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Membrane-based humidity pump: performance and limitations
Journal of Membrane Science 171 (2000) 207–216
Membrane-based humidity pump: performance and limitations L.Z. Zhang∗ , Y. Jiang, Y.P. Zhang Department of Thermal Engineering, Tsinghua University, Beijing 100084, PR China Received 20 May 1999; received in revised form 14 December 1999; accepted 16 December 1999
Abstract Moisture is usually transported from a fluid of high humidity to a fluid of relatively low humidity through a membrane. Membrane-based humidity pump works in another way: moisture is transported from a dryer air stream to a humid air stream under the driving force of thermal gradients in membrane. With humidity pump, a continuous air dehumidification can be realized by the utilization of low-grade waste heat. In this article, through finite difference simulations of the coupled heat and mass transfer in the unit, the performance and limitations of a membrane-based humidity pump are analyzed. The effects of various thermodynamic and dynamic parameters of membrane on the performance of humidity pump are discussed. It is found that even though the operational parameters can be optimized to enhance the thermo-osmosis rate of water vapor, the key role is played by a factor named humidity pump. Furthermore, when the humidity pump factor is bigger than 0.02 mK−1/7.5 kJ1/3 , the permeability is bigger than 1.0×10−5 kg m−2 s−1 , and the humidity pump can be used in commercial applications. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Microporous and porous membranes; Gas and vapor permeation; Humidity pump; Thermodynamics; Thermoosmosis
1. Introduction With the advances in cooling technology, independent humidity control techniques are strongly desired in air-conditioning industry. The most widely practiced techniques of dehumidification include cooling coils, fixed adsorbent beds, absorption tower and rotary wheel desiccant. These methods are bulky and very energy consuming since a large amount of energy is wasted in vapor phase change or desiccant regeneration [1]. The development in membrane science (especially pervaporation and gas separation) provides a new alternative to these traditional techniques. In recent years, membrane-based air dehumidification ∗ Corresponding author. Tel.: +86-10-62772072; fax: +86-10-62770544. E-mail address: [email protected] (L.Z. Zhang)
has drawn much attention since it offers a stable and continuous operable system that combines long life with low energy consumption [2–6]. In these systems, moisture is transferred from a fluid of high vapor partial pressure to a fluid of low vapor partial pressure under the driving force of pressure gradients. These systems are very interesting and they continue to be actively pursued. However, they must be operated under very high pressure-difference and thus high membrane intensity is required, which may be very problematic. Besides, the use of compressors (or vacuum pumps) also increases mechanical complexity and energy consumption. In addition to pressure-forced membrane dehumidification, there is another way of dehumidification: thermally forced membrane dehumidification. Based on the theory of Thermo-osmosis, moisture can also be transferred from a dryer air stream to a humid air
0376-7388/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 7 3 8 8 ( 0 0 ) 0 0 3 0 4 - 5
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L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
stream under the driving force of thermal gradients in membrane. In analogy to a heat pump, we call this way of moisture transport as the humidity pump. The thermally forced dehumidification is more attractive since here low-grade waste heat can be used to dehumidify a supply air stream. Furthermore, since no pressure difference exists between the two sides of a membrane, the durability and reliability could be very high. In this paper, the heat and mass transfer mechanisms of a membrane-based humidity pump are studied. The effects of various thermodynamic and dynamic parameters on the permeability are discussed. Through finite difference simulations, the temperature and moisture distributions along the stream are obtained. The performance and the limitations of the humidity pump are investigated. The requirement for the membrane material of a humidity pump is discussed.
µvH2 O (T2 , pT , yH2 O ) = µH2 O (T1 , p1∗ ) −
Z
+RT1 lnyH2 O
T2
T1
SHv 2 O dT (3)
The chemical potential difference of the two air streams is µvH2 O (T1 , pT , yH2 O ) − µvH2 O (T2 , pT , yH2 O )
= µvH2 O (T1 , p1∗ ) + RT1 ln yH2 O − µvH2 O (T1 , p1∗ ) Z T2 SHv 2 O dT (4) −RT1 lnyH2 O + T1
Since
SHv 2 O
µv1 − µv2 =
>0 Z T2 T1
SHv 2 O dT > 0
(5)
2. Theory
So µvH2 O in the cool air at T1 has a higher chemical potential than that of the equivalent partial pressure water vapor in the hot gas. Thus, water will tend to move from the cold to the hot stream.
