Novel Membrane Module for Permeate Flux Augmentation and

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Novel Membrane Module for Permeate Flux Augmentation and Process Intensification Jogender Singh, Vaibhav Srivastava, and K.D.P. Nigam* Chemical Engineering Department, Indian Institute of Technology, Hauz Khas New Delhi 110016, India ABSTRACT: The present study offers a novel coiled flow inverter (CFI) membrane module for higher permeate flux without consuming extra material or energy compared to helical coil membrane module. The proposed CFI membrane module is fabricated by bending of helical coil at 90° with equal arm lengths before and after the bend. The mass transfer and shear stress in CFI membrane module are also compared with straight tube module in addition to the helical coiled membrane module for two different gas−liquid contact systems, viz., oxygenation and carbonation. The Sherwood number increases by 10−20% for oxygenation and up to 26% for carbonation process in CFI membrane module as compared to helical coil membrane module, under identical process conditions. The mass transfer in CFI membrane module is augmented because of the reduced radial gradient caused by intensified radial flow due to the complete flow inversion. The CFI membrane module offers 3.5- to 5.5-fold enhancement in Sherwood number. The number of merits of CFI module has been observed up to 2.5 for oxygenation and 2.7 for carbonation process, as compared to that of the straight tube module. The literature data on different helical coil membrane modules have been revisited over a wide range of design parameters, and an empirical correlation is proposed for Sherwood number.

1. INTRODUCTION The design and operation of membrane modules have been of great interest to researchers for improved permeate flux and reduced membrane fouling. A number of methods, either geometry perturbation or modifying flow conditions, have been tried to overcome the problems with the conventional membranes, viz., flooding, loading, and foaming. Some of these methods are pulsation, Taylor vortices, introducing roughness, Dean vortices, and air sparging.1−6 Kumar and Nigam7 have discussed the different mass transfer enhancement techniques. Each of the mass transfer enhancement technique has own advantages as well as disadvantages, for example, introducing roughness inside the membrane can be significantly effective for breaking concentration polarization. However, introducing roughness inside the membrane is difficult from the geometrical design point of view. Coiled tubes have vast applications in industry because of their compactness, enhanced mixing, and high heat and mass transfer coefficients due to Dean vortices. Several authors8−15 have carried out different studies to understand the hydrodynamic phenomena in curved tubes after the pioneer work of Dean. Membrane-based gas−liquid contactors have gas and liquid on opposite sides of the membrane. The gas gets dissolved in liquid after diffusing through membrane. These processes are attracting the attention of researchers because of their wide range of applications. Hollow fiber membrane modules based gas removal techniques provide several advantages over conventional techniques such as packed bed and bubble column. These modules offer high surface area per unit of contact volume, independent control of gas and liquid flow, and eliminate the problems such as flooding, © XXXX American Chemical Society

loading, weeping, and entrainment. Moreover, it is also easy to scale up or down. A significant savings can be achieved in terms of pressure drop because the major driving force is concentration difference. The saving in terms of material, cost and operational simplicity makes hollow fiber membrane modules a better choice for applications in offshore oil platforms. Esato and Eiseman16 were probably the first to use the microporous membrane for gas−liquid contacting. They have used polytetrafluoroethylene (PTFE) for oxygenation of blood. Removal of CO2 has been a major issue for a long time because of several factors such as membrane material and ideal solvent. Qi and Cussler17,18 proposed the use of hollow fiber membrane module for removing acidic gas such as CO2 using NaOH. The industrial applications of hollow fiber membrane module based gas−liquid contactors are limited because of lower mass transfer coefficient in spite of several other advantages. The use of hollow fiber membrane module has been limited to straight tubes with a shell and tube kind of design. Liquid flows inside the tube, and gas is in shell side. Geometry perturbation in membrane module has been tried in the form of transverse flow through rectangular cross section.19 Vashisth et al.15 performed a comprehensive study of transport processes in curved geometries. They reported that geometry perturbation in a curved tube may further enhance mass transfer coefficient. Received: December 21, 2015 Revised: March 8, 2016 Accepted: March 10, 2016

