Scale-up Design of a Spacer-Filled Disk-Type Membrane ... · Keywords: Membrane module, Membrane bioreactor, CFD, Spacer-filled disk, Wastewater treatment 1.0 INTRODUCTION Flat-sheet

* Corresponding to: [email protected]

Scale-up Design of a Spacer-Filled Disk-Type Membrane Module Using CFD

Yu-Ling Li, Kuo-Lun Tung*

R&D Center for Membrane Technology and Dept. of Chemical Engineering Chung Yuan University, Chung-Li, Taoyuan 320, Taiwan

ABSTRACT The scale-up design of a spacer-filled disk-type membrane module has been conducted by using computational flu-id dynamic (CFD) technique. A three-dimensional CFD technique was used to analyze fluid flow in the membrane module, permeate flux, permeate volumetric flow rate and the distribution of permeation rates on the membrane surfaces. The numerical results showed that there were variations in the volumetric flow rate and permeation rates with different membrane module sizes. As radius ratio of the collection tube to radius of the spacer-filled disk-type membrane module was smaller than 0.162, a series of membrane module could be considered instead of large membrane module sizes based on the same total membrane areas. Microscopic understanding derived from the CFD analysis can improve the design of collection tubes, spacer thicknesses and membrane module sizes to en-hance module performance and assist the construction of new designs. Keywords: Membrane module, Membrane bioreactor, CFD, Spacer-filled disk, Wastewater treatment

1.0 INTRODUCTION Flat-sheet membranes and tubular membranes are fabricated in several membrane modules. Plate and frame, rotating disk, spiral-wound configurations, annular-gap dynamic mem-brane modules and pleated membrane car-tridges are made with flat-sheet membranes; tubular, capillary and hollow-fiber geometries are made with tubular-membrane modules. Hence, membrane modules are chosen based on various treated targets. Computational flu-id dynamics (CFD) has been widely used to understand the hydrodynamic behavior of membrane processes, including membrane modules (Schwinge et al., 2004; Ghidossi et al., 2006a). Therefore, the optimum design of

membrane modules is an important topic when using the CFD technology.

A schematic drawing of a plate-and-frame module is described in Figure 1. Two mem-brane and feed spacers are placed in a sand-wich with their feed sides facing each other. Flat and frame membrane modules were one of the earliest types of membrane modules and were widely used in the separation process. It has been also used widely in a membrane bioreactor system. The optimiza-tion of the flat sheet module design and oper-ating conditions despond on the geometry (membrane plate spacing) and aeration inten-sity (bubble size) was obtained from the ex-perimental and CFD investigations results (Drews et al., 2010). The two-phase flow in a submerged flat sheet membrane module sys-tem was identified as the most effective flow profiles for fouling mitigation by using a gas-liquid two-phase CFD model (Ndinisa et al., 2006).

Journal of Water Sustainability, Volume 1, Issue 1, June 2011, 59–74 © University of Technology Sydney & Xi’an University of Architecture and Technology

DELL

打字机文本

DOI: 10.11912/jws.1.1.59-74

Y. L. Li, K. L. Tung / Journal of Water Sustainability 1 (2011) 59-74

60

Permeate Permeate

Membrane

Membrane

Spacer

Figure 1 A schematic drawing of a plate-and-frame membrane module.

Spiral wound modules are constructed by using two flat membranes placing together with their active sides facing away from each other as shown in Figure 2. They are sepa-rated by a sheet of permeate collection ma-terial. Another feed channel spacer is placed on either side of the envelope. Then, this whole assembly is rolled around in a perfo-rated center tube in a spiral or “jelly-roll” as-sembly. The feed solution is then pumped in from one side along the tube. The permeate and the concentrate drained from the other side. Substantial literature describes the com-plex structure of the spiral-wound membrane module (Li et al., 2002; Schwinge et al., 2004). Li and Tung (2008a) pointed that the appropriate cell types and periodic boundary conditions have been suggested based on the three-dimensional CFD analysis of spac-er-filled membrane module designs with var-ious spacer arrangements. Li and Tung (2008b) noted that the curvature of a spacer-filled channel affected the flow field in spir-

al-wound membrane modules. They also found that the shear stress at the inner wall was greater than that at the outer wall in a curved, spacer-filled channel by using a two-dimensional numerical scheme. The par-ticulate deposition on the membrane surface in a spacer-filled channel was investigated by a CFD technique (Li et al., 2006). In addition, Li et al. (2009) showed that a three-dimensional CFD technique and an ex-perimental setup with a curved channel filled with a two-layer-filament spacer were used to understand the fluid flow in the channel. A spacer with unequal filament diameters be-tween the inner layer and outer layers was adopted owing to mitigating the curvature ef-fect of the spacer-filled channel in a spir-al-wound membrane module. This type of spacer could be considered to reduce the im-balance in shear stress between the inner and outer walls so as to extend the life of a mem-brane module.

