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Cake properties as a function of time and location in microfiltration of activated sludge suspension from membrane bioreactors (MBRs)
Chemical Engineering Journal 302 (2016) 97–110
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Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Cake properties as a function of time and location in microfiltration of activated sludge suspension from membrane bioreactors (MBRs) Zhongya Zhu, Zhan Wang ⇑, Hao Wang, Yadong Kong, Kui Gao, Yanling Li Beijing Key Laboratory for Green Catalysis and Separation, Department of Chemistry and Chemical Engineering, Beijing University of Technology, Beijing 100124, PR China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Characteristic parameters of activated
sludge were determined by a fitting method. The location and resistance of skin layer were quantitatively analyzed. Cake properties varied sharply within the skin layer at the location of x/ L < 0.2. The structure of cake layer was opposite to that of the asymmetric membrane.
a r t i c l e
i n f o
Article history: Received 4 March 2016 Received in revised form 5 May 2016 Accepted 6 May 2016 Available online 7 May 2016 Keywords: Microfiltration Activated sludge Cake properties Skin layer
a b s t r a c t How to determine characteristic parameters in Tiller’s power-law expressions is crucial to analyze cake properties in microfiltration using conventional cake filtration theory. In this study, these characteristic parameters of activated sludge from MBRs were determined by fitting experimental data to our proposed equation, and then cake properties were analyzed from two aspects of time and location. In addition, the relative cake resistance (Rx/Rc), and the resistance and location of the skin layer under different operating conditions were quantitatively analyzed by our developed equations. Results indicated that variations of cake properties with time were inconspicuous, while cake properties varied sharply over location until the relative thickness (x/L) reached 0.2. The cake consisted of a skin layer (at the location of x/L < 0.2) below a loose layer, which was opposite to the structure of asymmetric membrane. More than 70% of cake resistance concentrated in the skin layer whose thickness was only 20% of cake thickness. Predictions of permeate flux determined by obtained cake properties showed good agreement with experimental data. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Membrane bioreactor (MBR) technologies have already been widely used in wastewater treatment [1]. However, membrane fouling limits widespread applications of MBRs [2]. Sludge cake formation on the membrane surface is generally considered as the dominant reason for membrane fouling in MBRs [3]. In order ⇑ Corresponding author. E-mail address: [email protected] (Z. Wang). http://dx.doi.org/10.1016/j.cej.2016.05.031 1385-8947/Ó 2016 Elsevier B.V. All rights reserved.
to alleviate membrane fouling in MBRs, it is significant to acquire extensive knowledge about cake properties. Researches about cake properties were focused on two aspects: global cake properties and local cake properties. As to global cake properties, the common method to determine them (such as specific cake resistance, porosity and permeability) was compression – permeability (C–P) measurement [4]. Other methods were also developed to determine global cake properties, such as combining the instantaneous filtration rate with the instantaneous pressure drop across the cake [5], plotting t/V vs. V or 4t/4V vs. 4V [6],
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Nomenclature k k0 ps pl pa n x/L x L 4pc 4P 4pm s J w Rc Rx/Rc Rm cs
the permeability (m2) the value of k at zero-stress state (m2) the solid compressive pressure (Pa) the pore liquid pressure (Pa) the normalizing parameter of compressive pressure (Pa) empirical constant the relative cake thickness the distance apart away from the membrane surface (m) the cake thickness (m) the pressure drop across cake (Pa) the applied pressure (Pa) the pressure drop across membrane (Pa) the particle volume fraction of feed suspension the permeate flux (m3 m2 s1) the cake mass per unit membrane surface (g/m2) the resistance of the whole cake layer (1/m) the relative cake resistance that is the ratio of the resistance of the layer from 0 to x to the total cake resistance the intrinsic membrane resistance (1/m) the mass of activated sludge per unit suspension volume (g/mL)
rebuilding the cake recovered from the membrane unit by static filtration [7], combining confocal laser scanning microscope (CLSM) and image analysis technique [8]. It was concluded that cake properties were influenced by the pressure drop across the filter cake, and the relation between them cake agreed well with Tiller’s empirical equations [9]. In addition, filter cake properties in dead-end microfiltration of microbial suspensions were also affected by cell size and shape, cell surface properties (including charge), ionic environment, fermentation medium components, and ageing effects [10]. As to local cake properties, the common method to determine them (such as local cake porosity, specific cake resistance and permeability) was substituting values of the solid compressive pressure measured by pressure probes into Tiller’s empirical expressions [11]. In order to improve the accuracy of these empirical expressions, Tiller and Leu proposed the power-law expressions describing relationships between local cake properties and solid compressive pressures [12]. Tien et al. developed different relationships between the pore liquid pressure and the solid compressive pressure to determine local cake properties and cake filtration performance [13]. These researches provided a guide to applying conventional cake theory to determine local properties of cake formed in membrane filtration. In addition, local cake properties could also be determined by other methods such as a revised dynamic simulation method [14], an iterative method [15], a c-attenuation method [16], an electrochemical method combined with a step transient method [17] and NMR imaging [18]. As to membrane filtration, although local cake properties could be measured by these analysis techniques, some disadvantages such as complicated operating procedures and high operating costs hindered their wide use. So the application of conventional cake filtration theory to determine local cake properties in membrane filtration seemed more potential, and the key was to determine characteristic parameters in Tiller’s power-law expressions. Although C–P measurement, which used pressure probes to record the solid compressive pressure distribution within the cake, can be used to determine these characteristic parameters in conventional cake filtration [19], it was not suitable for the case of microfiltration in laboratory scale because the formed cake was so thin that it was very difficult to detect the solid compressive pressure distribution within the cake, even impossible. Therefore,
Vs MLSS TMP Jw V A t R2 Rskin
the volume of suspension filtrated (mL) mixed liquor suspended solids concentration (g L1) the transmembrane pressure (Pa) the pure water permeate flux (m3 m2 s1) the cumulative filtrate volume (m3) the effective membrane area (m2) the filtration time (s) correlation coefficient the resistance of the skin layer (1/m)
Greek letters es the cake solidosity e0s the value of es at zero-stress state e the cake porosity a the specific cake resistance (m/kg) a0 the value of a at zero-stress state (m/kg) b empirical constant d empirical constant l the dynamic viscosity of filtrate (Pa s) qs the density of sludge (kg/m3)
how to resolve this problem was urgent. In terms of compressible cakes, some research found that a relative dense layer (skin layer) was formed near the membrane surface during the cake formation process and that the resistance of skin layer was close to the overall filtration resistance though its thickness was only about 10–20% of the entire cake thickness [19,20]. However, these studies only made rough estimates of the resistance and location of the skin layer. Few studies quantitatively analyzed the location of the skin layer in the cake layer and its resistance in microfiltration of activated sludge suspension from MBRs. In addition, quantitative analysis on variations of the relative cake resistance (Rx/Rc, the ratio of the resistance of the layer from 0 to x to the total cake resistance) with time and location was also rarely reported. Therefore, the objective of this work was to propose a method to determine characteristic parameters in the power-law expressions for activated sludge from MBRs, and then quantitatively analyze variations of cake properties with both time and location using conventional cake filtration theory. Furthermore, based on our proposed equations, variations of the relative cake resistance (Rx/Rc) with time and location, and the resistance and location of skin layer were also analyzed. 2. Theory Tiller and Leu [12] proposed the following power-law expressions to describe the relationships between local cake properties and the solid compressive pressure.
es ¼ e0s ð1 þ ps =pa Þb
ð1Þ
k ¼ k ð1 þ ps =pa Þd
ð2Þ
a ¼ a0 ð1 þ ps =pa Þn
ð3Þ
0
where es, k and a denote cake solidosity, permeability and specific 0
cake resistance, respectively. e0s , k and a0 are the values of es, k and a at the state where ps = 0. ps is the solid compressive pressure. pa is the normalizing parameter of ps and the exponents b, d and n signify compression effects due to ps. Two of the three equations are
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Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110 Table 1 Operating conditions of different bioreactors.
Table 3 Characteristic parameters of activated sludge from the literature [23].
