SO SÁNH CÁC GIẢI PHÁP KHÁC Sử DỤNG CƠ CHẾ CHẾ ĐỘ NHIỀU

Fluid mechanics plays an important role in pressuredriven membrane processes. This manifests itself through the convective motion of fluids and its influence on the motion of dissolved and suspended solutes. In this review, we compare impact with crossflow filtration and summarize the advantages and limitations of different membrane permeators. Then, we present results from recent theoretical studies of flow in an annulus with porous walls, and from recent experiments showing the effect of transmembrane flux on the friction coefficient of a flowing fluid inside a porous tube with suction. We also compare the porous tube with a porous twowalled slit for capturing suspended colloids. The performance of several commercial modules are compared in light of the theory. Under the assumptions of the theoretical models, and all things being equal (besides fractional recovery per unit length), tubular systems will capture more particles from dilute suspensions than slits with two porous walls. This is expected since the fractional recovery for a tube is 2.67 times that for a s

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

Review

MEMBRANE MODULES: COMPARISON OF DIFFERENT

a porous tube with suction We also compare the porous tube with a porous two-walled slit for capturing suspended colloids The performance of several commercial modules are compared in light of the theory Under the assumptions of the theoretical models, and all things being equal (besides fractional recovery per unit length), tubular systems will capture more particles from dilute suspensions than slits with two porous walls This is expected since the fractional recovery for a tube is 2.67 times that for a slit, when u,/U,,,, L/R and L/l are kept the same Finally, we also report on a recent significant extension of the lift theory for all laminar flows (even Rep 1) in which results from the previous theory (for Re G 1) hold Experimental measurements for particle trajectories in porous ducts support these developments

During the modern development of membrane separation processes, early workers recognized the intimate relationship between mass transfer and con- vective fluid flow [l-4] With the appearance of a comprehensive treatise dealing with momentum, energy, and mass transport [ 51 models of varying complexity were developed linking convective fluid flow and mass transport for pressure-driven membrane processes Although membranes have been packaged in pressure modules of various designs, in a majority the feed solution moves across the membrane in tangential flow (also called cross-flow), allow-

*Presented in part at the Summer School on Engineering Aspects of Membrane Processes, Aar- hus, Denmark, June Z-6,1986

0376-7388/88/$03.50 0 1988 Elsevier Science Publishers B.V

ing fluid to be removed laterally by suction through the duct or channel walls

It has been known for some time that the performance of a pressure-driven membrane process is related to the tangential fluid mechanics across the mem- brane surface and that the build-up of dissolved solutes (ions, macromole-

at the membrane-solution interface through an understanding of the fluid me- chanics and mass transfer [ 6-91

Until recently, very little theoretical analysis has been reported on the effect

of even dilute suspensions (colloids) on membrane performance However, during the past few years, several different groups have begun to investigate this problem using different approaches Belfort and co-workers [ 10-131, us- ing perturbation methods, have shown that inertial lift balanced against suc- tion drag is responsible for the tubular pinch effect in dilute suspensions at low Reynolds number flows Leonard and Vassilieff [ 141 have postulated a moving cake-layer and solved this problem using the method of characteristics Re- cently, Davis and Leighton [ 15,351 have invoked a “shear-induced hydrody- namic diffusion” mechanism to describe the lateral migration of particles away from the polarized cake layer Cohen and Probstein [ 161, balancing suction drag with first-order reaction, have concluded that electrochemical interac- tions can explain the existence of a threshold permeation velocity

Since mass transport to a membrane surface is dependent on the fluid flow (or non-flow) above that surface, clearly, a detailed understanding of the fluid mechanics in various ducts (slits, tubes and annuli) is a prerequisite to study- ing mass transport problems such as concentration polarization and fouling These analyses (of fluid mechanics and mass transport) are thus different for different module designs It should therefore not be surprising that when pro- cessing a similar feed solution with similar membranes in different modules at about the same volumetric through-put, radically different performance is ob- served! In this review, after comparing impact with cross-flow filtration and summarizing the advantages and limitations of different membrane permea- tors, we present some new results on laminar flow in synthetic membrane ducts

