Ind. Eng. Chem. Res. 1996,34,813-819
813
MATERIALS AND INTERFACES Pilot Production of Polysulfone Hollow Fiber for Ultrafiltration Using Orthogonal Array Experimentation Chau Jen Lee,* Shih Sheng Wang, and Gwo Chin Lin Department of Chemical Engineering, National Tsing Hua University Hsinchu, Taiwan, R.O.C.
Wei Hu and Lien Tai Chen Man-made Fiber Research Division, Union Chemical Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan, R.O.C.
Hollow fiber membranes (HFM) have been in use for many industrial and specialty applications. Although a great deal of research has been done in the past, the making of hollow fibers for a specified application is still a n extremely difficult problem. Until now, the material formulation and the operating variables and conditions during spinning of fibers are specified more or less by trial-and-error method. In this study, the experimental design based on orthogonal array experimentation has been employed for discussing the relationship between the molecular weight cut-off (MWCO) and the dry-wet spinning conditions for making polysulfone hollow fibers for ultrafiltration. The factors considered in the experimental design included the contents of polysulfone (PSU) and poly(vinylpyrro1idone) (PVP) in the dope solution, the temperature of spinneret and the coagulation bath, the content of N-methyl-2-pyrrolidone (NMP) in bore liquid, the air gap length, and the relative humidity. The results indicate that the MWCO of the HFM was controlled by the PVP content and the temperature of the coagulation bath.
1. Introduction The application of ultrafiltration membranes for separation of dissolved solutes of different sizes has received increasing interest in recent years. In comparison with the tubular, plate-and-frame, spiralwound, and capillary modules, the hollow fiber modules are more compact generally and have a high packing density up to 30 000 m2/m3(Mulder, 1991). Disadvantages of hollow fiber modules include high fouling tendency. Consequently, pretreatment of the feed stream may be needed prior t o separation with hollow fiber systems. Polysulfone (PSU) is the second most widely used membrane material for applications in both largescale and laboratory-scale operations (Staude and Breitbach, 1991). The PSU membranes have the intrinsic advantage of being operable in a wide range of pH and temperature (up to 378 K). Furthermore, PSU membranes are also resistant to chlorine oxidation and, thus, are applicable equally well in areas where cellulose acetate membranes have been traditionally used (Nowak, 1989). The solute rejection method was employed in this study for determining the pore size of hollow fiber membrane. Poly(ethy1ene glycols), having a narrow molecular weight distribution ranging from 600 t o 50 000 Da, were used as the solute. MWCO is defined as the molecular weight that was 90% rejected by the membrane. Larger MWCO implies larger pore size of the membrane. The diameter of a solute molecule can be computed by the apparent equivalent spherical diameter (Schwarz et al., 1987) or the Stokes radius
* To whom correspondence should be addressed. E-mail address:
[email protected].
(Kassotis et al., 1985). Concentration polarization and membrane fouling can affect the determination of MWCO. Therefore, the determination of MWCO should be carried out at a low driving force and at low feed concentration. An orthogonal array was employed in this study as a tool for systematic experimental design. Experiments using an orthogonal array allow several effects of factors to be simultaneously determined efficiently. A matrix experiment consists of a set of experiments in which the settings of the various process factors change from row to row according to the orthogonal array, similar t o those 18 rows in columns 2-9 of Table 2. One of the advantages of utilizing orthogonal array is the simplicity of data analysis. Effects of the various factors can be determined by computing simple averages. An additive model, which states that the total effect of several factors is equal to the sum of effects of individual factors, was used as an approximation in orthogonal array experimental design (Phadke, 1989). Interactions between factors are considered as errors in the additive model. A second advantage is that it produces more reliable estimates on effects of factors with fewer experiments than those of the traditional methods, e.g., experiments with one factor a t a time. A third advantage is that the relative importance of various factors can be determined here; in addition, the order of factors can be ranked by using the variance ratio. The number of controlling factors could be reduced by pooling the sum of squares together which corresponds to the factors having the lowest mean square. Consequently, significantly smaller number of experiments may be required. A primary goal of using the orthogonal array for designing experiments lies in the determination of the optimum level for each factor. The additive model can
0888-5885/95l2634-0813$09.00l0 0 1995 American Chemical Society
814 Ind. Eng. Chem. Res., Vol. 34,No. 3, 1995 Table 1. Factors and Levels"
I Choose factors
factors
1
A.PSU content (%) B.PVP content (%)
20 20
C.spinneret temp ("C) D.coagulation bath temp ("C) E.N M P content in bore liquid (%) F.air gap length (cm) G.air humidity (%)
10 10 0
7 50
levels 2
3
28 15 25 30 33 25 75
10 40 50 50 40 100
Choose a response function, I-
t Calculate average response and variance ratio
t
The initial experimental condition of each factor is italicized, i.e., AlBlC2D2ElF3G2.