A

DOI: 10.1021/acs.iecr.5b04865 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Recently, some authors have started focusing on coiled hollow fiber membrane modules to enhance the mass transfer. The effect of cross-flow system on mass transfer inside tube has been also investigated. Ghogomu et al.20 compared four different geometries, viz., straight tube, helical coil, twisted, and meander shaped. They reported 1.4 times enhancement in permeate flux for all curved geometries as compared to the straight module. Liu et al.21 predicted the dependency of mass transfer on various factors such as wind angle, tube diameter, and coil diameter and developed a new correlation for Sherwood number. Sh = CDe αSc 0.33

(1)

The values of α and C were varied from 0.35−0.55 and 0.24− 0.264, respectively, on the basis of the wind angle. The mass transfer enhancement in helical coil module was approximately 2−3.5 times to that of straight modules. Moulin et al.22 performed a similar study and reported that the mass transfer coefficient was enhanced by 2−4 times relative to that of the straight tube module. Moulin et al.22 proposed a Sherwood number correlation considering the effect of tube pitch and curvature ratio of helical coil membrane module. The curvature ratio (λ) is defined as the ratio of curvature diameter and tube diameter. Tube pitch (Pt) is center to center distance between two turns of the helical coiled tube. Sh = 0.14De 0.75Sc 0.33

Figure 1. Diffusion process in a membrane module.

through liquid film. The overall mass transfer has been calculated. 1 1 1 1 = + + K K Gmg KMmm KL (3)

(2)

The coiled membrane modules show a significant enhancement in mass transfer rate. However, it remains a great challenge to reduce fouling and energy consumption and to enhance the membrane permeate flux, which are still barrier for wide application of membrane separation in water treatment. Saxena and Nigam23 proposed a new technique, “the bending of helical coil at 90°”, to cause multiple flow inversions. The centrally located 90° bend between two helical coils of equal arm lengths induces a flow inversion, which narrows the RTD. The plug flow behavior of CFI recently prompted researchers to use it for different applications in process industry. It has been reported that CFI has superior performance as compared to coiled tubes for many applications such as polymerization reactor,24−26 liquid−liquid extraction,27 microreactor for metal extraction,28 inline mixer,12 pharma application in protein refolding,29 heat exchanger,30−32 and other heat and mass transfer applications.31,33−35 The ease of fabrication, compactness, and narrower RTD of CFI establish its superiority over other devices. Hence, in the present study, the mass transfer performance of CFI as hollow fiber membrane module has been investigated under the laminar flow condition, using computational fluid dynamics. The velocity profiles were also analyzed because they elucidate the basic physics behind the mass transfer enhancement in helical coil and CFI modules. The number of merits of CFI over straight module has been also calculated in terms of mass transfer enhancement and energy consumption.

mg =

d0/di md

ml =

dlm/di md

(4)

(5) 21,22

A similar equation was used by previous investigators for overall mass transfer in helical coil. However, because of the assumption of presence of pure gas, no resistance is present in the gas phase. It can be seen from eq 3 that the total resistance to mass transfer is the sum of the resistance of liquid boundary layer, membrane, and gas boundary layer. For a hydrophobic membrane, the pores are filled with stripping gas. In addition, because of the low solubility of gas, the equilibrium constant mg of gas in liquid is very high. Therefore, compared with that of the liquid film, the mass transfer resistance caused by gas film and membrane can be considered negligible, i.e., the overall mass transfer process was limited by the liquid boundary layer resistance. Therefore, the effective resistance to mass transfer lies in the liquid phase, and eq 3 reduces to K = KL (6) 2.2. Geometry and Grid System. The mass transfer performance of three different hollow fiber membrane modules, viz., straight tube, helical coil, and CFI, have been investigated in the present study. The details of the geometry and system of coordinates considered are shown in Figure 2a−c, where dt and dc are the tube and coil diameter, respectively. The straight, helical coil, and CFI membrane modules were considered of identical length and tube diameter. The tube pitch (Pt) is defined as distance between two turns of coiled geometry. In the present study, the value of tube pitch (Pt) is equal to 10.6 mm for helical and CFI membrane modules. In case of CFI module, a 90° bend was introduced at midway in between two helical coils of the same length. Two different CFI membrane modules with three and six 90° bends have been tested to investigate the effect of number of 90° bends on mass transfer permeate flux. The effect of curvature ratio (λ) on mass

