Investigation of Shell Side Heat Transfer in Cross-Flow Designed

Article pubs.acs.org/IECR

Investigation of Shell Side Heat Transfer in Cross-Flow Designed Vacuum Membrane Distillation Module Bingwei Qi, Baoan Li,* and Shichang Wang Chemical Engineering Research Center, School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, and Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072, PR China ABSTRACT: This paper focuses on the investigation of heat transfer in a cross-flow designed vacuum membrane distillation (VMD) module. The employment of cross-flow membrane module could ensure significant reduction of temperature polarization effect at a relatively low range of Reynolds numbers. According to most literature on VMD, the heat transfer coefficients are usually estimated by the commonly used correlations for nonporous and rigid heat exchangers. However, due to the complex flow regime in module channel, the applicability of these formulas is questioned. In this work, the heat transfer in the shell side of VMD module was studied numerically and experimentally in the Reynolds range from 7.12 to 52.18. The experimental Nusselt numbers obtained in this work are relatively higher than those predicted in the literature for given conditions. The possible reasons leading to the considerable enhancement of heat transfer are analyzed and discussed. of dual layer hydrophilic−hydrophobic polyvinylidene fluoride (PVDF) hollow fiber membranes in DCMD, at feed inlet temperature of 90 °C, which is much higher than most of the previous reports. Later, Peng7 reported that dual-layer PVDF hollow fibers can significantly enhance the permeate flux of DCMD mainly due to lower mass transfer resistance via the architecture of morphological characteristics. During their experiments, a superior flux of 98.6 L/m2 h was obtained at an inlet feed temperature of 80.2 °C. According to Li and Sirkar’s results,8 in VMD, membrane module MXFR#3 containing larger size fibers having a much more open coating and larger pore size yielded at a high Reynolds number a water vapor flux as high as 71 L/m2 h from a 85 °C hot feed in crossflow. MD is characterized by simultaneous heat and mass transfer. In a VMD configuration (see Figure 1), the evaporation of water at the feed side membrane interface results in a simultaneous reduction of the temperature and increase of the solute concentration, referred to as temperature and concentration polarization, respectively.8 As vacuum is applied in the permeate side, there is no boundary layer on this side and this implies that the heat conducted through the membrane can be neglected.9 Normally, the net driving force of the VMD process is the partial vapor pressure (thermally driven) difference between the feed side and permeate side at the membrane surface. Clearly, in order to increase this net driving force, the membrane surface temperature in the feed side must be increased (a higher temperature means higher partial vapor pressure according to the Antoine equation) and the vapor pressure in the permeate side must be decreased (i.e., higher vacuum level). For a given

1. INTRODUCTION Membrane distillation (MD) is an evaporation process of feed volatile components through a hydrophobic membrane.1 The evaporation process takes place at the vapor−liquid interface supported by the membrane pores. Unlike other membrane processes (e.g., pervaporation process), in MD, the membrane does not alter the vapor/liquid equilibrium but only acts as a physical support.2 One side of the membrane is always brought into contact with the feed solution (i.e., feed side), while the other side (i.e., permeate side) differs from each other according to different condensing or removing methods of vapor. As known, membrane distillation can be classified into four configurations: direct contact membrane distillation (DCMD), vacuum membrane distillation (VMD), sweeping gas membrane distillation (SGMD), and air gap membrane distillation (AGMD). MD can substitute several conventional separation processes due to its outstanding features, such as low operating temperatures (typically below 323.15−333.15 K) and pressures, 100% (theoretical) rejection of nonvolatile components, and space saving. Therefore, MD has become an active area of research and used in seawater desalination, industrial water treatment3 and even food industry.4 Despite the successful development mentioned above, further enhancement of the performance of MD is needed, i.e., to get more permeate flux. Generally, there are two major factors determining the permeate flux of MD, i.e., effective driving force and mass transfer resistance. Through the first factor, low thermal conductivity of membrane and good fabricated membrane modules are needed so as to reduce the undesirable temperature polarization, which leads to a lower transmembrane driving force.5 Via the second factor, membranes with characteristics of large mean pore size and porosity, open-cell pore structure, thin functional layer, and small tortuosity are required in order to achieve a lower mass transfer resistance. Bonyadi and Chung6 have reported that flux enhancement as high as 55 L/m2 h was achieved via fabrication © 2012 American Chemical Society