t Predict the value of q under optimum condition by additive inodel
Table 2. Orthogonal Array (L18 Table) and Experimental Results
t Confirmation experiments tinder optimum condition
exp. no. 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1
Choose optimum conditions
0 1 2 3 4 5 6 7 8
A
B
C
D
E
F
G
e
1 1 1 1 1 1 1 1 1
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 1 2 2 3 3 2 3 3 1 1 2 3 2 1 3 2 1 2 2 3 3 1 1 1 3 2 1 3 2 3 1 1 2 2 3
1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1
2 2 2 2 2 2 2 2 2
1 1 1 2 2 2 3 3 3
MWCO(Da1 3 690 3 730 50 000 33 350 50 000 50 000 5 360 50 000 50 000 50 000 23 970 9 000 50 000 50 000 50 000 50 000 4 620 50 000
va -76.00 -75.95 -92.04 -87.37 -92.04 -92.04 -73.33 -92.04 -92.04 -92.04 -82.90 -60.04 -92.04 -92.04 -92.04 -92.04 -74.66 -92.04
The overall mean value ( m )of 7 was equal to -85.70.
be applied toward predicting the value of response under optimum conditions. After the optimum conditions are chosen and the responses under optimum conditions are predicted, confirmation experiments should be performed along with the observed value of response being compared with the prediction. Matrix experimentation, followed by confirmation experiments, is a powerful tool for detecting the presence of interactions among the control factors (Phadke, 1989). A situation in which the predicted response under the optimum conditions matches the observed response would infer that those interactions are probably not essential and that the additive model is a good approximation. However, a situation in which the predicted response does not match the observed response would infer that the interactions are essential. A situation in which interactions occur would require that product terms be made available in the model. A model for such a situation requires more factors than an additive model and consequently requires more experiments to estimate all of the factors. A flow chart of orthogonal array experimental design is shown in Figure 1. The orthogonal array L18, which contains seven three-level columns and one two-level column, is sufficient for examination of the effects of the seven control factors. The L18 array and the assignment of the control factors to the columns are listed in Table 2. The control orthogonal array for this study is the submatrix of L18 as formed by the columns assigned to the seven control factors, that is, one two-level factor and six three-level factors. For easy operation, PSU content is chosen as the 2-level factor and the other six factors (Le., PVP content, spinneret temperature, coagulation temperature, NMP content, air gap length, air humidity)
1
No strong interaction among factors. Additive model is
adequatelv to describe the dependence of 0 .
1
Figure 1. Flow chart of orthogonal array experimental design.
for three levels. The ninth column (column e) of Table 2 is empty for error estimation. The purposes of this study lie in preparing ultrafiltration hollow fiber membranes with a specified MWCO of 10000 as well as determining the effects of the spinning and coagulation conditions on MWCO through an orthogonal array experimentation. 2. Experimental Section
2.1. Materials. Polysulfone Udel-3500 (in powder form) was purchased from Union Carbide and poly(vinylpyrrolidone) (K30, % = 18 000 g/mol), from Janssen Chimica. The solvent, N-methyl-2-pyrrolidone (N") was also from Janssen Chimica. Water was used as nonsolvent. Poly(ethy1ene glycols) coded PEG 600, PEG 1500, PEG 6000, PEG 10000, and PEG 35000 were purchased from Merck (Germany), while PEG 4000 was from Nakarai Chemicals (Japan). The molecular weight of each PEG was determined by gel permeation chromatography -(GPC; Shimadzu LC-SA). The dispersity (Mw/Mn)of each PEG was less than 1.1. Therefore, the effect of molecular weight distribution of each PEG on MWCO was minimal. The weight-average molecular weight was used t o determine MWCO. 2.2. Dry Jet Wet Spinning. Polymer solutions were prepared by dissolving predetermined amounts of PSU and PVP in NMP. Filtered polymer solutions were debubbled before being used. A tube-in-orifice spinneret was used in the spinning process. The dope was placed in a pressure vessel that was subsequently pumped to the spinneret by a metering gear pump. The vessel pressure was kept at 1atm and in contact with dry air. Nitrogen gas was used for dope pumping, but it would not form any bubble in the dope. The polymer solution flowed through a ring nozzle while the bore liquid was fed through the inner tube of the spinneret. The fiber passed through an air gap before it entered a water bath. Spinning and coagulation conditions are listed in Tables 1 and 2 (orthogonal array of L18). After spinning and coagulation, the fiber was rinsed with water for 1 day and finally dried at room temperature.
