Preparation and Characterization of Ceramic Membranes
3.3 Results and discussion
3.3.4 Identification of competent flux decline mechanism
The identification of competent flux decline mechanism is very important for any MF processes. The decline in permeate flux during dead end MF of o/w emulsions was analyzed using different membrane pore blocking models as discussed in section 3.2. To find the most prominent fouling mechanism among the pore blocking models, linear plots corresponding to Eqs. (4) - (7) were prepared. Figures 3.5 - 3.8 illustrate the fitness of complete pore blocking, standard pore blocking, intermediate pore blocking and cake filtration model, respectively for all oil concentrations. From all figures, it was observed that the experimental data sets followed two linear trends corresponding to initial phase of 5 - 10 minutes and the rest upto 30 minutes. It can also be observed in these figures that initial phases were 10, 8, 7 and 5 minutes for initial oil concentrations of 50, 75, 100 and 150 mg/L, respectively. A reduction in initial time regime with oil concentration was due to the presence of higher amount of oil droplets at higher oil concentrations which facilitated pore blocking within lesser time frames.
Overall, the flux decline with time occurred due to two different pore blocking mechanisms.
Similar trends results were also observed during treatment of oily wastewater with a polymeric membrane [91]. Henceforth, the experimental flux data was further analyzed separately in two time regimes, namely the initial regime (during the first 5 - 10 minutes of MF) and the later regime to identify the most competent combinations of models in both the regimes. In order to visualize the most competent fouling phenomena during the initial phases, linear regression analysis was carried out to obtain slope, intercept as well as correlation coefficients (R2) of all flux data. To find the most prominent fouling mechanism, values of R2 were considered. Table 3.2 summarized the calculated values of all the models for both regimes namely initial and later regime. For the initial regime, it can be critically
observed from Fig. 3.8 that there exists negative intercept for cake filtration model. As negative intercept values infer to negative initial permeate flux, this model could not be justified physically and henceforth was ignored in the subsequent analysis of flux decline for initial regime. Further, it can be also observed in Table 3.2 for the same regime that R2 values for all other models (standard pore blocking, complete pore blocking and intermediate pore
0 4 8 12 16 20 24 28 32
9.0 9.5 10.0 10.5 11.0 11.5(a)
Oil Concentration: 50 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
Ln (J-1 , m2 .s/m3 )
Time (minute)
0 4 8 12 16 20 24 28 32
9.0 9.5 10.0 10.5 11.0 11.5(b)
Oil Concentration: 75 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
Ln (J-1 , m2 .s/m3 )
Time (minute)
0 4 8 12 16 20 24 28 32
9.0 9.5 10.0 10.5 11.0 11.5(c)
Oil Concentration: 100 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
Ln (J-1 , m2 .s/m3 )
Time (minute)
0 4 8 12 16 20 24 28 32
9.0 9.5 10.0 10.5 11.0 11.5 (d)
Oil Concentration: 150 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
Ln (J-1 , m2 .s/m3 )
Time (minute)
Figure 3.5: Linear plot of permeate flux variation with time for complete pore blocking model. Initial oil concentration: (a) 50 mg/L, (b) 75 mg/L, (c) 100 mg/L and (d) 150 mg/L.
blocking) were in appreciable range (0.954 - 0.999). To further analyze the applicability of various models, percent error of experimental flux and predicted permeate flux using slope and intercept values for the models were evaluated and analyzed. Percent error of permeate flux was calculated using the expression:
0 4 8 12 16 20 24 28 32
100 150 200 250 300(a)
Oil Concentration: 50 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J -0.5 , m.s0.5 /m1.5
Time (minute)
0 4 8 12 16 20 24 28 32
100 150 200 250 300 (b)
Oil Concentration: 75 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J -0.5 , m.s0.5 /m1.5
Time (minute)
0 4 8 12 16 20 24 28 32
100 150 200 250 300 (c)
Oil Concentration: 100 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J -0.5 , m.s0.5 /m1.5
Time (minute)
0 4 8 12 16 20 24 28 32
100 150 200 250 300(d)
Oil Concentration: 150 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J -0.5 , m.s0.5 /m1.5
Time (minute)
Figure 3.6: Linear plot of permeate flux variation with time for standard pore blocking model. Initial oil concentration: (a) 50 mg/L, (b) 75 mg/L, (c) 100 mg/L and (d) 150 mg/L.
100 (%)
exp
exp ⎟⎟×
⎠
⎞
⎜⎜
⎝
⎛ −
= J
J
Error J cal (3.8)
Figure 3.9a shows results obtained from error analysis for experimental condition of 150 mg/L initial oil concentration and 41.37 kPa trans-membrane pressure drop. Based on the observations from Fig. 3.9a, it can be inferred that intermediate pore blocking model is the
0 4 8 12 16 20 24 28 32
0 1 2 3 4 5 6 7 8(a)
Oil Concentration: 50 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-1 X 10-4 , m2 .s/m3
Time (minute)
0 4 8 12 16 20 24 28 32
0 1 2 3 4 5 6 7 8 9 (b)
Oil Concentration: 75 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-1 X 10-4 , m2 .s/m3
Time (minute)
0 4 8 12 16 20 24 28 32
0 1 2 3 4 5 6 7 8 9 (c)
Oil Concentration: 100 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-1 X 10-4 , m2 .s/m3
Time (minute)
0 4 8 12 16 20 24 28 32
0 1 2 3 4 5 6 7 8 9(d)
Oil Concentration: 150 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-1 X 10-4 , m2 .s/m3
Time (minute)
Figure 3.7: Linear plot of permeate flux variation with time for intermediate pore blocking model at various initial oil concentrations: (a) 50 mg/L, (b) 75 mg/L, (c) 100 mg/L and (d) 150 mg/L.