2.1. Thermodynamic basis for humidity pump
2.2. Heat and mass transfer in the unit
Unlike isothermal separations where the pressure gradients across the membrane drives the gas transfer, the Humidity Pump is driven by the temperature difference between the two air streams separated by a hydrophilic membrane. Assuming the two air streams have the same equivalent partial pressure, but different temperature (Air stream 1 is cooler than stream 2), then the chemical potential of water vapor in the hotter stream can be expressed as
A conceptual diagram of a humidity pump is shown in Fig. 1. A stream of fresh air is divided into two flows: feed and sweep. The feed and the sweep flow through the membrane counter-currently, while exchanging moisture and heat. The feed represents fresh air intake of a HVAC system that needs to be dehumidified in summer. The sweep acts as a driving force and a transport stream. Before entering the membrane unit, the sweep first flows through a surface-to-surface heat exchanger where it recovers the heat from the dehumidified feed. The sweep is then heated through a second exchanger of low-grade waste heat to a desired value. The temperature difference between these two air streams generates a thermal gradient in membrane, which is the driving force of vapor reverse-osmosis. Since humidity
µvH2 O (T2 , pT , yH2 O ) Z ∗ = µH2 O (T1 , p1 ) +
T2
∂µvH2 O ∂T
T1
Z +
yH2 O
∂µvH2 O
yH2 O=1
∂yH2 O
!
! dyH2 O
dT p,yH2 O =1
(1)
p,T1
Since SHv 2 O = −
∂µvH2 O ∂T
! (2) p,yH
=1 2O
Eq. (1) can be simplified as
Fig. 1. Conceptual diagram of a humidity pump.
L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
Fig. 2. Cross-section view of an elementary cell (surrounded by the dashed lines) in the humidity pump.
infiltrates from the feed to the sweep continuously, the vapor partial pressure in the feed is usually lower than that in the sweep. The vapor permeates through the membrane in a counter-pressure-gradient way. This is the reason why it is called a humidity pump. To increase packing density, a practical humidity pump is an air-to-air heat exchanger incorporates a cubic core where the feed and the sweep flow in thin, parallel, alternating membrane layers. For reasons of symmetry, the calculation domain is selected as the two-dimensional elementary cell represented in Fig. 2 by the system boundary (dashed lines) and consists in half the volume distributed between two consecutive layers. This humidity pump is developed from a membranebased Energy Recovery Ventilator, where vapor is transferred under pressure gradients. A novel porous hydrophilic zeolite membrane [3] is considered for moisture transfer. The adsorption isotherms and the diffusivity of the membrane material are experimentally obtained, which are the bases of simulation. To aid in the model set up, several assumptions are made: 1. Heat and mass transfer processes are in steady state. 2. Heat conduction and vapor diffusion in the two air streams are negligible compared to energy transport and vapor convection by bulk flow. 3. Adsorption of vapor and membrane material is in equilibrium adsorption-state. 4. Both the heat conductivity and the water diffusivity in the membrane are constants. 5. Temperature and concentration distributions in the thickness direction in membrane are linear. 6. Water vapor diffusion in the membrane only occurs in the thickness direction. 7. Heat and moisture transfer in the air streams is one-dimensional (in x direction), and heat
209
transfer in membrane is two-dimensional (x and z). With the above assumptions, it is easy to deduce that the water osmosis rate in the membrane is a constant in the thickness direction. On the other hand, many studies of water-permeable membrane have already revealed that the selectivity of water/air is very high (in the range of 460–30 000) [5], thus the air permeation through the membrane is negligible. For porous hydrophilic membrane, the fundamental mass transfer of permeation from the feed side to the sweep side can be considered to occur in three steps [7,8], i.e.: 1. adsorption at the feed side of the membrane, 2. diffusion through the membrane, 3. desorption at the sweep side of the membrane. 2.2.1. Governing equations for the module Feed m ˙ 1 cp1 m ˙1
2h1 ∂Tf1 + (Tf1 − Ts1 ) = 0 ∂x H1
2k1 ∂ω1 + (ρw1 − ρs1 ) = 0 ∂x H1
(6) (7)
Sweep can flow through the unit counter-currently or concurrently. For counter flow, the model is m ˙ 2 cp2 m ˙2
2h2 ∂Tf2 + (Tf2 (x 0 ) − Ts2 (x 0 )) = 0 0 ∂x H2
2k2 ∂ω2 + (ρw2 (x 0 ) − ρs2 (x 0 )) = 0 0 ∂x H2
(8) (9)
where, coordinate x 0 = L − x. If the sweep flows concurrently, then the model for the sweep becomes m ˙ 2 cp2 m ˙2
2h2 ∂Tf2 + (Tf2 − Ts2 ) = 0 ∂x H2
2k2 ∂ω2 + (ρw2 − ρs2 ) = 0 ∂x H2
(10) (11)
Membrane m ˙ w cpw
∂Tm ∂ 2 Tm ∂ 2 Tm − λm − λ =0 m ∂z ∂x 2 ∂z2
m ˙ w = −Dwm
∂C C1s − C2s = Dwm ∂z δ
(12) (13)
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L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
Surface 1 (Feed side) ∂Tm −λm = h1 (Tf1 − Tm ) + m ˙ w Lw ∂z z=0
where C1s , C2s are water concentration in membrane at two surfaces (kg m−3 ), δ is the membrane thickness. The direction of water osmosis is determined by the concentration difference between two sides of membrane. If m ˙ w is positive, the unit is working in ERV mode; if m ˙ w is negative, the unit works as a humidity pump. Ideal gas state equation for water vapor:
Surface 2 (sweep side): ∂Tm = −h2 (Tf2 − Tm ) + m ˙ w Lw −λm ∂z z=δ
Pv = ρv Rv T
where Lw is the latent heat of water (kJ kg−1 ).
