough generally occurred faster with higher flow rate. Breakthrough time reaching saturation was increased significantly with decrease in flow rate. At low flow rate of
influent, MB had more time to be in contact with the adsorbent, which resulted in greater removal of MB molecules in the column. Although MB adsorption was a fast process, diffusion effects were lower due to the insufficient residence time of dyes in the column at higher flow rates. Hence lower flow rates were desirable for the effective removal of MB in column mode. Similar trend was observed for MB removal using modified wheat straw( Zhang et al.,2) 5.4 Estimation of breakthrough curves In order to describe the fixed-bed column behavior and to scale it up for industrial applications, three models, Thomas, Adams Bohart and Yoon Nelson were used to fit the experimental data in the column. Although linear least-square regressive analysis is often used to obtain the model parameters, non-linear regressive analysis is adopted to determine the relative parameters. 5.4. Thomas model Thomas model was applied to the experimental data with respect to different bed height. A non-linear regression analysis was used on each set of data to determine the Thomas model parameters of q and K Th. The determined coefficients and the R 2 were also obtained using non- linear regression analysis according Eq. (2.33 ). The results were listed in Table- 5.7.
C/Co C/Co 5.4.. Effect of bed Height.2 Experimental Predicted 2 4 6 Time( min) Fig-5.2 Thomas model parameters at bed height, 5 cm using non-linear regression for adsorption of MB onto PTMF (C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6).2 Exp Pred 2 4 6 8 Time(min) Fig-5.22 Thomas model parameters at bed height, 8 cm using non-linear regression for adsorption of MB onto PTMF (C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6)
C/Co.2 Exp Pred 2 4 6 8 time(min) Fig-5.23 Thomas model parameters at bed height, cm using non-linear regression for adsorption of MB onto PTMF (C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6) Table-5.7 Thomas model parameters at different bed height using non-linear regression for adsorption of MB onto PTMF ( C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6) Sl.no Bed Height(cm) q o (mg/g) K Th ( ml/ mg.min) R 2 SS 5 25.93.394.99.3 2 8 27.4.79.995.425 3 3.39.676.9959.8 As shown in Table-5.7, when bed height increased, the value of q o increased while the value of K Th decreased. The increase in q o can be explained due to an increase in the surface area of the biosorbent, which provided more binding sites for the adsorption. The K Th decreased with increasing bed height indicating the reduced reaction rate which was ascribed to longer contact time for higher bed depth. From Fig-5.2,5.22 and 5.23, it was observed that experimental values were in agreement with predicted values. This fact was confirmed by high R 2 values in Table- 5.7. These results were in agreement with those referred to the literatures ( Han et al.,29)
C/Co C/Co 5.4..2 Effect of initial MB concentration.2 Exp Pred 2 4 6 8 Time,t(min) Fig-5.24 Thomas model parameters at initial concentration of mg/l using non-linear regression for adsorption of MB onto PTMF (bed height =8cm, flow rate = 7.5mL/min, ph=6).2 Exp Pred 2 4 6 Time(min) Fig-5.25 Thomas model parameters at initial concentration of 5 mg/l using non-linear regression for adsorption of MB onto PTMF (bed height =8cm, flow rate = 7.5mL/min, ph=6)
C/Co Table-5.8 Thomas model parameters at different initial concentrations using non-linear regression for adsorption of MB onto PTMF.(bed height =8cm, flow rate = 7.5mL/min, ph=6) Sl.no Concentration (mg/l) q o (mg/g) K Th ( ml/ mg.min) R 2 SS 5 27.4.79.995.425 2 39.47.228.9877.66 3 5 54.93.9847.585 When the MB concentration was increased from 5mg/L to 5 mg/l (Table-5.8), the q e increased and K Th decreased due to the fact that the rate of mass transfer in the column turned slowly for higher concentration of MB, which was result in lengthening the contact time between solute and adsorbent and improved adsorption capacity. From Fig-5.22, 5.24 and 5.25, it was observed that experimental values are in agreement with predicted values. This fact was confirmed by high R 2 values in Table- 5.8. The results are in agreement with the works reported previously on various fixed-bed adsorption systems (Ahmed & Hameed,2, Chen et al.,22). 5.4..3 Effect of Flow rate.9.7.5.3. Exp Pred 2 4 6 8 Time(min) Fig-5.26 Thomas model parameters at flow rate of 4.8 ml/min using non-linear regression for adsorption of MB onto PTMF (C o = mg/l bed height= 8cm, ph=6)