2. MATHEMATICAL FORMULATION AND BACKGROUND 2.1. Mass Transfer in Membrane Modules. The physical model considered for the mass transfer performance of two systems, viz., O2−water and CO2−water, is shown in Figure 1. Pure gas is assumed in the shell side of the membrane module. The transfer of gas takes place in three steps: diffusion through gas phase, diffusion through membrane, and mass transfer B


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Figure 2. Schematic diagram. (a) Straight tube module, (b) helical coil module, and (c) CFI module.

2.3. Governing Equation. The Cartesian coordinate system (x, y, z) is considered to represent the CFI module in numerical simulation. The fluid enters at a constant velocity, free from the gas to be absorbed at tube inlet. Mass transfer and flow profile developed as the fluid moves through the membrane module. A constant gas concentration is assumed at the tube wall because pure gas is present in the shell side. The temperature and pressure have been also assumed constant in the shell side. The mass transfer can be evaluated using eq 7, on the basis of the above assumptions.

transfer performances of helical coil and CFI membrane modules has been also investigated using three different curvature ratios (7.75, 10, and 15). The details of the considered geometries are given in Table 1. Table 1. Design Parameters of Membrane Modules di (mm) dc (mm)

geometry straight modules helical coil modules

CFI modules

1 2 3 1 2 3 4 1 2 3 4

3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2

24.8 32 24.8 48 24.8 32 24.8 48

λ

7.75 10 7.75 15 7.75 10 7.75 15

number L (m) of turns 0.71 1.23 2.47 1.23 1.78 2.47 2.58 1.23 1.78 2.47 2.58

16 16 28 16 16 16 28 16

no. of 90° bends (Nb)

⎯→ ⎯ ∂ (ρYi ) + ∇·(ρvY ⃗ i ) = −∇· Ji ∂t

(7)

Yi is the local mass fraction of ith species and Ji is the diffusion flux of species i, which increases because of concentration gradients between the tube and shell side of membrane module. The diffusion flux has been calculated under laminar flow conditions.

3 3 6 3

⎯→ ⎯

Ji = −ρDi ,m∇Yi

A commercial CFD package called FLUENT (ANSYS 13.0), was used to simulate the fluid flow and species mass transport in straight, helical coil, and CFI membrane modules. The mathematical model consists of solving the Navier−Stokes, continuity, and species transport equations for a steady, laminar flow of an incompressible homogeneous Newtonian fluid. An unstructured nonuniform hexahedral grid system is used to discretize the species transport equation. Grid test has been performed to elucidate the change in species mass fraction with increase/decrease in the number of cells. For each 90° bend, 5000, 10 000, and 15 000 hexahedral cells were tested to optimize the grid size. It was found that 10 000 hexahedral cells provided efficient and fairly accurate convergence. The pressure velocity coupling was solved using the SIMPLE algorithm. First-order upwind scheme was used to solve species transport equation. The under relaxation factors for pressure, density, body forces, momentum, and species transport were taken 0.3, 0.9, 0.9, 0.7, and 0.9, respectively, to accelerate the convergence. The final discrete equation for any property is the sum of linear equations resulting from neighboring nodes. The residual convergence criteria were taken as 10−6 for ux, uy, uz, and P and 10−8 for species mass fraction.