Tubular modules are usually made with ce-


61

ramic membranes. The skin layer is cast from the tubular supporter of stainless steel or ce-ramic (Figure 3 (a)) and the channels of a monolith (Figure 3 (b)). Several configura-tions by changing parameters, including the diameter, membrane geometry and the form of the channels (cylindrical, square-section, triangular, hexagonal, etc.), were studied by with CFD to efficiently increase the area of the membrane unit containing the ceramic membranes (Ghidossi et al., 2010).

The hollow-fiber module has been widely used in separation processes. A schematic drawing of a hollow-fiber module is depicted in Figure 4. Base on different operation con-ditions, there are two kinds of hollow-fiber modules: “Inside-out (Tube-side feed)” (Fig-ure 4 (a).) and “Outside-In (Shell-side feed)” (Figure 4 (b).). Controlling production quanti-ties, mitigating fouling and clogging pheno-mena depended on selecting a suitable oper-ating pressure and fiber locations within the module. The hydraulic-path variation within the connection box for the hollow-fiber mod-ule was caused by the geometry of the per-meate outlet (Glucina et al., 2009). The

CFD results found vortex zones at the side where is opposite to the feed inlet. Owing to the increasing recirculation velocity in these vortex zones, the risk of clogging should be reduced. Ghidossi et al. (2006b) determined the degree of clogged hollow fibers and esti-mated modular energy consumption by using a CFD technique to calculate the pressure drop with adjustments to the inlet velocities, inlet pressures, internal diameters and per-meabilities of the hollow fibers. However, lit-tle emphasis has been placed on studying the membrane module size and its effect on the performance of a membrane module.

In this study, a spacer-filled disk-type membrane module was optimized by consi-dering the collection-tube size, spacer thick-ness and membrane module sizes. Fluid flow in the membrane module and permeate flux, permeate volumetric flow rate and the distri-bution of permeation rates on the membrane surfaces were analyzed by a three-dimensional CFD technique. The pur-pose was to obtain the optimum conditions and configurations to yield a module design with maximum performance.

Figure 2 A schematic drawing of a spiral-wound membrane module (Li et al., 2006).


62

Feed

Retentate

Permeate

(a) stainless steel or ceramic supporter

(b) monolith supporte

Figure 3 A schematic drawing of a tubular membrane module.


63

(a) Inside-out or Tube-side feed.

(b) Outside-in or shell-side feed.

Figure 4 A schematic drawing of a hollow fiber membrane module.

2.0 THEORETICAL STUDY 2.1 The Simulated System Two membrane layers, one spacer layer and a collection tube were established in the spac-er-filled disk-type membrane module, as shown in Figure 5 (a). The membrane struc-ture contained a skin layer and a support layer. The selective skin layer was a laminated po-lyacrylonitrile (PAN) nanofiber membrane with an average pore size of approximately 0.27 μm. A nonwoven polyethylene tereph-thalate (PET) fabric was regarded as the sup-port layer. This geometry configuration was symmetrical, as shown in Figure 5 (b). Faces ABHG, BCIH, JKED, KLFE and CILF were defined as symmetrical planes. Faces GHKJ,

ABED and BCFE were set as the walls. Faces ADJG and HKLI were regarded as the pres-sure inlet and outlet boundaries, respectively. In addition, Zones AGJDEBHK and BCIHKLFE were the membrane layer and spacer layer individually. In order to minimize the large computational time, this simplified system would be adopted. The geometric pa-rameters of the spacer-filled disk-type mem-brane module (i.e., membrane radius, mem-brane thickness, collection-tube radius and spacer thickness) used in this study are listed in Table 1. The body-fitted structure grids were used for the CFD analysis in this study. The computational grids with 81,000–237,500 cells for the different cases were used as shown in Figure 5 (c).