Received: Revised: Accepted: Published: 11463

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Figure 1. Schematic diagram of the VMD process.

presence of feed circulation. In short, the heat transfer on the feed side of VMD is not always the same as that of “pure” heat exchanger. Therefore, the conventional heat transfer correlations for nonporous and rigid heat exchangers should be questioned before using them to estimate the heat transfer of VMD. The experimental heat transfer correlations were compared with those commonly used in publications, and the differences between them are analyzed and discussed. In our earlier works,5,8 several novel membranes and devices for both DCMD and VMD have been presented due to their excellent performances in enhancing heat transfer rate and thus high water permeate flux. In this work, a cross-flow VMD module with packing fraction of hollow fibers (0.26) was designed on the basis of the method introduced by Li and Sirkar.5,8 The excellent heat transfer performances are analyzed and discussed in details in term of Nusselt, Reynolds, and Prandtl numbers based on experimental results.

bulk temperature, the key point to increase the membrane/ interface temperature on the feed side or reduce the temperature polarization effect is to increase the heat transfer coefficient. In fact, since the earliest reports of membrane distillation by Findley10 and Gore11 and later brief review in Sirkar,12 as well as a more extensive review of membrane distillation by Lawson and Lloyd,1 the importance of heat transfer coefficients in MD performance has been specially emphasized. The heat transfer on the feed side of VMD is very complex due to its interaction with mass transfer and the instable flow regime. Phattaranawik pointed out that in a DCMD process, the maximum heat transfer due to mass transfer across the heat boundary on the feed side is 12.9% at a bulk temperature of 368 K, which is termed as the Dufour effect.13 However, the socalled Dufour effect decreases almost linearly with decreasing temperatures. Referring to the temperature range (333.15− 353.15 K) tested in this work, the Dufour effect was not taken into account. Additionally, due to the presence of hollow fiber bundles, a more turbulent flow regime occurs in the module channel, and therefore, the mass (no mass boundary layer when pure water is employed in this work) and heat boundary layer is minimized. In other words, the thickness of the heat boundary layer varies with the instable flow regime and so does the heat transfer rate through the heat boundary layer. There are plenty of publications about how to estimate the heat transfer coefficient for both parallel-flow and crossflow. 14−21 They are usually the well-known empirical correlations developed for nonporous and rigid heat exchangers. As a basic property, there are numerous pores at the membrane surface (Figure 1), both the liquid−vapor interface and liquid−solid interface therefore appear simultaneously. According to Ramon’s research,9 in the presence of liquid−vapor interface, the degree of temperature polarization was reduced and a corresponding increase in the evaporation mass flux was observed. More specially, when the slip coefficient was set at l0 = 0.1, the mass flux was increased by as much as 10.2%, at a bulk temperature of 333.15 K and bulk velocity of 0.5 m/s. In addition, the membrane (hydrophobic hollow fiber in this paper) may deform22 and vibrate in the

2. THEORY 2.1. Mass and Heat Transfer. In VMD, the relationship between the permeate flux (i.e., mass of water vapor transferred per unit of surface area and of time, kg/m2 h) and the pressure difference across the membrane is usually described as J = C ΔP = C(Pfm − Ppm)

(1)

where C is the net mass transport coefficient of VMD. The coefficient C is usually dependent on the temperature and geometric characteristics of membrane, which represents a quantitative measure of membrane resistance. ΔP is the pressure difference across the membrane. Ppm is the pressure at the membrane/interface on the permeate side. Pfm is the vapor partial pressure at the feed/membrane interface evaluated by the Antoine equation, which can be expressed by8 ⎛ 3816.44 ⎞ Pfm = exp⎜23.1964 − ⎟ Tfm − 46.13 ⎠ ⎝

(2)

Mass transport across the membrane is usually described by a variety of theories based on the Gas−Dusty model,23−25 such as the Knudsen model, the Poseuille model, the Knudsen− 11464

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feed side (i.e., Qf) and the permeate side (i.e., Qp) equal to Qm once the steady state of heat transfer is reached. So we get

Poseuille transition model, and the molecular diffusion model. We can decide which model is the control one according to the nominal pore size and the molecular mean free path of vapor. If the molecular mean free path of the transporting vapor is larger compared with the average membrane pore size, the molecular−pore wall collisions are dominant over the molecular−molecular collisions and the Knudsen model will be the prevailing mechanism that describes the vapor transfer through the membrane pores. In this case, the membrane mass transfer coefficient can be expressed as1,26−28 εr ⎛⎜ M ⎞⎟ τδ ⎝ RT̅ ⎠