(8)

where Di,m is the diffusion coefficient for species i in the mixture. 2.4. Boundary Conditions. The boundary conditions of mass transfer in all membrane modules is as follows: z = 0, CA = 0 r = 0,

∂CA =0 ∂r

r = R , CA = CA,m

(9)

(10) (11)

CA,m is the gas concentration in liquid phase at the membrane boundary toward the tube. The value of the CA,m was calculated using Henry’s law, in terms of mass fraction of the gas phase in equilibrium condition. The concentration distribution varies along the tube radius because of secondary flow. Hence to calculate the driving force, it is necessary to calculate the average concentration through membrane wall. The overall mass transfer coefficient is also calculated. K= C

Q L(C L,out − C L,in) AΔC LM

(12) DOI: 10.1021/acs.iecr.5b04865 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 3. Velocity contour in (a) helical coil membrane module at different velocities, viz., v = 0.023, 0.07, 0.13, and 0.3 m/s. (b) CFI membrane module at different axial lengths, viz., inlet, φ = 180°, after the first 90° bend and after the second 90° bend for v = 0.3 m2.

A is the total effective area of membrane module, and ΔCLM is the log means concentration difference. The aim of calculating log mean concentration was to derive the value of the average concentration difference for the specific geometries (straight tube, helical coil, and CFI). The log mean concentration was computed using analysis relating the concentrations to the area (and mass transfer coefficient, flow rate, and distribution coefficient). It is emphasized in the literature that the equation for mass contactors becomes equivalent to those described for heat exchangers. Our recent papers30,32,36 elucidate that log mean temperature difference can be successfully applied in case of CFI as heat exchanger. Hence, the log mean concentration difference can be used in case of coiled flow inverter membrane module. Other researchers have also used log mean concentration difference for mass transfer in coiled modules.21,22 ΔC LM =

* − C L,out) − (C L,out * − C L,in) (C L,in * − C L,out)/(C L,out * − C L,in)) Ln((C L,in

3. RESULTS AND DISCUSSION The performance of novel CFI membrane module has been analyzed in terms of flow profile and Sherwood number. The proposed CFI membrane module offer significant improvement in permeate flux as compared to helical coil and conventional straight membrane modules for identical process flow parameters. 3.1. Flow Inversion and Hydrodynamics. The performance of any membrane module is significantly affected by both the geometrical design of membrane and solvent velocity. The velocity profile controls the rate of mass transfer, particularly in curved membrane modules. Hence, the velocity profiles have been analyzed to elucidate the physics of mass transfer augmentation in CFI membrane module. The velocity contours have been computed at the outlet of helical coil membrane module for different solvent velocities as shown in Figure 3a. It may be noted for lower value of solvent velocity (v = 0.023 m/s) that the velocity contour at the outlet of helical coil membrane module has a negligible difference from that of straight tube membrane module. The location of the maximum velocity shift toward the outer wall with increase in value of solvent velocity (from 0.023 to 0.3 m/s), and the contours take the familiar C shape in helical coil membrane module. Here, the inner wall means the tube wall toward the center of curvature of helical coil and CFI. The outer wall means the tube wall in opposite direction of the center of curvature of helical coil and CFI modules. This trend reveals the development of the centrifugal force in helical coil module with increase in solvent velocity. The velocity profile takes parabolic shape near the outer wall with further increase in the solvent velocity. Figure 3b shows the velocity contours at different cross sections of the CFI membrane module in axial direction. Here, φ is the circumferential angle, a measure of the axial length in helical coil and CFI membrane modules. It may be noted from Figure 3b that the location of maximum velocity shift toward the outer wall with increase in the value of curvature angle φ = 0−180°. This result shows that a minimum axial length is vital for the flow to be fully developed. It may be further noted that the Dean vortices are completely inverted by 90° after each bend in CFI membrane module. The Dean vortices before each 90° bend vanish and reappear in a plane perpendicular to the previous plane. The reason for this phenomenon is the

(13)

