Modeling of Cross-Flow Filtration Processes in an Airlift Ceramic

The model was tested by the ultrafiltration of T2000 dextran at different gas flow rates with an external-loop airlift ceramic membrane reactor. The m...
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Ind. Eng. Chem. Res. 2009, 48, 10637–10642

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Modeling of Cross-Flow Filtration Processes in an Airlift Ceramic Membrane Reactor Feng Zhang, Wenheng Jing, and Weihong Xing* State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing UniVersity of Technology, Nanjing 210009, China

Air sparging is recognized as an effective way to overcome concentration polarization in membrane filtration processes. The mechanism of flux enhancement in the case of slug flow in tubular ceramic membrane is discussed in this Article. The region near the gas slug is divided into three different zones: gas slug zone, wake zone, and remaining liquid slug zone. Air sparging significantly increases shear stress and flow instabilities, and consequently lowers concentration polarization for the gas slug zone and the wake zone. A novel model based on hydrodynamics of air-liquid two-phase flow is developed to predicting permeate flux in such processes. The dimensionless groups of filtrate resistance number and shear stress number are used to analyze the cake resistance induced by the concentration polarization, and, from these, the average permeate flux for air sparged ultrafiltration can be calculated. The model was tested by the ultrafiltration of T2000 dextran at different gas flow rates with an external-loop airlift ceramic membrane reactor. The model is validated with experimental data with an error of 10%. Experimental results show that air sparging can enhance the permeate flux significantly. Introduction Cross-flow ultrafiltration plays an important role in many industrial separation processes, especially in the food and biochemical industries for concentration, purification, and separation of macromolecules from solutions.1,2 The principal limitation for the wider application of this technique lies in the flux decline associated with fouling and concentration polarization on the membrane surface. The performance of these systems can be improved by promoting turbulence on the membrane surface, thus increasing the wall shear stress.3-6 The formation of gas-liquid two-phase cross-flow on the membrane surface by air sparging has been shown to reduce concentration polarization and fouling in ultrafiltration.7-9 Several mechanisms for this enhancement have been identified, including bubbleinduced secondary flow, physical displacement of the mass transfer, reduction in membrane fouling, increase in superficial cross-flow velocity, and pressure pulsing caused by slugs for different membrane geometry. For hollow-fiber membrane systems, high shear stresses10 and physical displacement of the mass-transfer boundary layer11 were thought to be the main reasons for flux improvement. However, it was postulated that for tubular membranes, the bubble-induced secondary flow12 played a major role in the enhancement of ultrafiltration by creating local velocity and pressure fluctuations related to intermittency. It is now necessary to understand which hydrodynamic parameters are responsible for the flux enhancement. The hydrodynamics of gas-liquid two-phase flow has been characterized by Collins and Bendiksen13,14 for tubes of large diameter. Cabassud and Schwartz15,16 studied the characterization of gas-liquid two-phase flow inside capillaries. Yet very few studies are available on gas-liquid two-phase flow inside the multichannel of the tubular membrane. The aim of this Article is to characterize some relevant hydrodynamic parameters, such as liquid circulation velocity, length of gas and liquid slugs, and wall shear stress, and to * To whom correspondence should be addressed. Tel.: +86-2583172288. Fax: +86-25-83172292. E-mail: [email protected].

