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Optimization model of submerged hollow fiber membrane modules
Journal of Membrane Science 234 (2004) 147–156
Optimization model of submerged hollow fiber membrane modules Seong-Hoon Yoon a,∗ , Hyung-Soo Kim b , Ik-Tae Yeom b b
a Global Research Center, Nalco Company, Naperville, IL 60563-1198, USA Department of Civil Engineering, SungKyunKwan University, Suwon 440-746, South Korea
Received 8 May 2003; received in revised form 14 January 2004; accepted 20 January 2004
Abstract A practical method to obtain optimum design parameters of vertically mounted submerged hollow fiber module was demonstrated to minimize the energy consumption for aeration. Assuming maximum allowable pressure difference in both ends of hollow fiber membrane was 5%, maximum allowable fiber length was calculated for various fluxes and fiber diameters. In case there was no limitation in fiber length, permeate throughput from unit footprint simply increased with fiber diameter. However, if there was a limitation in fiber length/water depth, optimum range of fiber length and lumen diameter existed. For one-side suction, optimum range of outer fiber diameter and fiber length were estimated to be 2.26–3.25 mm and 1.01–1.90 m, respectively, when operating flux was 20–50 l/m2 h and a ratio of lumen and outer diameter was 1:2. In the case of two-side suction, fiber length of 1.01–1.90 m and diameter of 1.34–2.05 mm were the optimum range. Finally, optimum design lines, showing the best combinations of lumen diameter and fiber length, were obtained for one-side and two-side suctions. © 2004 Elsevier B.V. All rights reserved. Keywords: Modules; Economics; Water treatment; Submerged membrane
1. Introduction Since submerged membrane concept was developed in 1980s [1], it has become one of the most competitive ways of water/wastewater treatment method due to the simplicity and resistance against membrane fouling comparing to cross-flow filtration [2,3]. In fact, hollow fiber and flat plate type submerged membranes are rapidly replacing conventional filtration processes in raw water and wastewater treatments. Especially, hollow fiber type submerged membranes are becoming more popular for large-scale water treatments because of compactness. In submerged hollow fiber membrane process, negative pressure is applied to the lumen side of fiber to obtain permeate through the porous membrane. In the mean while, air is supplied from the bottom of the module to scour outer membrane surface. Some extent of internal pressure drop will occur while permeate is flowing the fiber lumen, where pressure is the lowest at the permeate exit. The trans-membrane pressure (TMP), which is obtained from the difference between inside and outside pressure, will be the highest at the ∗ Corresponding author. Tel.: +1-630-305-1012; fax: +1-630-305-2982. E-mail address: [email protected] (S.-H. Yoon).
0376-7388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2004.01.018
exit and the lowest at the starting point of flow. Therefore local flux at the permeate exit is the highest and this will result in the most rapid membrane fouling in this area [4–7]. Once permeate exit is fouled under high flux, more water will permeate the vicinity of the fouled segment to meet constant flow and this chain reaction results in the propagation of membrane fouling to the other end of fiber. Therefore, axial pressure drop in the lumen side of fiber should be minimized for the prevention of accelerated membrane fouling by unequal filtration along the fibers. Chang and Fane [4] and Chang et al. [5] have extensively analyzed axial pressure drop in hollow fiber to derive ranges of optimum lumen diameter and fiber length. In their studies, all design parameters of submerged membrane module were optimized with the assumption of constant critical flux in order to achieve minimum suction energy. However, two arguable points could be found from the optimization processes, e.g. (1) the assumption of constant critical flux and (2) the goal of optimization that was suction energy minimization. Although critical flux above which fouling is dramatically accelerated exists in most cases, the value is not constant but variable depending on feed water conditions. For example, the extent of membrane fouling in membrane bioreactor (MBR) process is highly dependant on the biological
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condition that is variable with time [8]. Therefore module design may not be able to entirely rely on the critical flux concept. Instead, modules should be optimized for a range of standard flux with which membrane fouling is not severe for most of the operating time. Of course, the standard flux range, which is implicating critical flux concept in itself, is variable with membrane chemistry and morphology, types of feed solution, etc. In terms of the efficiency of filtration, module should be optimized to minimize scouring air rather than suction energy because aeration takes majority of energy in submerged membrane process. In vertically mounted hollow fiber membrane module, more efficient use of scouring air can be achieved with longer fibers. However, many problems are associated with long hollow fibers: (1) pressure drop in lumen side could be intolerable; (2) energy for aeration increases because of water depth; (3) if big fiber is used to reduce axial pressure drop, fiber packing density decreases; (4) uniformity of up-flow velocity on the top of the module is questionable because of coalescence of bubbles; (5) handling and maintenance problem, etc. As above, all design parameters are inter-connected and should be optimized considering all parameters together. This study aimed to elucidate the relationships among the design parameters and derive optimum ranges of fiber diameter and length that allow maximum energy efficiency.
2. Theory 2.1. Pressure drop inside a hollow fiber membrane [6] In submerged hollow fiber membrane which has closed bottom and open top, the liquid permeated from outside flows upward by the negative pressure applied to lumen side as shown in Fig. 1. While permeate is flowing toward exit, more and more permeate is added to the flow and the flow velocity is increasing along the fiber. Consequently, the rate of pressure drop also increases along the fiber. The pressure drop inside a hollow fiber can be written as Eq. (1), where multiplication of the cross-sectional area of flow channel ((π/4)Di2 ) and an increment of flow velocity (dv) in an infinitesimal block of fiber equals to the amount of water permeated in the same block (πD0 J dx). This equation can be rearranged to Eq. (1 ). π 2 D dv = πD0 J dx (1) 4 i 4D0 J dv = (1 ) dx Di2 where Di and D0 are lumen and outer diameter of hollow fiber membrane, J is the flux, v is the flow velocity inside the fiber, and x is a distance from the starting point of flow. Pressure drop in the lumen side can be described as Eq. (2) using Hagen–Poiseuille equation, where no slip on lumen
Fig. 1. Schematics of vertically mounted hollow fiber module. Left figure shows the flow in the lumen of hollow fiber and right one shows a module in water.