CL* is the equilibrium concentration of gas at inlet (CL,in * ) or outlet (CL,out * ). The equilibrium concentrations were calculated by Henry’s law. The value of diffusion constant and Henry’s constant were taken from Perry’s Handbook. The Sherwood number (Sh) was computed in terms of the ratio of total mass transfer rate to the diffusive mass transport rate. K Sh = (14) D/L where L is a characteristic length (m), D is mass diffusivity (m2/s), and K is the mass transfer coefficient (m/s). The values of the mass flux, pressure drop, and shear stress were computed using the postprocessing tool of FLUENT software. In the case of no-slip wall conditions, FLUENT uses the properties of the flow adjacent to the wall/fluid boundary to predict the shear stress on the fluid at the wall. The shear stress calculation under laminar flow condition simply depends on the velocity gradient at the wall.

τ = μ∂u/∂y

(15)

μ is the dynamic viscosity of the fluid, u is the velocity of the fluid along the boundary, and y is the height above the boundary. D


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streamline that previously had the lowest concentration. Thus, in helical flow, a 90° degree change in the direction of centrifugal force causes a flow inversion. Hence, CFI membrane module provide much better mass transfer performance as compare to helical coil membrane module. The effect of the flow inversion has been expressed in detail in our previous studies.12,23,33−35 The effect of solvent velocity on mass fractions of oxygen has been also investigated. Figure 5 shows that the concentration

reorientation of centrifugal force after each 90° bend. The patterns of axial profile development at various axial lengths are clearly related to the fluid dynamics of CFI membrane module. Hence, in CFI membrane module, the direction of centrifugal force changes by 90° after each bend. The points at which velocity was maximum before changing the direction of centrifugal force are now lying on the streamline, which corresponds to the lowest velocity, and the new points of maximum velocity are induced on the streamline that previously had the lowest velocity. Thus, in helical flow a 90° change in the direction of centrifugal force causes a flow inversion. Therefore, the radial mixing between the fluid elements of different ages augments after the 90° bends in CFI membrane modules. Hence, CFI module provides higher mixing and improved mass transfer as compared to those of conventional helical coil and straight membrane modules. 3.2. Oxygenation Process of Water. The oxygenation process is becoming increasingly important in wastewater treatment and biomedical applications such as a bubble-free supply of oxygen with blood in the human body. The concentration contours have been examined in order to elucidate the physics of flow in complex coiled membrane modules. In Figure 4, the species transport contours are plotted at the

Figure 5. Convective transport vs diffusion transport: Species mass fraction at 360° in CFI membrane module with different velocities, viz., v = 0.023, 0.07, 0.13, and 0.3 m/s.

contours become more and more uniform with increase in solvent velocity (from 0.023 to 0.3 m/s) because of the decrease in concentration gradient. The species transport contours elucidate the dominance of convective transport over diffusion due to augmented centrifugal force with increase in the solvent velocity. The enhanced radial mixing at higher velocities caused by 90° flow inversion is the probable reason for lower concentration gradients in CFI membrane module. The present computed results of straight and helical coil membrane modules are verified against the known experimental results of Moulin et al.22 as shown in Figure 6. The Sherwood number of straight and helical coiled membrane module computed in the present study are comparable with the experimental results reported in the literature.22 It may also be noted that the slope of the Sherwood number curve is steeper in helical coil than that of straight membrane module. This result reveals that a significant improvement of mass transfer rate in helical coil as compared to straight membrane module at higher Reynolds number. The Sherwood number in helical coil membrane module increases up to 5 times that of straight membrane module, which is in agreement to the experimental results.22 The present computational results are in good agreement to the correlation developed on the basis of experimental results by Moulin et al.22 The Sherwood number of all three membrane modules have been compared for the oxygenation process with variation in Reynolds number as shown in Figure 7. It may be noted that the mass transfer enhancement strongly depends on Reynolds number in helical coil and CFI membrane modules. The CFI membrane module offer 3.5- to 5.5-fold higher Sherwood number to that of conventional straight membrane module for