identify their effect on steady permeate flux in the case of slug flow in the multichannel of the ceramic membrane. A novel model describing the relationships of the gas velocities, hydrodynamics of gas-liquid two-phase flow, and permeate flux is developed. The flux prediction model is based on dividing the membrane surface area into different zones depending on the hydrodynamics in the vicinity of the membrane.17 Simulation results with respect to flux performance will be presented in comparison to the experimental data. Experimental Section The Membrane Equipment. The experimental setup, similar to that described elsewhere,18 is shown in Figure 1. Different from the traditional riser in the external loop reactors, tubular ceramic membrane module is a part of the new riser. The reactor was made from a transparent plastic column for ease of visual observation. A 6 L plastic vessel was placed above the downflow region as a holding tank. Four liters of feed T2000 dextran solution was charged into this vessel, leaving an empty space to act as a gas-liquid separator. The cross-section ratio of the membrane and the reactor is 3:10. A transparent tube was vertically parallel to the membrane to allow direct observation of the flow pattern inside the membrane. Experiments were carried out using a 19-channel tubular zirconia membrane with 0.05 µm mean pore size and a length of 0.5 m. The inner diameter of each channel was 0.004 m. The filtering area was 0.11 m2. The membrane was cleaned with 1% NaClO solution for 30 min after each experiment, followed by thorough rinsing with distilled water. Operations. Experiments were conducted under different superficial gas velocities from 0.07 to 0.63 m/s. The temperature was maintained at room temperature (25 ( 3 °C). All filtration experiments were carried out for a minimum time period of 120 min so as to allow the permeate flux to reach a steady state. All experiments were carried out repeatedly, and all of the reported results proved to be reproducible. The liquid slug length and gas slug were determined by visualization using a SONY video camera for different gas and

10.1021/ie900512g CCC: $40.75  2009 American Chemical Society Published on Web 10/02/2009

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Figure 1. Schematic of the airlift ceramic membrane bioreactor system.

liquid superficial velocities. For each gas velocity, about 100 gas slugs and 100 liquid slugs were measured. Theory Gas-Liquid Two-Phase Flow in the Channel of Ceramic Membrane. Gas-liquid two-phase flow in a vertical direction can be classified into three flow regimes: bubbles flow, slugs flow, and annular flow. The transition from one type of flow to another is linked to the air injection ratio εr defined as: UG εr ) UG + ULm QG UG ) Am

(1)

(2)

where UG and ULm are the superficial air and liquid velocities based on membrane cross-section, QG is the gas flow rate, and Am is the cross-sectional area of the membrane. Inside the ceramic membrane channel, the injection ratio is always between 0.15 and 0.8. Consequently, Taylor bubbles are formed inside the channel of ceramic membrane. The spaces between consecutive gas slugs are made up of liquid slugs; the liquid slugs do not contain any small dispersed bubbles. The gas slug is cylindrical and surrounded by a thin liquid film. It is assumed that a liquid slug is made up of two regions: a turbulent wake region following the gas slug and the remaining liquid slug region. Liquid Circulation Velocity. For Newtonian fluids and nonNewtonian media, the energy balance over an airlift loop may be written19 as E i ) E R + ED + EB + ET + EF

(3)

where Ei is the energy input due to isothermal gas expansion, ED is the energy dissipation due to stagnant gas in the downcomer, ER is the energy dissipation due to wakes behind

bubbles in the riser, and EB and ET are the energy dissipation due to fluid turn around at the bottom and the top of the reactor. ED, ER, and (EB + ET) are given, respectively, by the following equations:19 ED ) FLghDULdAdεd

(4)

ER ) Ei - FLghDULrArεr

(5)

[

()

KT Ar 2 1 1 3 Ar + K EB + ET ) FLULr B 2 Ad (1 - ε )2 (1 - εr)2 d

]

(6)

The gas-liquid two phases are almost completely separated at the top of the reactor, and gas hold-up in the downcomer is often less than 1%, which leads to εd ) 0. EF is the energy loss due to friction in the riser, the downcomer, and the channel of membrane; wall friction loss in the multichannel tubular ceramic membrane channel is much larger than wall friction losses in the downcomer and the other part of the riser. EF ) ∆PLrULrAr + ∆PLdULdAd + ∆PLmULmAm

(7)

Furthermore, the continuity equation for the liquid flow between the riser and the downcomer can be written as ULrAr ) ULdAd ) ULmAm

(8)

Substitution of eqs 4-8 into eq 3 gives: KT 1 3 Ar[ + Ei ) Ei - FLghDULrArεr + FLULr 2 (1 - εr)2 Ar 2 KB ] + ULrAr(∆PLr + ∆PLd + ∆PLm) Ad

()

(9)

For external loop devices, KT ) KB ) 5.19 The energy loss due to friction in the riser, downcomer sections, and in multichannel

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tubular ceramic membrane may be related by means of the Fanning equation in the following form: 1 h ∆P ) f FU2L 2 D



(1 - εr)2

(17)