most appropriate model to account for the flux decline mechanism during the initial regime with the lowest errors. Similar observations were also observed for other experimental conditions (different initial oil concentrations and different ∆P) as well. On the other hand, for the later regime error analysis was carried out for all the models. Figure 3.9b shows results obtained from error analysis using Eq. (3.8) for 75 mg/L initial oil concentration and ∆P of 124.11 kPa. Based on the observations from Fig. 3.9b, it can be inferred errors were minimum
0 4 8 12 16 20 24 28 32
0 10 20 30 40 50 60
(a)
Oil Concentration: 50 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-2 X 10-8 , m4 .s2 /m6
Time (minute)
0 4 8 12 16 20 24 28 32
0 10 20 30 40 50 60 70 (b)
Oil Concentration: 75mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-2 X 10-8 , m4 .s2 /m6
Time (minute)
0 4 8 12 16 20 24 28 32
0 10 20 30 40 50 60 70(c)
Oil Concentration: 100 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-2 X 10-8 , m4 .s2 /m6
Time (minute)
0 4 8 12 16 20 24 28 32
0 10 20 30 40 50 60 70 (d)
Oil Concentration: 150 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J-2 X 10-8 , m4 .s2 /m6
Time (minute)
Figure 3.8: Linear plot of permeate flux variation with time for cake filtration model.
Initial oil concentration: (a) 50 mg/L, (b) 75 mg/L, (c) 100 mg/L and (d) 150 mg/L.
Table 3.2: Correlation coefficients obtained from linear regression analysis of permeate flux data for various membrane pore blocking models.
for cake filtration model. Hence cake filtration model was selected as the most appropriate pore blocking model to represent the flux decline during the later regime with lowest error.
Therefore, based on the physical observation as well as the fitness of the cake filtration model, Complete pore
blocking
Standard pore blocking
Intermediate pore blocking
Cake filtration C
(mg/L)
Pressure (kPa)
Initial regime
Final regime
Initial regime
Final regime
Initial regime
Final regime
Initial regime
Final regime 41.37 0.963 0.972 0.984 0.982 0.995 0.989 0.992 0.997 82.74 0.955 0.978 0.985 0.983 0.998 0.987 0.981 0.994 124.11 0.954 0.977 0.986 0.982 0.999 0.986 0.981 0.991 165.47 0.960 0.987 0.988 0.991 0.998 0.994 0.977 0.998 50
206.84 0.962 0.962 0.988 0.972 0.999 0.989 0.983 0.989 41.37 0.974 0.964 0.991 0.976 0.998 0.986 0.988 0.997 82.74 0.975 0.950 0.993 0.962 0.999 0.973 0.981 0.994 124.11 0.964 0.982 0.989 0.987 0.999 0.991 0.982 0.996 165.47 0.967 0.982 0.991 0.987 1.000 0.991 0.978 0.996 75
206.84 0.970 0.962 0.992 0.973 1.000 0.982 0.978 0.994 41.37 0.981 0.959 0.993 0.973 0.998 0.984 0.990 0.996 82.74 0.974 0.946 0.991 0.961 0.998 0.973 0.986 0.999 124.11 0.966 0.914 0.987 0.935 0.997 0.993 0.989 0.998 165.47 0.978 0.963 0.993 0.972 0.997 0.980 0.971 0.991 100
206.84 0.970 0.967 0.992 0.976 0.998 0.984 0.967 0.994 41.37 0.993 0.968 0.997 0.979 0.999 0.988 0.992 0.997 82.74 0.989 0.950 0.996 0.968 0.999 0.982 0.994 0.998 124.11 0.986 0.958 0.996 0.972 0.999 0.983 0.989 0.996 150
165.47 0.989 0.959 0.997 0.974 1.000 0.985 0.987 0.997 206.84 0.984 0.944 0.996 0.963 1.000 0.978 0.985 0.996
it was inferred that a thin layer of oil droplets formed during the membrane process justifies the fitness of a cake layer model. Therefore, it was herewith inferred that intermediate pore blocking followed with cake filtration represent the most competent combination of fouling mechanisms for the observed membrane flux decline. Table 3.3 summarized the final values of slope and intercept for both regimes. Based on these values predicted values of flux were calculated. Table 3.4 summarized the values of maximum and average errors for all data sets.
Figure 3.10 presents a parity plot between experimental and calculated flux based on the combinations of the two most appropriate models in the initial and later regimes. As shown, a good fitness between experimental and evaluated values was observed and henceforth, the suggested model combination was inferred to be applicable for the analysis, design, planning and scheduling of time dependent MF processes for oil-water emulsion separation in the process industries.