C/Co.2 Exp Pred 2 3 4 5 Time(min) Fig-5.27 Thomas model parameters at flow rate of ml/min using non-linear regression (C o = mg/ L, bed height= 8cm, ph=6) Table-5.9 Thomas model parameters at different flow rate using non-linear regression for adsorption of MB onto PTMF (C o = mg/l, bed height= 8cm, ph=6) Sl.no Flow rate(ml/min) q o (mg/g) K Th ( ml/ mg.min) R 2 SS 4.8 44.68.768.986.8 2 7.5 39.47.228.9877.66 3 38.89.574.9994.838 From Table-5.9, when the flow rate increased the MB removal efficiency decreased. This was attributed to the fact that short contact time between solute and adsorbent would reduce the adsorption efficiency. The K Th increased with the increase in flow rate due to faster mass transfer at higher flow rate. From Fig-5.24, 5.26 and 5.27, it was observed that experimental and predicted breakthrough values were overlapping. This fact was confirmed by high R 2 values in Table- 5.9.Similar findings were obtained by researchers (Song et al.,2, Han et al.,29)
C/Co 5.4.2 Yoon Nelson Model Yoon-Nelson model was applied to the experimental data with respect to different bed height, initial concentration of MB and flow rate. A non-linear regression analysis was used on each set of data to determine the Yoon-Nelson model parameters of τ and K YN. The determined coefficients and the R 2 were also obtained using non- linear regression analysis according Eq. (2.38). The results are listed in Table- 5.,5. and 5.2. 5.4.2. Effect of bed height.2 Experimental Predicted 2 4 6 Time,t(min) Fig-5.28 Yoon-Nelson model parameters at bed height of 5 cm using non-linear regression for adsorption of MB onto PTMF (C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6)
C/Co C/Co.2 Exp Pred 2 4 6 8 Time,t (min) Fig-5.29 Yoon-Nelson model parameters at bed height of 8 cm using non-linear regression for adsorption of MB onto PTMF (C o = 5mg/L, flow rate = 7.5 ml/min, ph=6).2 Exp Pred 2 4 6 8 Time, t(min) Fig-5.3 Yoon-Nelson model parameters at bed height of cm using non-linear regression for adsorption of MB onto PTMF (C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6) Table-5. Yoon-Nelson model parameters at different bed height using non-linear regression for adsorption of MB onto PTMF(C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6) Sl.no Bed Height(cm) τ (min) K YN (/min) R 2 SS 5 24.35.59.99.3 2 8 366.86.995.425 3 494.48.84.9959.8
C/Co C/Co 5.4.2.2 Effect of initial MB concentration.2 Exp Pred 2 4 6 8 Time, t (min) Fig-5.3 Yoon-Nelson model parameters at initial concentration of mg/l using non-linear regression. for adsorption of MB onto PTMF (bed height =8cm, flow rate = 7.5mL/min, ph=6).2 Exp Pred 2 4 6 Time,t (min) Fig-5.32 Yoon-Nelson model parameters at initial concentration of 5 mg/l using non-linear regression for adsorption of MB onto PTMF (bed height =8cm, flow rate = 7.5mL/min, ph=6) Table-5. : Yoon-Nelson model parameters at different initial concentrations using non-linear for adsorption of MB onto PTMF regression. (bed height =8cm, flow rate = 7.5mL/min, ph=6) Sl.no Concentration(mg/L) τ (min) K YN (/min) R 2 SS 5 366.86.995.425 2 278.9.23.9877.65 3 5 234.99.39.9847.585
C/Co C/Co 5.4.2.3 Effect of flow rate Exp Pred 2 4 6 8 Time,t (min) Fig-5.33 Yoon-Nelson model parameters at flow rate of 4.6 ml/min using non-linear regression for adsorption of MB onto PTMF (C o = mg/l, bed height= 8cm, ph=6).2 Exp Pred 2 3 4 5 Time, t(min) Fig- 5.34 Yoon-Nelson model parameters at flow rate of ml/min using non-linear regression for adsorption of MB onto PTMF (C o = mg/l, bed height= 8cm, ph=6) Table-5.2: Yoon-Nelson model parameters at different flow rate using non-linear regression for adsorption of MB onto PTMF (C o = mg/l, bed height= 8cm, ph=6) Sl.no Flow rate (ml/min) τ (min) K YN (/min) R 2 SS 4.8 493.39.79.986.8 2 7.5 278.9.23.9877.65 3.5 98.2.57.9794.838