surface is assumed. The static pressure in lumen side is not necessary in this equation because it always matches with outside static pressure as long as whole fiber is immersed in water dp 32µv (2) =− 2 dx Di where p is the lumen side pressure. For simplicity, flux can be assumed to be proportional to TMP and written as Eq. (3) J = k(p0 − p)
(3)
where k is a permeability constant and p0 is an outside pressure of hollow fiber membrane. Here, p0 can be set to be “zero” because it is always offset by lumen side static pressure. In this study, maximum pressure difference in axial direction will be restricted to less than 5% to ensure almost equal filtration in all segments of the fiber. Therefore, all segments of fiber would be similarly fouled during the course of filtration. It was assumed that permeability constants are same for all segments of hollow fiber. Lee [9] combined above equations with several different pore-blocking theories and predicted TMP increase in the filtration of starch solution using submerged hollow fiber membranes. In his work, the model based on above equations predicts experimental results excellently in the range of experimental condition. 2.2. Evaluation of pressure difference in both ends of fibers In most of the water treatment plants, membranes are operated under constant flux mode to meet water demand [2],
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where average flux of membrane is not affected by membrane fouling status but affected by water demand. Therefore, axial pressure drop in the fiber is rarely affected by the extent of membrane fouling. As mentioned in Section 1, difference of TMP in both ends of fiber, defined as Eq. (4), should be controlled properly to reduce membrane fouling. All flux values in this equation can be replaced with pressures because flux is proportional to TMP as shown in Eq. (3) Jx=L − Jx=0 Px=L − Px=0 Df = = (4) Jx=0 Px=0
Here d is a distance between two adjacent fibers and assumed to be equal to outer fiber diameter in this study for simplicity. However, measured diameters can be used when optimization procedure is performed for real membrane fiber. The number density of membranes in the cross-section of module, N/Am , can be calculated by dividing R by cross-sectional area of one hollow fiber. Membrane packing density, aN/Am , can be obtained by the multiplication of N/Am and each fiber’s surface area, a N 2 =√ Am 3(D0 + d)2
(6)
2.3. Effect of packing density on productivity per footprint
2πD0 L aN =√ Am 3(D0 + d)2
(6 )
Packing density can be defined by total surface area of membrane per cross-sectional area of a module [4] because this value is directly proportional to the efficiency of up-flow utilization as well as membrane area per footprint. According to this definition, packing density simply increases with longer fibers. However, if longer fiber is used to increase productivity, fiber diameter should be also increased to minimize axial pressure and this affects packing density negatively. In addition, more energy is necessary for supplying scouring air to deeper position. There may exist a combination of optimum fiber diameter and length allowing maximum output per footprint. Fig. 2 shows a cross-section of the potting area in module. It was assumed that all hollow fibers are regularly spaced in the potting area and this will be helpful in preventing particle build up [10]. In this figure, all hollow fibers are potted in the three corners of regular triangles. The ratio of total cross-sectional area of membranes in potting area, R, can be calculated by dividing the total membrane cross-sectional area in a triangle by the area of a triangle
where Am is a cross-sectional area of module, L is the fiber length. In submerged hollow fiber membrane process, modules need empty spaces among fiber bundles. These empty spaces not only become the path of up-flow but also facilitate the mass transfer between the inside and outside of fiber bundles. Thus, fiber bundles take only some portion of the total footprint on which aeration is performed. The ratio of membrane potting area in the total footprint, ε, should be multiplied to consider the effect of the empty space. In this study, it was assumed that only half of the total footprint is filled with fiber bundles (ε = 0.5) and the other half of the area is used for aeration. This assumption does not affect results because packing density in unit footprint is equally reduced by the empty space for all cases
R = √
(π/8)D02 πD02 = √ 2 3(D0 + d)2 3/4 (D0 + d)2
Q 2πεD0 LJ =√ A 3(D0 + d)2
(7)
where A is the total footprint on which membrane modules are installed and aeration is performed.
(5)
Fig. 2. Schematic of the cross-section of potting area in a module. Hollow fiber membranes are assumed to be placed evenly. It is assumed that lumen diameter is half of outer diameter in this study.
2.4. Effect of module configuration on aeration efficiency There are two kinds of energy consumptions in submerged membrane process, i.e. aeration for membrane scouring and permeate suction, i.e. air scouring and permeate suction. In this calculation, only the energy for air scouring was considered not only because it consumes majority of energy during filtration but also because suction energy is hardly affected by module design when axial internal pressure drop is limited to less than 5%. The specific aeration rate, Qair /A, was assumed to be 5 m3 air/min m2 footprint considering the practical value of 3–6 m3 air/min m2 footprint in commercial plants [11]. Although the specific aeration rate is decreasing due to recent progress, this value does not affect the results because aeration intensity proportionally affects all module dimensions. The sum of Lb , Lh , and Lw shown in Fig. 1 and the total friction loss by pipeline and nozzle were assumed to be 1 m H2 O, respectively. With this assumption, total head loss in
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aeration can be calculated by adding 2 m to the fiber length, e.g. total head loss for 1.5 m fiber becomes 3.5 m. Electricity consumption was calculated using a modified equation from Wagner and Popel’s (1998) work [12]. According to this equation, power consumption, P (kW), is proportional to aeration rate, Qair (m3 /min), and 0.8 power of head loss, H (m), for a screw compressor P = 0.306Qair H 0.8
(8)
Finally the equation showing specific flow rate, Q/P, meaning flow rate per unit power (m3 permeate/s kW) was derived by dividing Eq. (7) by Eq. (8) Q πεD0 LJ = P 0.265(D0 + d)2 (Qair /A)H 0.8
(9)
2.5. Verification of flow stability in the lumen All of the equations shown above are driven with the assumption of laminar flow in the lumen. By calculating Reynolds number, this assumption should be verified. In hollow fiber membrane, Reynolds number is the highest in the exit because of the fastest flow velocity. The flow velocity in the exit can be calculated by dividing the flow rate in the exit by cross-sectional area of lumen as Eq. (10). In this study, outer fiber diameter was assumed to be twice of inner diameter. The maximum Reynolds number can be calculated using Eq. (10 ) vmzx =
πD0 LJ 8LJ = 2 Di πDi /4
Remax =
(10)
Di vmax 8LJ = ν ν
(10 )
Here ν is a kinematic viscosity of water. If the maximum Reynolds number in a fiber is less than 2300, the flow in the lumen can be assumed as laminar flow and the assumption of laminar flow in lumen can be justified. All assumptions used in this study are summarized in Table 1 and the procedures of obtaining optimum design parameter are shown in Fig. 3.
Fig. 3. Flow chart of the optimization process to obtain optimum design parameters of submerged hollow fiber module.
3. Results and discussion 3.1. Pressure profile in hollow fiber membrane According to Eq. (4), Df decreases during the course of filtration mainly because the denominator, Px=0 , increases while the numerator, Px=L − Px=0 , is almost constant. It is noticeable that Df is not constant for all TMPs but variable even in a same fiber according to TMP. Therefore, module can hardly be optimized for all operating pressure ranges but can be optimized for typical operating pressure range. A typical range of suction pressure with which membrane is operated in most of the time has been known to be 20–30 kPa in MBR process. In this study, module will be
Table 1 All assumptions used in this study Items
Assumptions/values
Etc
References
Flow condition in fiber Permeability, k
Laminar flow Same in all segments of fibers Di :D0 = 1:2 Calculated with Eq. (6) Regularly spaced Assumed D0 equals d 0.5 5 m3 air/min m2 5%
Verified with Eq. (10 ) –
– –
Can be replaced with measured values Can be replaced with measured values Being pursued to space fibers regularly Being pursued to space fibers regularly Does not affect results because it affects all parameters equally Does not affect results because it affects all parameters equally Operational parameters with which modules will be operated
Arbitrary – [10] Arbitrary [11] Arbitrary
20–50 LMH 30 kPa
Operational parameters with which modules will be operated Operational parameters with which modules will be operated
[11,13] [14]
Fiber dimension Fiber potting density Fiber spacing in module Ratio of potting area in footprint, ε Specific aeration, Qair /A Maximum allowable TMP difference in both ends of fibers, Df,max Flux TMP
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Fig. 4. Pressure profiles inside a hollow fiber membrane when average pressure in lumen side of hollow fiber is 30 kPa. L = 1 m, Di = 1 mm, D0 = 2 mm.