Bioreactors
MLSS (g L1)
Temperature (°C)
DO (mg L1)
pH
SRT (d)
HRT (h)
Material
e0s
qsa0 (m2)
k0 (m2)
b
n
d
pa (kPa)
1 2 3
2.5 3.5 4.5
31 23 19
2.5 3.5 6.5
6.2 6.7 8.7
160 80 140
11 12 19
Activated sludge
0.05
3.62 1014
5.53 1014
0.26
1.40
1.66
0.19
independent, and the relationship among es, k and a and that among n, d and b can be expressed as [13]
a ¼ 1=ðes kqs Þ
ð4Þ
d¼ nþb
ð5Þ
where qs is the density of particles. Relationships between local cake properties and the relative cake thickness (x/L) can be expressed as [11,12,21]
"
1 !#1d ps x Dp 1d 1þ c ¼ 1þ 1 1 1 L pa pa
ð6Þ
ð7Þ
b " #1d ! Dpc 1d x þ1 1þ 1 1 L pa
ð8Þ
ð9Þ
n " #1d ! Dpc 1d x þ1 a¼a 1þ 1 1 L pa
ð10Þ
0
Differentiating pl with respect to x yields d @pl p Ch xi1d 1þC 1 ¼ a L @x 1 d L
ð14Þ
and
C ¼ ð1 þ Dpc =pa Þ1d 1
ð15Þ
Combining Eqs. (11), (13) and (14) yields 0
J¼
k
pa
C
ð16Þ
l 1d L 0
dL s k pa C ¼ dt e0s s l 1 d L
ð17Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " # u u 2s k0 p Z t Dpc 1d a t L¼ 1þ 1 dt e0s s l 1 d 0 pa
d " #1d ! Dpc 1d x k¼k þ1 1þ 1 1 L pa
ð18Þ
Substituting Eqs. (15) and (18) into Eq. (16) yields
1d 1 þ Dppac 1 J ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1d Rt 2lsð1dÞ D pc 1 þ 1 dt pa k0 p ðe0 sÞ 0 a
ð19Þ
s
Substituting Eq. (5) into Eq. (19) yields
0
ð11Þ
where pl and ps denote the pore liquid pressure and solid compressive pressure, respectively. Dpc is the pressure drop across cake. x is the distance apart away from the membrane surface. L is the cake thickness. e denotes the cake porosity. 4P is the applied pressure. The growth rate of cake thickness [21] can be expressed as
dL e0 k @pl ¼ 0 s dt es s l @x
ð13Þ x¼0
Integrating Eq. (17) from t = 0 to t = t, one has
b " #1d ! Dpc 1d x 0 þ1 e ¼ 1 es 1þ 1 1 L pa
Combining Eqs. (11), (12), (14) and (16), one has
1 " !#1d p l DP x Dp 1d 1þ c ¼ 1þ 1 1 þ1 pa L pa pa
es ¼ e0s
k @pl l @x
J¼
J
ð12Þ
x¼L
where s is the particle volume fraction of feed suspension. l is the dynamic viscosity of filtrate. J is the permeate flux. Based on the assumption that the solid phase velocity is negligible [21], the flux J can be expressed as
1nb 1 þ Dppc 1 a J ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1nb Rt 2lsð1dÞ D pc 1 þ 1 dt p k0 p ðe0 sÞ 0 a
ð20Þ
a
s
The resistance of the layer from 0 to x can be expressed as
Z
Rx ¼ 0
Z
x
a dw ¼ qs
0
x
ð21Þ
a es dx
where x is the distance away from the membrane surface. qs is the density of particles. w is the cake mass per unit membrane surface. Combining Eqs. (8), (10) and (21) yields 1 1 L Rx ¼ qs e0s a0 ð1 dÞ ð½Cð1 x=LÞ þ 11d ð1 þ CÞ1d Þ C
ð22Þ
Table 2 Characteristic parameters of activated sludge determined by Eq. (20) under different conditions (0.1 lm PAN membrane used as the filter media). MLSS (g/L)
2.5
Pressure (kPa)
60
90
120
150
60
90
120
150
60
90
120
e0s a0 1011 (m/kg)
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
3.12 5.53 0.26 1.40 1.66 0.19 0.9741
3.12 5.53 0.26 1.40 1.66 0.19 0.9780
3.12 5.53 0.26 1.40 1.66 0.19 0.9707
3.12 5.53 0.26 1.40 1.66 0.19 0.9757
3.12 5.53 0.26 1.40 1.66 0.45 0.9813
3.12 5.53 0.26 1.40 1.66 0.45 0.9863
3.12 5.53 0.26 1.40 1.66 0.45 0.9870
3.12 5.53 0.26 1.40 1.66 0.45 0.9882
3.12 5.53 0.26 1.40 1.66 3.00 0.9756
3.12 5.53 0.26 1.40 1.66 3.00 0.9821
3.12 5.53 0.26 1.40 1.66 3.00 0.9840
3.12 5.53 0.26 1.40 1.66 3.00 0.9887
k0 1014 (m2) b n d pa (kPa) R2
3.5
4.5 150
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Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
Table 4 Characteristic parameters of activated sludge determined by Eq. (20) under other conditions (PVDF membrane with mean pore size of 0.1 lm and 0.22 lm used as the filter media). MLSS (g/L)
Mean pore size (lm)
Pressure (kPa)
e0s
a0 1011 (m/kg)
k0 1014 (m2)
b
n
d
pa (kPa)
R2
5.0
0.1
25 30 40
0.05 0.05 0.05
3.12 3.12 3.12
5.53 5.53 5.53
0.26 0.26 0.26
1.40 1.40 1.40
1.66 1.66 1.66
0.03 0.07 0.10
0.9897 0.9746 0.9750
4.0
0.1 0.22
20 20
0.05 0.05
3.12 3.12
5.53 5.53
0.26 0.26
1.40 1.40
1.66 1.66
0.07 0.25
0.9845 0.9784
Table 5 Characteristic parameters of kaolin determined by Eq. (20) under different conditions (0.1 lm PES membrane used as the filter media). Concentration (g/L)
Pressure (kPa)
e0s
a0 1014 (m/kg)
k0 1014 (m2)
b
n
d
pa (kPa)
R2
12.0
40 80 120
0.32 0.32 0.32
2.88 2.88 2.88
1.09 1.09 1.09
0.09 0.09 0.09
0.55 0.55 0.55
0.64 0.64 0.64
0.30 0.26 0.50
0.9934 0.9819 0.9904
Fig. 1. The variation of cake thickness with time at (a) different MLSSs for 60 kPa, and (b) different TMPs for 4.5 g/L.
Fig. 2. Cake mass per unit membrane surface area as a function of cake thickness at (a) different MLSSs for 60 kPa and (b) different TMPs for 2.5 g/L. 1
Substituting x = L into Eq. (22) yields the resistance of the whole cake layer (Rc). That is 1 L Rc ¼ qs e0s a0 ð1 dÞ ½1 ð1 þ CÞ1d C
Dividing Eq. (22) by Eq. (23), one has
ð23Þ
1
Rx ½Cð1 x=LÞ þ 11d ð1 þ CÞ1d ¼ 1 Rc 1 ð1 þ CÞ1d
ð24Þ
where Rx/Rc denotes the relative cake resistance that is the ratio of the resistance of the layer from 0 to x to the total cake resistance. Sludge cake formation on the membrane surface is generally regarded as the dominant reason for membrane fouling in MBRs
Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
101
[3]. Therefore, the permeate flux can be approximately expressed as
J¼
DP
ð25Þ
l ðRm þ Rc Þ
where Rm is the intrinsic resistance of membrane. Substituting Eq. (23) into Eq. (25), one has
J¼
DP
h
1
l Rm qs e0s a0 ð1 dÞ CL 1 ð1 þ CÞ1d
i
ð26Þ
3. Materials and methods 3.1. Experimental setup and operation The filtration experiments of activated sludge suspension were conducted in a constant pressure microfiltration system which was described in the previous work of our laboratory [22] at four different pressures of 60, 90, 120 and 150 kPa and the agitation speed was set at 200 rpm. The effective filtration area was 24.0 cm2. The membrane used in this experiment was 0.1 lm polyacrylonitrile (PAN) flat sheet microfiltration membrane which was obtained from Beijing Ande Membrane Separation Technology and Engineering (Beijing) Co., Ltd.. The activated sludge suspension obtained from MBRs was chosen as the feed suspension in the experiment. The bioreactor, an intermittent mode, has an effective volume of 25 L. Different operating parameters of the bioreactors, such as mixed liquor suspended solids concentration (MLSS), temperature, dissolved oxygen (DO), pH, sludge retention time (SRT) and hydraulic retention time (HRT), were shown in Table 1. 3.2. Evaluation of intrinsic membrane resistances The intrinsic resistance of 0.1 lm PAN membrane (Rm) was measured by filtering de-ionized (DI) water through the virgin PAN membrane and calculated based on the following equation.
Rm ¼ TMP=ðlJ w Þ
ð27Þ
where Jw is the pure water permeate flux. TMP denotes transmembrane pressure. 3.3. Evaluation of the pressure drop across cake and cake mass Cake formation plays a dominant role in membrane fouling of MBRs [3]. So the pressure drop across cake can be approximately determined based on Darcy’s equation.
Dpc ¼ DP Dpm ¼ DP lRm J
ð28Þ
and
J ¼ ðdV=dtÞ=A
ð29Þ
where 4pc is the pressure drop across cake. 4pm is the pressure drop across membrane. 4P is the applied pressure. l is the dynamic viscosity of filtrate. V is the cumulative filtrate volume. A is the effective membrane area. t is the filtration time. Based on the mass balance, the cake mass per unit membrane area (w) can be expressed as [10]
w ¼ cs V s =A
ð30Þ
Fig. 3. Cake porosity as a function of filtration time (t) and location (x/L) under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
where cs is the mass of activated sludge per unit suspension volume. Vs is the volume of suspension filtrated. Because activated sludge suspensions used in our experiments are very dilute, Vs approximately equals to V (cumulative filtrate volume).