(14)
where Pv is the partial pressure of water vapor (Pa), Rv is the ideal gas constant for water vapor. The relation between Pv and total pressure of atmosphere P is calculated by Pv =
ωP ω + 0.622
(15)
Water concentration in membrane is determined by the isotherms of membrane material as following in the Dubinin and Radushkevich form (the D–R equation) [9]: ( 2 ) P0 (16) C = C0 exp −γ Tm ln Pv
(23)
(24)
2.2.3. Heat and mass transfer in boundary layers Heat transfer in boundary layers is described by Nusselt correlations in which the Nusselt number, Nu, is related to the Reynolds number, Re, and the Prandtl number, Pr. A product, Re Pr de /L, is helpful in obtaining the Nusselt number. For values of Re Pr de /L less than approximately 100, Hausen’s correlation is often recommended for the estimation of heat transfer coefficients in the laminar flow regime [10] 0.085[Re Pr(de /L)] νb 0.14 (25) Nu = Nulim + νs 1 + 0.047 [RePr(de /L)]0.67
Tf1 |x=0 = Tf1i
(17)
Where de is the hydraulic diameter of the flow channel, ν is the dynamic viscosity (kg m−1 s−1 ) and L is the length of the flow channel. Subscript ‘b’ refers to bulk and ‘s’ refers to surface. For laminar flow at higher values of Re Pr de /L, the Siedel–Tate correlation is often recommended [10] 0.14 0.33 νb (26) Nu = 1.86[Re Pr(de /L)] νs
ω1 |x=0 = ω1i
(18)
For turbulent flow, the Dittus–Boelter correlation is recommended [10]
where C0 and γ are coefficients, P is the vapor pressure in the voids of membrane, P0 is the corresponding saturated pressure of vapor. 2.2.2. Boundary conditions Feed
Nu = 0.023Re0.8 Pr n
Sweep Tf2 |x 0 =0 = Tf2i ω2 y=0 = ω2i where x 0 = L − x. Membrane ∂Tm =0 ∂x x=0 ∂Tm =0 ∂x x=L
(19) (20)
(21) (22)
(27)
in which n=0.4 if the fluid is being heated and n=0.3 if the fluid is being cooled. For pipe flow, the lower limiting value of the Nusselt number (Nulim ) is 3.658. For flow in rectangular channels, Nulim is dependent on the geometry of the flow channel [11]. Hydraulic diameter for rectangular flow channel is 4bH (28) de = 2(b + H ) where b is the width of the channel.
L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
211
Mass transfer in boundary layers is often described by Sherwood correlations in which the Sherwood number, Sh, is
Table 1 Some parameters of the humidity pump Symbol
Value
Unit
kde Sh = Dva
A L H1 H2 b
5.21 0.72 0.01 0.01 0.24 20
m2 m m m m m
(29)
where Dva is the diffusivity of vapor in air (m2 s−1 ). Convective mass transfer can be an analogy to convective heat transfer [11]. Then we have Sh = Nu
(30)
i.e. h k= ρa cpa Le
(31)
where ρ a is the density of humid air; cpa is the specific heat of humid air; Le is the Lewis number which is defined as Le =
λa ρa cpa Dva
␦
(32)
3. Results and discussion The parameters in the model are strongly coupled. To overcome this problem, the nonlinearty of the equations is solved by iterative techniques. The two-dimensional equations of the membrane are calculated by the means of ADI (alternating direction
implicit) method [12]. It should be noted that since the membrane thickness is very small compared to the length and width, all variables must be in double-precision format, to alleviate numeric error. A case study is considered. Some parameters of the humidity pump are shown in Table 1. Using the model, the temperature and the humidity are calculated for both the feed and the sweep. The parameters of the air streams at inlets are, Feed: t1 =30◦ C, ω1 =0.019 kg kg−1 ; sweep: t2 =50◦ C, ˙1 = ω2 =ω1 =0.019 kg kg−1 ; air mass flow rates G ˙2 = G ˙ = 0.05 kg s−1 . G The temperature distributions of the feed, the sweep, and the membrane are shown in Fig. 3. The temperature distributions are very linear. A temperature difference of 3.5◦ C between the feed and the sweep can be maintained throughout the membrane length. The temperature of the membrane is half the sum of feed
Fig. 3. Temperature distribution along membrane length.