C/Co From Table-5.2, as the flow rate increased the K YN increased while τ decreased. This was due to the fact that higher flow rate would result in the insufficiency of the adsorption and adsorption equilibrium early. The time required for 5% breakthrough increased with increase in bed height for PTMF adsorbent but was found to decrease with increase in MB concentration. A similar observation was made during sorption study using treated chitosan (Auta & Hameed, 24). However the same trend was also observed when the initial MB concentration (Table-5. ) which seemed quite abnormal because higher MB concentration would prolong the rate of mass transfer in column which usually extended the contact time between solute and adsorbent in column. Therefore Yoon-Nelson model was not the proper one also. 5.4.3 Adam-Bohart Model Adam-Bohart model was applied to the experimental data with respect to different bed height, initial concentration of MB and flow rate. A non-linear regression analysis was used on each set of data to determine the Adam-Bohart model parameters of N o and K AB. The determined coefficients and the R 2 were also obtained using non- linear regression analysis according Eq. (2.37). The results are listed in Table- 5.22,5.23 and 5.24. 5.4.3. Effect of bed height.2 Exp Pred 2 4 6 8 Time(min) Fig-5.35 Adam-Bohart model parameters at bed height of 8 cm using non-linear regression for adsorption of MB onto PTMF (C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6)
C/Co Table-5.3 : Adam-Bohart model parameters at different bed height using non-linear regression for adsorption of MB onto PTMF (C o = 5 mg/l, flow rate = 7.5 ml/min, ph=6) Sl.no Bed Height(cm) K AB (ml/min.mg) No (g/l) R 2 SS 5.632 228.25.7723 292 2 8.523 259.6 582.557 3.548 92.33 9.5262 5.4.3.2Effect of initial concentration of dye.2 Exp Pred 2 3 4 5 6 Time(min) Fig-5.36 Adam-Bohart model parameters at initial concentration of mg/l using non-linear regression for adsorption of MB onto PTMF (bed height=8 cm, flow rate = 7.5 ml/min, ph=6) Table -5.4: Adam-Bohart model parameters at different initial concentration using non-linear regression for adsorption of MB onto PTMF (flow rate = 7.5 ml/min, bed height= 8cm, ph=6) Sl.no Concentration(mg/L) K AB (ml/min.mg) No (g/l) R 2 SS 5.523 259.6 582.557 2.299 3425. 5 292 3 5.238 4273.56 242.5362 5.4.3.3 Effect of flow rate Table-5.5 Adam-Bohart model parameters at different flow rate using non-linear regression for adsorption of MB onto PTMF (C o = mg/l, bed height= 8cm, ph=6) Sl.no Flow rate (ml/min) K AB (ml/min.mg) No (g/l) R 2 SS 4.8.26 7697.89 67.573 2 7.5.299 3425. 5 292 3.359 839.5 5.5658
Adams Bohart model was only applicable to describe the experimental data at the initial part of the breakthrough curves but the variation in bed height, initial concentration of MB and flow rate did not provide any good agreement even in the initial portion of the breakthrough curve. The fitted results by Adams Bohart model were also shown in Table-5.3,5.4 and 5.5 (selected plots shown). The determination coefficients R 2 showed unsatisfactory fitness. Besides, the fitted kinetic constant K AB and adsorption capacity N were irrelevant to bed height, flow rate and initial solution concentration. They were inconsistent with the assumption of this model, which required that K AB should be proportional to the residual capacity of PTMF and the concentration of MB. Consequently, Adams Bohart model was not a proper one to describe the adsorption behaviors of PTMF in column. Similar trend was reported for modified wheat straw (Zhang et al.,2). 5.5 Fixed bed studies PTMFAC The experiments of three different bed height 5cm, 8cm, cm respectively were operated at influent MB concentration of 5 mg/l and flow rate of 7.5 ml/ min at ph of 6.Also, experiments with three different MB concentration (5,,5 mg/l) were performed at 8 cm bed height, 7.5 ml/ min flow rate and ph of 6.The effect of flow rate (4.6, 7.5 and ml/min) experiments were studied at 8cm bed height, mg/l and ph of 6.