Qf = Qm = Qp

As mentioned above, the heat transfer on the feed side of VMD is usually estimated by empirical heat transfer correlations for nonporous and rigid heat exchangers, which are presented in Table 1. Table 1. Heat Transfer Correlations Commonly Used for Turbulent Cross-Flow

1/2

C = 1.064

(3)

where ε, τ, r, and δ are the porosity, pore tortuosity, pore size, and the effective thickness of the hydrophobic membrane, respectively. M is the water molecular mass. R is the gas constant, and T̅ is the average membrane temperature. Moreover, it has been reported that for membranes with a pore radius smaller than 0.6 μm, the dominant transport mechanism may be assumed to be Knudsen diffusion.29 As shown in Figure 1, the feed solution evaporates at the liquid−vapor interface and transfers through the porous hydrophobic hollow fiber wall in the presence of the pressure difference across the membrane. Simultaneously, the latent heat transfers from the feed side to the permeate side of membrane, which results in the temperature polarization in the feed side. The heat transfer process in the feed side can be divided into three parts: (1) the heat transfers from the bulk field to the surface of membrane, (2) the water evaporates at the liquid− vapor interface and the latent heat transfers through the membrane accompanying the transmembrane vapor flux, and (3) the vapor is condensed and the latent heat is released. Convective heat transfer and conductive heat transfer are normally considered in the VMD process. The heat transfer conducted near the surface of membrane is considered as convection, which can be expressed as30 Q f = hf (Tf − Tfm)

Qm

no.

correlation

1

Nu = 2(Red × Pr) (μ/μw) 0.14a Nu = (0.5Red1/2 + 0.2Red2/3)Pr1/3(μ/μw)0.14 Nu = 1.05Red0.4Pr0.36(Pr/ Prw)0.25bc Nu = 0.35FaRed0.57Pr0.31 d Nu = 0.206(Recosθ)0.63Pr0.36

2 3 4 5

1/3

comments

ref

tube banks with 10 or more rows, Re < 100 tube banks with 10 or more rows, 1 < Re < 105 1 < Red < 5 × 102

20

1.25 < a′, b′ < 3 cross-flow: θ = 0

31 22

20 16−21

a Red is the diameter-based Reynolds number. bAll properties except Prw are evaluated at the arithmetic mean of the fluid inlet and outlet temperatures. cAll properties appearing in the equation are evaluated at the film temperature. dFa = 1 + 0.1a′ + 0.34/b′, where a′ = SL/do, b′ = ST/do, SL is the distance between centerlines of tubes in adjacent longitudinal rows, ST is the distance between centerlines of tubes in adjacent transverse rows, and do is the outer diameter of hollow fiber.

However, in order to describe the exact heat transfer coefficient in this work, i.e., shell side heat transfer in the presence of phase change, a general form of channel-average heat transfer correlation is proposed: Nu = aRebPr c

(7)

In this equation, Re and Pr are the Reynolds number [Re = (interstitial velocity)dρ/μ] and Prandtl number [Pr = cpμ/λ]. a, b, and c represent the characteristic constants of the module design and liquid flow regime. Here, interstitial velocity is defined as

(4)

where hf is the heat transfer coefficient of the heat boundary layer on the feed side. Tf and Tfm are the bulk temperature and membrane/interface temperature of the feed side, respectively. The heat transfer across the membrane (i.e., Qm) is known as the sum of the conductive heat and the latent heat of water evaporation transferred with the vapor through the membrane. The heat conducted through the membrane (i.e., through the solid polymeric wall as well as through the vapor space) is invalid for permeate flux. This heat loss can be neglected due to the low pressure in the permeate side of membrane in the VMD process as well as high porosity (0.65 in this work) and larger membrane wall thickness (e.g., the hollow fibers with a wall thickness of 220 μm were selected in this paper).9 Therefore, Qm can be described as k = m (Tfm − Tpm) + J ΔH ≈ J ΔH δ

(6)

interstitial velocity volumetric flow rate = open area for flow through the shell side