We then present an analysis of particle dynamics in Poiseuille flow in porous ducts and show how this theory can be used to compare different commercial modules

2.0 Impact versus cross-flow filtration

Membrane filtration is usually carried out by flowing the feed solution per- pendicular to the membrane (usually called impact or dead-ended filtration)

or across the membrane surface (usually called tangential or cross-flow filtra- tion) A qualitative comparison of these two modes of filtration can be made with reference to Fig 1 A non-uniform spatial permeation velocity is charac- teristic of both systems However, the spatial permeate profile is relatively easy

a 1 BATCH ( impact or dead ended 1

IFEED IN

PERMEATE

WITH MIXING

PERMEATE vw UNSTIRRED

b 1 CROSS - FLOW CONTINUOUS

MASS TRANSFER IN POROUS DUCTS WITH SUCTION

Fig 1 Different flow conditions above a membrane Feed solution flows (a) perpendicularly to- wards membrane surface, and (b) tangentially across membrane surface

to estimate for the cross-flow system and difficult for the dead-ended system More important, however, are the temporal effects Since all the feed solution minus the retained solutes passes through the membrane in the impact system, flux decline with time is usually severe

For the cross-flow system, however, wall shear, inertial lift, shear-induced diffusion, and cross-flow of the cake are all mechanisms that could reduce the build-up of foulant on the membrane surface, thereby mediating flux decline Only for very small feed volumes and for dilute solutions is impact or dead- ended filtration used Cross-flow filtration is the dominant mode of operation for most pressure-driven membrane processes (hyperfiltration, ultrafiltration and microfiltration) In order to increase wall shear and scour the membrane surface many ingenious designs have been developed such as those shown in Fig 2 Thus, increased axial flow rate ( laminar to turbulent ) , physical inserts, Taylor vorticies, roughness, and pulsating flow have been used in commercial modules

248

EFFECT ON PERFORMANCE

INCREASE MIXING TO SCOUR MEMBRANE SURFACE

o) INCREASE FLOW RATE

(Low 9, I High 9 1

b) INSERTS

c) TAYLOR VORTICES

Spin inner Tube

d) ROUGH /MOVING SURFACE

1 &Membrane

Stamped Plastic Disc e) PULSATING FLOW

Fig 2 Methods for disturbing the mass transfer boundary layer

The main requirement of a membrane permeator or module is that it house the membranes in such a way that the feed stream is sealed from the permeate stream Other requirements are concerned with the following:

1 Mechanical stability, such as supporting a fragile membrane under the op- erating differential pressures (100-1500 psi) for microfiltration, ultrafiltra- tion and hyperfiltration

2 Hydrodynamic considerations, such as minimizing concentration polari- zation, including the build-up of solute and fouling layers on or in the mem- brane surface, to impede membrane performance

3 Economic considerations, such as obtaining high membrane-packing den- sity to reduce capital costs of the pressure vessels and designing the unit for ease of membrane replacement

Commercial permeators that meet these requirements can be classified into

TABLE 1

Reverse osmosis membrane permeators

Class Designation Description of available designs Manufacture? Tubular

4a 4b 5a

Brine flow outside flexible rigid support tube

Brine flow between alternate leaves of a spiral wrap

Brine flow outside flexible hollow-fiber membranes

Brine flow inside flexible hollow-fiber membranes

Horizontal filterpress design with brine flow radially between leaves Same as 4a with whole unit spinning

A dynamic precoat membrane is laid down on a porous support Taylor vortices are used to shear the membrane

L Israel Desalination Engineering, Tel Baruch, Israel; M Kalle, West Germany; N Nitto Electric Co., Osaka, Japan; P Osmonics, Inc., Hopkins, Minnesota; Q Paterson Candy Int., Laverstoke Mills, Whit- church, Hamps, U.K.; R Raypak, Inc., Westlake Village, California; S Toray Industries, Inc., Otsu, Shiga, Japan; T Toyobo Co., Ltd., Kataka Reseach Center, Otsu, Shiga, Japan; U UOP Fluid Systems Div., San Diego, California

five broad design categories based on the membrane geometry: tubular, spiral wound (wrap), hollow fiber, flat plate, and dynamic Nearly all of these per- meators or variants thereof have been produced commercially