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L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
Fig. 4. Humidity distribution along membrane length.
temperature and sweep temperature. Due to small resistance of membrane material and small thickness, the temperature difference between the two sides of membrane is very small (in the order of 10−4◦ C). The small temperature difference results in a limited performance, which will be discussed later. This result is a sharp contrast to the analysis by M. Tasaka et al. [13]. The difference may be attributed to the difference of flows studied (they studied the Thermo-osmosis between two liquid flows). The humidity distributions of the fluids are shown in Fig. 4. As can be seen, the humidity pump mode is
realized throughout the membrane length. The sweep absorbs the moisture from the feed and drives them away. Humidity distribution is linear both for the feed and for the sweep. No re-mix occurs. The moisture osmosis rate along the membrane length is shown in Fig. 5. The value is very stable. The reason for this phenomenon is that a stable temperature difference between two sides of membrane can be quarantined by counter flow arrangement. Numerical results found that the counter flow arrangement is superior to concurrent flow arrangement for both the heat transfer and the mass transfer. Thus, counter-flow
Fig. 5. Vapor reverse-osmosis rate along membrane length.
L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
213
Fig. 6. Influence of thickness on vapor reverse-osmosis rate.
humidity pump performs better than concurrent flow humidity pump. The thickness of the membrane is another important factor. The influence of membrane thickness on humidity pump performance is shown in Fig. 6. As can be seen, vapor osmosis rate decreases with an increase in thickness. It should be noted that the performance of a humidity pump is determined by two resistance: thermal resistance and mass transfer resistance. The bigger the thickness, the greater the thermal resistance and the mass transfer resistance. A greater thermal resistance is beneficial for the performance since the bigger the temperature difference, the larger the osmosis rate. However, a greater mass transfer resistance is detrimental to humidity pump performance. These are two opposite effects. For the present material, the effect of mass transfer resistance is more important than that of thermal resistance. Therefore, performance decreases with an increase in thickness. Since the driving force of water osmosis is the temperature difference of the two fluids. The permeability of the membrane increases with a rise in temperature difference of two inlets, as shown in Fig. 7. The permeability can be raised 10 times higher when the temperature difference of inlets is increased from 20 to 100◦ C. In Fig. 8 are shown the effects of mass flow rate of two fluids on permeability. As can be seen, the permeability increases with an increasing mass flow
rate. This is due to a greater temperature difference and a smaller vapor partial pressure difference between the two fluids resulted from increased mass flow. When the flow rate is bigger than 0.2 kg s−1 , the step of increase tends to be smaller. Even though the permeability is increased, the dehumidification effectiveness of the humidity pump decreases, which is undesirable. From above analysis, it is clear that humidity pump can be realized by the use of waste heat. However, the performance is very limited. The water vapor transfer rate is relatively small. For practical applications, an osmosis rate in the order of 10−5 kg m−2 s−1 is required to keep the bulk and investment within the economic limits. New membrane material that has a better performance is desired. To investigate the effects of parameters of material on humidity pump performance, a new coefficient which reflects both the adsorption characters and the thermodynamic and dynamic parameters of the membrane material should be defined. In simulations, we found that the humidity pump performance is very sensitive to a factor shown as following. ψ = γ 0.2
Dwm λm
1/3 (33)
where γ is the coefficient in adsorption isotherm (Eq. (16)) of membrane material, Dwm is the diffusivity of
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L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
Fig. 7. Effects of temperature difference on permeability.
water in membrane (m2 s−1 ), and λm is the thermal conductivity of membrane material (kW mK−1 ). We define this dimensional parameter the humidity pump factor. For the present membrane material, the value of ψ is about 0.006 mK−1/7.5 kJ1/3 . The corresponding vapor osmosis rate is in the order of 10−7 kg m−2 s−1 . The variations of humidity pump performance with different humidity pump factor are shown in Fig. 9. As can be seen, the water osmosis rate increases with a rise in ψ. When the ψ is smaller than 0.035 mK−1/7.5 kJ1/3 , the step of increase is very
large. When the ψ is bigger than 0.035 mK−1/7.5 kJ1/3 , the step of increase tends to be small. A further increase in ψ has little merit in further increasing the performance. On the other hand, when ψ is bigger than 0.02 mK−1/7.5 kJ1/3 , the water osmosis rate is bigger than 1.0−5 kg m−2 s−1 , and the humidity pump can be used in practical systems. Thus, new material with humidity pump factor ψ bigger than 0.02 mK−1/7.5 kJ1/3 is desired for the implementation of membrane-based Humidity Pump.