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Fig. 4. The distribution of pore liquid pressure within the cake under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
4. Results and discussion 4.1. Determination of characteristic parameters in the power-law expressions The permeate flux (J) and the pressure drop across cake (4pc) were calculated by substituting experimental data (V vs. t) into Eqs. (29) and (28), respectively. Then, these values (J vs. 4pc) were fit to Eq. (20) to determine the characteristic parameters in the power-law expressions (Eqs. (1)–(3)) and the results were shown
in Table 2. And comparisons of experimental results (determined by Eq. (29)) and model predictions (determined by Eq. (20)) of the permeate flux under different conditions were shown in Figs. S1–S3 in Supplementary Material. It was found that the values of R2 (correlation coefficient) were close to 1.0 (Table 2) and the model predictions of permeate flux agreed well with the experimental results of permeate flux (Figs. S1–S3), which suggested that the obtained characteristic parameters of activated sludge were valid. Moreover, these obtained characteristic parameters were also consistent with those from the literature [23] (shown in Table 3).
Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
103
Fig. 4 (continued)
4.2. Validation and applicability of the proposed equation In order to validate the proposed equation (Eq. (20)) used to determine characteristic parameters, the proposed equation was applied to other systems (filtrating activated sludge suspension through 0.1 lm and 0.22 lm PVDF membrane and filtrating kaolin suspension through 0.1 lm PES membrane in dead-end microfiltration system). The experimental data used for testing the proposed equation were obtained from the literature our laboratory had published [22]. The results (obtained characteristic parameters) were shown in Tables 4 and 5, and the comparisons of experimental results and model predictions (determined by Eq. (20)) for the permeate flux under different conditions were shown in Figs. S4–S6 in Supplementary Material. The values of R2 (correlation coefficient) were close to 1.0 (Tables 4 and 5) and the model predictions for permeate flux (Eq. (20)) were consistent with the experimental results (Figs. S4–S6), which suggested that the obtained characteristic parameters were valid. Moreover, obtained characteristic parameters of kaolin and activated sludge (determined by Eq. (20)) also agreed well with those reported in the literature [23]. In addition, it was concluded that the characteristic parameters in Tiller’s power-law expressions mainly depended on types of feed suspensions rather than operating conditions. 4.3. Cake thickness Fig. 1 showed some typical results of variations of cake thickness (L) with time (t), and other results were shown in Fig. S7. Herein, L was determined by substituting 4pc and t into Eq. (18). And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). Fig. 2 indicated variations of mass per unit membrane surface area (w) with the cake thickness (L) under different conditions. Herein, w was determined by Eq. (30). Fig. 1 indicated that the variation trend of cake thickness with time could be divided into two stages. In the first stage, the cake
thickness increased over time in a quickly decreased growth rate. In the second stage, it increased over time in a rarely changed growth rate. For example, as shown in Fig. 1(a), L increased by 1.28 mm while the cake growth rate decreased by 5.21 times from 0 s to 1200 s at 60 kPa for 2.5 g/L. From 1200 s to 2400 s, L increased by 0.54 mm, while the growth rate only decreased by 0.40 times. This variation of cake thickness with time was in agreement with that described in the literature [21]. The reason behind this phenomenon was stated as follows. L could be expressed as the term cs V=ðAqs ð1 eÞÞ[14]. Here, cs, A, and qs was constant at given conditions. e(average cake porosity) was determined by the slope (qs ð1 eÞ) of the cake mass per unit membrane surface area (w) vs. the cake thickness (L) plot [24].The relationship between w and L was nearly linear under different conditions (Fig. 2), which suggested that the average cake porosity rarely varied with time. Therefore, the variation trend of L was consistent with that of V. V increased over time at a decreased rate in the initial filtration stage and then V increased over time at a nearly constant rate in constant pressure microfiltration [22], which was corresponding to the variation trend of L. In addition, the slope of the w vs. L plot decreased as MLSS increased, which suggested that MLSS had a positive influence on average cake porosity. This was true for the case of local cake porosity described in Fig. 3. However, the slope of the w vs. L plot increased as TMP increased, which indicated that TMP had a negative influence on average cake porosity. This was consistent with the case of local cake porosity described in Fig. 3. Fig. 1 also indicated that the cake thickness was influenced by MLSS and TMP. MLSS had a positive influence on the cake thickness, and this influence was evident. For example, the cake thickness increased by 5.07 mm (3.96 times) with MLSS rising from 2.5 g/L to 4.5 g/L at 1200 s for 60 kPa. This was attributed to the fact that the increase of MLSS accelerated the formation of the fouling layer [1]. TMP also had a positive influence, while this influence was inconspicuous. For example, the cake thickness only increased by 0.36 mm (0.06 times) when TMP rose from 60 kPa to 150 kPa at 1200 s for 4.5 g/L, which was due to that the increase of TMP would
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Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
Fig. 5. The distribution of solid compressive stress within the cake under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
accelerate the deposition of particles [7], while higher compression happened within the cake at higher TMP due to that activated sludge was of much compressibility [23]. 4.4. Cake porosity Fig. 3 indicated variations of cake porosity (e) with time (t) and location (x/L) under different conditions. Herein, e was calculated by substituting 4pc and x/L into Eq. (9). And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). The cake porosity decreased over time at any distance away from the membrane surface (x), while this variation was not obvious. For example, e only decreased by 0.004 (0.51%) with the
time increasing from 10 min to 40 min at x = 0 when TMP and MLSS were 60 kPa and 2.5 g/L, respectively (Fig. 3(a)). This phenomenon could be explained by the fact that the cake formed by activated sludge was of high compressibility [23] and the pressure drop across the cake layer increased over time. However, e increased over x. This variation was evident, especially at the location of x/ L < 0.2. The variation of e with x/L increasing from 0 to 0.2 accounted for about 80% of that with x/L increasing from 0 to 1.0 (Fig. 3(a)–(c)). So there existed a relatively dense cake layer on the membrane surface. e within this dense layer was relative smaller and changed greatly over x, which was due to the fact that the solid compressive stress exported on this layer was larger and its variation within this layer was obvious [20]. However, the layer
Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
105
Fig. 5 (continued)
above the dense layer was very loose. e within this loose layer was close to that before compression and rarely varied over x. This could be explained by the fact that the solid compressive stress of this layer was close to zero (Fig. 5). It was also found that e was influenced by TMP and MLSS, especially at the location of x/L < 0.2. e decreased when TMP was elevated, which was owing to the fact that the compressive stress within the cake increased with the increase of TMP (Fig. 5). Moreover, the farther the distance apart away from the membrane surface was, the weaker the influence of TMP on cake porosity was. When it got to the top layer of the cake, the influence of TMP was so weak that it could be neglected. As shown in Fig. 3(a), e at the location of x/L = 0 decreased by 0.064 (8.1%) with TMP increasing from 60 kPa to 150 kPa at 10 min for MLSS of 2.5 g/L, while e at the location of x/L = 0.9 only decreased by 3.0 105 (0.003%) with TMP increasing from 60 kPa to 150 kPa at the same condition, which was caused by that the influence of TMP on the solid compressive stress became weaker as the distance apart away from the membrane surface grew farther (Fig. 5). In addition, e increased as MLSS increased, which can be explained by the fact that increasing MLSS went against the closer packing of particles [25] and that the negative surface charge of the major components (extracellular polymeric substances (EPS)) of sludge cake was increased with the rising MLSS, resulting in the increase of repulsive electrostatic interactions between approaching surfaces [26]. Moreover, the variation of e caused by the increase of MLSS at the location of x/L < 0.2 was more obvious. For example, e at the location of x/L = 0 increased by 0.145 (20.2%) with MLSS increasing from 2.5 g/L to 4.5 g/L at the time of 20 min for TMP of 150 kPa, which was due to the fact that the increase of MLSS had a relative evident influence on the solid compressive pressure at the location of x/L < 0.2 (Fig. 5). 4.5. Pore liquid pressure and solid compressive stress within the cake Figs. 4 and 5 respectively showed that the distributions of pore liquid pressure (pl) and solid compressive stress (ps) within the cake under different conditions. Herein, pl and ps were determined