For example, reverse osmosis subclasses within each subcategory are de- scribed in Table 1 A sketch of each of the major commercial reverse osmosis

TABLE 2

Comparison of reverse osmosis membrane permeators

Module design Packing Water flux Salt Water output Flow channel Ease of

density at 6000 psi rejection per unit volume size cleaning ( m’/m3 ) (cm/set ) lo5 (set-‘) (cm)

a Data for spaghetti permeator obtained from Ref [ 171 The flow channel dimension can vary from zero (tubes touching) to about 0.125 in

b Two different spiral-wound designs are commercially available In the one case (UOP, CA) the per- meate spirals to the center manifold, whereas for the other design (Toray, Japan) the brine stream spirals to the center manifold Their performances are essentially equivalent

’ Data for fiber with brine flow inside obtained from Ref [ 181 Maximum internal pressure for this unit

is 28 atm (410 psi)

d Data for flat-plate design obtained from Ref [ 191

e Data for dynamic membrane design estimated from Ref [ 201

membrane permeators is shown in Fig 3 Several performance and structural characteristics for the different permeators are also presented in Table 2 The first thing to notice in Table 2 is that the permeator with the lowest water output per unit volume (tubular with inside axial feed flow) is most easily cleaned, whereas the permeator with the highest water output per unit volume (fibers with feed flow on the outside) is the most difficult to clean Ease of cleaning is especially important for a turbid feed such as wastewater

or a typical fermentation broth Permeators that offer a compromise include the fiber design with feed flow inside the bore, and the dynamic membrane concept The flow channel size, in the penultimate column in Table 2, is pre- sented as a measure of the cross-sectional area available for feed flow In a crude calculation, a large value of flow channel size should indicate little chance

of fluid hold-up due to blockage from flowtables or suspended solids A small value suggests that a high degree of prefiltering is necessary

3.1 Rigid tube

The membrane is cast as a tube on the inside of a porous support tube (e.g., paper or cloth), which is placed inside a pressure vessel The feed stream flows through the tube while the product permeates the membrane radially The pressure vessel may be a steel pipe with perforated holes (rigid design), or, if the support tube can withstand the pressure differential, a plastic or low-pres- sure housing (helical design) can collect the product Rods or spheres some- times placed inside the tube, along the center line, increase fluid velocity and axial shear at the membrane solution interface Sanderson [ 211 reports the production of a relatively inexpensive tubular vessel made from cast plastic elements held together with a rod By slightly misaligning the elements, the cast membrane tube will have protrusions desirable for fluid mixing (see Fig 2) Reynolds numbers as high as 130,000 have been used in tubular systems [ 22 ] Tubular units are easily cleaned, and many operating data exist for them Their disadvantages include low permeate rate per unit volume and high vol- ume hold-up per unit area of membrane

3.2 Spiral-wound module

Several flat or planar membranes are sandwiched between porous plastic screen supports and then formed into a “Swiss roll” The edges of the mem- branes are sealed to each other and the central perforated tube The resultant spiral-wrap module is fitted into a tubular steel pressure vessel, such as a 4-in nominal pipe The pressurized feed solution is fed into the pipe so that it flows through the plastic mesh screens along the surface of the membranes The product, which permeates the membranes, flows into the closed alternate com- partments and spirals radially toward the weep holes in the central tube, to be removed Advantages of this design include fairly high water output per unit membrane area, and vast amount of operating data

Recently, the spiral-wrap design is increasingly being used to recover pro- teins in the biotechnology field However, because of the small dimensions of the flow channel it has a danger of plugging This design is one of the leading contenders for large-scale commercial applications for bioprocessing

3.3 Hollow fiber

Several million down to a few hundred hollow fibers (100 to 200 ,um outside diameter) are bundled together in either a U-shape configuration (for feed flow on the outside) or in a straight configuration (for feed flow on the inside) The ends of the fibers are glued into a tube sheet while making sure each fiber

is not blocked Thus, for the case in which the feed flows at high pressure on the outside of the hollow fibers, the product permeates radially inward through

the unsupported fiber The product then moves inside the hollow fiber bore to the product collection chamber For the other case, where the design is similar

to a typical heat exchanger, the feed flows into the bore of the hollow fibers at one end and, after moving along the inside of the fiber, flows out of the other end of the unit The product continually permeates radially outward through the fiber walls