optimized assuming the average suction pressure in lumen is 30 kPa. The permeability constant, k, was calculated with Eq. (3) for a range of fluxes, assuming the average TMP of 30 kPa. Here, initial k is obtained according to the initial TMP of a new membrane under specified flux and then k will decrease during the course of filtration due to TMP increase. Pressure profiles in the hollow fiber membrane can be calculated using Eqs. (1)–(3). Here, the pressure drop in the potted segment was neglected because the length of potted membrane is much shorter than that of unspotted membrane. Fig. 4 shows pressure profiles for a range of fluxes in a hollow fiber membrane of which lumen diameter is 1 mm. The pressure difference in both ends of the fiber increases from 1.3 to 7.6% when flux increases from 10 to 60 LMH. 3.2. Maximum allowable fiber length Assuming maximum allowable pressure difference in both ends of fiber is 5%, maximum allowable fiber length for each lumen size can be calculated for a given flux. After repeating the calculations performed to get Fig. 4 for many different fiber lengths, diameters and fluxes, Df was calculated using Eq. (4). Finally, maximum allowable fiber lengths were obtained for each combination of flux and lumen size with which pressure difference, Df , became exactly 5%. Fig. 5 was obtained assuming outer fiber diameter was twice of the lumen diameter. According to this figure, fiber length should be shorter when standard operating flux is higher for a same fiber diameter. In other words, fiber diameter should be larger for higher standard operating flux when fiber length is fixed. One example is that the maximum allowable fiber length is 1.46 m when outer diameter is 2 mm and flux is 20 LMH.
3.3. Module design for minimum footprint As discussed in Section 3.2, longer hollow fibers are feasible with bigger fibers because of less pressure drop in the lumen. With the longer and bigger fibers, module footprint and the amount of aeration may also decrease in spite of a negative effect, i.e. lower fiber density. Other possible negative impacts of the longer fibers include uneven up-flow pattern in the top of the module and difficult maintenance/ handling. Permeate throughput per unit footprint can be calculated using Eq. (7), where total number density of fibers (N/A) is multiplied by each membrane’s surface area (2πD0 L) and flux (J). If maximum allowable fiber length, Lmax , is inserted to Eq. (7) instead of L, maximum permeate throughput from unit footprint is obtained. In this calculation, outer fiber diameter and distance between two adjacent fibers were assumed to be equal as mentioned in Section 2.3. Maximum permeate throughput from unit footprint increases with fiber diameter as shown in Fig. 6. It was turned out that the positive effect resulted by the fiber elongation was dominant over the negative effect by the reduced fiber number density for a range of parameters considered in this calculation. Therefore long fibers having big lumen diameter would be better for intensive use of footprint. 3.4. Design parameters for maximum energy efficiency In Section 3.3, module design parameters to obtain maximum throughput from unit footprint were studied. In real situation, however, membrane length can hardly be increased over certain level because of handling/maintenance problem as well as aeration cost. In this study, efficiency of aeration utilization was investigated for various fiber diameters and
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Fig. 5. Maximum allowable fiber length as functions of flux and outer fiber diameter under a constraint of 5% pressure difference in both ends of a hollow fiber. Di : D0 = 1 : 2.
lengths while membrane length was limited to 3 m. When membrane length is 3 m, scouring air is supplied to the depth of 4 m because of the spaces above and below the membrane as shown in Section 2.4. Assuming 1 m head loss in air sparger and pipeline, total maximum head loss for aeration becomes 5 m. Power efficiencies can be obtained using Eq. (9), which is a measure of permeate flow rate per unit power. The maximum allowable fiber lengths for each flux and diameter shown in Fig. 5 were inserted into Eq. (9) with a restriction of 3 m in length. If maximum fiber length was bigger than 3, 3 m was used as a fiber length.
Fig. 7 shows a flow rate per unit power as functions of flux and fiber diameter. In the figure, the higher the flux, the higher the energy efficiency. Each curve has an inflection point in the right side as well as a maximum point in the middle. The inflection point is resulted by the restriction of fiber length, i.e. 3 m. The almost flat area in each curve can be regarded as an optimum range of fiber diameter. To obtain optimum range, one dotted line was drawn horizontally from the inflection point to the left side. In the figure, the optimum range of fiber diameter is between the inflection point and the intersecting point between the horizontal line and a curve. It is
Fig. 6. Maximum output per footprint as functions of fiber diameter and flux. Maximum output is calculated with maximum allowable fiber length. Di : D0 = 1 : 2.
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Fig. 7. Effect of outer diameter of fiber on energy efficiency for some flux conditions. Di : D0 = 1 : 2.
noticeable that 2 mm fiber is always in the optimum range for all fluxes and this may suggest there is a common optimum fiber diameter for a broad range of flux. The optimum ranges of fiber diameter for each flux, which give reasonably high energy efficiency, can be extracted from the six curves in Fig. 7. Results are summarized in Fig. 8, where optimum fiber diameter is increasing with flux. In this calculation, the ratio of lumen and outer diameter was assumed to be 1:2. Now a method to design a module of which operating flux ranges from 20 to 50 LMH will be discussed. The optimum range of fiber diameter obtained from Fig. 7 can be plotted
as Fig. 9, where two curves in the graph are high and low limit of outer fiber diameter, respectively. In this figure, the upper curve is corresponding to a fiber length of 3 m because all values on this curve were collected from the inflection points. On the other hand, all of the values on the lower curve are corresponding to a fiber length of around 0.65 m. This means optimum range of fiber length is always between 0.65 and 3 m when flux is fixed to a certain value. For the first step to derive optimum design parameters for the flux of 20–50 LMH, one rectangle can be drawn between two curves as shown in Fig. 9. While this rectangle covers
Fig. 8. Outer and lumen diameter of fiber to obtain maximum energy efficiency when one-side suction is performed. Di : D0 = 1 : 2.