Fig. 8. Influence of mass flow rate of fluids on permeability.
L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
215
Fig. 9. Variation of permeability of the humidity pump with ψ.
4. Conclusions In this paper, the mathematical model for a counter flow membrane-based humidity pump is set up. The thermodynamic basis for dehumidification is presented. Using a hydrophilic porous membrane core, the performance and limitations of the Humidity Pump is analyzed. It is found that the thermally driven water reverse-osmosis can be realized when the heating and cooling fluids have a certain temperature difference. The performance of Humidity pump decreases with an increase in thickness, but increases with increasing temperature difference between two inlets. The performance of humidity pump is mainly determined by a parameter named humidity pump factor ψ. The value of ψ of present material is very small, resulting in limited performance. For practical systems, new material with ψ bigger than 0.02 mK−1/7.5 kJ1/3 is desired. It’s our future research direction.
5. Nomenclature a A b cp
Thermal diffusivity (m2 /s) Membrane area (m2 ) Width of the flow channel (m) Specific heat (kJ kg−1 K−1 )
C de D Dva Dwm ˙ G h H k L Lw m ˙ P P∗ Q R S T x, y, z yH2 O λ δ ω ν µ
Water concentration in membrane (kg m−3 ) Hydraulic diameter (m) Moisture transfer rate (kg s−1 ) Diffusivity of vapor in air (m2 s−1 ) Diffusivity of water in membrane (m2 s−1 ) Total mass flow rate of air streams (kg s−1 ) Convective heat transfer coefficient (kW m−2 K−1 ) Height of the flow channel (m) Convective mass transfer coefficient (m s−1 ) Length of the flow channel (m) Latent heat of evaporization of water (kJ kg−1 ) Mass flow-rate for unit cross-section area (kg m−2 s−1 ) Pressure (Pa) Reference pressure (Pa) Heat transfer rate (kW) Ideal gas constant (kJ kg−1 K−1 ) Entropy (kJ kg−1 K−1 ) Tempareture (K) Coordinates (m) Mole fraction of vapor in air Thermal conductivity (kW m−1 K−1 ) Thickness of membrane (m) Humidity (kg water/kg air) Dynamic viscosity (Pas) Chemical potential (kJ kg−1 )
216
ρ ψ
L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
Density (kg m−3 ) Humidity pump factor (mK−1/7.5 kJ1/3 )
Subscripts a Air f Fluids I Inlet m Membrane s Surface v Vapor w Water 1 Feed, feed inlet 2 Sweep, sweep inlet 3 Feed outlet 4 Sweep outlet
Acknowledgements This project is funded and approved by UTRC (United Technologies Research Center of USA). References [1] G.W. Brundrett, Handbook of dehumidification technology, Butterworths, London, 1987.
[2] U. Sander, H. Janssen, Industrial application of vapour permeation, J. Membr. Sci. 61 (1991) 113–129. [3] J.Q. Wang, Z. Li, Synthesis of zeolite membrane and its application in removal of moisture from gases, Membr. Sci. Technol. 18 (1998) 54–58. [4] C.Y. Pan, C.D. Jensen, C. Bielech, H.W. Habgood, Permeation of water vapor through cellulose triacetate membranes in hollow fiber form, J. Appl. Polym. Sci. 22 (1978) 2307– 2323. [5] K.L. Wang, S.H. Mccray, D.D. Newbold, E.L. Cusseler, Hollow fiber air drying, J. Membr. Sci. 72 (1992) 231– 244. [6] J.S. Cha, R. Li, K.K. Sirkar, Removal of water vapor and VOCs from nitrogen in a hydrophilic hollow fiber gel membrane permeator, J. Membr. Sci. 119 (1996) 139– 153. [7] S.H. Chen, R.C. Ruaan, J.Y. Lai, Sorption and transport mechanism of gases in polycarbonate membranes, J. Membr. Sci. 134 (1997) 143–150. [8] M. Asaeda, L.D. Du, Separation of alcohol/water gaseous mixtures by thin ceramic membrane, J. Chem. Eng. Jpn. 19 (1986) 72–77. [9] M. Suzuki, Adsorption engineering, Kodansha, Tokyo, 1989. [10] H.O.E. Karlsson, T. Gun, Heat transfer in pervaporation, J. Membr. Sci. 119 (1996) 295–306. [11] F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, 3rd Edition, Wiley, New York, 1990. [12] R. Peyret, T.D. Taylor, Computational Methods for Fluid flow, Springer, New York, 1990. [13] M. Tasaka, H. Futamura, The effects of temperature on thermoosmosis, J. Membr. Sci. 28 (1986) 183–190.