64

Cross sectional view

SymmetrySymmetry

Top view

Spacer

Collection tube

(a)

(b)

(c)

Figure 5 Schematic diagrams of the spacer-filled disk-type membrane module: (a) construc-tion, (b) simulated system and (c) computational grids.


65

Table 1 The geometric parameters of the spacer-filled disk-type membrane module.

Parameter Value (mm)

Disk-type membrane radius (R) 092.5, 185.0, 277.5

Membrane thickness (hm) 0.2

Collection-tube radius (Rtube) 05, 10, 15, 20, 25, 30 (R = 092.5) 10, 20, 30, 40, 50, 60 (R = 185.0) 15, 30, 45, 60, 75, 90 (R = 277.5)

Spacer thickness (hsp) 0.50, 0.75, 1.00, 1.50

2.2 Governing Equations and Numerical

Calculations The simulation model was assumed to be at steady state and isothermal; the wall was as-sumed to have a no-slip boundary condition. The flow field was analyzed by solving the continuity equation and the momen-tum-balance equations of the system. The go-verning equations for the steady-state fluid flow in the spacer-filled disk-type membrane module are the continuity and momentum equations, i.e.:

(I) Continuity Equation 0=∇u (1)

(II) Momentum Equation

upDtDu 2∇+−∇= μρ (2)

The membrane-permeation effect was in-vestigated to study the fluid flow through the membrane module. The transmembrane pres-sure (TMP) gradient across the membrane was regarded as the driving force, and the permeate flux J was defined by Darcy’s equa-tion as follows:

)(TMP

cm RRμJ

+= (3)

where Rm is the resistance of the clean mem-brane. Because a single phase was used in this study, the resistance of the cake, Rc, would be neglected. In addition, the resistance of the spacer was also neglected since its val-ue was far smaller than that of membrane. The SIMPLEC (semi-implicit method for pres-

sure-linked equations, consistent) algorithm and the QUICK differencing scheme with the velocity and pressure components were used to analyze the flow field. Water was regarded as the fluid in this simulation study. The sum of the normalized residuals of all variables converged to 1 × 10-4. The flow field in the membrane module was calculated by using the commercially available CFD software FLUENT®. 3.0 RESULTS AND DISCUSSION Three spacer-filled disk-type membrane mod-ule sizes (R = 92.5, 185 and 277.5 mm), six values of the collection-tube size (R* = 0.054, 0.108, 0.162, 0.216, 0.27 and 0.324) and four spacer thicknesses (hsp = 0.50, 0.75, 1.00 and 1.50 mm) were chosen in the analysis. Based on the simulation results obtained from the module, the effects of the collection-tube size, spacer thickness, membrane module sizes on the permeate flux, permeate volumetric flow rate, permeation-rate distributions and dimen-sionless permeation rate are discussed com-prehensively in the following sections. 3.1 The Effect of Membrane Module Con-

figurations on the Performance of The Membrane Module

In order to obtain the Rm value in advance for this simulation work, it would be estimated from a preliminary dead-end filtration expe-riment (Tung et al., 2010). According to the


66

flux and TMP values using Eq. (3), the Rm values were obtained. In addition, the flux was calculated by CFD with the experimental Rm value. Figure 6 describes that the CFD si-mulation data agreed well with the experi-

mental results. It also confirmed the validity of the simulation assumptions. Hence, the Rm value of 2.0 × 1010 1/m was used to calculate the flow field in this work at a TMP values of 1.0 bar.

TMP (bar)0.5 1.0 1.5 2.0 2.5

J . 1

03 (m3 / m

2 . s)

4.0

5.0

6.0

7.0

8.0CFDExp. data

Figure 6 The pure-water flux at various TMP values

Rtube (mm)0 8 16 24 32

J . 1

05 (m3 / m

2 . s)

350

375

400

425

450

Q (m

3 / day

)

18

19

20

21

22

Figure 7 The effect of collection-tube size on the permeate flux and permeate volumetric flow

rate for pure-water at a TMP of 1.0 bar and an hsp of 0.75 mm.


67

The simulated system of the spacer-filled disk-type membrane module is indicated in Figure 5 (b). The effect of six values of the collection-tube size on the permeate flux and permeate volumetric flow rate at a TMP of 1.0 bar and a spacer thicknesses of 0.75 mm is shown in Figure 7. As the collection-tube size increased, the permeate flux also increased. There was an apparent increase in the per-meate flux when increasing the tube size up to 15 mm. Only slight flux increased when the size of the collection-tube was more than 15mm.