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Fig. 9. Optimum range of outer fiber diameter and length for the flux range of 20–50 LMH when suction is performed from one side of membrane.
largest area between the two curves, the two sides of the rectangle are located on the lines of 20 and 50 LMH. For the second step, two horizontal sides of the rectangle are extended to y-axis, where corresponding values are 1.59 and 3.25 mm as shown in Fig. 9. Then, fiber lengths corresponding to the four corners are obtained from the data in Fig. 5, considering fiber diameter and flux in the points. In Fig. 9, the optimum ranges of fiber length are 1.03–3.00 and 0.65–1.90 m for 20 and 50 LMH, respectively. Thus, the common range, which means optimum fiber length, becomes 1.03 and 1.90 m. For the last step, fiber diameters corresponding to the common range of fiber lengths will be found for the two
extreme fluxes, i.e. 20 and 50 LMH. One more dotted line that corresponds to the fiber length of 1.03 m is drawn and an intersecting point with right side of the rectangle will be found. The y-value of the intersection becomes the lower limit of fiber diameter while y-value of the upper side of the rectangle becomes higher limit. From the graph, the optimum outer fiber diameter becomes 2.16–3.25 mm when fiber length ranges between 1.03 and 1.90 m. These procedures can be repeated for two-side suction, where permeate is sucked from both ends of hollow fiber. In two-side suction, fiber length can be doubled without additional pressure drop because effective fiber length becomes half of the total length. According to Fig. 10, optimum fiber
Fig. 10. Optimum range of outer fiber diameter and length for the flux range of 20–50 LMH when suction is performed from both sides of a hollow fiber.
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Fig. 11. Optimum design lines for the hollow fiber modules operated between 20 and 50 LMH to maximize energy efficiency. Di : D0 = 1 : 2.
diameters for two-side suction are smaller than those for one-side suction shown in Fig. 8. By repeating the same procedures performed in above three paragraphs, optimum design parameters for 20–50 LMH can be obtained, i.e. fiber length of 1.01–1.90 m and diameter of 1.34–2.05 mm (law data is not shown). The optimum ranges of parameters obtained above are part of the bold lines indicating 50 LMH in Figs. 9 and 10, because these two lines represent the strictest condition in the range of flux, 20–50 LMH. Some part of a curve indicating 50 LMH in Fig. 5, which corresponds to the fiber diameter of 2.16–3.25 mm, will be the design curve for one-side suction (data for two-side suction is not shown here). Finally, optimum design lines for one-side and two-side suctions can be drawn as shown in Fig. 11. Reynolds number can be calculated using Eq. (10 ) to verify the flow stability in the lumen side. As indicated in the equation, Reynolds number is not a function of fiber diameter but a function of fiber length. When flux is 50 LMH, Reynolds number ranges from 11 to 21 depending on fiber length, which is well below 2300. Therefore, initial assumption about flow stability is confirmed and the mathematical analysis to obtain pressure drop can be justified.
(1) External pressure type submerged hollow fiber membranes suffer from internal pressure drop caused by permeate flow in the lumen side. The maximum allowable fiber length increases with fiber diameter when TMP difference between the two ends of fiber is limited to 5%. (2) If there is no limitation in water depth and energy efficiency, permeate throughput from unit footprint increases with fiber diameter. This means longer fibers, which have bigger lumens, provide better efficiency of footprint usage. (3) When maximum fiber length is limited to 3 m and one-side suction is performed, the optimum design parameters that allow reasonable energy efficiencies at 30 kPa are fiber diameter of 2.16–3.25 mm and fiber length of 1.03–1.90 m. In the case of two-side suction, where permeate is sucked from both ends of fibers, fiber length of 1.01–1.90 m and diameter of 1.34–2.05 mm were the optimum for the same flux and TMP.
Nomenclature A
4. Conclusions
Am
Optimum design parameters of vertically mounted hollow fiber membranes were calculated with some assumptions, e.g. lumen diameter is half of outer diameter, permeate flow does not slip on the lumen surface, fibers are evenly distributed on potting area, flux is proportional to transmembrane pressure, permeability is same in all segments of fibers, flux ranges between 20 and 50 LMH, etc. The conclusions drawn in this study are summarized as follows.
d Df Di D0 H J
total footprint on which aeration is performed (m2 ) cross-sectional area of a module on which fiber bundle is potted (m2 ) distance among fibers (m) pressure difference between both ends of fiber lumen diameter of fiber (m) outer diameter of fiber (m) pressure head (m) flux (m s−1 )
156
k L Lb Lh Lw LMH p P Q Qair R TMP v x
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permeability constant (kg−1 m2 s) fiber length (m) flow development area (m) thickness of header for permeate collection (m) water depth on the top of modules (m) flux unit (l/m2 h) pressure in lumen side (Pa) power for aeration (kW) total permeate flow from a module (m3 s−1 ) air flow rate (m3 min−1 ) ratio of the area occupied by membrane in the potting area of module trans-membrane pressure (kPa) flow velocity inside hollow fiber (m s−1 ) distance from dead end (m)
Greek letters ε area ratio of fiber bundle in total footprint on which aeration is performed ν kinematic viscosity of water (m−2 s)
References [1] K. Yamamoto, M. Hiasa, T. Mahmood, T. Matsuo, Direct solid– liquid separation using hollow fiber membrane in an activated sludge aeration tank, Water Sci. Technol. 21 (1989) 43–54. [2] I.-S. Chang, P. Clech, B. Jefferson, J. Simon, Membrane fouling in membrane bioreactors for wastewater treatment, J. Environ. Eng. 128 (11) (2002) 1018–1029.
[3] K.-J. Kim, S.-H. Yoon, Wastewater treatment using membrane bioreactors, J. Korean Ind. Eng. Chem. 12 (3) (2001) 239–248 (in Korean). [4] S. Chang, A. Fane, The effect of fibre diameter on filtration and flux distribution-relevance to submerged hollow fibre modules, J. Membr. Sci. 184 (2001) 221–231. [5] S. Chang, A. Fane, S. Vigneswaran, Modeling and optimizing submerged hollow fiber membrane module, AIChE Journal 48 (10) (2002) 2203–2212. [6] S.-H. Yoon, H.-S. Kim, Effect of operating flux on membrane fouling in submerged membrane filtration process, J. Korean Soc. Environ. Eng. 21 (9) (1999) 1707–1716 (in Korean). [7] K. Fujida, S. Takijawa, A simulation of pore plugging in external pressure type hollow fiber membrane and the evaluation of operational methods, J. JWWA 64 (3) (1995) 12–23 (in Japanese). [8] I.-J. Kang, Factors affecting filtration performance of submerged microfiltration membranes in a membrane coupled sequencing batch reactor, Ph.D. Dissertation, Seoul National University, Seoul, South Korea, 2002. [9] H.-M. Lee, Development of TMP variation prediction model in the submerged type hollow fiber membrane filtration, M.S. Thesis, Seoul National University, 2002. [10] I. Crossley, S. Pedersen, A. Janson, Zenon introduces a new reinforced hollow fiber membrane system, in: Proceedings of the Membrane Technology Conference, AWWA, Atlanta, GA, 2003. [11] S. Judd, Submerged membrane bioreactors: flat plate or hollow fiber? Filtr. Separat. June (2002) 30–31. [12] M. Wagner, J. Popel, Oxygen transfer and aeration efficiency— influence of diffuser submergence, diffuser density, and blower type, Water Sci. Technol. 38 (3) (1998) 1–6. [13] M. White, L. Schideman, L. Rago, Key considerations for integrating low-pressure membrane filtration into existing treatment facilities, in: Proceedings of the Membrane Technology Conference, AWWA, Atlanta, GA, 2003. [14] J. Lee, W. Ahn, C. Lee, Comparison of the filtration characteristics between attached and suspended growth microorganisms in submerged membrane bioreactor, Water Res. 35 (10) (2001) 2435– 2445.