5.5. Effect of different bed depth on breakthrough curve Fig-5.37 Breakthrough curves for methylene blue adsorption onto PTMFAC at different bed height (initial concentrations= 5 mg/l, flow rate = 7.5 ml/min, ph=6) From the Fig-5.37, it was seen that as bed height increased, MB had more time to contact with PTMFAC that resulted in higher removal efficiency of MB. So the higher bed column resulted in a decrease in the solute concentration in the effluent at the same time. The slope of the breakthrough curve decreased with increasing bed height, which resulted in broadened mass transfer zone. Higher uptake was observed at the highest bed height due to an increase in the surface area of the adsorbent, which provided more binding sites for the adsorption. At lower adsorbent bed height, axial dispersion phenomenon predominated and reduced the diffusion of MB adsorbate (Foo & Hameed,22).Also, increase in PTMFAC bed height 5 to cm indicated a dramatic increase of adsorption uptake and in the volume of MB solution to be treated.
5.5.2 The effect of initial MB concentration on breakthrough curve Fig-5.38 Breakthrough curves for methylene blue adsorption onto PTMFAC at different initial concentrations ( bed height= 8cm, flow rate = 7.5 ml/min, ph=6) From the Fig-5.38, an inverse relationship between the initial dye concentrations and the breakthrough time and volume of treated solution was observed (Foo & Hameed,22) i.e., breakthrough time decreased with increasing influent MB concentration. At lower influent MB concentrations, breakthrough were dispersed, slower and delayed, since the lower concentration gradient causes reduced transport of dye. As influent dye concentration increased, sharper breakthrough curves were obtained. The driving force for adsorption is the concentration difference between the solute on the adsorbent and the solute in the solution because high concentration differences provides a higher driving force, which favors the adsorption process.. Further, at high initial dye concentrations, a sharper breakthrough curve indicated shortened mass transfer zone and higher adsorption rates. Therefore, when quick dye uptake is desired, which is often the case, operating with high initial dye concentrations appears to be favorable.
Similar findings were reported in the case of MB adsorption by activated carbon prepared from oil palm shell ( I.A.W Tan et al.,28) 5.5.3 Effect of flow rate on breakthrough curve Breakthrough generally occurred faster with higher flow rate as seen from Fig-5.39. This behavior is primarily associated with the insufficient residence time for the MB solution within the bed and the diffusion limitations of MB into the pores of PTMFAC at higher feed flow rates ( Foo & Hameed, 22). Moreover, the higher turbulence at higher feed flow rates could lead to a weaker interaction and intraparticle mass transfer between the MB molecules and PTMFAC for the adsorption to be taken place. At low flow rate of influent, MB had more time to be in contact with the adsorbent, which resulted in greater removal of MB molecules in the column. Fig.-5.39 Breakthrough curves for methylene blue adsorption onto PTMFAC at different flow rate (initial concentrations = mg/l, bed height= 8cm, ph=6)
5.6 Estimation of breakthrough curves In order to describe the fixed-bed column behavior and to scale it up for industrial applications, three models, Thomas, Adams Bohart and Yoon Nelson were used to fit the experimental data in the column. Although linear least-square regressive analysis is often used to obtain the model parameters, non-linear regressive analysis is adopted to determine the relative parameters. 5.6. Thomas model Thomas model was applied to the experimental data with respect to different bed height. A non-linear regression analysis was used on each set of data to determine the Thomas model parameters of q and K Th. The determined coefficients and the R 2 were also obtained using nonlinear regression analysis according Eq. (2.33). The results are listed in Table- 5.6,5.7 and 5.8. 5.6.. Effect of bed height Table-5.6 Thomas model parameters at different bed height using non-linear regression for adsorption of MB onto PTMFAC.(Co=5 mg/l, flow rate = 7.5mL/min, ph=6) Sl.no Bed Height (cm) q o (mg/g) K Th ( ml/ mg.min) R 2 SS 5 2.57 622.9854.38 2 8 2.75 474.996.46 3 27.94.77.997.694 5.6..2 Effect of initial concentration Table 5-7: Thomas model parameters at different initial concentrations using non-linear regression for adsorption of MB onto PTMFAC.(bed height =8cm, flow rate = 7.5mL/min, ph=6) Sl.no Concentration (mg/l) q o (mg/g) K Th ( ml/ mg.min) R 2 SS 5 2.75 474.996.46 2 34.4.547.9842.682 3 5 43.79.3.998.38