Nf )

µRcU ∆P

(18)

(11)

1 τ ) fFLU2 8

0.3164 for turbulent flow Re0.25

(12)

The plot of the resistance number against the shear stress number leads to straight lines:22

() Ar Ad

2

2ghDεr hr Ar 2 hd Ar 2 hm + fr + fd + fm Dr Ad Dd Am Dm (13)

()

( )

where ULr is the superficial liquid velocity in the riser. Equation 13 is our general equation for liquid velocity prediction in airlift membrane reactors. Flux Prediction. For the purpose of modeling, a gas slug zone, a wake zone, and a remaining liquid slug zone can be considered as one unit; the ceramic module is considered to be composed of a train of such units moving along the length of the membrane. The permeate flux can be expressed by the resistance-in-series model as: J)

∆P µ(Rm + Rp + Rc)

(14)

where ∆P is the transmembrane pressure, µ is the viscosity of filtrate, Rm is the intrinsic membrane resistance, Rp is the pore blocking resistance, and Rc is cake resistance induced by the concentration polarization of microspheres. Experimentally,20 Rm and Rp can be determined from the value of flux. First, pure water flux (J1) was determined using a clean membrane. Rm can be calculated with eq 15: Rm )

∆P µJ1

(15)

The determination of the pore blocking resistance is based on conditions where the cake layer has effectively been removed. The total resistance was measured after intensive surface cleaning with sponge balls, and the membrane that was rinsed with pure water measured afterward was J2. Rp can be calculated with eq 16: Rp )

∆P - Rm µJ2

(19)

Nf ) a + bNs

ULr )

+ KB

FLU2 ∆P

FLU2 is linked to the shear stress τ against the membrane wall by the following relationship:

Equation 9 can be written in terms of ULr explicitly:

KT

Ns )

64 for laminar flow Re

f) f)

dimensionless groups, the shear stress number (Ns) and filtration resistance number (Nf), are defined as follows:

(10)

where f is the friction factor, which depends on the Reynolds number in the considered phase, h is the length of friction region, D is the diameter of friction region, F is density of the liquid, and UL is the superficial liquid velocity. The friction factor is then obtained by one of the following relationships:

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(16)

It was found that air sparging cannot reduce Rp for all of the filtration experiments. Rc is assumed to be a function of the liquid density FL and the liquid velocity U near the membrane. According to the analysis of flux behavior by the dimensionless groups,21 two

(20)

where a is the intercept with the Nf-axis and b is the gradient of the straight line. By substitution of eq 20 into eq 14, the permeate flux in these three different zones can be calculated: Jgs )

Jlr )

∆PUgs τgs a∆P + µ(Rm + Rp)Ugs + 8b f ∆PUr τr a∆P + µ(Rm + Rp)Ur + 8b f ∆PUlw

Jlw )

a∆P + µ(Rm + Rp)Ulw + 8b

τlw f

(21)

(22)

(23)

where Ugs, Ur, and Ulw are the liquid velocity near the wall in the gas slug zone, remaining liquid slug zone, and wake zone. Using eqs 21-23, the values of Jgs, Jr, and Jlw can be determined. From eq 24, the average permeate flux for gas sparged ultrafiltration can be calculated. Jave ) [LgsJgs + LrJr + LlwJlw]/(Lgs + Lls)

(24)

The model was tested by the ultrafiltration of dextran T2000 solution in an external-loop airlift ceramic membrane reactor at different gas flow rates. Results and Discussion Liquid Circulation Velocity (ULr). Liquid circulation velocity is an important hydrodynamic design parameter of an airlift membrane reactor, and it has an important influence on shear stress. To correlate the experimental data on liquid circulation, the approach proposed by Chisti et al.19 was chosen. However, wall friction loss in the multichannel tubular ceramic membrane channel is much larger than wall friction losses in the downcomer and the other part of the riser. The liquid velocities calculated with our model were shown in Figure 2. The model was validated with experimental data with an error less than 10%. The model will be essential for designing suitable operational strategies and process designs for the external-loop airlift membrane reactor. Effects of Gas Superficial Velocities on Gas and Liquid Slug Lengths (Lgs, Lls). Inside the ceramic membrane channel, the injection ratio is always between 0.15 and 0.8. Consequently,

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Lls 1 ) 62.8 dt (ReEo)0.39

Figure 2. Influence of superficial gas velocity on superficial liquid velocity.