Optimization model of submerged hollow fiber membrane modules Seong-Hoon Yoon a,∗ , Hyung-Soo Kim b , Ik-Tae Yeom b b
a Global Research Center, Nalco Company, Naperville, IL 60563-1198, USA Department of Civil Engineering, SungKyunKwan University, Suwon 440-746, South Korea
Received 8 May 2003; received in revised form 14 January 2004; accepted 20 January 2004
Abstract A practical method to obtain optimum design parameters of vertically mounted submerged hollow fiber module was demonstrated to minimize the energy consumption for aeration. Assuming maximum allowable pressure difference in both ends of hollow fiber membrane was 5%, maximum allowable fiber length was calculated for various fluxes and fiber diameters. In case there was no limitation in fiber length, permeate throughput from unit footprint simply increased with fiber diameter. However, if there was a limitation in fiber length/water depth, optimum range of fiber length and lumen diameter existed. For one-side suction, optimum range of outer fiber diameter and fiber length were estimated to be 2.26–3.25 mm and 1.01–1.90 m, respectively, when operating flux was 20–50 l/m2 h and a ratio of lumen and outer diameter was 1:2. In the case of two-side suction, fiber length of 1.01–1.90 m and diameter of 1.34–2.05 mm were the optimum range. Finally, optimum design lines, showing the best combinations of lumen diameter and fiber length, were obtained for one-side and two-side suctions. © 2004 Elsevier B.V. All rights reserved. Keywords: Modules; Economics; Water treatment; Submerged membrane
1. Introduction Since submerged membrane concept was developed in 1980s [1], it has become one of the most competitive ways of water/wastewater treatment method due to the simplicity and resistance against membrane fouling comparing to cross-flow filtration [2,3]. In fact, hollow fiber and flat plate type submerged membranes are rapidly replacing conventional filtration processes in raw water and wastewater treatments. Especially, hollow fiber type submerged membranes are becoming more popular for large-scale water treatments because of compactness. In submerged hollow fiber membrane process, negative pressure is applied to the lumen side of fiber to obtain permeate through the porous membrane. In the mean while, air is supplied from the bottom of the module to scour outer membrane surface. Some extent of internal pressure drop will occur while permeate is flowing the fiber lumen, where pressure is the lowest at the permeate exit. The trans-membrane pressure (TMP), which is obtained from the difference between inside and outside pressure, will be the highest at the ∗ Corresponding author. Tel.: +1-630-305-1012; fax: +1-630-305-2982. E-mail address: [email protected] (S.-H. Yoon).
0376-7388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2004.01.018
exit and the lowest at the starting point of flow. Therefore local flux at the permeate exit is the highest and this will result in the most rapid membrane fouling in this area [4–7]. Once permeate exit is fouled under high flux, more water will permeate the vicinity of the fouled segment to meet constant flow and this chain reaction results in the propagation of membrane fouling to the other end of fiber. Therefore, axial pressure drop in the lumen side of fiber should be minimized for the prevention of accelerated membrane fouling by unequal filtration along the fibers. Chang and Fane [4] and Chang et al. [5] have extensively analyzed axial pressure drop in hollow fiber to derive ranges of optimum lumen diameter and fiber length. In their studies, all design parameters of submerged membrane module were optimized with the assumption of constant critical flux in order to achieve minimum suction energy. However, two arguable points could be found from the optimization processes, e.g. (1) the assumption of constant critical flux and (2) the goal of optimization that was suction energy minimization. Although critical flux above which fouling is dramatically accelerated exists in most cases, the value is not constant but variable depending on feed water conditions. For example, the extent of membrane fouling in membrane bioreactor (MBR) process is highly dependant on the biological
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condition that is variable with time [8]. Therefore module design may not be able to entirely rely on the critical flux concept. Instead, modules should be optimized for a range of standard flux with which membrane fouling is not severe for most of the operating time. Of course, the standard flux range, which is implicating critical flux concept in itself, is variable with membrane chemistry and morphology, types of feed solution, etc. In terms of the efficiency of filtration, module should be optimized to minimize scouring air rather than suction energy because aeration takes majority of energy in submerged membrane process. In vertically mounted hollow fiber membrane module, more efficient use of scouring air can be achieved with longer fibers. However, many problems are associated with long hollow fibers: (1) pressure drop in lumen side could be intolerable; (2) energy for aeration increases because of water depth; (3) if big fiber is used to reduce axial pressure drop, fiber packing density decreases; (4) uniformity of up-flow velocity on the top of the module is questionable because of coalescence of bubbles; (5) handling and maintenance problem, etc. As above, all design parameters are inter-connected and should be optimized considering all parameters together. This study aimed to elucidate the relationships among the design parameters and derive optimum ranges of fiber diameter and length that allow maximum energy efficiency.
2. Theory 2.1. Pressure drop inside a hollow fiber membrane [6] In submerged hollow fiber membrane which has closed bottom and open top, the liquid permeated from outside flows upward by the negative pressure applied to lumen side as shown in Fig. 1. While permeate is flowing toward exit, more and more permeate is added to the flow and the flow velocity is increasing along the fiber. Consequently, the rate of pressure drop also increases along the fiber. The pressure drop inside a hollow fiber can be written as Eq. (1), where multiplication of the cross-sectional area of flow channel ((π/4)Di2 ) and an increment of flow velocity (dv) in an infinitesimal block of fiber equals to the amount of water permeated in the same block (πD0 J dx). This equation can be rearranged to Eq. (1 ). π 2 D dv = πD0 J dx (1) 4 i 4D0 J dv = (1 ) dx Di2 where Di and D0 are lumen and outer diameter of hollow fiber membrane, J is the flux, v is the flow velocity inside the fiber, and x is a distance from the starting point of flow. Pressure drop in the lumen side can be described as Eq. (2) using Hagen–Poiseuille equation, where no slip on lumen
Fig. 1. Schematics of vertically mounted hollow fiber module. Left figure shows the flow in the lumen of hollow fiber and right one shows a module in water.