(8)

and the open area for flow through the shell side is expressed by the frame cross sectional area (60 × 40, mm2) minus fiber projected area (no. of fibers in one layer × do × L, mm2). 2.2. Mass and Heat Transfer Coefficients Obtaining Method. Equation 4 can be rewritten as

Tf − Tfm =

Q hf

(9)

28

Schofield proposed that, when the feed is pure water and the temperature difference across the membrane is low (less than 10 K, approximately 5 K in this work), eq 5 could be rewritten as

(5)

where km is the conductive heat transfer coefficient of membrane. δ is the effective thickness of membrane. J is the permeate flux. ΔH is the latent heat of water evaporation. As the heat loss from the membrane module to the environment is negligible (the MD system was insulated in this work), it is assumed that both the heat transfer rate on the

Q = J ΔH = C ΔP ΔH = C ΔH(Pfm − Ppm) = C ΔH ⎛ dP ⎞ ⎜ ⎟ (T − T ) pm ⎝ dT ⎠T̅ fm

(10)

Therefore, the following equation is obtained 11465

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Q

( ddTP )T̅

C ΔH

(11)

where Tpm is the membrane/interface temperature of the permeate side. As there is vacuum applied in the permeate side, the value of Tpm is considered approximately equal to Tp. T̅ is the average temperature of membrane. Here, dP/dT can be evaluated by the Clausius−Clapeyron equation: ⎛ P ΔHM ⎞ ⎛ dP ⎞ ⎜ ⎟ = ⎜ ⎟ ⎝ dT ⎠T̅ ⎝ RT 2 ⎠T ̅

(12)

The following relation is obtained by combining eqs 9 and 11: Tf − Tpm Q

=

1 C ΔH

1 dP dT T ̅

( )

+

1 hf

Figure 2. (a) Rectangular cross-flow membrane module with face box, face plate, module frame, and assembly. (b) Cross section of the module.

To clearly show the feed flow regime, by CFD simulation, Figure 3 schematically illustrates the 2D velocity vectors of feed

(13)

Q is evaluated by eq 5. Therefore, a graph of (Tf − Tpm)/Q plotted against 1/(dP/dT)T̅ should yield a straight line with a slope of

k=

1 C ΔH

(14)

and an intercept of 1/hf. 2.3. Calculation of Tfm. An iterative method was used to obtain the value of Tfm. As there is a vacuum applied on the permeate side and the length of the hollow fiber membrane is only 60 mm, the recorded Tp was assumed to be equal to Tpm. First, an initial temperature value T between Tf and Tp was given. The mean average of T and Tp, (T + Tp)/2, was assigned to T̅ in eq 3 to obtain a first value of the mass transfer coefficient C. Then, the obtained C was used to calculate the value of Pfm for given Ppm in eq 1. Finally, referring to the Antoine equation, the corresponding value of Tfm was worked out. If the calculated Tfm equals the initial temperature value T, the process was finished. Otherwise, a new initial temperature value T′ was used to repeat the iterative process until Tfm = T′. By this method, the temperature polarization coefficient (TPC) can also be evaluated according to TPC = Tfm/Tf.8

Figure 3. Velocity vectors of feed solution across the hollow fiber in a staggered manner (bulk inlet interstitial velocity of 0.083 m/s).

solution across the hollow fibers in a staggered manner. In Figure 3, the feed flows around the hollow fibers and yields a relatively higher velocity among the hollow fibers in one layer. Later, these higher velocity flow paths are impeded by the next layer of hollow fibers, which were arranged in a staggered manner. Repeating of this process leads to more turbulence of feed solution at a low range of Reynolds numbers. The packing fraction of membrane module in this work is 0.26. 3.2. Experimental System. The laboratory system designed to conduct VMD experiments is presented in Figure 4. The pipes and membrane module of the VMD system were both insulated in order to minimize the heat loss to the surroundings. The feed temperatures varied from 333.15 to 353.15 K, while the vacuum level in the permeate side was maintained at 0.085 MPa. The vacuum level is defined as the difference between atmospheric pressure and absolute pressure. In the present work, pure water was employed as the feed fluid. The feed liquid circulated on the shell side and the vacuum was applied in the lumen side of the hollow fiber membrane. During the experiments, the module was maintained in a horizontal position. Pure water flowed into the module perpendicularly from the bottom inlet and