Ind. Eng. Chem. Res., Vol. 34,No. 3, 1995 815
2.3. Determination of MWCO. A cartridge was prepared with each specific PSU fiber made to determine the MWCO. By placing a bundle of 100 fibers of internal diameter around 350 pm and an external diameter of 650 pm in a casing of an acrylic resin outer shell with an internal diameter of 18 mm and external diameter of 25 mm and of 20 cm length, the cartridge was sealed at each end with an epoxy resin. The molecular weight cut-off of each cartridge was determined by measuring the rejection of 0.1 wt % PEG (quite low feed concentration) in an Amicon DC-2 concentrator/ dialyzer. PEG solutions were prepared by dissolving an equal weight of each PEG of different molecular weights in deionized water. PEG concentrations were measured by gel permeation chromatography (GPC; Shimadzu LC-SA). The feed solution was fed and circulated through the tube side of the hollow fiber cartridge, and the deionized water was circulated through the shell side. Due to different cross-sectional areas in shell and tube sides, the circulation rates of both sides must be adjusted carefully to maintain the pressure difference (P)across membrane at a minimum and to keep constant volumes of both sides. The rejection coefficient is defined as
R = 1 - (C2/C1)
(1)
1.0
a
y
e
R 0.4
L Exp. data by dialysis
0
Os2 0.0 0
Exp. data by ultrafiltration
20000
40000
60000
Molecular weight (dalton)
Figure 2. Rejection characteristics (MWCO) of membrane. Comparisonof experimental results by dialysis method with those by ultrafiltration method. At 25 "C, ( 0 )A€'FZ 0, (0)AP = 10 psi.
A response function vi is defined as
qz = -10 log(Mwcoi - 1oooo~2 The overall mean ( m )of
For dialysis at equilibrium,
(4)
vi is defined as R
Cl,V1 = ClV1 + c2v2
m = (&)in
(5)
i=l
where VI and V2 represent the volumes of feed solution and shell-side deionized water, respectively; C1 and C2 are the concentrations of feed solution and of shell-side solution, respectively; Clo is the initial concentration of feed solution. Substituting eq 2 into eq 1,
(3) VI and VZ were 250 and 400 mL, respectively. Samples of the tube-side solution were taken after it reached steady state. All experiments were operated at a low driving force (AP M 0) and at a low feed concentration (0.1 wt %) to minimize concentration polarization and membrane fouling. MWCO was defined as the molecular weight that was 90% rejected by the membrane. The interpolating method was used to estimate molecular weight for 90% rejection. The dialysis method that was applied in the determination of MWCO must be ensured. A commercialized hollow fiber cartridge, h i c o n HlP10-43, with MWCO of 10 000 was used to characterize the standard. Furthermore, the rejection coefficients ( R ) determined by the dialysis method were compared with those determined by the ultrafiltration method (using poly(ethy1ene glycols)) at 10 psi, as shown in Figure 2. The shapes of the two curves were similar to each other with the difference of MWCO between two curves falling within 3%. The characterization results of the dialysis method were consistent with that of the ultrafiltration method. The MWCO characterization of membrane by the dialysis method was found as reliable as that by the ultrafiltration method. 3. Results and Discussion 3.1. Effects of Factors. The results of MWCO determination for each cartridge are listed in Table 3.