Effects of Superficial Gas Velocity on Wake of the Slugs (Llw, Reδ). Research on bubble dynamics in fluidized beds23 and enhanced heat transfer24 indicated that the wake following a bubble can be divided into two parts, a primary wake zone and a remaining liquid slug zone. To achieve most enhancement with minimum gas flow rate, the gap between two adjacent bubbles should just be the size of the primary wake. The length of the wake is theoretically estimated using the empirical relationship given by Campos and Guedes de Carvalho25 for a two-phase flow in tubes. The dimensionless wake length, Llw/dt, increased with Reδ: L1w ) 0.3 + 0.014 × Reδ dt Reδ )

Figure 3. Influence of superficial gas velocity on gas and liquid slug lengths.

(UB - UG)dt 4υ

Figure 5. Lls/dt versus 1/ReEo.

Two empirical correlations (eqs 25 and 26) were presented to find dimensionless numbers providing a good description of these lengths. It should be pointed out that our experimental data indicate an agreement with the S. Laborie correlation.15 Lgs Re0.97 ) 0.0074 1.94 dt Eo

(27)

(28)

where Reδ is the Reynolds number in the film flowing around the bubble. The wake is closed and axisymmetric with internal recirculatory flow when Reδ < 50. The wake is closed and unaxisymmetric with internal recirculatory flow when 50 < Reδ < 90. The wake is open and perfectly mixed when Reδ > 90. The length of the wake increased when UG increased (see Table 1). The flow pattern in the wake was transit from transitional flow to turbulent flow when UG increased from 0.056 to 0.464 m/s. Wall Shear Stress (τ). To characterize the slug flow in the channel of ceramic membrane, the wall shear stresses have been calculated. Figure 6 shows the shear stresses under different gas flow rates in the gas slug zone, the wake zone, and the remaining liquid slug zone with eq 19. The results of shear stress calculations for gas-sparged ultrafiltration indicate that the highest shear stress can be expected in the gas slug zone. The

Figure 4. Lgs/dt versus Re/Eo2.

Taylor bubbles are formed inside the channel of ceramic membrane. The spaces between consecutive gas slugs are made up of liquid slugs; the liquid slugs do not contain any small dispersed bubbles. Figure 3 shows the influence of gas superficial velocity on gas and liquid slug lengths. Gas slug length Lgs increased when UG increased, and Lgs is a linear function of UG when UG is less than 0.49 m/s. Liquid slug length Lls decreased when UG increased. Figure 4 plots log(Lgs/dt) versus log(Re/Eo2), and Figure 5 plots log(Lls/dt) versus log(1/ReEo).

(26)

(25) Figure 6. Influence of superficial gas velocity on wall shear stress.

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The model was validated with experimental data with an error of 10%. Conclusion

Figure 7. Resistance number against shear stress number at different crossflow velocities.

Air sparging has shown its efficiency to improve flux in the case of slug flow in tubular ceramic membrane. Shear stress created by slug flow scours the membrane surface to alleviate concentration polarization for the wake region and the slug region, and this would result in an increase in the average permeate flux. Increasing gas velocity also results in an increase in the permeate flux due to an increase in the length of tubular membrane under the influence of turbulence. Hydrodynamics of slug flow in multichannel tubular ceramic membrane was characterized. The membrane surface area is divided into three zones depending on the hydrodynamic regime in the vicinity of the membrane. Liquid circulation velocities, lengths of the three zones, and shear stresses have been calculated. From this, the average permeate flux for air-sparged ultrafiltration can be predicted. There is reasonably good agreement between theoretically predicted data and experimental data obtained by the air-water two-phase cross-flow ultrafiltration experiments using the multichannel tubular membranes. Acknowledgment

Figure 8. Effect of superficial gas velocity on permeate flux (∆P ) 0.04 MPa, C ) 2 g/L). Table 1. Effects of Superficial Gas Velocity on Reδ, Llw UG (m/s)