C/Co C/Co 5.6..3 Effect of flow rate Table-5.8 Thomas model parameters at different flow rate using non-linear regression for adsorption of MB onto PTMFAC (concentration= mg/l, bed height= 8cm, ph=6) Sl.no Flow rate (ml/min) q o (mg/g) K Th ( ml/ mg.min) R 2 SS 4.8 38.49.7.9958.92 2 7.5 34.4.547.9842.682 3 34.45 668.9945.82.2 Exp Pred 2 3 4 Time(min) Fig-5.4 Thomas model parameters at bed height of 5cm of PTMFAC using non-linear regression for adsorption of MB onto PTMFAC (concentration= 5 mg/l, flow rate = 7.5 ml/min, ph=6).2 Exp Pred 2 3 4 5 6 Time(min) Fig-5.4 Thomas model parameters at bed height of 8cm of PTMFAC using non-linear regression for adsorption of MB onto PTMFAC (concentration= 5 mg/l, flow rate = 7.5 ml/min, ph=6)
C/Co C/Co.9.7.5.3. Exp Pred 2 4 6 8 Time(min) Fig-5.42 Thomas model parameters at bed height of cm of PTMFAC using non-linear regression for adsorption of MB onto PTMFAC (concentration= 5 mg/l, flow rate = 7.5 ml/min, ph=6).2 Exp Pred 2 4 6 Time(min) Fig-5.43 Thomas model parameters at initial concentration of mg/l using non-linear regression for adsorption of MB onto PTMFAC.(bed height =8cm, flow rate = 7.5mL/min, ph=6)
C/Co.9.7.5.3. Exp Pred 2 4 6 8 Time(min) Fig-5.44 Thomson model parameters at flow rate of 4.8 ml/min using non-linear regression for adsorption of MB onto PTMFAC (concentration= ppm, bed height= 8cm, ph=6) As shown in Table-5.5, when bed height increased, the value of q o increased while the value of K Th decreased. The increase in q o can be explained due to an increase in the surface area of the biosorbent, which provided more binding sites for the adsorption. The K Th decreased with increasing bed height indicating the reduced reaction rate which was ascribed to longer contact time for higher bed depth. When the MB concentration was increased from 5mg/L to 5 mg/l (Table-5.6), the q o increased and K Th decreased due to the fact that the rate of mass transfer in the column turned slowly for higher concentration of MB, which was result in lengthening the contact time between solute and adsorbent and improved adsorption capacity From Table-5.7, when the flow rate increased the MB removal efficiency decreased. This was attributed to the fact that short contact time between solute and adsorbent would reduce the adsorption efficiency. The K Th increased with the increase in flow rate due to faster mass transfer at higher flow rate. Similar finding were reported by many researchers (Han et al.,29,ahmad and Hameed, 2)
5.6.2 Yoon-Nelson Model Yoon-Nelson model was applied to the experimental data with respect to different bed height, initial concentration of MB and flow rate. A non-linear regression analysis was used on each set of data to determine the Yoon-Nelson model parameters of τ and K YN. The determined coefficients and the R 2 were also obtained using non- linear regression analysis according Eq. (2.38). The results are listed in Table- 5.9,5.2 and 5.2. 5.6.2. Effect of bed height Table-5.9 Yoon-Nelson model parameters at different bed height using non-linear regression for adsorption of MB onto PTMFAC (concentration= 5 mg/l, flow rate = 7.5 ml/min, ph=6) Sl.no Bed Height(cm) τ (min) K YN (/min) R 2 SS 5 86.49.23.9854.38 2 8 29.7.24.996.46 3 454.57.85.997.694 5.6.2.2 Effect of initial concentration Table-5.2 Yoon-Nelson model parameters at different initial concentrations using non-linear regression for adsorption of MB onto PTMFAC.(bed height =8cm, flow rate = 7.5mL/min, ph=6) Sl.no Concentration(mg/L) τ (min) K YN (/min) R 2 SS 5 29.7.24.996.46 2 24.24.55.9842.682 3 5 22.37.96.999.38 5.6.2.3 Effect of flow rate Table-5.2 Yoon-Nelson model parameters at different flow rate using non-linear regression for adsorption of MB onto PTMFAC (concentration= mg/l, bed height= 8cm, ph=6) Sl.no Flow rate (ml/min) τ (min) K YN (/min) R 2 SS 4.8 425.2.8.9958.92 2 7.5 24.24.55.9842.682 3.5 69..267.9946.82