by substituting 4pc and x/L into Eqs. (7) and (6), respectively. And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). From Fig. 4, it was found that pl increased firstly and then tended to be constant over the distance apart away from the membrane surface (x) at time t. More specifically, pl varied sharply when x/L was less than 0.2, while it rarely changed when x/L was more than 0.2. However, pl decreased over time, while this variation was very little, especially at the location of x/L > 0.2. In addition, pl was influenced by TMP and MLSS. pl increased as TMP was increased in the range of 60 kPa to 150 kPa. The more the increase of TMP was, the more the increase of pl was. The increase of pl caused by the elevated TMP became more evident over x until x/L reached 0.2. pl also increased with the increase of MLSS in the range of 2.5 g/L to 4.5 g/L, while this increase was very small. As shown in Fig. 5, ps decreased sharply over x at time t until x/L was 0.2. ps was close to 0 when x/L was more than 0.2. However, ps increased over time, while this increase was subtle, especially when x/L was more than 0.2. In addition, ps was also influenced by TMP and MLSS. It increased as TMP was elevated in the range of 60 kPa to 150 kPa, while it decreased with the increase of MLSS in the range of 2.5 g/L to 4.5 g/L, which was corresponding to that cake porosity decreased as TMP was elevated while it increased as MLSS was increased (Fig. 4). Moreover, the decrease of ps with x/L rising from 0 to 0.2 became more evident when TMP was elevated, while it rarely varied when MLSS was increased. 4.6. The specific cake resistance and relative cake resistance Figs 6 and 7 respectively indicated the distribution of specific cake resistance (a) within the cake and the variation of relative cake resistance (Rx/Rc) with location (x/L) under different conditions. Herein, a and Rx/Rc were determined by substituting 4pc and x/L into Eqs. (10) and (24), respectively. And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). From Fig. 6, it was found that a decreased first and then tended to keep constant over the distance apart away from the membrane
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Fig. 6. The distribution of specific resistance within the cake under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
surface (x). The decrease of a over x was very evident when x/L was less than 0.2, while it was inconspicuous when x/L was more than 0.2. However, a increased over time. This increase was very little, especially at the location of x/L > 0.2. In addition, a was influenced by TMP and MLSS. a increased as TMP was elevated in the range of 60 kPa to 150 kPa, which was due to the fact that increasing TMP would accelerate the deposition of particles and enlarge the drag force leading to cake compression [27]. However, it decreased as MLSS was increased in the range of 2.5 g/L to 4.5 g/L. This was consistent with the fact that membrane fouling would be reduced with the increase of MLSS at low MLSS (MLSS < 6 g/L) while membrane fouling would be aggravated with the increase of MLSS at high MLSS (MLSS > 15 g/L) [1,28]. This phenomenon was explained as follows: (1) the increase of pH with the increase of MLSS (shown in Table 1) reduced the adsorption of the protein and humic acid
(major components of activated sludge) on the membrane surface and increased electrostatic repulsion among the protein or humic acid molecules due to the increase of negative surface charges of the protein and humic acid molecules with the rising pH, which resulted in mitigation of membrane fouling [26,29]; (2) the increase of pH caused by the increase of MLSS was of benefit to the hydrolysis of PAN molecules in the membrane surface resulting in the increase of the hydrophilicity of PAN membrane. The decrease of a with x/L increasing from 0 to 0.2 became more obvious when TMP was increased, while it was reverse for the case that MLSS was increased. As indicated in Fig. 7, Rx/Rc increased sharply as x/L increased in the range of 0 to 0.2, while it rarely changed when x/L was more than 0.2. For example, Rx/Rc increased by 0.934 as x/L increased from 0 to 0.2 at 30 min for TMP of 60 kPa and MLSS of 3.5 g/L, while
Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
107
Fig. 6 (continued)
it only increased 0.066 with x/L increasing from 0.2 to 1.0. Rx/Rc increased over time, while this variation was very little. Moreover, Rx/Rc was also influenced by TMP and MLSS. Rx/Rc increased with the increase of TMP in the range of 60 kPa to 150 kPa, while its increase was inconspicuous at lower concentration. However, Rx/ Rc decreased with MLSS increasing in the range of 2.5 g/L to 4.5 g/ L, which agreed with the fact that membrane fouling would mitigate with the increase of MLSS at low MLSS (MLSS < 6 g/L) [1,28]. In addition, there existed a thin layer near the membrane surface. The thickness of this layer was only 20% of the total cake thickness, but its resistance accounted for more than 70% of the total cake resistance.
4.7. The location and resistance of the skin layer As described in Figs. 3–7, cake properties (the cake porosity, the liquid pressure, the compressive stress, the specific cake resistance and the relative cake resistance) varied sharply as x/L increased in the range of 0 to 0.2, which suggested that the skin layer was formed at the location of x/L < 0.2 (i.e. from the membrane surface to x = 0.2 L). Moreover, from Fig. 7, it was found that the resistance of the skin layer accounted for more than 70% of the total cake resistance while its thickness was only 20% of the total cake thickness. In order to acquire more quantitative information about the resistance of the skin layer (Rskin), the values of Rskin under different conditions were determined by submitting x/L = 0.2 into the derived equation (Eq. (22)), and some typical results were shown in Fig. 8. The variation trend of Rskin with time could be divided into two stages. In the first stage, Rskin increased over time in a gradually decreased rate. In the second stage, it increased in a nearly constant rate. In addition, Rskin was influenced by TMP and MLSS. Rskin increased as TMP was elevated, which was caused by the fact that increasing TMP was in favor of the increase of the drag force exerted on the particle surfaces resulting into more cake compression [27]. However, Rskin decreased as MLSS was elevated, which
was due to the fact that the increase of MLSS reduced the adsorption of the protein and humic acid (major components of activated sludge) on the membrane surface [26,29]. 4.8. The structure of the fouled membrane Based on the analysis above, it was concluded that the cake structure formed in microfiltration of activated sludge suspension was asymmetric and consisted of a skin layer and a loose layer. The cake layer became looser over the distance away from the membrane surface (x). The skin layer which was relatively dense was near the membrane surface and its thickness was 20% of the total cake thickness. The porosity within this skin layer changed sharply over x. Above the skin layer, there existed a layer that is very loose. The porosity within this loose layer rarely changed over. The cake layer structure that the skin layer was below the loose layer was opposite to the asymmetric membrane structure that the selective skin layer was above the porous sublayer. For the asymmetric microporous membrane, it consisted of a selective skin layer above a porous sublayer. The selective skin layer whose thickness was 0.1–1.0 lm was relative dense, while the porous sublayer whose thickness was 100–200 lm was very loose [30]. The schematic diagram of the fouling membrane structure for microfiltration of activated sludge suspension was shown in Fig. 9. 4.9. Comparisons of model predictions and experimental results In order to further verify the obtained results (cake properties), comparisons between experimental results and model predictions were necessary. Herein, the permeate flux of the membrane was chosen as the indicator, which was due to the fact that direct measurements of local cake properties in microfiltration of activated sludge suspension was very difficult and permeate flux could be determined by obtained cake properties. The flux predictions were determined based on Eq. (26) which was derived from combining
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Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
Fig. 8. The resistance of the skin layer (Rskin) as a function of time under different TMPs for 2.5 g/L (a), and different MLSSs for 90 kPa (b).
be served as an evidence for the validity of obtained cake properties and proposed equations.
5. Conclusions
Fig. 7. The variation of relative cake resistance with location (x/L) under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
expressions of cake solidosity, specific cake resistance and the resistance of the layer from 0 to x (Eqs. (8), (10) and (21)) with Darcy’s equation (Eq. (25)). The experimental results of flux were determined based on Eq. (29). The comparisons of model predictions and experimental results of flux at MLSS of 2.5 g/L were shown in Fig. 10. The results at other MLSSs were shown in Figs. S8 and S9 in Supplementary Material. It was found that the model predictions determined by Eq. (26) showed good agreement with experimental results under different conditions, which could
Characteristic parameters in Tiller’s power-law expressions for activated sludge were determined by fitting experimental data to the proposed equation (Eq. (20)) in microfiltration of activated sludge suspension, and then cake properties were analyzed from two aspects of time and location using conventional cake filtration theory. Furthermore, the relative cake resistance and the resistance of the skin layer were quantitatively analyzed using our proposed equations. Results showed that: (1) The proposed method to determine characteristic parameters in Tiller’s power-law expressions was not only applicable to activated sludge system, but also other similar system. (2) Cake properties varied sharply over location until the location of x/L = 0.2, while they varied slightly with time. (3) The cake layer consisted of a skin layer below a loose layer, which was opposite to the structure of the asymmetric microporous membrane. The skin layer was at the location of x/L < 0.2 and its resistance accounted for more than 70%
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109
Fig. 9. The schematic diagram of the fouling membrane structure for microfiltration of activated sludge suspension (MLSS = 2.5 g/L, TMP = 150 kPa, t = 40 min).
Fig. 10. Comparisons of model predictions and experimental results of flux at MLSS of 2.5 g/L.
of the cake resistance. The resistance of the skin layer increased as TMP was elevated while it decreased as MLSS was increased. (4) Good agreements between model predictions of permeate flux with experimental results under different conditions confirmed our proposed equations.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cej.2016.05.031.
References Acknowledgements The authors wish to express their sincere gratitude to National Natural Science Foundation of China (Project No. 21176006 and No. 21476006).