One spacer-filled channel and two mem-brane layers on each side were fabricated in the disk-type membrane module. Because of different collection-tube sizes and spacer thicknesses, the filtration area and the total collection volume differed among the mod-ules. In addition to the permeate flux, the permeate volumetric flow rate should be con-sidered owing to the difference in the filtra-tion area and spacer thickness. Figure 7 illu-strates the effect of collection-tube size on the permeate volumetric flow rate at a TMP of

1.0 bar and a spacer thickness of 0.75 mm. There was a maximum value for the permeate volumetric flow rate with a collection-tube size of 15 mm. As the collection-tube size in-creased, the permeate flux would be enhanced; however, the filtration area decreased. Con-sequently, the permeate volumetric flow rate decreased after a sharp increase in the smaller collection-tube sizes.

Four spacer thicknesses ranging from 0.5 mm to 1.5 mm were simulated in this study. The effect of the spacer thicknesses on the permeate flux and permeate volumetric flow rate at a TMP of 1.0 bar and a collection-tube size of 15 mm is shown in Figure 8. As the spacer thickness was increased, the permeate flux and the permeate volumetric flow rate also increased. However, the cost of pumping power and spacer thickness should be consi-dered. The pumping power and spacer cost are increased as the spacer thickness is in-creased. Therefore, the last resort for improv-ing the performance of a spacer-filled disk-type membrane module should be in-creasing the spacer thickness.

hsp (mm)0.0 0.5 1.0 1.5 2.0

J . 1

05 (m3 / m

2 . s)

350

375

400

425

450

Q (m

3 / day

)

20

21

22

23

24

Figure 8 The effect of spacer thickness on the permeate flux and permeate volumetric flow

rate for pure-water at a TMP of 1.0 bar and an Rtube of 15 mm.


68

3.2 The Effect of Membrane Module Sizes on the Performance of The Membrane Module

Many membrane module sizes depended on various requirements; three values of membrane module size were considered in Table 1. Table 2 shows the effect of membrane module sizes with the permeate volumetric flow rate and different spacer thicknesses. As the spacer-filled disk-type membrane module sizes (R) increased to 185.0 and 277.5 mm, the membrane area would be enhanced to fourfold and ninefold membrane areas based on the R value of 92.5

mm individually. As the membrane areas increased, the permeable volumetric flow rate would be enhanced. However, the permeable volumetric flow rate would not rise to fourfold and ninefold quantity even with an increase of spacer thicknesses. With the same spacer thickness, the relationship between membrane areas and Qi / Q1 would be closed to the straight line if the collection-tube size increased as shown in Figure 9. As the line was not straight, a series of membrane module could be considered rather than large membrane module sizes based on the same total membrane areas.

Table 2 The permeate volumetric flow rate at various spacer thicknesses and membrane

module sizes.

hsp (mm) R (mm) Q (m3/Day)

0.50 092.5 017.19 ~ 021.11 185.0 045.97 ~ 076.10 277.5 074.25 ~ 155.00

0.75 092.5 019.80 ~ 021.89 185.0 059.92 ~ 081.70 277.5 103.90 ~ 172.22

1.00 092.5 021.04 ~ 022.19 185.0 068.90 ~ 084.31 277.5 125.84 ~ 180.72

1.50 092.5 022.10 ~ 022.58 185.0 078.75 ~ 087.19 277.5 154.14 ~ 189.39

In addition to the pure water flux, the dis-

tribution of permeation rates on the membrane was estimated for the performance of the spacer-filled disk-type membrane module. Effects of the collection-tube sizes and mem-brane module size on the distribution of the permeation rates on the membrane at an hsp of 0.75 mm and a TMP of 1.0 bar are shown in Figure 10. The permeation rates ranged from 2.00 × 10-3 to 5.00 × 10-3 m/s and are shown

here in color-contoured deciles. The ratius radio of the collection tube to radius of the spacer-filled disk-type membrane module was defined as:

RRR tube* = (4)

There was a wide distribution of permea-tion rates; the lowest permeation rate was at an R* of 0.054; especially for an R of 277.5