3. EXPERIMENTS 3.1. Membrane and Membrane Module. Polypropylene (PP) hollow fibers with a porosity of 0.65 and nominal pore size of 0.2 μm, supplied from Memclean Sci & Tech Ltd. (Tianjin, China), were employed in this work. The inner and outer diameters of the hollow fiber membrane are 610 and 1050 μm, respectively. The inner diameter of the hollow fiber is larger compared with that used in Li’s work (330 μm), which ensures that the vapor undergoes only a low pressure drop on the lumen side. The membrane module was assembled in our lab according to the method introduced by Li,5 with scales of 60 mm length, 40 mm width, and 24 mm height and active membrane area of 0.0425 m2. As shown in Figure 2, the membrane module consists of four main parts, the face box, the face plate, the module frame, and the hollow fiber membranes packed in. The plow groove in the face box served as a buffer for feed flow. The face plate is characterized by smaller holes in the center and progressive larger holes further away, which acted as a fluid distributor to ensure a uniform flow through the hollow fiber bundles. 11466

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Figure 4. Experimental system established for heat transfer investigation of VMD: (1−8) valves, (9) feed reservoir, (10) peristaltic pump, (11, 14, 17, 19, 21) Pt-100 probes, (12, 20) flow meter (13) hollow fiber membrane module, (15, 16) pressure indicators, (18) heat exchanger, (22, 23) containers, (24) pressure indicator and regulator, (25) needle valve in bypass loop, (26) main on/off valve, and (27) vacuum pump.

4. RESULTS AND DISCUSSION The relationships between water permeate performances and interstitial velocities of feed at different inlet temperatures are illustrated in Figure 5. Obviously, the permeate flux increases

discharged from the top outlet, while the two lateral openings were connected with the vacuum system to keep a low-pressure environment on the lumen side of the hollow fiber. Before pure water was pumped into the module, it had been kept in a container (feed reservoir) and heated to the preset temperature. The recirculation rates of the feed solution were regulated by a digital Masterflex peristaltic pump. In order to investigate the heat transfer mechanism in the module channel, different flow rates were studied in the experiments (i.e., 60−435 cm/min). In this case, the Reynolds numbers fall into the range of 7.12− 52.18. When the water vapor was drawn from the membrane module into the heat exchanger equipped in the VMD system, it was condensed to liquid water. In more detail, for the permeate flux (19.46 kg/m2 h) in this work, the feed inlet and outlet temperatures of the VMD module were 353.15 and 350.75 K at a volumetric flow rate of 0.198 m 3 /h (corresponding to 400 cm/min), while the inlet and outlet temperatures of cooling medium (tap water) of the heat exchanger were 290.45 and 300.05 K at a volumetric flow rate of 0.05 m3/h, which indicates that approximately 99.1% of the vapor was condensed to liquid at a vacuum level of 0.085 MPa in the heat exchanger. The position of the heat exchanger was higher than those of the permeate containers; condensed water therefore flowed into the main container, while valves 1, 3, and 6 were switched on and 2, 7, and 8 off. The temperatures of the fluid at the entrance (Tin) and the exit (Tout) on the feed side and the temperature of the permeate side exit (Tp) were recorded with 0.1 °C accuracy. The average bulk temperatures in the module channel were evaluated by Tf = (Tin + Tout)/2, and the average temperatures of the hollow fiber membrane were estimated by T̅ = (Tfm + Tp)/2. Both collectors were placed on two balances, respectively. Permeate collector a served as the main device, while collector b was a standby one. Before recording the permeate flux, valves 1, 3, and 6 were switched on to connect collector a with the vacuum pump; therefore, collector a was linked with the vacuum system and used as the main collector. As more and more water assembled in collector a during the experiments, the water was discharged from valve 5. Valves 1 and 3 were switched off when water was discharging, collector a was separated from the vacuum system, and collector b took effect instead for the sake of stability of the vacuum level.

Figure 5. Variations of water permeate flux with interstitial velocity of feed at different temperatures.

with the interstitial velocity as well as the temperature. For specific temperatures, the permeate flux becomes less sensitive to the increasing interstitial velocity. While the effect of temperature on the permeate flux increases with increasing temperatures. These trends have also been reported in previously work.8 Specially, variation of TPC with interstitial velocity at an inlet temperature of 333.15 K is illustrated in Figure 6. The TPC increases with velocity quickly (100−300 cm/min) and later a slight increase was observed (300−400 cm/min). Therefore, it is deduced that in this case low feed velocity (