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Contents lists available at ScienceDirect
Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Cake properties as a function of time and location in microfiltration of activated sludge suspension from membrane bioreactors (MBRs) Zhongya Zhu, Zhan Wang ⇑, Hao Wang, Yadong Kong, Kui Gao, Yanling Li Beijing Key Laboratory for Green Catalysis and Separation, Department of Chemistry and Chemical Engineering, Beijing University of Technology, Beijing 100124, PR China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Characteristic parameters of activated
sludge were determined by a fitting method. The location and resistance of skin layer were quantitatively analyzed. Cake properties varied sharply within the skin layer at the location of x/ L < 0.2. The structure of cake layer was opposite to that of the asymmetric membrane.
a r t i c l e
i n f o
Article history: Received 4 March 2016 Received in revised form 5 May 2016 Accepted 6 May 2016 Available online 7 May 2016 Keywords: Microfiltration Activated sludge Cake properties Skin layer
a b s t r a c t How to determine characteristic parameters in Tiller’s power-law expressions is crucial to analyze cake properties in microfiltration using conventional cake filtration theory. In this study, these characteristic parameters of activated sludge from MBRs were determined by fitting experimental data to our proposed equation, and then cake properties were analyzed from two aspects of time and location. In addition, the relative cake resistance (Rx/Rc), and the resistance and location of the skin layer under different operating conditions were quantitatively analyzed by our developed equations. Results indicated that variations of cake properties with time were inconspicuous, while cake properties varied sharply over location until the relative thickness (x/L) reached 0.2. The cake consisted of a skin layer (at the location of x/L < 0.2) below a loose layer, which was opposite to the structure of asymmetric membrane. More than 70% of cake resistance concentrated in the skin layer whose thickness was only 20% of cake thickness. Predictions of permeate flux determined by obtained cake properties showed good agreement with experimental data. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Membrane bioreactor (MBR) technologies have already been widely used in wastewater treatment [1]. However, membrane fouling limits widespread applications of MBRs [2]. Sludge cake formation on the membrane surface is generally considered as the dominant reason for membrane fouling in MBRs [3]. In order ⇑ Corresponding author. E-mail address: [email protected] (Z. Wang). http://dx.doi.org/10.1016/j.cej.2016.05.031 1385-8947/Ó 2016 Elsevier B.V. All rights reserved.
to alleviate membrane fouling in MBRs, it is significant to acquire extensive knowledge about cake properties. Researches about cake properties were focused on two aspects: global cake properties and local cake properties. As to global cake properties, the common method to determine them (such as specific cake resistance, porosity and permeability) was compression – permeability (C–P) measurement [4]. Other methods were also developed to determine global cake properties, such as combining the instantaneous filtration rate with the instantaneous pressure drop across the cake [5], plotting t/V vs. V or 4t/4V vs. 4V [6],
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Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
Nomenclature k k0 ps pl pa n x/L x L 4pc 4P 4pm s J w Rc Rx/Rc Rm cs
the permeability (m2) the value of k at zero-stress state (m2) the solid compressive pressure (Pa) the pore liquid pressure (Pa) the normalizing parameter of compressive pressure (Pa) empirical constant the relative cake thickness the distance apart away from the membrane surface (m) the cake thickness (m) the pressure drop across cake (Pa) the applied pressure (Pa) the pressure drop across membrane (Pa) the particle volume fraction of feed suspension the permeate flux (m3 m2 s1) the cake mass per unit membrane surface (g/m2) the resistance of the whole cake layer (1/m) the relative cake resistance that is the ratio of the resistance of the layer from 0 to x to the total cake resistance the intrinsic membrane resistance (1/m) the mass of activated sludge per unit suspension volume (g/mL)
rebuilding the cake recovered from the membrane unit by static filtration [7], combining confocal laser scanning microscope (CLSM) and image analysis technique [8]. It was concluded that cake properties were influenced by the pressure drop across the filter cake, and the relation between them cake agreed well with Tiller’s empirical equations [9]. In addition, filter cake properties in dead-end microfiltration of microbial suspensions were also affected by cell size and shape, cell surface properties (including charge), ionic environment, fermentation medium components, and ageing effects [10]. As to local cake properties, the common method to determine them (such as local cake porosity, specific cake resistance and permeability) was substituting values of the solid compressive pressure measured by pressure probes into Tiller’s empirical expressions [11]. In order to improve the accuracy of these empirical expressions, Tiller and Leu proposed the power-law expressions describing relationships between local cake properties and solid compressive pressures [12]. Tien et al. developed different relationships between the pore liquid pressure and the solid compressive pressure to determine local cake properties and cake filtration performance [13]. These researches provided a guide to applying conventional cake theory to determine local properties of cake formed in membrane filtration. In addition, local cake properties could also be determined by other methods such as a revised dynamic simulation method [14], an iterative method [15], a c-attenuation method [16], an electrochemical method combined with a step transient method [17] and NMR imaging [18]. As to membrane filtration, although local cake properties could be measured by these analysis techniques, some disadvantages such as complicated operating procedures and high operating costs hindered their wide use. So the application of conventional cake filtration theory to determine local cake properties in membrane filtration seemed more potential, and the key was to determine characteristic parameters in Tiller’s power-law expressions. Although C–P measurement, which used pressure probes to record the solid compressive pressure distribution within the cake, can be used to determine these characteristic parameters in conventional cake filtration [19], it was not suitable for the case of microfiltration in laboratory scale because the formed cake was so thin that it was very difficult to detect the solid compressive pressure distribution within the cake, even impossible. Therefore,
Vs MLSS TMP Jw V A t R2 Rskin
the volume of suspension filtrated (mL) mixed liquor suspended solids concentration (g L1) the transmembrane pressure (Pa) the pure water permeate flux (m3 m2 s1) the cumulative filtrate volume (m3) the effective membrane area (m2) the filtration time (s) correlation coefficient the resistance of the skin layer (1/m)
Greek letters es the cake solidosity e0s the value of es at zero-stress state e the cake porosity a the specific cake resistance (m/kg) a0 the value of a at zero-stress state (m/kg) b empirical constant d empirical constant l the dynamic viscosity of filtrate (Pa s) qs the density of sludge (kg/m3)
how to resolve this problem was urgent. In terms of compressible cakes, some research found that a relative dense layer (skin layer) was formed near the membrane surface during the cake formation process and that the resistance of skin layer was close to the overall filtration resistance though its thickness was only about 10–20% of the entire cake thickness [19,20]. However, these studies only made rough estimates of the resistance and location of the skin layer. Few studies quantitatively analyzed the location of the skin layer in the cake layer and its resistance in microfiltration of activated sludge suspension from MBRs. In addition, quantitative analysis on variations of the relative cake resistance (Rx/Rc, the ratio of the resistance of the layer from 0 to x to the total cake resistance) with time and location was also rarely reported. Therefore, the objective of this work was to propose a method to determine characteristic parameters in the power-law expressions for activated sludge from MBRs, and then quantitatively analyze variations of cake properties with both time and location using conventional cake filtration theory. Furthermore, based on our proposed equations, variations of the relative cake resistance (Rx/Rc) with time and location, and the resistance and location of skin layer were also analyzed. 2. Theory Tiller and Leu [12] proposed the following power-law expressions to describe the relationships between local cake properties and the solid compressive pressure.
es ¼ e0s ð1 þ ps =pa Þb
ð1Þ
k ¼ k ð1 þ ps =pa Þd
ð2Þ
a ¼ a0 ð1 þ ps =pa Þn
ð3Þ
0
where es, k and a denote cake solidosity, permeability and specific 0
cake resistance, respectively. e0s , k and a0 are the values of es, k and a at the state where ps = 0. ps is the solid compressive pressure. pa is the normalizing parameter of ps and the exponents b, d and n signify compression effects due to ps. Two of the three equations are
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Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110 Table 1 Operating conditions of different bioreactors.
Table 3 Characteristic parameters of activated sludge from the literature [23].