C/Co C/Co.2 Exp Pred 2 4 6 Time, t (min) Fig-5.45 Yoon-Nelson model parameters at bed height of 8 cm using non-linear regression for adsorption of MB onto PTMFAC (concentration= 5 mg/l, flow rate = 7.5 ml/min, ph=6).2 Exp Pred 2 3 4 5 6 Time,t(min) Fig-5.46 Yoon-Nelson model parameters at initial concentration of mg/l using non-linear regression for adsorption of MB onto PTMFAC (bed height= 8cm, flow rate = 7.5 ml/min, ph=6)
C/Co Exp Pred 2 4 6 8 Time, t (min) Fig-5.47 Yoon-Nelson model parameters at flow rate of 4.8 ml/ min using non-linear regression for adsorption of MB onto PTMFAC (concentration= mg/l, bed height= 8cm, ph=6) From Table-5.2, as the flow rate increased the K YN increased while τ decreased. This was due to the fact that higher flow rate would result in the insufficiency of the adsorption and adsorption equilibrium early. However the same trend was also observed when the initial MB concentration (Table-5.2) which seemed quite abnormal because higher MB concentration would prolong the rate of mass transfer in column which usually extended the contact time between solute and adsorbent in column. Therefore Yoon-Nelson model was not the proper model for this study(zhang et al.,2) 5.6.3 Adam-Bohart Model Adam-Bohart model was applied to the experimental data with respect to different bed height, initial concentration of MB and flow rate. A non-linear regression analysis was used on each set of data to determine the Adam-Bohart model parameters of N o and K AB. The determined
coefficients and the R 2 were also obtained using non- linear regression analysis according Eq. (2.37). The results are listed in Table- 5.22,5.23 and 5.24. 5.6.3. Effect of bed height Table-5.22 Adam-Bohart model parameters at different bed height using non-linear regression for adsorption of MB onto PTMFAC (concentration= 5 mg/l, flow rate = 7.5 ml/min, ph=6) Sl.no Bed Height(cm) K AB (ml/min.mg) No R 2 SS 5.45 58.7 3 938 2 8.829 494.66 747 429 3.729 628.23.9384.323 5.6.3.2 Effect of initial concentration Table-5.23 Adam-Bohart model parameters at different initial concentration using non-linear regression for adsorption of MB onto PTMFAC (flow rate = 7.5 ml/min, bed height= 8cm, ph=6) Sl.no Concentration(mg/L) K AB (ml/min.mg) No R 2 SS 5.829 494.66 747 429 2.39 285.98 63.5746 3 5.34 344.8 99.587 5.6.3.3 Effect of flow rate Table-5.24 Adam-Bohart model parameters at different flow rate using non-linear regression for adsorption of MB onto PTMFAC (concentration= mg/l, bed height= 8cm, ph=6) Sl.no Flow rate (ml/min) K AB (ml/min.mg) No R 2 SS 4.8.354 6232. 937 67 2 7.5.39 285.98 63.5746 3.742 79.57.948 297
C/Co C/Co.2 Exp Pred 2 3 4 5 6 Time(min) Fig-5.48 Adam-Bohart model parameters at bed height of 8 cm using non-linear regression for adsorption of MB onto PTMFAC (concentration= 5 ppm, flow rate = 7.5 ml/min, ph=6).2 Exp Pred 2 3 4 5 6 Time(min) Fig-5.49 Adam-Bohart model parameters at initial concentration of mg/l using non-linear regression for adsorption of MB onto PTMFAC (concentration= ppm, bed height= 8cm, ph=6) Adams Bohart model was only applicable to describe the experimental data at the initial part of the breakthrough curves but the variation in bed height, initial concentration of MB and flow rate did not provide any good agreement even in the initial portion of the breakthrough curve as shown in Fig-5.48 and 5.49. The fitted results by Adams Bohart model were also shown in