69

mm (Figure 10 (c)). The distribution of the permeation rates on the membrane was not uniform. The widest range of permeation rates (2.30 × 10-3 – 5.00 × 10-3 m/s) on the mem-brane was at an R’ of 0.054 and an R of 277.5 mm (Figure 10 (c)). The narrowest range of permeation rates (4.70 × 10-3 – 5.00 × 10-3 m/s; a single color contour) on the membrane were at cases of Figs. 10 (d), (g), (j), (m), (n), (p), (q). Therefore, the distribution of the permea-tion rates on the membrane was non uniform and was improved by increasing the collec-tion-tube size. In addition, the distribution of the permeation rates on the membrane was more deteriorated by enhancing the mem-brane module size. In order to quantify the variation of the per-meation rates, the dimensionless radius and the dimensionless permeation rate, ξ and ζ, respectively, were defined as:

tube

tube

RRRr

−−

=ξ (5)

maxuu

=ζ (6)

Here, a ξ value close to 1 reveals a position near the exterior of the membrane module,

and a ξ value close to 0 is a position near the collection tube. Figure 11 shows the effect of the dimensionless radius on the dimensionless permeation rate at an hsp of 0.75 mm and a TMP of 1.0 bar with various collection-tube sizes and membrane module sizes. The ζ val-ue would decrease as the ξ value increased. The ζ value kept a constant value at a ξ value of 0.5 to 1.0. In other words, the variation of the permeation rates was not evident in this range. In addition, the variation of permeation rate is greater at lower ζ values. The highest permeation rate occurred near the collection tube because the suction force was enhanced when the distance from the collection tube was reduced. The variation of the permeation rates would be more obvious with the en-hancement of membrane module sizes rather than collection-tube sizes. However, the ζ value was maintained at 0.8 when the R* val-ue was larger than 0.162; even if an R of 277.5 mm. Therefore, a series of membrane module could be considered rather than large membrane module sizes based on the same total membrane areas as the R* value was smaller than 0.162.

A (m2)0.00 0.13 0.26 0.39 0.52

Qi /

Q92

.5 (-

)

0

3

6

9

12

Figure 9 The relationship between membrane areas and Qi / Q92.5 at a TMP of 1.0 bar.


70

Figure 10 The effect of membrane module size with various collection-tube sizes on the per-meation rate at a TMP of 1.0 bar and an hsp of 0.75 mm

R* = 0.054 R* = 0.108

(a) Rtube = 5 mm, R = 92.5 mm

(d) Rtube = 10 mm, R = 92.5 mm

(b) Rtube = 10 mm, R = 185 mm

(e) Rtube = 20 mm, R = 185 mm

(c) Rtube = 15 mm, R = 277.5 mm

(f) Rtube = 30 mm, R = 277.5 mm


71

Figure 10 Continued

R* = 0.162 R* = 0.216

(g) Rtube = 15 mm, R = 92.5 mm

(j) Rtube = 20 mm, R = 92.5 mm

(h) Rtube = 30 mm, R = 185 mm

(k) Rtube = 40 mm, R = 185 mm

(i) Rtube = 45 mm, R = 277.5 mm

(l) Rtube = 60 mm, R = 277.5 mm


72

R* = 0.270 R* = 0.324

(m) Rtube = 25 mm, R = 92.5 mm

(p) Rtube = 30 mm, R = 92.5 mm

(n) Rtube = 50 mm, R = 185 mm

(q) Rtube = 60 mm, R = 185 mm

(o) Rtube = 75 mm, R = 277.5 mm

(r) Rtube = 90 mm, R = 277.5 mm

Figure 10 Continued


73

ξ (-)0.00 0.25 0.50 0.75 1.00

ζ (-

)

0.2

0.4

0.6

0.8

1.0

Figure 11 The effect of the dimensionless radius on the dimensionless permeation rate at a TMP of 1.0 bar and an hsp of 0.75 mm with various membrane module sizes and R*.

4.0 CONCLUSIONS Effects of varying membrane module confi-gurations and sizes on the fluid flow through a spacer-filled disk-type membrane module were analyzed by the CFD technique. Various structural configurations and module sizes including R* values, spacer thicknesses and membrane module sizes were modeled in this study. The numerical results of the permeate flux, the permeate volumetric flow rate, the distribution of permeation rates and the varia-tion of permeation rates showed that varia-tions in the structural configuration and membrane module size caused inherent changes in the hydrodynamic behavior. The enhancement of permeate volumetric flow rate could use a series of membrane modules rather than increasing membrane module sizes as the R* value was smaller than 0.162. The

study also showed that the CFD tool could enhance the performance of a membrane module and promoted new module designs.