Bioreactors
MLSS (g L1)
Temperature (°C)
DO (mg L1)
pH
SRT (d)
HRT (h)
Material
e0s
qsa0 (m2)
k0 (m2)
b
n
d
pa (kPa)
1 2 3
2.5 3.5 4.5
31 23 19
2.5 3.5 6.5
6.2 6.7 8.7
160 80 140
11 12 19
Activated sludge
0.05
3.62 1014
5.53 1014
0.26
1.40
1.66
0.19
independent, and the relationship among es, k and a and that among n, d and b can be expressed as [13]
a ¼ 1=ðes kqs Þ
ð4Þ
d¼ nþb
ð5Þ
where qs is the density of particles. Relationships between local cake properties and the relative cake thickness (x/L) can be expressed as [11,12,21]
"
1 !#1d ps x Dp 1d 1þ c ¼ 1þ 1 1 1 L pa pa
ð6Þ
ð7Þ
b " #1d ! Dpc 1d x þ1 1þ 1 1 L pa
ð8Þ
ð9Þ
n " #1d ! Dpc 1d x þ1 a¼a 1þ 1 1 L pa
ð10Þ
0
Differentiating pl with respect to x yields d @pl p Ch xi1d 1þC 1 ¼ a L @x 1 d L
ð14Þ
and
C ¼ ð1 þ Dpc =pa Þ1d 1
ð15Þ
Combining Eqs. (11), (13) and (14) yields 0
J¼
k
pa
C
ð16Þ
l 1d L 0
dL s k pa C ¼ dt e0s s l 1 d L
ð17Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " # u u 2s k0 p Z t Dpc 1d a t L¼ 1þ 1 dt e0s s l 1 d 0 pa
d " #1d ! Dpc 1d x k¼k þ1 1þ 1 1 L pa
ð18Þ
Substituting Eqs. (15) and (18) into Eq. (16) yields
1d 1 þ Dppac 1 J ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1d Rt 2lsð1dÞ D pc 1 þ 1 dt pa k0 p ðe0 sÞ 0 a
ð19Þ
s
Substituting Eq. (5) into Eq. (19) yields
0
ð11Þ
where pl and ps denote the pore liquid pressure and solid compressive pressure, respectively. Dpc is the pressure drop across cake. x is the distance apart away from the membrane surface. L is the cake thickness. e denotes the cake porosity. 4P is the applied pressure. The growth rate of cake thickness [21] can be expressed as
dL e0 k @pl ¼ 0 s dt es s l @x
ð13Þ x¼0
Integrating Eq. (17) from t = 0 to t = t, one has
b " #1d ! Dpc 1d x 0 þ1 e ¼ 1 es 1þ 1 1 L pa
Combining Eqs. (11), (12), (14) and (16), one has
1 " !#1d p l DP x Dp 1d 1þ c ¼ 1þ 1 1 þ1 pa L pa pa
es ¼ e0s
k @pl l @x
J¼
J
ð12Þ
x¼L
where s is the particle volume fraction of feed suspension. l is the dynamic viscosity of filtrate. J is the permeate flux. Based on the assumption that the solid phase velocity is negligible [21], the flux J can be expressed as
1nb 1 þ Dppc 1 a J ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1nb Rt 2lsð1dÞ D pc 1 þ 1 dt p k0 p ðe0 sÞ 0 a
ð20Þ
a
s
The resistance of the layer from 0 to x can be expressed as
Z
Rx ¼ 0
Z
x
a dw ¼ qs
0
x
ð21Þ
a es dx
where x is the distance away from the membrane surface. qs is the density of particles. w is the cake mass per unit membrane surface. Combining Eqs. (8), (10) and (21) yields 1 1 L Rx ¼ qs e0s a0 ð1 dÞ ð½Cð1 x=LÞ þ 11d ð1 þ CÞ1d Þ C
ð22Þ
Table 2 Characteristic parameters of activated sludge determined by Eq. (20) under different conditions (0.1 lm PAN membrane used as the filter media). MLSS (g/L)
2.5
Pressure (kPa)
60
90
120
150
60
90
120
150
60
90
120
e0s a0 1011 (m/kg)
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
3.12 5.53 0.26 1.40 1.66 0.19 0.9741
3.12 5.53 0.26 1.40 1.66 0.19 0.9780
3.12 5.53 0.26 1.40 1.66 0.19 0.9707
3.12 5.53 0.26 1.40 1.66 0.19 0.9757
3.12 5.53 0.26 1.40 1.66 0.45 0.9813
3.12 5.53 0.26 1.40 1.66 0.45 0.9863
3.12 5.53 0.26 1.40 1.66 0.45 0.9870
3.12 5.53 0.26 1.40 1.66 0.45 0.9882
3.12 5.53 0.26 1.40 1.66 3.00 0.9756
3.12 5.53 0.26 1.40 1.66 3.00 0.9821
3.12 5.53 0.26 1.40 1.66 3.00 0.9840
3.12 5.53 0.26 1.40 1.66 3.00 0.9887
k0 1014 (m2) b n d pa (kPa) R2
3.5
4.5 150
100
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Table 4 Characteristic parameters of activated sludge determined by Eq. (20) under other conditions (PVDF membrane with mean pore size of 0.1 lm and 0.22 lm used as the filter media). MLSS (g/L)
Mean pore size (lm)
Pressure (kPa)
e0s
a0 1011 (m/kg)
k0 1014 (m2)
b
n
d
pa (kPa)
R2
5.0
0.1
25 30 40
0.05 0.05 0.05
3.12 3.12 3.12
5.53 5.53 5.53
0.26 0.26 0.26
1.40 1.40 1.40
1.66 1.66 1.66
0.03 0.07 0.10
0.9897 0.9746 0.9750
4.0
0.1 0.22
20 20
0.05 0.05
3.12 3.12
5.53 5.53
0.26 0.26
1.40 1.40
1.66 1.66
0.07 0.25
0.9845 0.9784
Table 5 Characteristic parameters of kaolin determined by Eq. (20) under different conditions (0.1 lm PES membrane used as the filter media). Concentration (g/L)
Pressure (kPa)
e0s
a0 1014 (m/kg)
k0 1014 (m2)
b
n
d
pa (kPa)
R2
12.0
40 80 120
0.32 0.32 0.32
2.88 2.88 2.88
1.09 1.09 1.09
0.09 0.09 0.09
0.55 0.55 0.55
0.64 0.64 0.64
0.30 0.26 0.50
0.9934 0.9819 0.9904
Fig. 1. The variation of cake thickness with time at (a) different MLSSs for 60 kPa, and (b) different TMPs for 4.5 g/L.
Fig. 2. Cake mass per unit membrane surface area as a function of cake thickness at (a) different MLSSs for 60 kPa and (b) different TMPs for 2.5 g/L. 1
Substituting x = L into Eq. (22) yields the resistance of the whole cake layer (Rc). That is 1 L Rc ¼ qs e0s a0 ð1 dÞ ½1 ð1 þ CÞ1d C
Dividing Eq. (22) by Eq. (23), one has
ð23Þ
1
Rx ½Cð1 x=LÞ þ 11d ð1 þ CÞ1d ¼ 1 Rc 1 ð1 þ CÞ1d
ð24Þ
where Rx/Rc denotes the relative cake resistance that is the ratio of the resistance of the layer from 0 to x to the total cake resistance. Sludge cake formation on the membrane surface is generally regarded as the dominant reason for membrane fouling in MBRs
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101
[3]. Therefore, the permeate flux can be approximately expressed as
J¼
DP
ð25Þ
l ðRm þ Rc Þ
where Rm is the intrinsic resistance of membrane. Substituting Eq. (23) into Eq. (25), one has
J¼
DP
h
1
l Rm qs e0s a0 ð1 dÞ CL 1 ð1 þ CÞ1d
i
ð26Þ
3. Materials and methods 3.1. Experimental setup and operation The filtration experiments of activated sludge suspension were conducted in a constant pressure microfiltration system which was described in the previous work of our laboratory [22] at four different pressures of 60, 90, 120 and 150 kPa and the agitation speed was set at 200 rpm. The effective filtration area was 24.0 cm2. The membrane used in this experiment was 0.1 lm polyacrylonitrile (PAN) flat sheet microfiltration membrane which was obtained from Beijing Ande Membrane Separation Technology and Engineering (Beijing) Co., Ltd.. The activated sludge suspension obtained from MBRs was chosen as the feed suspension in the experiment. The bioreactor, an intermittent mode, has an effective volume of 25 L. Different operating parameters of the bioreactors, such as mixed liquor suspended solids concentration (MLSS), temperature, dissolved oxygen (DO), pH, sludge retention time (SRT) and hydraulic retention time (HRT), were shown in Table 1. 3.2. Evaluation of intrinsic membrane resistances The intrinsic resistance of 0.1 lm PAN membrane (Rm) was measured by filtering de-ionized (DI) water through the virgin PAN membrane and calculated based on the following equation.
Rm ¼ TMP=ðlJ w Þ
ð27Þ
where Jw is the pure water permeate flux. TMP denotes transmembrane pressure. 3.3. Evaluation of the pressure drop across cake and cake mass Cake formation plays a dominant role in membrane fouling of MBRs [3]. So the pressure drop across cake can be approximately determined based on Darcy’s equation.
Dpc ¼ DP Dpm ¼ DP lRm J
ð28Þ
and
J ¼ ðdV=dtÞ=A
ð29Þ
where 4pc is the pressure drop across cake. 4pm is the pressure drop across membrane. 4P is the applied pressure. l is the dynamic viscosity of filtrate. V is the cumulative filtrate volume. A is the effective membrane area. t is the filtration time. Based on the mass balance, the cake mass per unit membrane area (w) can be expressed as [10]
w ¼ cs V s =A
ð30Þ
Fig. 3. Cake porosity as a function of filtration time (t) and location (x/L) under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
where cs is the mass of activated sludge per unit suspension volume. Vs is the volume of suspension filtrated. Because activated sludge suspensions used in our experiments are very dilute, Vs approximately equals to V (cumulative filtrate volume).