Table-5.22, 5.23 and 5.24. The determination coefficients R 2 showed unsatisfactory fitness. Besides, the fitted kinetic constant K AB and adsorption capacity N were irrelevant to bed height, flow rate and initial solution concentration. They were inconsistent with the assumption of this model, which required that K AB should be proportional to the residual capacity of PTMF and the concentration of MB. Consequently, Adams Bohart model was not a proper one to describe the adsorption behaviors of PTMF in column also. Similar trend was observed by authors (Zhang et al.,2, Auta & Hameed,24). 5.7 Fixed bed studies- ASD The experiments of three different bed height 4cm, 6cm, 8 cm respectively were operated at influent MB concentration of mg/l and flow rate of.5 ml/ min at ph of 7.Also, experiments with three different MB concentration (5,75, mg/l) were performed at 6 cm bed height, 8.5 ml/ min flow rate and ph of 7.The effect of flow rate (6.5, 8.5 and.5 ml/min) experiments were studied at 6cm bed height, mg/l and ph of 7. 5.7. Breakthrough curves 5.7.. Effect of bed height on breakthrough curves Fig-5.5 (a) gave the breakthrough curve at different bed depth at the same influent concentration (C = mg/l) and flow rate (F =.5 ml/min), respectively. From Fig-5.5(a), as the bed height increases, MB had more time to contact with ASD that resulted in higher removal efficiency of MB ions in column. So the higher bed column results in a decrease in the
solute concentration in the effluent at the same time. The slope of breakthrough curve decreased with increasing bed height, which resulted in a broadened mass transfer zone. High uptake was observed at the highest bed height of 8cm due to an increase in the surface area of biosorbent, which provided more binding sites for the sorption (Han et al.,27). 5.7..2. Effect of flow rate on breakthrough curve The breakthrough curves were shown in Fig.5.5 (b). It was shown that breakthrough generally occurred faster with higher flow rate. Breakthrough time reaching saturation was increased significantly with a decreased in the flow rate. When at a low rate of influent, MB had more time to contact with ASD that resulted in higher removal of MB ions in column. The variation in the slope of the breakthrough curve and adsorption capacity may be explained on the basis of mass transfer fundamentals. The reason is that at higher flow rate the rate of mass transfer gets increases, i.e. the amount of dye adsorbed onto unit bed height (mass transfer zone) gets increased with increasing flow rate leading to faster saturation at higher flow rate (Han et al.,27; Markovska & Meshko,2) 5.7..3 Effect of influent MB concentration on breakthrough curve The effect of influent MB concentration on the shape of the breakthrough curves was shown in Fig-5.5 (c). From Fig-5.5(c), in the interval of 2 min, the value of C t /C reached.5,.3 and.96 when influent concentration was 5, 75 and mg/l, respectively. It is illustrated that the breakthrough time decreased with increasing influent MB concentration. At lower influent MB concentrations, breakthrough curves were dispersed and breakthrough occurred slower.
Ct/Co Ct/Co.2. a).2.. Z = 4 cm Z = 6 cm Z = 8 cm 5 5 2 25 3. 6.5 ml/min 8.5 ml/min.5 ml/min 5 5 2 25 3 35 t (min) t (min) b).2.. 5 ppm 75 ppm ppm 2 3 4 5 6 c) Fig-5.5 a) Effect of Bed Height, b) Effect of flow rate, c) Effect of influent MB concentration on breakthrough curve for ASD.
5.7.2 Modified dose response model: Yan et al. proposed a modified dose response model, which minimizes the error that results from use of the Thomas model, especially with lower and higher breakthrough curve times. The nonlinear Modified dose-response model is represented as (Vijayaraghavan & Yun, 28) ( ) (5.2) Where as Where, ɑ is Modified dose-response model constant ( ) (5.3) 5.8 Chi square test (χ 2 ) It is basically the sum of the sum of the squares of the differences between the experimental data and theoretically predicted data from models. ( ) ( 5.4 ) 5.9 Evaluation of Breakthrough curves Experimental data obtained from column studies were fitted to the three models Thomas,Yoon- Nelson and Modified dose-response. The parameters and values of and according to nonlinear regressive analysis were listed in Tables-5.24, respectively. All model parameters were evaluated using a non-linear regression with Microsoft Excel solver Add-in.