surface is assumed. The static pressure in lumen side is not necessary in this equation because it always matches with outside static pressure as long as whole fiber is immersed in water dp 32µv (2) =− 2 dx Di where p is the lumen side pressure. For simplicity, flux can be assumed to be proportional to TMP and written as Eq. (3) J = k(p0 − p)
(3)
where k is a permeability constant and p0 is an outside pressure of hollow fiber membrane. Here, p0 can be set to be “zero” because it is always offset by lumen side static pressure. In this study, maximum pressure difference in axial direction will be restricted to less than 5% to ensure almost equal filtration in all segments of the fiber. Therefore, all segments of fiber would be similarly fouled during the course of filtration. It was assumed that permeability constants are same for all segments of hollow fiber. Lee [9] combined above equations with several different pore-blocking theories and predicted TMP increase in the filtration of starch solution using submerged hollow fiber membranes. In his work, the model based on above equations predicts experimental results excellently in the range of experimental condition. 2.2. Evaluation of pressure difference in both ends of fibers In most of the water treatment plants, membranes are operated under constant flux mode to meet water demand [2],
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where average flux of membrane is not affected by membrane fouling status but affected by water demand. Therefore, axial pressure drop in the fiber is rarely affected by the extent of membrane fouling. As mentioned in Section 1, difference of TMP in both ends of fiber, defined as Eq. (4), should be controlled properly to reduce membrane fouling. All flux values in this equation can be replaced with pressures because flux is proportional to TMP as shown in Eq. (3) Jx=L − Jx=0 Px=L − Px=0 Df = = (4) Jx=0 Px=0
Here d is a distance between two adjacent fibers and assumed to be equal to outer fiber diameter in this study for simplicity. However, measured diameters can be used when optimization procedure is performed for real membrane fiber. The number density of membranes in the cross-section of module, N/Am , can be calculated by dividing R by cross-sectional area of one hollow fiber. Membrane packing density, aN/Am , can be obtained by the multiplication of N/Am and each fiber’s surface area, a N 2 =√ Am 3(D0 + d)2
(6)
2.3. Effect of packing density on productivity per footprint
2πD0 L aN =√ Am 3(D0 + d)2
(6 )
Packing density can be defined by total surface area of membrane per cross-sectional area of a module [4] because this value is directly proportional to the efficiency of up-flow utilization as well as membrane area per footprint. According to this definition, packing density simply increases with longer fibers. However, if longer fiber is used to increase productivity, fiber diameter should be also increased to minimize axial pressure and this affects packing density negatively. In addition, more energy is necessary for supplying scouring air to deeper position. There may exist a combination of optimum fiber diameter and length allowing maximum output per footprint. Fig. 2 shows a cross-section of the potting area in module. It was assumed that all hollow fibers are regularly spaced in the potting area and this will be helpful in preventing particle build up [10]. In this figure, all hollow fibers are potted in the three corners of regular triangles. The ratio of total cross-sectional area of membranes in potting area, R, can be calculated by dividing the total membrane cross-sectional area in a triangle by the area of a triangle
where Am is a cross-sectional area of module, L is the fiber length. In submerged hollow fiber membrane process, modules need empty spaces among fiber bundles. These empty spaces not only become the path of up-flow but also facilitate the mass transfer between the inside and outside of fiber bundles. Thus, fiber bundles take only some portion of the total footprint on which aeration is performed. The ratio of membrane potting area in the total footprint, ε, should be multiplied to consider the effect of the empty space. In this study, it was assumed that only half of the total footprint is filled with fiber bundles (ε = 0.5) and the other half of the area is used for aeration. This assumption does not affect results because packing density in unit footprint is equally reduced by the empty space for all cases
R = √
(π/8)D02 πD02 = √ 2 3(D0 + d)2 3/4 (D0 + d)2
Q 2πεD0 LJ =√ A 3(D0 + d)2
(7)
where A is the total footprint on which membrane modules are installed and aeration is performed.
(5)
Fig. 2. Schematic of the cross-section of potting area in a module. Hollow fiber membranes are assumed to be placed evenly. It is assumed that lumen diameter is half of outer diameter in this study.
2.4. Effect of module configuration on aeration efficiency There are two kinds of energy consumptions in submerged membrane process, i.e. aeration for membrane scouring and permeate suction, i.e. air scouring and permeate suction. In this calculation, only the energy for air scouring was considered not only because it consumes majority of energy during filtration but also because suction energy is hardly affected by module design when axial internal pressure drop is limited to less than 5%. The specific aeration rate, Qair /A, was assumed to be 5 m3 air/min m2 footprint considering the practical value of 3–6 m3 air/min m2 footprint in commercial plants [11]. Although the specific aeration rate is decreasing due to recent progress, this value does not affect the results because aeration intensity proportionally affects all module dimensions. The sum of Lb , Lh , and Lw shown in Fig. 1 and the total friction loss by pipeline and nozzle were assumed to be 1 m H2 O, respectively. With this assumption, total head loss in
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aeration can be calculated by adding 2 m to the fiber length, e.g. total head loss for 1.5 m fiber becomes 3.5 m. Electricity consumption was calculated using a modified equation from Wagner and Popel’s (1998) work [12]. According to this equation, power consumption, P (kW), is proportional to aeration rate, Qair (m3 /min), and 0.8 power of head loss, H (m), for a screw compressor P = 0.306Qair H 0.8
(8)
Finally the equation showing specific flow rate, Q/P, meaning flow rate per unit power (m3 permeate/s kW) was derived by dividing Eq. (7) by Eq. (8) Q πεD0 LJ = P 0.265(D0 + d)2 (Qair /A)H 0.8
(9)
2.5. Verification of flow stability in the lumen All of the equations shown above are driven with the assumption of laminar flow in the lumen. By calculating Reynolds number, this assumption should be verified. In hollow fiber membrane, Reynolds number is the highest in the exit because of the fastest flow velocity. The flow velocity in the exit can be calculated by dividing the flow rate in the exit by cross-sectional area of lumen as Eq. (10). In this study, outer fiber diameter was assumed to be twice of inner diameter. The maximum Reynolds number can be calculated using Eq. (10 ) vmzx =
πD0 LJ 8LJ = 2 Di πDi /4
Remax =
(10)
Di vmax 8LJ = ν ν
(10 )
Here ν is a kinematic viscosity of water. If the maximum Reynolds number in a fiber is less than 2300, the flow in the lumen can be assumed as laminar flow and the assumption of laminar flow in lumen can be justified. All assumptions used in this study are summarized in Table 1 and the procedures of obtaining optimum design parameter are shown in Fig. 3.
Fig. 3. Flow chart of the optimization process to obtain optimum design parameters of submerged hollow fiber module.