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Fig. 4. The distribution of pore liquid pressure within the cake under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
4. Results and discussion 4.1. Determination of characteristic parameters in the power-law expressions The permeate flux (J) and the pressure drop across cake (4pc) were calculated by substituting experimental data (V vs. t) into Eqs. (29) and (28), respectively. Then, these values (J vs. 4pc) were fit to Eq. (20) to determine the characteristic parameters in the power-law expressions (Eqs. (1)–(3)) and the results were shown
in Table 2. And comparisons of experimental results (determined by Eq. (29)) and model predictions (determined by Eq. (20)) of the permeate flux under different conditions were shown in Figs. S1–S3 in Supplementary Material. It was found that the values of R2 (correlation coefficient) were close to 1.0 (Table 2) and the model predictions of permeate flux agreed well with the experimental results of permeate flux (Figs. S1–S3), which suggested that the obtained characteristic parameters of activated sludge were valid. Moreover, these obtained characteristic parameters were also consistent with those from the literature [23] (shown in Table 3).
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103
Fig. 4 (continued)
4.2. Validation and applicability of the proposed equation In order to validate the proposed equation (Eq. (20)) used to determine characteristic parameters, the proposed equation was applied to other systems (filtrating activated sludge suspension through 0.1 lm and 0.22 lm PVDF membrane and filtrating kaolin suspension through 0.1 lm PES membrane in dead-end microfiltration system). The experimental data used for testing the proposed equation were obtained from the literature our laboratory had published [22]. The results (obtained characteristic parameters) were shown in Tables 4 and 5, and the comparisons of experimental results and model predictions (determined by Eq. (20)) for the permeate flux under different conditions were shown in Figs. S4–S6 in Supplementary Material. The values of R2 (correlation coefficient) were close to 1.0 (Tables 4 and 5) and the model predictions for permeate flux (Eq. (20)) were consistent with the experimental results (Figs. S4–S6), which suggested that the obtained characteristic parameters were valid. Moreover, obtained characteristic parameters of kaolin and activated sludge (determined by Eq. (20)) also agreed well with those reported in the literature [23]. In addition, it was concluded that the characteristic parameters in Tiller’s power-law expressions mainly depended on types of feed suspensions rather than operating conditions. 4.3. Cake thickness Fig. 1 showed some typical results of variations of cake thickness (L) with time (t), and other results were shown in Fig. S7. Herein, L was determined by substituting 4pc and t into Eq. (18). And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). Fig. 2 indicated variations of mass per unit membrane surface area (w) with the cake thickness (L) under different conditions. Herein, w was determined by Eq. (30). Fig. 1 indicated that the variation trend of cake thickness with time could be divided into two stages. In the first stage, the cake
thickness increased over time in a quickly decreased growth rate. In the second stage, it increased over time in a rarely changed growth rate. For example, as shown in Fig. 1(a), L increased by 1.28 mm while the cake growth rate decreased by 5.21 times from 0 s to 1200 s at 60 kPa for 2.5 g/L. From 1200 s to 2400 s, L increased by 0.54 mm, while the growth rate only decreased by 0.40 times. This variation of cake thickness with time was in agreement with that described in the literature [21]. The reason behind this phenomenon was stated as follows. L could be expressed as the term cs V=ðAqs ð1 eÞÞ[14]. Here, cs, A, and qs was constant at given conditions. e(average cake porosity) was determined by the slope (qs ð1 eÞ) of the cake mass per unit membrane surface area (w) vs. the cake thickness (L) plot [24].The relationship between w and L was nearly linear under different conditions (Fig. 2), which suggested that the average cake porosity rarely varied with time. Therefore, the variation trend of L was consistent with that of V. V increased over time at a decreased rate in the initial filtration stage and then V increased over time at a nearly constant rate in constant pressure microfiltration [22], which was corresponding to the variation trend of L. In addition, the slope of the w vs. L plot decreased as MLSS increased, which suggested that MLSS had a positive influence on average cake porosity. This was true for the case of local cake porosity described in Fig. 3. However, the slope of the w vs. L plot increased as TMP increased, which indicated that TMP had a negative influence on average cake porosity. This was consistent with the case of local cake porosity described in Fig. 3. Fig. 1 also indicated that the cake thickness was influenced by MLSS and TMP. MLSS had a positive influence on the cake thickness, and this influence was evident. For example, the cake thickness increased by 5.07 mm (3.96 times) with MLSS rising from 2.5 g/L to 4.5 g/L at 1200 s for 60 kPa. This was attributed to the fact that the increase of MLSS accelerated the formation of the fouling layer [1]. TMP also had a positive influence, while this influence was inconspicuous. For example, the cake thickness only increased by 0.36 mm (0.06 times) when TMP rose from 60 kPa to 150 kPa at 1200 s for 4.5 g/L, which was due to that the increase of TMP would
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Fig. 5. The distribution of solid compressive stress within the cake under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
accelerate the deposition of particles [7], while higher compression happened within the cake at higher TMP due to that activated sludge was of much compressibility [23]. 4.4. Cake porosity Fig. 3 indicated variations of cake porosity (e) with time (t) and location (x/L) under different conditions. Herein, e was calculated by substituting 4pc and x/L into Eq. (9). And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). The cake porosity decreased over time at any distance away from the membrane surface (x), while this variation was not obvious. For example, e only decreased by 0.004 (0.51%) with the
time increasing from 10 min to 40 min at x = 0 when TMP and MLSS were 60 kPa and 2.5 g/L, respectively (Fig. 3(a)). This phenomenon could be explained by the fact that the cake formed by activated sludge was of high compressibility [23] and the pressure drop across the cake layer increased over time. However, e increased over x. This variation was evident, especially at the location of x/ L < 0.2. The variation of e with x/L increasing from 0 to 0.2 accounted for about 80% of that with x/L increasing from 0 to 1.0 (Fig. 3(a)–(c)). So there existed a relatively dense cake layer on the membrane surface. e within this dense layer was relative smaller and changed greatly over x, which was due to the fact that the solid compressive stress exported on this layer was larger and its variation within this layer was obvious [20]. However, the layer
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105
Fig. 5 (continued)
above the dense layer was very loose. e within this loose layer was close to that before compression and rarely varied over x. This could be explained by the fact that the solid compressive stress of this layer was close to zero (Fig. 5). It was also found that e was influenced by TMP and MLSS, especially at the location of x/L < 0.2. e decreased when TMP was elevated, which was owing to the fact that the compressive stress within the cake increased with the increase of TMP (Fig. 5). Moreover, the farther the distance apart away from the membrane surface was, the weaker the influence of TMP on cake porosity was. When it got to the top layer of the cake, the influence of TMP was so weak that it could be neglected. As shown in Fig. 3(a), e at the location of x/L = 0 decreased by 0.064 (8.1%) with TMP increasing from 60 kPa to 150 kPa at 10 min for MLSS of 2.5 g/L, while e at the location of x/L = 0.9 only decreased by 3.0 105 (0.003%) with TMP increasing from 60 kPa to 150 kPa at the same condition, which was caused by that the influence of TMP on the solid compressive stress became weaker as the distance apart away from the membrane surface grew farther (Fig. 5). In addition, e increased as MLSS increased, which can be explained by the fact that increasing MLSS went against the closer packing of particles [25] and that the negative surface charge of the major components (extracellular polymeric substances (EPS)) of sludge cake was increased with the rising MLSS, resulting in the increase of repulsive electrostatic interactions between approaching surfaces [26]. Moreover, the variation of e caused by the increase of MLSS at the location of x/L < 0.2 was more obvious. For example, e at the location of x/L = 0 increased by 0.145 (20.2%) with MLSS increasing from 2.5 g/L to 4.5 g/L at the time of 20 min for TMP of 150 kPa, which was due to the fact that the increase of MLSS had a relative evident influence on the solid compressive pressure at the location of x/L < 0.2 (Fig. 5). 4.5. Pore liquid pressure and solid compressive stress within the cake Figs. 4 and 5 respectively showed that the distributions of pore liquid pressure (pl) and solid compressive stress (ps) within the cake under different conditions. Herein, pl and ps were determined