Membrane-based humidity pump: performance and limitations L.Z. Zhang∗ , Y. Jiang, Y.P. Zhang Department of Thermal Engineering, Tsinghua University, Beijing 100084, PR China Received 20 May 1999; received in revised form 14 December 1999; accepted 16 December 1999
Abstract Moisture is usually transported from a fluid of high humidity to a fluid of relatively low humidity through a membrane. Membrane-based humidity pump works in another way: moisture is transported from a dryer air stream to a humid air stream under the driving force of thermal gradients in membrane. With humidity pump, a continuous air dehumidification can be realized by the utilization of low-grade waste heat. In this article, through finite difference simulations of the coupled heat and mass transfer in the unit, the performance and limitations of a membrane-based humidity pump are analyzed. The effects of various thermodynamic and dynamic parameters of membrane on the performance of humidity pump are discussed. It is found that even though the operational parameters can be optimized to enhance the thermo-osmosis rate of water vapor, the key role is played by a factor named humidity pump. Furthermore, when the humidity pump factor is bigger than 0.02 mK−1/7.5 kJ1/3 , the permeability is bigger than 1.0×10−5 kg m−2 s−1 , and the humidity pump can be used in commercial applications. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Microporous and porous membranes; Gas and vapor permeation; Humidity pump; Thermodynamics; Thermoosmosis
1. Introduction With the advances in cooling technology, independent humidity control techniques are strongly desired in air-conditioning industry. The most widely practiced techniques of dehumidification include cooling coils, fixed adsorbent beds, absorption tower and rotary wheel desiccant. These methods are bulky and very energy consuming since a large amount of energy is wasted in vapor phase change or desiccant regeneration [1]. The development in membrane science (especially pervaporation and gas separation) provides a new alternative to these traditional techniques. In recent years, membrane-based air dehumidification ∗ Corresponding author. Tel.: +86-10-62772072; fax: +86-10-62770544. E-mail address: [email protected] (L.Z. Zhang)
has drawn much attention since it offers a stable and continuous operable system that combines long life with low energy consumption [2–6]. In these systems, moisture is transferred from a fluid of high vapor partial pressure to a fluid of low vapor partial pressure under the driving force of pressure gradients. These systems are very interesting and they continue to be actively pursued. However, they must be operated under very high pressure-difference and thus high membrane intensity is required, which may be very problematic. Besides, the use of compressors (or vacuum pumps) also increases mechanical complexity and energy consumption. In addition to pressure-forced membrane dehumidification, there is another way of dehumidification: thermally forced membrane dehumidification. Based on the theory of Thermo-osmosis, moisture can also be transferred from a dryer air stream to a humid air
0376-7388/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 7 3 8 8 ( 0 0 ) 0 0 3 0 4 - 5
208
L.Z. Zhang et al. / Journal of Membrane Science 171 (2000) 207–216
stream under the driving force of thermal gradients in membrane. In analogy to a heat pump, we call this way of moisture transport as the humidity pump. The thermally forced dehumidification is more attractive since here low-grade waste heat can be used to dehumidify a supply air stream. Furthermore, since no pressure difference exists between the two sides of a membrane, the durability and reliability could be very high. In this paper, the heat and mass transfer mechanisms of a membrane-based humidity pump are studied. The effects of various thermodynamic and dynamic parameters on the permeability are discussed. Through finite difference simulations, the temperature and moisture distributions along the stream are obtained. The performance and the limitations of the humidity pump are investigated. The requirement for the membrane material of a humidity pump is discussed.
µvH2 O (T2 , pT , yH2 O ) = µH2 O (T1 , p1∗ ) −
Z
+RT1 lnyH2 O
T2
T1
SHv 2 O dT (3)
The chemical potential difference of the two air streams is µvH2 O (T1 , pT , yH2 O ) − µvH2 O (T2 , pT , yH2 O )
= µvH2 O (T1 , p1∗ ) + RT1 ln yH2 O − µvH2 O (T1 , p1∗ ) Z T2 SHv 2 O dT (4) −RT1 lnyH2 O + T1
Since
SHv 2 O
µv1 − µv2 =
>0 Z T2 T1
SHv 2 O dT > 0
(5)
2. Theory
So µvH2 O in the cool air at T1 has a higher chemical potential than that of the equivalent partial pressure water vapor in the hot gas. Thus, water will tend to move from the cold to the hot stream.