3. Results and discussion 3.1. Pressure profile in hollow fiber membrane According to Eq. (4), Df decreases during the course of filtration mainly because the denominator, Px=0 , increases while the numerator, Px=L − Px=0 , is almost constant. It is noticeable that Df is not constant for all TMPs but variable even in a same fiber according to TMP. Therefore, module can hardly be optimized for all operating pressure ranges but can be optimized for typical operating pressure range. A typical range of suction pressure with which membrane is operated in most of the time has been known to be 20–30 kPa in MBR process. In this study, module will be
Table 1 All assumptions used in this study Items
Assumptions/values
Etc
References
Flow condition in fiber Permeability, k
Laminar flow Same in all segments of fibers Di :D0 = 1:2 Calculated with Eq. (6) Regularly spaced Assumed D0 equals d 0.5 5 m3 air/min m2 5%
Verified with Eq. (10 ) –
– –
Can be replaced with measured values Can be replaced with measured values Being pursued to space fibers regularly Being pursued to space fibers regularly Does not affect results because it affects all parameters equally Does not affect results because it affects all parameters equally Operational parameters with which modules will be operated
Arbitrary – [10] Arbitrary [11] Arbitrary
20–50 LMH 30 kPa
Operational parameters with which modules will be operated Operational parameters with which modules will be operated
[11,13] [14]
Fiber dimension Fiber potting density Fiber spacing in module Ratio of potting area in footprint, ε Specific aeration, Qair /A Maximum allowable TMP difference in both ends of fibers, Df,max Flux TMP
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Fig. 4. Pressure profiles inside a hollow fiber membrane when average pressure in lumen side of hollow fiber is 30 kPa. L = 1 m, Di = 1 mm, D0 = 2 mm.
optimized assuming the average suction pressure in lumen is 30 kPa. The permeability constant, k, was calculated with Eq. (3) for a range of fluxes, assuming the average TMP of 30 kPa. Here, initial k is obtained according to the initial TMP of a new membrane under specified flux and then k will decrease during the course of filtration due to TMP increase. Pressure profiles in the hollow fiber membrane can be calculated using Eqs. (1)–(3). Here, the pressure drop in the potted segment was neglected because the length of potted membrane is much shorter than that of unspotted membrane. Fig. 4 shows pressure profiles for a range of fluxes in a hollow fiber membrane of which lumen diameter is 1 mm. The pressure difference in both ends of the fiber increases from 1.3 to 7.6% when flux increases from 10 to 60 LMH. 3.2. Maximum allowable fiber length Assuming maximum allowable pressure difference in both ends of fiber is 5%, maximum allowable fiber length for each lumen size can be calculated for a given flux. After repeating the calculations performed to get Fig. 4 for many different fiber lengths, diameters and fluxes, Df was calculated using Eq. (4). Finally, maximum allowable fiber lengths were obtained for each combination of flux and lumen size with which pressure difference, Df , became exactly 5%. Fig. 5 was obtained assuming outer fiber diameter was twice of the lumen diameter. According to this figure, fiber length should be shorter when standard operating flux is higher for a same fiber diameter. In other words, fiber diameter should be larger for higher standard operating flux when fiber length is fixed. One example is that the maximum allowable fiber length is 1.46 m when outer diameter is 2 mm and flux is 20 LMH.
3.3. Module design for minimum footprint As discussed in Section 3.2, longer hollow fibers are feasible with bigger fibers because of less pressure drop in the lumen. With the longer and bigger fibers, module footprint and the amount of aeration may also decrease in spite of a negative effect, i.e. lower fiber density. Other possible negative impacts of the longer fibers include uneven up-flow pattern in the top of the module and difficult maintenance/ handling. Permeate throughput per unit footprint can be calculated using Eq. (7), where total number density of fibers (N/A) is multiplied by each membrane’s surface area (2πD0 L) and flux (J). If maximum allowable fiber length, Lmax , is inserted to Eq. (7) instead of L, maximum permeate throughput from unit footprint is obtained. In this calculation, outer fiber diameter and distance between two adjacent fibers were assumed to be equal as mentioned in Section 2.3. Maximum permeate throughput from unit footprint increases with fiber diameter as shown in Fig. 6. It was turned out that the positive effect resulted by the fiber elongation was dominant over the negative effect by the reduced fiber number density for a range of parameters considered in this calculation. Therefore long fibers having big lumen diameter would be better for intensive use of footprint. 3.4. Design parameters for maximum energy efficiency In Section 3.3, module design parameters to obtain maximum throughput from unit footprint were studied. In real situation, however, membrane length can hardly be increased over certain level because of handling/maintenance problem as well as aeration cost. In this study, efficiency of aeration utilization was investigated for various fiber diameters and
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Fig. 5. Maximum allowable fiber length as functions of flux and outer fiber diameter under a constraint of 5% pressure difference in both ends of a hollow fiber. Di : D0 = 1 : 2.
lengths while membrane length was limited to 3 m. When membrane length is 3 m, scouring air is supplied to the depth of 4 m because of the spaces above and below the membrane as shown in Section 2.4. Assuming 1 m head loss in air sparger and pipeline, total maximum head loss for aeration becomes 5 m. Power efficiencies can be obtained using Eq. (9), which is a measure of permeate flow rate per unit power. The maximum allowable fiber lengths for each flux and diameter shown in Fig. 5 were inserted into Eq. (9) with a restriction of 3 m in length. If maximum fiber length was bigger than 3, 3 m was used as a fiber length.
Fig. 7 shows a flow rate per unit power as functions of flux and fiber diameter. In the figure, the higher the flux, the higher the energy efficiency. Each curve has an inflection point in the right side as well as a maximum point in the middle. The inflection point is resulted by the restriction of fiber length, i.e. 3 m. The almost flat area in each curve can be regarded as an optimum range of fiber diameter. To obtain optimum range, one dotted line was drawn horizontally from the inflection point to the left side. In the figure, the optimum range of fiber diameter is between the inflection point and the intersecting point between the horizontal line and a curve. It is
Fig. 6. Maximum output per footprint as functions of fiber diameter and flux. Maximum output is calculated with maximum allowable fiber length. Di : D0 = 1 : 2.
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Fig. 7. Effect of outer diameter of fiber on energy efficiency for some flux conditions. Di : D0 = 1 : 2.
noticeable that 2 mm fiber is always in the optimum range for all fluxes and this may suggest there is a common optimum fiber diameter for a broad range of flux. The optimum ranges of fiber diameter for each flux, which give reasonably high energy efficiency, can be extracted from the six curves in Fig. 7. Results are summarized in Fig. 8, where optimum fiber diameter is increasing with flux. In this calculation, the ratio of lumen and outer diameter was assumed to be 1:2. Now a method to design a module of which operating flux ranges from 20 to 50 LMH will be discussed. The optimum range of fiber diameter obtained from Fig. 7 can be plotted
as Fig. 9, where two curves in the graph are high and low limit of outer fiber diameter, respectively. In this figure, the upper curve is corresponding to a fiber length of 3 m because all values on this curve were collected from the inflection points. On the other hand, all of the values on the lower curve are corresponding to a fiber length of around 0.65 m. This means optimum range of fiber length is always between 0.65 and 3 m when flux is fixed to a certain value. For the first step to derive optimum design parameters for the flux of 20–50 LMH, one rectangle can be drawn between two curves as shown in Fig. 9. While this rectangle covers
Fig. 8. Outer and lumen diameter of fiber to obtain maximum energy efficiency when one-side suction is performed. Di : D0 = 1 : 2.