m is equal t o -85.70 for 18 experiments (Table 2). The average response for each factor level can be calculated by the following way. For example, the PVP content maintained itself at level B1 for experiments 1,2,3,10, 11, and 12; the average response of factor level B1 as denoted by mgl is given by mB1 = (1/6)(ql + q 2
+ q 3 + VlO + 711 + 712) (6)
The average response for level B2 and B3 of PVP content, as well as those for the various levels of the other factors, can be obtained in a similar way. The average rj for each level of seven factors was obtained, as listed in Table 3, by taking the numerical value of vi listed in Table 2. 3.2. Analysis on the Relative Importance of Various Factors. The relative effect of these factors can be obtained by the decomposition of variance, which is commonly named the analysis of variance (ANOVA). An important purpose of ANOVA is for determining the relative importance of various factors. The results of ANOVA are listed in Table 4. The total sum of squares (SS) is defined by 18
18
(7) = (-76.00)2
+ (-75.95)2 + ... + (-92.04)2
- 18(-85.71)2
= 1576.14 The effect of a factor level is defined as the deviation caused from the overall mean. Thus,the effect of PVP content at level B1 is given by ( m ~ l - m). The sum of squares due t o factor B is equal t o the total squared deviation for factor B from the overall mean. Six experiments were performed at each level of factor B. Consequently,
816 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 Table 3. Average Response of Each Factor Level MWCO 32 900 37 510 23 400 47 230 35 000 32 070 30 380 43 170 27 600 28 010 50 000 30 500 32 680 42 440 27 880 39 510 38 220 35 450 27 280 42 890
factor levels A1 A2 B1 B2 B3
c1 c2
c3 D1 D2 D3 El E2 E3 F1 F2 F3 G1 G2 G3
rl
-85.87 -85.53 -79.83 -91.26 -86.02 -85.47 -84.93 -86.71 -84.16 -80.91 -92.04 -84.73 -83.25 -89.14 -81.13 -88.58 -87.40 -84.03 -83.34 -89.74
Table 4. Analysis of Variance of qa factors
df
SS
mean SS
A B C D E F G error total (errorIb
1 2 2 2 2 2 2
0.51 393.08 9.95 393.25 112.72 192.36 148.00 326.25 1576.14 (336.72)
0.51 196.54 4.98 196.63 56.36 96.18 74.00 81.56 92.71 (48.10)
4 17 (7)
F 4.09 4.09 1.17 2.00 1.54
contribution (%) 0.0 24.9 0.6 25.0 7.2 12.2 9.4 20.7 100.0
a df, degrees of freedom; SS, sum of squares. The sum of squares of factors A and C were added to form the pooled error sum of squares shown in parentheses.
+
+
SS due to factor B = 6(mB,- mI2 6(mB2 - m)' 6(m~3 - m )2 = 393.08
(8)
As such, factor B is responsible for 393.08l1576.14 x 100% = 24.9% of the variance of 7. Factor D may be responsible for the largest portion, i.e., 25% of the variance of r. Factors B and D thus account for nearly 50% of the total variance of 7. Factors B, D, F, and G account for around 72% of the variance of 7. Hence, 72 % of the total variation of r is actually controlled by factors B, D, F, and G. The mean square of a factor was computed by dividing the sum of squares by the degrees of freedom (do. The sums of squares for factors A and C were much smaller than those of other factors. An approximation of the error variance was obtained by pooling the sum of squares of factors A and C. The variance ratio, denoted by F in Table 4, was the ratio of mean square due to a factor and the mean error square. A value of F less than 1, meant that the effect of factor was smaller than the error of additive model and, therefore, was insignificant. A value of F larger than 2, meant that factor was not trivial. Whereas, a value larger than 4 meant that the effect of factor was rather significant. Our results indicate that factors B and D exerted the most significant effect on MWCO. The more important the factor, the more it would influence the process response 7 for the larger value of F. Therefore, value of F could be used to rank the order of the factors. In this study, the order of importance that influenced the MWCO was foundtobe D > B > F > G > E C > A.