2.1. Thermodynamic basis for humidity pump
2.2. Heat and mass transfer in the unit
Unlike isothermal separations where the pressure gradients across the membrane drives the gas transfer, the Humidity Pump is driven by the temperature difference between the two air streams separated by a hydrophilic membrane. Assuming the two air streams have the same equivalent partial pressure, but different temperature (Air stream 1 is cooler than stream 2), then the chemical potential of water vapor in the hotter stream can be expressed as
A conceptual diagram of a humidity pump is shown in Fig. 1. A stream of fresh air is divided into two flows: feed and sweep. The feed and the sweep flow through the membrane counter-currently, while exchanging moisture and heat. The feed represents fresh air intake of a HVAC system that needs to be dehumidified in summer. The sweep acts as a driving force and a transport stream. Before entering the membrane unit, the sweep first flows through a surface-to-surface heat exchanger where it recovers the heat from the dehumidified feed. The sweep is then heated through a second exchanger of low-grade waste heat to a desired value. The temperature difference between these two air streams generates a thermal gradient in membrane, which is the driving force of vapor reverse-osmosis. Since humidity
µvH2 O (T2 , pT , yH2 O ) Z ∗ = µH2 O (T1 , p1 ) +
T2
∂µvH2 O ∂T
T1
Z +
yH2 O
∂µvH2 O
yH2 O=1
∂yH2 O
!
! dyH2 O
dT p,yH2 O =1
(1)
p,T1
Since SHv 2 O = −
∂µvH2 O ∂T
! (2) p,yH
=1 2O
Eq. (1) can be simplified as
Fig. 1. Conceptual diagram of a humidity pump.
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Fig. 2. Cross-section view of an elementary cell (surrounded by the dashed lines) in the humidity pump.
infiltrates from the feed to the sweep continuously, the vapor partial pressure in the feed is usually lower than that in the sweep. The vapor permeates through the membrane in a counter-pressure-gradient way. This is the reason why it is called a humidity pump. To increase packing density, a practical humidity pump is an air-to-air heat exchanger incorporates a cubic core where the feed and the sweep flow in thin, parallel, alternating membrane layers. For reasons of symmetry, the calculation domain is selected as the two-dimensional elementary cell represented in Fig. 2 by the system boundary (dashed lines) and consists in half the volume distributed between two consecutive layers. This humidity pump is developed from a membranebased Energy Recovery Ventilator, where vapor is transferred under pressure gradients. A novel porous hydrophilic zeolite membrane [3] is considered for moisture transfer. The adsorption isotherms and the diffusivity of the membrane material are experimentally obtained, which are the bases of simulation. To aid in the model set up, several assumptions are made: 1. Heat and mass transfer processes are in steady state. 2. Heat conduction and vapor diffusion in the two air streams are negligible compared to energy transport and vapor convection by bulk flow. 3. Adsorption of vapor and membrane material is in equilibrium adsorption-state. 4. Both the heat conductivity and the water diffusivity in the membrane are constants. 5. Temperature and concentration distributions in the thickness direction in membrane are linear. 6. Water vapor diffusion in the membrane only occurs in the thickness direction. 7. Heat and moisture transfer in the air streams is one-dimensional (in x direction), and heat
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transfer in membrane is two-dimensional (x and z). With the above assumptions, it is easy to deduce that the water osmosis rate in the membrane is a constant in the thickness direction. On the other hand, many studies of water-permeable membrane have already revealed that the selectivity of water/air is very high (in the range of 460–30 000) [5], thus the air permeation through the membrane is negligible. For porous hydrophilic membrane, the fundamental mass transfer of permeation from the feed side to the sweep side can be considered to occur in three steps [7,8], i.e.: 1. adsorption at the feed side of the membrane, 2. diffusion through the membrane, 3. desorption at the sweep side of the membrane. 2.2.1. Governing equations for the module Feed m ˙ 1 cp1 m ˙1
2h1 ∂Tf1 + (Tf1 − Ts1 ) = 0 ∂x H1
2k1 ∂ω1 + (ρw1 − ρs1 ) = 0 ∂x H1
(6) (7)
Sweep can flow through the unit counter-currently or concurrently. For counter flow, the model is m ˙ 2 cp2 m ˙2
2h2 ∂Tf2 + (Tf2 (x 0 ) − Ts2 (x 0 )) = 0 0 ∂x H2
2k2 ∂ω2 + (ρw2 (x 0 ) − ρs2 (x 0 )) = 0 0 ∂x H2
(8) (9)
where, coordinate x 0 = L − x. If the sweep flows concurrently, then the model for the sweep becomes m ˙ 2 cp2 m ˙2
2h2 ∂Tf2 + (Tf2 − Ts2 ) = 0 ∂x H2
2k2 ∂ω2 + (ρw2 − ρs2 ) = 0 ∂x H2
(10) (11)
Membrane m ˙ w cpw
∂Tm ∂ 2 Tm ∂ 2 Tm − λm − λ =0 m ∂z ∂x 2 ∂z2
m ˙ w = −Dwm
∂C C1s − C2s = Dwm ∂z δ
(12) (13)
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Surface 1 (Feed side) ∂Tm −λm = h1 (Tf1 − Tm ) + m ˙ w Lw ∂z z=0
where C1s , C2s are water concentration in membrane at two surfaces (kg m−3 ), δ is the membrane thickness. The direction of water osmosis is determined by the concentration difference between two sides of membrane. If m ˙ w is positive, the unit is working in ERV mode; if m ˙ w is negative, the unit works as a humidity pump. Ideal gas state equation for water vapor:
Surface 2 (sweep side): ∂Tm = −h2 (Tf2 − Tm ) + m ˙ w Lw −λm ∂z z=δ
Pv = ρv Rv T
where Lw is the latent heat of water (kJ kg−1 ).