UB (m/s)

Reδ

Llw (mm)

0.056 0.116 0.232 0.348 0.464

0.137 0.209 0.348 0.488 0.627

68 78 97 116 136

5.0 5.5 6.6 7.7 8.8

Nomenclature

Taylor bubble moves faster than the liquid slug ahead of itself. Thus, the liquid flow induces two alternate shear stresses near the membrane wall: τgas is generated by the liquid film near the gas slugs, and τliq is generated by the liquid slugs. Comparison with Experimental Data. Figure 7 shows the plot of the resistance number against the shear stress number at different liquid velocities for one-phase cross-flow operation. A linear relationship was found between the parameters Nf and Ns. It can be written as: Nf ) (-4.95 × 105) × Ns + (1.18 × 105)

This work is supported by the key program of the National Natural Science Foundation of China (20636020), National Basic Research Program of China (2009CB623403), the National 863 Plans Projects of China (No. 2006AA03Z534), China Postdoctoral Science Foundation (No. 20060400927), and Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0601023B).

(29)

A negative slope and an intersection with the Ns-axis mean that gas sparging can eliminate the cake resistance induced by the concentration polarization of microspheres. Figure 8 shows the steady flux of simulation with eq 24 and experiment results under different gas flow rates. The changing pattern of flux versus UG can be divided into two regions, an increasing flux region and a plateau region. τgs increased greatly, but τr and τlw increased slowly with the increase of UG in the increasing flux region. According to eq 29, the increase of τ would help to eliminate the cake resistance induced by the concentration polarization. Jgs would increase greatly, but Jlw and Jr increased slowly with the increase of UG. Lqs and Llw also increased when UG increased. Based on these conclusions, Jave would increase with the increase of UG. However, Rc was smaller than Rm when the shear stress was larger than 25 Pa. In the plateau region, τgs was larger than 26 Pa when UG was larger than 0.464 m/s. The increase of τgs had less effect on Rc, so the increase in UG would not lead to the increase of Jgs.

Ar ) cross-sectional area (riser) Ad ) cross-sectional area (downcomer) Am ) cross-sectional area (membrane) dt ) inner diameter of tubular membrane Ei ) energy input to reactor EB ) energy loss in bottom of reactor ED ) energy dissipation in downcomer EF ) energy loss due to friction ER ) energy dissipation in riser Eo ) Eo¨tvo¨s number ET ) energy loss in headspace of reactor f ) friction factor Jave ) average permeate flux g ) acceleration due to gravity hd ) height of the downcomer hm ) height of the membrane hr ) height of the remaining part of the riser hD ) gas-liquid dispersion height KB ) frictional loss coefficient for the bottom of reactor KT ) frictional loss coefficient for the top of reactor L ) length of membrane Lgs ) length of gas slug Lr ) length of remaining liquid slug zone Lls ) length of liquid slug Llw ) length of wake in the liquid slug Nf ) resistance number, dimensionless Ns ) shear stress number, dimensionless ∆P ) trans-membrane pressure ∆PLd ) frictional pressure drop in the downcomer ∆PLm ) frictional pressure drop in the membrane

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∆PLr ) frictional pressure drop in the remaining part of the riser U ) liquid velocity near the wall UB ) slug bubble velocity UG ) superficial gas velocity (based on membrane cross-section) ULm ) superficial liquid velocity (based on membrane cross-section) ULr ) superficial liquid velocity (based on riser cross-section) Ugs ) liquid velocity near the wall in gas slug zone Ur ) liquid velocity near the wall in the remaining liquid slug zone Ulw ) liquid velocity near the wall in the wake zone εr ) voidage fraction in the riser εd ) voidage fraction in the downcomer Rp ) pore blocking resistance Rc ) cake resistance Rm ) membrane resistance FL ) liquid density Re ) Reynolds number in the liquid slug Reδ ) Reynolds number in the film flowing around the bubble ν ) kinematic viscosity τ ) shear stress µ ) dynamic viscosity

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ReceiVed for reView March 30, 2009 ReVised manuscript receiVed July 23, 2009 Accepted September 24, 2009 IE900512G