3.3. Effects of Various Factors on MWCO. For a given solute, the higher rejection coefficient of a membrane meant a smaller pore size. MWCO is defined as the molecular weight that was 90% rejected by the membrane. Larger MWCO means that the membrane has a larger pore size. Effects of factors for average responses are plotted in Figure 3. The variance ratios of A and C were less than 1, i.e., effects of factors of A and C were smaller than the error of additive model. Consequently, the effects of factors of A and C could be neglected in the experimental ranges. The effects of the other five factors are discussed below. 3.3.1. Effect of P W Content on MWCO. PVP was chosen as a nonsolvent additive and could be added to the PSU solution in a wide concentration range. Furthermore, it greatly increased the viscosity of the PSU dope, which was generally helpful for the spinning of hollow fiber. PVP is a water-soluble polymer that could be extracted into water after the fiber was rinsed with water; consequently, a higher PVP concentration could contribute t o a higher porosity. The addition of PVP to the polymer solution also accelerated the gelling of membrane, favoring the formation of more open structures. However, PVP also rapidly increased the viscosity of dope solution (Tam et al., 1993) to cause formation of a less porous top skin layer. The formation of polymer structure was discussed by Tam et al. (1993) as being a function of the exchange rate between solvent and nonsolvent during the gelation step. A fast exchange rate favored the formation of fingerlike voids in a membrane, and a slow ex6hange rate formed sponge membranes. The exchange rate was partially governed by the viscosity of spinning dope. Consequently, a higher F"concentration was generally associated with higher viscosity of spinning dope and subsequently lowered the exchange rate that led t o a less porous skin layer. Thus, two competitive effects on MWCO simultaneously appeared, in which MWCO increased at PVP concentration ranging from 10 to 15 wt %; however, MWCO rapidly decreased from 15 to 20 wt % as found in this study. Some other authors (Lafreniere et al., 1987; Kesting, 1985; Tweddle, 1983; Liu et al., 1992) have studied the effect of nonsolvent additive in polymer solution on the performance of membranes. Tweddle et al. reported no influence of PVP concentration ranging from 0 to 6% on rejection coefficients (R).Tam et al. reported that pore size decreased with PVP concentration increasing in the range from 0 to 30%. However, Liu et al. reported that R decreased with increasing PVP concentration (i.e,, pore size increased with increasing PVP concentration) ranging from 4 to 17%. A more detailed effect of PVP on performance of poly(ether sulfone) (PES)ultrafiltration membranes was reported by Lafreniere et al. (1987).They described that R had two maximum points and R was strongly dependent on PVP concentration at 15% PES. Furthermore, the curve was shifted to the left, keeping a similar shape at 20% PES. Lafreniere et al. have given a more clear picture of the effect of nonsolvent additive on the pore size. PVP content was the second most important variable whose contribution to the variance of 7 was 24.9% in this study. 3.3.2. Effect of Coagulation Bath Temperature on MWCO. The coagulation bath temperature influenced the rate of phase-inversion process, and also, the structure of the membranes obtained. Increasing the coagulant bath temperature (factor D) led toward a larger MWCO, as observed in Figure 3. Similar results
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 817
3.0
5 -100
A1A2
BlB2B3
ClC2C3
DlD2D3
ElE2E3
FlMF3
GlG2G3
factor levels Figure 3. Plot of effects of factors (for the detailed legend of factors and levels refer to Table 1).
were reported by Kassotis et al. (19851, Kesting (19851, and Nowak (1989) in which the average pore size of the films increased with an increasing coagulation bath temperature in their systems. Also, coagulation bath temperature was the most important variable whose contribution to the variation of r was 25%. 3.3.3. Effect of NMP Content in Bore Liquid on MWCO. NMP was the solvent of spinning dope that contained PSU. The lower interfacial PSU concentration that yields a more porous top layer was found in higher NMP content in bore liquid. A similar result in which solute rejection decreased with an increasing NMP concentration in bore liquid was reported by Doi and Hamanaka (1991). They said, “This may be an effect of the increased coagulant mixability, in which microphase separation in dope slowed down at the interface, thereby increasing polymer particle growth and ultimately resulting in larger interparticle openings.” MWCO is increased with an increasing NMP content (factor E) in bore liquid, as indicated in Figure 3. 3.3.4. Effect of Air Gap Length on MWCO. Since the spinneret was at a distance above the coagulant bath, the viscous polymer liquid relaxed from shear flow and was elongated under the effect of its own mass. The micropores in the top skin layer would be similarly elongated; i.e., MWCO enlarged and the longer air gap produced, the higher MWCO. However, the longer air gap length meant the longer polymer solution in air (i.e., more evaporation time) which allowed more solvent to evaporate. This resulted in a higher concentration of polymer solution subsequently entering the coagulation bath and a less porous top skin layer. With these two competitive effects, the MWCO increased at air gap length (factor F in Figure 3) ranging from 7 to 25 cm. However, MWCO was almost the same at an air gap length ranging from 25 to 40 cm. Now& (1989) reported when evaporation time increased, R increased slightly (from about 97% to 99%, almost no change). Bodzek and Konieczny (1993) reported no influence of the evaporation time of solvent on the performance of the obtained membranes, probably due t o the weak solvent volatility. Therefore, the solvent volatility also influenced the effect of air gap length on MWCO. The air gap length was the third most important variable whose contribution to the variation of 7 was 12.2%.