The shell-side feed hollow-fiber design (i.e., feed on the outside) is very compact, low in cost, has a low water hold-up and, because of the compressive strength of the small diameter fibers, can withstand fairly high differential pressures (400 psi) It unfortunately plugs easily and is very difficult to clean The inside-feed hollow-fiber design has the advantage of well-controlled hy- drodynamics of the feed; which improves the possibility of cleaning These modules can also be cleaned by backflushing or reversing the permeate flow This design has become very popular in biomedical and biochemical applications

3.4 Plate and frame

Sheet flow in narrow slits with one or two permeable walls per slit are com- mercially available in plate and frame permeators The permeate is manifolded separately from the feed stream and can be combined within or outside the module Some manufacturers have introduced multiple axial flow channels in place of sheet flows thereby increasing the average axial velocity and wall shear rate [ 231, General advantages of this design include low volume hold-up per unit membrane area (attractive for recovering valuable biologicals) and the ability to process highly viscous solutions because of the thin channel height ( 0.3-0.6 mm ) Its disadvantages include susceptibility to channel plugging and difficulties in cleaning With the new designs cartridge membrane replacement

is extremely quick and easy

3 In contrast to the reverse osmosis hollow fiber design with brine flow on the shell or outside of the fiber, the capillary or bore-side ultrafiltration hollow

Brian and coworkers [ 1,3] were early in recognizing the importance of mass transfer and frictional pressure drop in the axial direction of membrane ducts Using similarity and constant wall flux assumptions and a perturbation method in wall Reynolds number (Re,) to solve the Navier-Stokes problem, Chatterjee and Belfort [ 251 have obtained analytical (and numerical) solu- tions for steady laminar incompressible flow in an idealized spiral-wound membrane duct They use an annular idealization of the spiral-wound geom- etry and give criteria for which this assumption is reasonable Typical axial and radial velocity profiles are shown in Fig 4, while the pressure drop versus axial distance and the coordinates of the annulus are shown in Fig 5 for suction and injection

In Fig 6 we present a summary of recent experimental data for the flow of water through a porous stainless steel microfilter tube from Belfort and Nagata [ 91 The data are presented as the friction coefficient, C, versus axial Rey-

nolds number, Re, with the net average wall Reynolds number, Re,, as a pa-

CENTERLINE OF CONCENTRIC CYLINDERS

Fig 5 (a) Pressure drop versus axial distance and (b) co-ordinate system for flow in an annulus with two porous walls

rameter The experimental conditions are given in the figure legend The following observations are noteworthy: (1) with no net wall flux (Re, = 0) , Cf

is much higher for flow in a porous tube than for Poiseuille flow in a non-porous tube; (ii) transition from laminar to turbulent for flow in the porous tube is shifted to Re = 4000 from the usual value of 2100 for Poiseuille flow in a non-

porous tube; (iii) at a given Reynolds value in the laminar regime the C, value rises to a maximum at about Re,= 0.23-0.33 and drops down again as Re,

increases to Re, = 2 This maximum is not observed for turbulent flow See Fig

7

Explanations for these effects are still unclear However, we have shown that for the case of no net flow (Re,= 0 ) in a porous tube, the fluid permeates the tube and moves axially both inside and outside the tube to the downstream exit of the tube This has been called the Starling effect Reverse radial flow

meation ( Re, - - 0 ) , and (b ) porous tube with Re, > 0 (suction) The porous stainless steel tube

had the following dimensions: IL30 cm, di=1.99f0.01, d0=6.15f0.10 Nominal pore size 0.8

pm Ultrafiltered deionized water was used at 30°C (after Ref [ 91)

occurs in the last 1/5th of the tube length for Re = 30,000 A combination of

momentum loss and axial flow reversal is suspected as a cause for the laminar flow results shown in Fig 7