ACKNOWLEDGEMENTS

We thank the Center-of-Excellence (COE) Program on Membrane Technology with the Ministry of Education (MOE), R.O.C., the Taiwan Textile Research Institute project, and the National Science Council (NSC) for their financial support.

NOMENCLATURE

J permeate flux, m3/m2day p pressure, Pa Q permeate volumetric flow rate,

m3/day Qi permeate volumetric flow rate based


74

on an R of i mm, with i∈ (92.5, 185.0 and 277.5)

Q92.5 permeate volumetric flow rate based on an R of 92.5 mm.

r radial position of the disk-type mem-brane module, mm

R radius of the spacer-filled disk-type membrane module, mm

Rc resistance of the cake, 1/m Rm resistance of the clean membrane,

1/m Rtube radius of the collection tube, mm R* the ratio of Rtube to R t time, s u permeation rate, m/s umax maximum permeation rate, m/s Greek letters ζ dimensionless permeation rate ξ dimensionless radius ρ fluid density, kg/m3 μ fluid viscosity, kg/m-s

REFERENCES

Drews A., Prieske H., Meyer E.-L., Senger G.

and Kraume M. (2010). Advantageous and detrimental effects of air sparging in membrane filtration: Bubble movement, exerted shear and particle classification. Desalination, 250, 1083-1086.

Ghidossi R., Veyret D. and Moulin P. (2006a). Computational fluid dynamics applied to membranes: State of the art and opportunities. Chem. Eng. Process., 45, 437-454.

Ghidossi R., Daurelle J.V., Veyret D. and Moulin P. (2006b). Simplified CFD approach of a hollow fiber ultrafiltration system. Chem. Eng. J., 123, 117-125.

Ghidossi R., Carretier E., Veyret D., Dhalerd D. and Moulinb P. (2010). Optimizing the compacity of ceramic membranes. J. Membr. Sci., 360, 483-492.

Glucina K., Derekx Q., Langlais C. and Laine J.-M. (2009). Use of advanced CFD tool to characterize hydrodynamic of

commercial UF membrane module. Desalination Water Treat., 9, 253-258.

Li F., Meindersma W., de Haan A.B. and Reith T. (2002). Optimization of commercial net spacers in spiral wound membrane modules, J. Membr. Sci., 208 (1-2), 289-302.

Li Y.L., Chang T.H., Wu C.Y., Chuang C.J. and Tung K.L. (2006). CFD analysis of particle deposition in the spacer-filled membrane module. J. Water Supply Res. Technol.-Aqua, 55 (7-8), 589-601.

Li Y.L. and Tung K.L. (2008a). CFD simulation of fluid flow through spacer-filled membrane module: selecting suitable cell types for periodic boundary conditions. Desalination, 233, 351–358.

Li Y.L. and Tung K.L. (2008b). The effect of curvature of a spacer-filled channel on fluid flow in spiral-wound membrane modules, J. Membr. Sci., 319 (1-2), 286-297.

Li Y.L., Tung K.L., Lu M.Y. and Huang S.H. (2009). Mitigating the curvature effect of the spacer-filled channel in a spiral-wound membrane module. J. Membr. Sci., 329 (1-2) , 106-118.

Ndinisa N.V., Fane A.G., Wiley D.E. and Fletcher D.F. (2006). Fouling control in a submerged flat sheet membrane system: Part II-Two-phase flow vharacterization and CFD simulations. Sep. Sci. Technol., 41 (7), 1411-1445.

Schwinge J., Neal P.R., Wiley D.E., Fletcher D.F. and Fane A.G. (2004). Spiral wound modules and spacers. Review and analysis. J. Membr. Sci., 242, 129-153.

Tung K.L., Li Y.L., Wang S.J., Nanda D., Hu C.C., Li C.L., Lai J.Y. and Huang J. (2010) Performance and effects of polymeric membranes on the dead-end microfiltration of protein solution during filtration cycles. J. Membr. Sci., 352 (1-2), 143-152.

Documents

Scale-up Design of a Spacer-Filled Disk-Type Membrane ... · Keywords: Membrane module, Membrane bioreactor, CFD, Spacer-filled disk, Wastewater treatment 1.0 INTRODUCTION Flat-sheet