3.3.5. Effect of Air Humidity on MWCO. Solvent would evaporate at a slower rate in the air with higher relative humidity. This subsequently delayed the phase separation that tended to produce a nonporous membrane with thick and dense top layers (smaller MWCO). However, a higher relative humidity led PSU solution to meet nonsolvent moisture in the air. This tended to produce a more open top layer (larger MWCO). With these opposite effects, the effect of air humidity (factor G in Figure 3) on MWCO became a nonlinear function. However, too high a humidity again resulted in the densification of the top layer structure. Thus, the MWCO decreased with relative humidity from 50% to about 75%, and the MWCO increased. 3.3.6. Effect of Dry and Wet Spinning Processes on Variation of 7 . The dry-wet spinning process consisted of two steps: dry spinning step and wet spinning step. The dry spinning process consisted of two variables: air gap length and relative humidity of air. These two variables contributed 21.6% of variation of r. About 57.7% of variation of r was contributed by the wet spinning process. The other 20.7% was the operating error or interaction among existing factors. The polysulfone content in dope solution has the lowest influence on MWCO and it seems to contradict common findings. It is explained that increasing polymer concentrations would result in a densification of the membrane structure and thus result in decreasing permeate rate. Therefore, higher polysulfone concentration will form a stronger sublayer. However, MWCO is mainly influenced by the skin layer which is mainly affected by evaporation conditions and coagulation conditions. Polysulfone content ranging from 20% t o 28% is not a relatively wide range. Therefore, the effect of PSU content is relatively smaller than other wider range factors. The other cause maybe resulted from the operating error and/or interaction among factors existing (about 20% of variation of 7). 3.4. Confirmation Experiments. A primary goal of conducting an orthogonal array to design experiments was to determine the optimum level for each factor. The optimum combination of setting was determined by separately examining the effect of each factor. Optimum conditions, i.e., AlBlC2D2E2FlG2, were determined in this study by the largest value of the average response in each factor. In most situations, when 7 was
818 Ind. Eng. Chem. Res., Vol. 34,No. 3, 1995 Table 5. Prediction of Initial Experimental Conditions and Optimum Conditions init exptl conditions opt conditions factors level effect level effect A B C D E F G m total
-0.17 5.88 -1.00 4.80 -3.44 -1.70 2.37 -85.70 -78.97
A1
B1 c3 D2 E3 F3 G2
A1 B1 c2 D2 E2 F1 G2
-0.17 5.88 0.77 4.80 2.46 4.57 2.37 -85.70 -65.03
Table 7. Comparison of Experimental Results with Prediction Data init exptl conditions opt conditions observed MWCO 16660 9200 pred by additive modela 18880 (13.3%) 8220 (10.68) a The error between observed and predicted MWCO is shown in parentheses.