Figure 4. Species transport due to flow inversion in CFI membrane module at different axial lengths, viz., inlet, φ = 30, 90, 180, 360, and 720°, after the first 90° bend and after the second 90° bend for a constant value (0.2 m/s) of solvent velocity.

different angular planes of CFI membrane module. Here, φ is the circumferential angle, a measure of the axial length in helical coil membrane module and CFI membrane module. The axial length in helical coil membrane module and CFI membrane module increases with increase in the value of φ. It may be noted from Figure 4 that there is no secondary flow at the inlet (φ = 0°) of CFI membrane module. However, the formation of Dean vortices are clearly visible with increase in the value of φ. The higher concentration zones shift toward the outer wall of CFI membrane module before the 90° bends. It may further be noted from Figure 4g,h that the Dean vortices are completely inverted by 90° after each bend in CFI. The Dean vortices before each 90° bend vanish and reappear in a plane perpendicular to the previous plane. The reason for this phenomenon is the reorientation of centrifugal force after each 90° bend. The patterns of axial profile development at various axial lengths are clearly related to the fluid dynamics of CFI membrane module. Hence, in CFI membrane module, the direction of centrifugal force changes by 90° after each bend. The points at which concentration was maximum before changing the direction of centrifugal force are now lying on the streamline, which corresponds to the lowest concentration, and the new points of maximum concentration are induced on the E


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Figure 8. Sh vs Re for carbonation process in CFI (Nb = 6), helical coil, and straight membrane modules of identical length (L = 2.47 m). Figure 6. Comparison of the present computed results with the experimental results reported in the literature.22

enhancement for carbonation process was same as that explained in the case of oxygenation process. The Sherwood number results for both oxygenation and carbonation processes are supported by mass transfer results in terms of amount of gas absorbed with respect to flow rate of the solvent as shown in Figure 9. It may be noted from Figure 9a that the amount of gas absorbed with respect to flow rate of solvent in CFI membrane module was up to 4.7-fold higher to

Figure 7. Comparison of Sh and Re for oxygenation process in CFI (Nb = 6), helical coil, and straight membrane modules of identical length (L = 2.47 m).

the oxygenation process. The CFI membrane module further enhances Sherwood number up to 20% as compared to the helical coil membrane module. The reason for the mass transfer enhancement in CFI module is not only the presence of the Dean vortices but also the flow inversion caused by the 90° bends. The action of secondary flow in radial direction improves the fluid mixing and the flow inversion by 90°, further intensifying the mixing of fluid, therefore resulting in higher mass transfer. 3.3. Carbonation Process of Water. The carbonation process has important application in the beverage industry. Adjusting carbonation level in a beverage is vital for its sparkle and tangy taste. The present CFI membrane module has been tested for the carbonation of water. The Sherwood number comparison for carbonation process has been shown in Figure 8 for all three membrane modules of identical design parameter and length (L = 2.47 m). The Sherwood number in CFI augments up to 26% as compared to that of helical coil module of identical design parameters. The reason for mass transfer

Figure 9. Amount of gas absorbed with respect to flow rate of the solvent for (a) oxygenation process and (b) carbonation process. F


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Industrial & Engineering Chemistry Research that of straight membrane module for the oxygenation process. The CFI membrane module further enhances mass transfer up to 18%, as compared to that of the helical coil membrane module. Similar mass transfer results were observed for carbonation process as shown in Figure 9b. The amount of gas absorbed with respect to flow rate of solvent in CFI augments up to 24% as compared to helical coil module of identical design parameters. However, it may be noted from Figure 9a,b that the mass transfer for carbonation process was considerably higher as compared to oxygenation process. The total quantity of CO2 absorbed was found to be higher as compared to O2 because the solubility of CO2 in water is higher than that in O2. The difference between the absorption of CO2 and O2 increases with increase in flow rate of the solvent. The probable reason behind this may be explained from Henry’s law, which states that the solubility of a gas in liquid at a particular temperature is proportional to the pressure of that gas above the liquid. The pressure is directly proportional to the density of gas according to ideal gas law; hence, CO2 dissolves more in water as compared to oxygen because it has a higher density. This result is quite significant from an industrial point of view since it predicts the amount of solvent needed to be passed per second for absorbing a given quantity of gas. 3.4. Effect of Curvature Ratio (λ). The mass transfer performance of the helical coil and CFI membrane modules have been investigated using three different curvature ratios of 7.75, 10, and 15 as shown in Figure 10. The curvature ratio is