Ct/Co Ct/Co Ct/Co.2. expt Thomas model modified doseresponse model. 5 5 2 25 3 35 t (min) Fig-5.5 Comparison of fitted curves and experimental data. for adsorption of MB onto ASD (C = mg/l, F = 6.5 ml/min, Z = 6 cm ).2 Expt Thomas model modified doseresponse model 5 5 2 25 3 t (min) Fig- 5.52 Comparison of fitted curves and experimental data for adsorption of MB onto ASD (C = mg/l, F = 8.5 ml/min, Z = 6 cm).2. Expt Thomas model modified doseresponse model. 25 5 75 25 5 75 2 t (min) Fig- 5.53 Comparison of fitted curves and experimental data for adsorption of MB onto ASD( C = mg/l, F =.5 ml/min, Z = 6 cm)
5.9. Thomas model Thomas model was applied to the experimental data with respect to different bed height, initial concentration of MB and flow rate. A non-linear regression analysis was used on each set of data to determine the Thomas model parameters of q o and K Th. The determined coefficients and the R 2 were also obtained using non- linear regression analysis according Eq. (2.33). The results are listed in Table- 5.25,5.26 and 5.27. 5.9.. Effect of bed height Table-5.25 Thomas model parameters at different bed height using non-linear regression for adsorption of MB onto ASD ( C o = mg/l, flow rate =.5 ml/min, ph=7) Sl.no Bed Height(cm) q o (mg/g) K Th ( ml/ mg.min) R 2 χ 2 4 32.7.9.987.635 2 6 35.8 275.9943.4 3 8 49.553.9968.223 5.9..2 Effect of initial concentration Table-5.26 Thomas model parameters at different MB concentration using non-linear regression for adsorption of MB onto ASD ( bed height= 6 cm, flow rate =8.5mL/min, ph=7) Sl.no Concentration(mg/L) q o (mg/g) K Th ( ml/ mg.min) R 2 χ 2 5 32.33 854.995. 2 75 33.228 8.9973. 3 35.66.3974.9978.3 5.9..3 Effect of flow rate Table-5.27 Thomas model parameters at different flow rate using non-linear regression for adsorption of MB onto ASD ( C o = mg/l, bed height =6 cm, ph=7) Sl.no Flow rate(ml/min) q o (mg/g) K Th ( ml/ mg.min) R 2 χ 2 6.5 35.87 925.9975.459 2 8.5 35.66.3974.9978.3 3.5 35.79 275.9943.4 5.9.2 Yoon Nelson model Yoon-Nelson model was applied to the experimental data with respect to different bed height, initial concentration of MB and flow rate. A non-linear regression analysis was used on each set
of data to determine the Yoon-Nelson model parameters of τ and K YN. The determined coefficients and the R 2 were also obtained using non- linear regression analysis according Eq. (2.38). The results are listed in Table- 5.28,5.29 and 5.3. 5.9.2. Effect of bed height Table- 5.28 Yoon-Nelson model parameters at different bed height using non-linear regression for adsorption of MB onto ASD (C o = mg/l, flow rate =.5 ml/min, ph=7) Sl.no Bed Height(cm) q o (mg/g) τ (min) K YN (/min) R 2 χ 2 4 32.74 73.5.2.9858.635 2 6 35.79 2.28.627.9948.4 3 8 49 88.32.55.9968.223 5.9.2.2 Effect of initial concentration Table- 5.29 Yoon-Nelson model parameters at different concentration using non-linear regression for adsorption of MB onto ASD (bed height = 6 cm, flow rate = 8.5 ml/min, ph=7) Sl.no Concentration (mg/l) q o (mg/g) τ (min) K YN (/min) R 2 χ 2 5 46.9 275.38.243.995. 2 8 39.95 88.96.3.9973. 3 34.37 5.62.397.9978.3 5.9.2.3 Effect of flow rate Table- 5.3 Yoon-Nelson model parameters at different bed height using non-linear regression for adsorption of MB onto ASD (C o = mg/l, bed height = 6 cm, ph=7) Sl.no Flow rate(ml/ min) q o (mg/g) τ (min) K YN (/min) R 2 χ 2 6.5 32.762 99.42.292.9985.459 2 8.5 34.368 5.62.397.9978.3 3.5 35.78 2.29.627.9948.4 5.9.3 Modified dose-response model Modified dose-response model was applied to the experimental data with respect to different bed height, initial concentration of MB and flow rate. A non-linear regression analysis was used on each set of data to determine model parameters of a and b. The determined coefficients and