experimental conditions to optimum conditions is equal to 18.37,Le.,
vOpt- qo = 18.3716
Table 6. Confirmation Experiments
predicted r,~ observed v Vobs - Vpre
= 10 log
initl exptl conditions
conditions
OP4
improvement
-78.97 -76.47 2.50
-65.04 -58.10 6.94
13.94 18.37
judiciously chosen, the relationship could be adequately approximated by the additive model. The additive model, which can be calculated by m adding total deviation from m for each factor setting, could be applied toward predicting the value of 11 under the optimum conditions, denoted by l;lopt, as follows:
+ (-85.87 + 85.71) + (79.83 + 85.71) + ... + (-83.34 + 85.71)
= -85.71
= -65.04 After the optimum conditions were obtained, and the responses under these conditions, at least one confirmation experiment with optimum factor settings must be conducted. Additionally, the observed value of 11 is compared with the predictions. If the predicted and observed values of 11 were close to each other, the additive model was then considered as being adequate for describing the dependence of 11 on the various factors. Two confirmation experiments were conducted in this study, one a t the optimum conditions and other at AlBlC3D2E3F3G2 (initial experimental conditions). The optimum conditions implied from the data analysis above are listed in Table 5 along with initial experimental conditions. Results from the confirmation experiments are summarized in Table 6. The differences between vobs and vpreare 2.50 for initial experimental conditions and 6.94 for optimum conditions. Thus, the observed responses for these two conditions were within their respective two-standard-deviation confidence limits (f14.46at 90% confidence level), i.e., -78.97 f 14.46 for initial experimental conditions and -65.04 f 14.46 for optimum conditions. Therefore, the additive model was adequate enough for describing the dependence of 7 on the various factors within the range of this study. There was no evidence of strong interactions occurring among the factors. Additionally, 11 under the optimum conditions was found to be better than the best among the 18 experiments. That is, the optimum conditions truly improved on r. The improvement of 17 from initial
MWCO, - 10000 - 10000
and thus,
Mwco, - 10000 Mwco,,, - 10000~= 8.3
(11)
This means that the difference between target value and operating M W C O has been improved 8.3 times from initial experimental conditions to optimum conditions. That is more evidence of no essential interaction occurring among factors. Therefore, AlBlC2D2E2FlG2 was chosen as the optimum conditions among 1458 (2l x 36=1458)combination conditions of factor settings. In order to prove the validity of the additive model, 1458 combination conditions of factor settings or more experiments must be done. That is not the purpose of utilizing an orthogonal array that produces more reliable estimates of factor effects with fewer experiments than those of traditional methods. In actual operation, only at least one confirmation experiment (two confirmation experiments in this study) should be used to check the validity of the additive model. In Table 7,the observed M W C O was compared with M W C O predicted by the additive model at optimum conditions and initial experimental conditions. The observed M W C O at optimum conditions was equal to 9200,reasonably close to the target value of 10 000. Additional experiments to achieve an M W C O even closer to the target seems t o be unnecessary. 4. Conclusion
Orthogonal array experimental design was employed
to analyze production of PSU hollow fibers in this study. 7, a process response parameter, was suitably used in determining the optimum conditions of each factor. An additive model adequately described the dependence of 7 on seven factors within the range of this study. The confirmation of optimum operating conditions for a polysulfone membrane was AlBlC2D2E2FlG2,which produced an M W C O of 9200 versus a target value of 10 000. Using the orthogonal array experimental design provided more reliable estimates of effects of factors with fewer experiments than those of conventional methods. Seven effects of factors were analyzed in this study by only 20 experiments. However, these experiments have provided a clear picture regarding those factors which influence the pore sizes of ultrafiltration membranes.
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 819
Acknowledgment The authors wish to acknowledge the financial support given through following projects: UCL 37D2310, NSC 77-0201-E007-05, and NTH 0982-08252.
Nomenclature ANOVA = analysis of variance df = degrees of freedom F = variance ratio m = overall mean of qi E = number-average molecular weight E = weight-average molecular weight MWCO = molecular weight cutoff MWCOo = molecular weight cutoff at initial experimental conditions n = number of qi R = rejection coefficient SS = sum of squares q = defined by eq 4 qopt= q at optimum conditions obs = observed pre = predicted 0 = at initial experimental conditions P = pressure difference between shell and tube sides Literature Cited Bodzek, M.; Konieczny, K. Ultrafiltration membranes made of vinyl chloride-vinyl acetate copolymer. J. Membr. Sci. 1993,76 (2-31, 269-280. Doi, S.; Hamanaka, K. Pore size control technique in the spinning of polysulfone hollow fiber ultrafiltration membranes. Desalination 1991,80, 167-180. Gotoh, M.; Tamiya, E.;. Karube, I. Preparation and performance of poly(viny1 butyral) membrane for ultrafiltration. J. Appl. Polym. Sci. 1993,48,67-73.
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