Figure 11. Effect of curvature ratio (λ) in CFI membrane module.

Figure 12. Comparison of present computed and experimental results21,22 with the proposed correlation.

incorporating the data from literature21,22 and present study. The following correlation is proposed with R2 value of 0.97. Sh = 1.62Re 0.75Sc 0.33(d t /dc)0.33 (L /d t)0.33 Figure 10. Effect of curvature ratio (λ) in helical coil membrane module.

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3.5. Pressure Drop Analysis. The coiled membrane modules provide significant augmentation in mass transfer as compared to that in straight membrane module. However, the pressure drop is an important consideration in coiled membrane modules. The pressure drop is observed to be higher in coiled membrane modules as compared to that of straight membrane modules because of the additional viscous dissipation caused by secondary flow. Figure 13 shows the pressure drop result of all three geometries. The pressure drop in both CFI and helical coil membrane module is higher as compared to straight modules. It is interesting to see that CFI membrane module provides significant improvement in mass transfer as compared to helical coil modules, practically at same pressure drop. The probable reason for this unexpected behavior is the influence of two factors, which affect the pressure drop in CFI: (i) dissipation of energy due to the mixing in fluid elements of different ages at the 90° bend

defined as the ratio of coil diameter to that of tube diameter. It may be noted from Figure 10 that the mass transfer performance of helical coil module improves with decrease in value of λ. In helical coil membrane module, the Sherwood number increases by 15%, with 50% decrease in the value of λ from 15 to 7.75. The CFI membrane module also shows a similar trend as apparent from Figure 11. The Sherwood number increases by 19%, with 50% decrease in the value of λ from 15 to 7.75. The reason behind this phenomena is the fact that the centrifugal force increases with decrease in the value of λ and hence augments secondary flow. To propose a Sh number correlation taking into consideration of different design and process parameters in helical coil membrane modules, a regression analysis was performed by G


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Figure 15. Shear stress comparison in CFI and helical coil membrane modules of identical length (L = 1.23 m) at different axial lengths, for v = 0.13 m/s.

Figure 13. Pressure drop comparison in CFI, helical coil, and straight membrane modules.

Figure 15 shows the comparison of the shear stress of all three membrane modules with the correlations reported in the literature.37 The present results of shear stress are in good agreement with the correlations.37 Moreover, it may be observed that the shear stress in helical coil and CFI membrane modules are practically same. Figure 15 shows the comparison of shear stress of helical coil and CFI membrane modules along the axial length, which is measured in terms of curvature angle (φ). Here, the angle of curvature shows the angle between the inlet and the final measuring point along the length of helical coil or CFI. For example, the fluid will travel by an angle of 360° after one turn and 720° after two turns of helical coil. A slight reduction in the shear stress of CFI membrane module has been observed after φ = 1440°. The reason behind this phenomena is the fact that the first 90° bend of CFI appears exactly at φ = 1440° which drastically reduces the axial gradients as already explained in case of pressure drop in CFI. CFI module gives significant augmentation in mass transfer as compared to that of straight tube module but at higher energy consumption in the form of pressure drop. Hence, it is desirable to compare the performance of CFI membrane module per unit energy with the straight membrane module. For this, a new parameter number of merits (Nm) is defined as

Figure 14. Shear stress comparison in CFI, helical coil, and straight membrane modules.