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Fig. 9. Optimum range of outer fiber diameter and length for the flux range of 20–50 LMH when suction is performed from one side of membrane.
largest area between the two curves, the two sides of the rectangle are located on the lines of 20 and 50 LMH. For the second step, two horizontal sides of the rectangle are extended to y-axis, where corresponding values are 1.59 and 3.25 mm as shown in Fig. 9. Then, fiber lengths corresponding to the four corners are obtained from the data in Fig. 5, considering fiber diameter and flux in the points. In Fig. 9, the optimum ranges of fiber length are 1.03–3.00 and 0.65–1.90 m for 20 and 50 LMH, respectively. Thus, the common range, which means optimum fiber length, becomes 1.03 and 1.90 m. For the last step, fiber diameters corresponding to the common range of fiber lengths will be found for the two
extreme fluxes, i.e. 20 and 50 LMH. One more dotted line that corresponds to the fiber length of 1.03 m is drawn and an intersecting point with right side of the rectangle will be found. The y-value of the intersection becomes the lower limit of fiber diameter while y-value of the upper side of the rectangle becomes higher limit. From the graph, the optimum outer fiber diameter becomes 2.16–3.25 mm when fiber length ranges between 1.03 and 1.90 m. These procedures can be repeated for two-side suction, where permeate is sucked from both ends of hollow fiber. In two-side suction, fiber length can be doubled without additional pressure drop because effective fiber length becomes half of the total length. According to Fig. 10, optimum fiber
Fig. 10. Optimum range of outer fiber diameter and length for the flux range of 20–50 LMH when suction is performed from both sides of a hollow fiber.
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Fig. 11. Optimum design lines for the hollow fiber modules operated between 20 and 50 LMH to maximize energy efficiency. Di : D0 = 1 : 2.
diameters for two-side suction are smaller than those for one-side suction shown in Fig. 8. By repeating the same procedures performed in above three paragraphs, optimum design parameters for 20–50 LMH can be obtained, i.e. fiber length of 1.01–1.90 m and diameter of 1.34–2.05 mm (law data is not shown). The optimum ranges of parameters obtained above are part of the bold lines indicating 50 LMH in Figs. 9 and 10, because these two lines represent the strictest condition in the range of flux, 20–50 LMH. Some part of a curve indicating 50 LMH in Fig. 5, which corresponds to the fiber diameter of 2.16–3.25 mm, will be the design curve for one-side suction (data for two-side suction is not shown here). Finally, optimum design lines for one-side and two-side suctions can be drawn as shown in Fig. 11. Reynolds number can be calculated using Eq. (10 ) to verify the flow stability in the lumen side. As indicated in the equation, Reynolds number is not a function of fiber diameter but a function of fiber length. When flux is 50 LMH, Reynolds number ranges from 11 to 21 depending on fiber length, which is well below 2300. Therefore, initial assumption about flow stability is confirmed and the mathematical analysis to obtain pressure drop can be justified.
(1) External pressure type submerged hollow fiber membranes suffer from internal pressure drop caused by permeate flow in the lumen side. The maximum allowable fiber length increases with fiber diameter when TMP difference between the two ends of fiber is limited to 5%. (2) If there is no limitation in water depth and energy efficiency, permeate throughput from unit footprint increases with fiber diameter. This means longer fibers, which have bigger lumens, provide better efficiency of footprint usage. (3) When maximum fiber length is limited to 3 m and one-side suction is performed, the optimum design parameters that allow reasonable energy efficiencies at 30 kPa are fiber diameter of 2.16–3.25 mm and fiber length of 1.03–1.90 m. In the case of two-side suction, where permeate is sucked from both ends of fibers, fiber length of 1.01–1.90 m and diameter of 1.34–2.05 mm were the optimum for the same flux and TMP.
Nomenclature A
4. Conclusions
Am
Optimum design parameters of vertically mounted hollow fiber membranes were calculated with some assumptions, e.g. lumen diameter is half of outer diameter, permeate flow does not slip on the lumen surface, fibers are evenly distributed on potting area, flux is proportional to transmembrane pressure, permeability is same in all segments of fibers, flux ranges between 20 and 50 LMH, etc. The conclusions drawn in this study are summarized as follows.
d Df Di D0 H J
total footprint on which aeration is performed (m2 ) cross-sectional area of a module on which fiber bundle is potted (m2 ) distance among fibers (m) pressure difference between both ends of fiber lumen diameter of fiber (m) outer diameter of fiber (m) pressure head (m) flux (m s−1 )
156
k L Lb Lh Lw LMH p P Q Qair R TMP v x
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permeability constant (kg−1 m2 s) fiber length (m) flow development area (m) thickness of header for permeate collection (m) water depth on the top of modules (m) flux unit (l/m2 h) pressure in lumen side (Pa) power for aeration (kW) total permeate flow from a module (m3 s−1 ) air flow rate (m3 min−1 ) ratio of the area occupied by membrane in the potting area of module trans-membrane pressure (kPa) flow velocity inside hollow fiber (m s−1 ) distance from dead end (m)
Greek letters ε area ratio of fiber bundle in total footprint on which aeration is performed ν kinematic viscosity of water (m−2 s)
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[3] K.-J. Kim, S.-H. Yoon, Wastewater treatment using membrane bioreactors, J. Korean Ind. Eng. Chem. 12 (3) (2001) 239–248 (in Korean). [4] S. Chang, A. Fane, The effect of fibre diameter on filtration and flux distribution-relevance to submerged hollow fibre modules, J. Membr. Sci. 184 (2001) 221–231. [5] S. Chang, A. Fane, S. Vigneswaran, Modeling and optimizing submerged hollow fiber membrane module, AIChE Journal 48 (10) (2002) 2203–2212. [6] S.-H. Yoon, H.-S. Kim, Effect of operating flux on membrane fouling in submerged membrane filtration process, J. Korean Soc. Environ. Eng. 21 (9) (1999) 1707–1716 (in Korean). [7] K. Fujida, S. Takijawa, A simulation of pore plugging in external pressure type hollow fiber membrane and the evaluation of operational methods, J. JWWA 64 (3) (1995) 12–23 (in Japanese). [8] I.-J. Kang, Factors affecting filtration performance of submerged microfiltration membranes in a membrane coupled sequencing batch reactor, Ph.D. Dissertation, Seoul National University, Seoul, South Korea, 2002. [9] H.-M. Lee, Development of TMP variation prediction model in the submerged type hollow fiber membrane filtration, M.S. Thesis, Seoul National University, 2002. [10] I. Crossley, S. Pedersen, A. Janson, Zenon introduces a new reinforced hollow fiber membrane system, in: Proceedings of the Membrane Technology Conference, AWWA, Atlanta, GA, 2003. [11] S. Judd, Submerged membrane bioreactors: flat plate or hollow fiber? Filtr. Separat. June (2002) 30–31. [12] M. Wagner, J. Popel, Oxygen transfer and aeration efficiency— influence of diffuser submergence, diffuser density, and blower type, Water Sci. Technol. 38 (3) (1998) 1–6. [13] M. White, L. Schideman, L. Rago, Key considerations for integrating low-pressure membrane filtration into existing treatment facilities, in: Proceedings of the Membrane Technology Conference, AWWA, Atlanta, GA, 2003. [14] J. Lee, W. Ahn, C. Lee, Comparison of the filtration characteristics between attached and suspended growth microorganisms in submerged membrane bioreactor, Water Res. 35 (10) (2001) 2435– 2445.