by substituting 4pc and x/L into Eqs. (7) and (6), respectively. And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). From Fig. 4, it was found that pl increased firstly and then tended to be constant over the distance apart away from the membrane surface (x) at time t. More specifically, pl varied sharply when x/L was less than 0.2, while it rarely changed when x/L was more than 0.2. However, pl decreased over time, while this variation was very little, especially at the location of x/L > 0.2. In addition, pl was influenced by TMP and MLSS. pl increased as TMP was increased in the range of 60 kPa to 150 kPa. The more the increase of TMP was, the more the increase of pl was. The increase of pl caused by the elevated TMP became more evident over x until x/L reached 0.2. pl also increased with the increase of MLSS in the range of 2.5 g/L to 4.5 g/L, while this increase was very small. As shown in Fig. 5, ps decreased sharply over x at time t until x/L was 0.2. ps was close to 0 when x/L was more than 0.2. However, ps increased over time, while this increase was subtle, especially when x/L was more than 0.2. In addition, ps was also influenced by TMP and MLSS. It increased as TMP was elevated in the range of 60 kPa to 150 kPa, while it decreased with the increase of MLSS in the range of 2.5 g/L to 4.5 g/L, which was corresponding to that cake porosity decreased as TMP was elevated while it increased as MLSS was increased (Fig. 4). Moreover, the decrease of ps with x/L rising from 0 to 0.2 became more evident when TMP was elevated, while it rarely varied when MLSS was increased. 4.6. The specific cake resistance and relative cake resistance Figs 6 and 7 respectively indicated the distribution of specific cake resistance (a) within the cake and the variation of relative cake resistance (Rx/Rc) with location (x/L) under different conditions. Herein, a and Rx/Rc were determined by substituting 4pc and x/L into Eqs. (10) and (24), respectively. And 4pc was determined by substituting experimental values of J determined by Eq. (29) into Eq. (28). From Fig. 6, it was found that a decreased first and then tended to keep constant over the distance apart away from the membrane
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Fig. 6. The distribution of specific resistance within the cake under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
surface (x). The decrease of a over x was very evident when x/L was less than 0.2, while it was inconspicuous when x/L was more than 0.2. However, a increased over time. This increase was very little, especially at the location of x/L > 0.2. In addition, a was influenced by TMP and MLSS. a increased as TMP was elevated in the range of 60 kPa to 150 kPa, which was due to the fact that increasing TMP would accelerate the deposition of particles and enlarge the drag force leading to cake compression [27]. However, it decreased as MLSS was increased in the range of 2.5 g/L to 4.5 g/L. This was consistent with the fact that membrane fouling would be reduced with the increase of MLSS at low MLSS (MLSS < 6 g/L) while membrane fouling would be aggravated with the increase of MLSS at high MLSS (MLSS > 15 g/L) [1,28]. This phenomenon was explained as follows: (1) the increase of pH with the increase of MLSS (shown in Table 1) reduced the adsorption of the protein and humic acid
(major components of activated sludge) on the membrane surface and increased electrostatic repulsion among the protein or humic acid molecules due to the increase of negative surface charges of the protein and humic acid molecules with the rising pH, which resulted in mitigation of membrane fouling [26,29]; (2) the increase of pH caused by the increase of MLSS was of benefit to the hydrolysis of PAN molecules in the membrane surface resulting in the increase of the hydrophilicity of PAN membrane. The decrease of a with x/L increasing from 0 to 0.2 became more obvious when TMP was increased, while it was reverse for the case that MLSS was increased. As indicated in Fig. 7, Rx/Rc increased sharply as x/L increased in the range of 0 to 0.2, while it rarely changed when x/L was more than 0.2. For example, Rx/Rc increased by 0.934 as x/L increased from 0 to 0.2 at 30 min for TMP of 60 kPa and MLSS of 3.5 g/L, while
Z. Zhu et al. / Chemical Engineering Journal 302 (2016) 97–110
107
Fig. 6 (continued)
it only increased 0.066 with x/L increasing from 0.2 to 1.0. Rx/Rc increased over time, while this variation was very little. Moreover, Rx/Rc was also influenced by TMP and MLSS. Rx/Rc increased with the increase of TMP in the range of 60 kPa to 150 kPa, while its increase was inconspicuous at lower concentration. However, Rx/ Rc decreased with MLSS increasing in the range of 2.5 g/L to 4.5 g/ L, which agreed with the fact that membrane fouling would mitigate with the increase of MLSS at low MLSS (MLSS < 6 g/L) [1,28]. In addition, there existed a thin layer near the membrane surface. The thickness of this layer was only 20% of the total cake thickness, but its resistance accounted for more than 70% of the total cake resistance.
4.7. The location and resistance of the skin layer As described in Figs. 3–7, cake properties (the cake porosity, the liquid pressure, the compressive stress, the specific cake resistance and the relative cake resistance) varied sharply as x/L increased in the range of 0 to 0.2, which suggested that the skin layer was formed at the location of x/L < 0.2 (i.e. from the membrane surface to x = 0.2 L). Moreover, from Fig. 7, it was found that the resistance of the skin layer accounted for more than 70% of the total cake resistance while its thickness was only 20% of the total cake thickness. In order to acquire more quantitative information about the resistance of the skin layer (Rskin), the values of Rskin under different conditions were determined by submitting x/L = 0.2 into the derived equation (Eq. (22)), and some typical results were shown in Fig. 8. The variation trend of Rskin with time could be divided into two stages. In the first stage, Rskin increased over time in a gradually decreased rate. In the second stage, it increased in a nearly constant rate. In addition, Rskin was influenced by TMP and MLSS. Rskin increased as TMP was elevated, which was caused by the fact that increasing TMP was in favor of the increase of the drag force exerted on the particle surfaces resulting into more cake compression [27]. However, Rskin decreased as MLSS was elevated, which
was due to the fact that the increase of MLSS reduced the adsorption of the protein and humic acid (major components of activated sludge) on the membrane surface [26,29]. 4.8. The structure of the fouled membrane Based on the analysis above, it was concluded that the cake structure formed in microfiltration of activated sludge suspension was asymmetric and consisted of a skin layer and a loose layer. The cake layer became looser over the distance away from the membrane surface (x). The skin layer which was relatively dense was near the membrane surface and its thickness was 20% of the total cake thickness. The porosity within this skin layer changed sharply over x. Above the skin layer, there existed a layer that is very loose. The porosity within this loose layer rarely changed over. The cake layer structure that the skin layer was below the loose layer was opposite to the asymmetric membrane structure that the selective skin layer was above the porous sublayer. For the asymmetric microporous membrane, it consisted of a selective skin layer above a porous sublayer. The selective skin layer whose thickness was 0.1–1.0 lm was relative dense, while the porous sublayer whose thickness was 100–200 lm was very loose [30]. The schematic diagram of the fouling membrane structure for microfiltration of activated sludge suspension was shown in Fig. 9. 4.9. Comparisons of model predictions and experimental results In order to further verify the obtained results (cake properties), comparisons between experimental results and model predictions were necessary. Herein, the permeate flux of the membrane was chosen as the indicator, which was due to the fact that direct measurements of local cake properties in microfiltration of activated sludge suspension was very difficult and permeate flux could be determined by obtained cake properties. The flux predictions were determined based on Eq. (26) which was derived from combining
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Fig. 8. The resistance of the skin layer (Rskin) as a function of time under different TMPs for 2.5 g/L (a), and different MLSSs for 90 kPa (b).
be served as an evidence for the validity of obtained cake properties and proposed equations.
5. Conclusions
Fig. 7. The variation of relative cake resistance with location (x/L) under different conditions. (a) 2.5 g/L, (b) 3.5 g/L and (c) 4.5 g/L.
expressions of cake solidosity, specific cake resistance and the resistance of the layer from 0 to x (Eqs. (8), (10) and (21)) with Darcy’s equation (Eq. (25)). The experimental results of flux were determined based on Eq. (29). The comparisons of model predictions and experimental results of flux at MLSS of 2.5 g/L were shown in Fig. 10. The results at other MLSSs were shown in Figs. S8 and S9 in Supplementary Material. It was found that the model predictions determined by Eq. (26) showed good agreement with experimental results under different conditions, which could
Characteristic parameters in Tiller’s power-law expressions for activated sludge were determined by fitting experimental data to the proposed equation (Eq. (20)) in microfiltration of activated sludge suspension, and then cake properties were analyzed from two aspects of time and location using conventional cake filtration theory. Furthermore, the relative cake resistance and the resistance of the skin layer were quantitatively analyzed using our proposed equations. Results showed that: (1) The proposed method to determine characteristic parameters in Tiller’s power-law expressions was not only applicable to activated sludge system, but also other similar system. (2) Cake properties varied sharply over location until the location of x/L = 0.2, while they varied slightly with time. (3) The cake layer consisted of a skin layer below a loose layer, which was opposite to the structure of the asymmetric microporous membrane. The skin layer was at the location of x/L < 0.2 and its resistance accounted for more than 70%
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Fig. 9. The schematic diagram of the fouling membrane structure for microfiltration of activated sludge suspension (MLSS = 2.5 g/L, TMP = 150 kPa, t = 40 min).
Fig. 10. Comparisons of model predictions and experimental results of flux at MLSS of 2.5 g/L.
of the cake resistance. The resistance of the skin layer increased as TMP was elevated while it decreased as MLSS was increased. (4) Good agreements between model predictions of permeate flux with experimental results under different conditions confirmed our proposed equations.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cej.2016.05.031.
References Acknowledgements The authors wish to express their sincere gratitude to National Natural Science Foundation of China (Project No. 21176006 and No. 21476006).
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