(The fluid elements of different ages means infinitesimal regions of the fluid continuum in isolation from its surroundings.) and (ii) viscous forces, which depend upon the axial velocity gradient. The first factor increases the pressure drop with increase in number of bends, whereas the second factor tends to reduce it, owing to the weaker velocity gradients caused by interchange of velocities at the bends. The first factor is less effective, but the second one shows its substantial effect as the residence time for the fastest moving fluid element shifted from 0.613 to 0.68 even for single bend, causing a reduction in pressure drop.23 3.6. Shear Stress Analysis. Friction factor fs for the fluid flow in a tube is defined by the wall shear stress τ = (fs /2)ρu 2

Number of merits (Nm) =

(19)

The number of merits of CFI compared to those of straight membrane module have been observed up to 2.5 for oxygenation and 2.7 for carbonation process, as shown in Figure 16. This suggests that the overall mass transfer performance of CFI membrane module is much higher than that of straight membrane module under identical conditions.

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4. CONCLUSIONS The performance superiority of novel CFI membrane module was investigated as compared to that of conventional helical coil and straight membrane modules. The proposed CFI membrane module significantly enhances the mass transfer as compared to conventional helical coil and straight membrane modules because of intensified radial mixing caused by flow

where fs/2 = 8/Re. The friction factor for the helical coil can be calculated using Mishra and Gupta37 correlation. fC /fs = 1 + 0.033(log De′)4

ShCFI ShSt τCFI τSt

(18)

fc and fs are the friction factors in helical coil and straight tube, respectively. H


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Industrial & Engineering Chemistry Research Q volumetric flow rate (m3/s) St straight membrane module v velocity of fluid (m/s) x, y, z master Cartesian coordinates Yi local mass fraction of ith species Greek Letters

α λ φ ρ τw μ

Dean number exponent curvature ratio (dc/dt) angle of curvature (°) density of the fluid (kg/m3) wall shear stress (N/m2) viscosity (kgf·s/m2)

Dimensionless numbers

⎛ De Dean number ⎜De = Re ⎝

⎛ De′ M o d i fi e d d e a n n u m b e r ⎜De′ = Re ⎝ 2⎤ ⎡ Pt where dc′ = dc⎢1 + πd ⎥ c ⎣ ⎦

Figure 16. Mass transfer performance per unit energy consumption in CFI module as compared to straight tube module.

( )

inversion. Higher permeate flux was achieved in CFI membrane module as compared to that in helical coil module of similar design parameters with negligible difference in pressure drop. The CFI membrane module offer up to 5.5-fold enhancement in Sherwood number as compared to straight tube module for identical process conditions. The number of merit of the proposed CFI membrane module was found up to 2.5 for oxygenation and 2.7 for carbonation process as compared to that of currently practiced straight tube membrane module. The CFI membrane module may find potential applications in the food and beverage industry for the oxygenation and carbonation process. The present study may be potentially helpful to design the new membrane unit for improved mass transfer efficiency.

■

dt ⎞ ⎟ dc ⎠

dt ⎞ ⎟, dc′ ⎠

Re Reynolds number (−) Sc Schmidt number (−) Sh Sherwood number (−) Subscripts

L, l liquid phase M membrane G, g gas phase

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +911126591020. E-mail: [email protected], [email protected]. Notes

The authors declare no competing financial interest.

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NOMENCLATURE A cross-sectional area, (m2) C dissolved concentration (ppm) CFI coiled flow inverter CFD computational fluid dynamics dc coil diameter (m) do external diameter of the membrane (m) dt tube diameter (m) fc friction factor in curved membrane modules fs friction factor in straight membrane modules DAB molecular diffusion coefficient (m2/s) K mass transfer coefficient (m/s) L length (m) m phase equilibrium constant md diffusion coefficient Nb number of 90° bends Nm number of merit p pressure (N/m2) Pt coil pitch (center to center distance between two coil, m) ΔP pressure drop (Pa) I


Article

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Novel Membrane Module for Permeate Flux Augmentation and

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