1 2 3 4 5
-3 -2 -1 0 1 2
(a)
Time (minute)
Error (%)
Initial oil concentration: 150 mg/L Pressure (kPa): 41.37
Intermediate pore blocking Standard pore blocking Complete pore blocking
9 12 15 18 21 24 27 30
-2 -1 0 1 2 3 (b)
Time (minute)
Error (%)
Initial oil concentration: 75 mg/L Pressure (kPa): 124.11
Cake filtration
Intermediate pore blocking Standard pore blocking Complete pore blocking
Figure 3.9: Variation of error (%) with time for the initial and final flux decline regimes (a) initial oil concentration: 150 mg/L and trans-membrane pressure: 41.37 kPa and (b) initial oil concentration: 75 mg/L and trans-membrane pressure: 124.11 kPa.
Table 3.3: Slope and intercept values obtained from linear regression analysis for initial (intermediate pore blocking) and final (cake filtration) flux decline regimes.
A critical analysis of the membrane permeation characteristics based on pore size distribution also yields conclusive insights upon pertinent flux decline phenomena. Based on SEM based pore size distributions summarized in chapter 2, it can be observed that the membrane pores varied from 0.15 - 2.5 µm. On the other hand, droplet size distribution for all oil
Initial regime
(Intermediate pore blocking)
Final regime (Cake filtration) C
(mg/L)
Pressure (kPa)
(J0−1) (ki) (J0−2)×10-7 (kC)×10-7
41.37 14458 3446.5 72.39 16.85
82.74 9204 3824 157.27 7.07
124.11 7447 3465 121.15 6.15
165.47 5667 3181 79.95 5.72
50
206.84 5888 2057 16.65 5.48
41.37 1492 3952 89.87 17.95 82.74 1009 4081 132.78 9.66
124.11 7905 4039 135.56 6.48
165.47 6174 3703 119.44 6.04
75
206.84 5185 2731 45.44 5.99
41.37 16650 4272 126.53 17.90 82.74 13128 4032 139.41 10.80
124.11 11666 3831 133.27 9.14
165.47 8024 4067 125.60 8.52
100
206.84 5725 4024 80.59 9.02
41.37 20296 4585 163.22 17.08
82.74 15708 4287 61.59 18.69
124.11 12714 4582 84.46 15.74
150
165.47 9829 4263 43.50 15.36
206.84 8251 4202 37.27 13.91
Table 3.4: A summary of errors evaluated using best fit flux decline models (intermediate pore blocking followed with cake filtration).
C (mg/L) Pressure (kPa) Maximum error Average error
41.37 4.03 0.90
82.74 4.38 0.74
124.11 3.86 0.79
165.47 2.93 0.78
50
206.84 3.50 1.23
41.37 3.39 0.77
82.74 2.33 0.71
124.11 1.83 0.49
165.47 2.42 0.47
75
206.84 2.64 0.92
41.37 1.86 0.61
82.74 3.20 0.71
124.11 4.72 0.95
165.47 3.62 1.30
100
206.84 3.52 1.10
41.37 2.78 0.74
82.74 3.64 0.80
124.11 2.45 0.79
150
165.47 1.48 0.60
206.84 3.24 0.97
concentrations varied from 0.04 - 100 µm (Fig. 3.2). Therefore, amongst these droplets it can be expected that droplets with size distributions 0.04 - 0.15 µm would not get rejected by the membrane and droplets with sizes above 2.5 µm (6 - 7.62 %) would be rejected fully by the membrane. Also droplets in the range 0.15 - 2.5 µm either enter the pores or rejected by the membrane and contribute to intermediate pore blocking and cake filtration. Therefore,
droplets with sizes above 2.5 µm contribute towards the formation of a thin oily layer over the membrane that is realized as cake filtration phenomena during filtration studies. Henceforth, it is apparent that the pertinent flux decline shall constitute an initial phase of intermediate pore blocking followed with cake filtration. These insights are in accordance with fouling phenomena trends evaluated previously in this section.
0 20 40 60 80 100 120 140
0 20 40 60 80 100 120 140(a)
Oil Concentration: 50 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
Jcal X 106 m3 /m2 .s
Jexp X 106 m3/m2.s
0 20 40 60 80 100 120 140
0 20 40 60 80 100 120 140(b)
Oil Concentration: 75 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
Jcal X 106 m3 /m2 .s
Jexp X 106 m3/m2.s
10 30 50 70 90 110
10 30 50 70 90 110(c)
Oil Concentration: 100 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
Jcal X 106 m3 /m2 .s
Jexp X 106 m3/m2.s
10 20 30 40 50 60 70 80 90
10 20 30 40 50 60 70 80 90(d)
Oil Concentration: 150 mg/L Pressure (kPa):
41.37 82.74 124.11 165.47 206.84
J cal X 106 m3 /m2 .s
Jexp X 106 m3/m2.s
Figure 3.10: Parity plot of experimental and evaluated permeate flux using a combination of intermediate pore blocking and cake filtration model.