(14)
where Pv is the partial pressure of water vapor (Pa), Rv is the ideal gas constant for water vapor. The relation between Pv and total pressure of atmosphere P is calculated by Pv =
ωP ω + 0.622
(15)
Water concentration in membrane is determined by the isotherms of membrane material as following in the Dubinin and Radushkevich form (the D–R equation) [9]: ( 2 ) P0 (16) C = C0 exp −γ Tm ln Pv
(23)
(24)
2.2.3. Heat and mass transfer in boundary layers Heat transfer in boundary layers is described by Nusselt correlations in which the Nusselt number, Nu, is related to the Reynolds number, Re, and the Prandtl number, Pr. A product, Re Pr de /L, is helpful in obtaining the Nusselt number. For values of Re Pr de /L less than approximately 100, Hausen’s correlation is often recommended for the estimation of heat transfer coefficients in the laminar flow regime [10] 0.085[Re Pr(de /L)] νb 0.14 (25) Nu = Nulim + νs 1 + 0.047 [RePr(de /L)]0.67
Tf1 |x=0 = Tf1i
(17)
Where de is the hydraulic diameter of the flow channel, ν is the dynamic viscosity (kg m−1 s−1 ) and L is the length of the flow channel. Subscript ‘b’ refers to bulk and ‘s’ refers to surface. For laminar flow at higher values of Re Pr de /L, the Siedel–Tate correlation is often recommended [10] 0.14 0.33 νb (26) Nu = 1.86[Re Pr(de /L)] νs
ω1 |x=0 = ω1i
(18)
For turbulent flow, the Dittus–Boelter correlation is recommended [10]
where C0 and γ are coefficients, P is the vapor pressure in the voids of membrane, P0 is the corresponding saturated pressure of vapor. 2.2.2. Boundary conditions Feed
Nu = 0.023Re0.8 Pr n
Sweep Tf2 |x 0 =0 = Tf2i ω2 y=0 = ω2i where x 0 = L − x. Membrane ∂Tm =0 ∂x x=0 ∂Tm =0 ∂x x=L
(19) (20)
(21) (22)
(27)
in which n=0.4 if the fluid is being heated and n=0.3 if the fluid is being cooled. For pipe flow, the lower limiting value of the Nusselt number (Nulim ) is 3.658. For flow in rectangular channels, Nulim is dependent on the geometry of the flow channel [11]. Hydraulic diameter for rectangular flow channel is 4bH (28) de = 2(b + H ) where b is the width of the channel.
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Mass transfer in boundary layers is often described by Sherwood correlations in which the Sherwood number, Sh, is
Table 1 Some parameters of the humidity pump Symbol
Value
Unit
kde Sh = Dva
A L H1 H2 b
5.21 0.72 0.01 0.01 0.24 20
m2 m m m m m
(29)
where Dva is the diffusivity of vapor in air (m2 s−1 ). Convective mass transfer can be an analogy to convective heat transfer [11]. Then we have Sh = Nu
(30)
i.e. h k= ρa cpa Le
(31)
where ρ a is the density of humid air; cpa is the specific heat of humid air; Le is the Lewis number which is defined as Le =
λa ρa cpa Dva
␦
(32)
3. Results and discussion The parameters in the model are strongly coupled. To overcome this problem, the nonlinearty of the equations is solved by iterative techniques. The two-dimensional equations of the membrane are calculated by the means of ADI (alternating direction
implicit) method [12]. It should be noted that since the membrane thickness is very small compared to the length and width, all variables must be in double-precision format, to alleviate numeric error. A case study is considered. Some parameters of the humidity pump are shown in Table 1. Using the model, the temperature and the humidity are calculated for both the feed and the sweep. The parameters of the air streams at inlets are, Feed: t1 =30◦ C, ω1 =0.019 kg kg−1 ; sweep: t2 =50◦ C, ˙1 = ω2 =ω1 =0.019 kg kg−1 ; air mass flow rates G ˙2 = G ˙ = 0.05 kg s−1 . G The temperature distributions of the feed, the sweep, and the membrane are shown in Fig. 3. The temperature distributions are very linear. A temperature difference of 3.5◦ C between the feed and the sweep can be maintained throughout the membrane length. The temperature of the membrane is half the sum of feed
Fig. 3. Temperature distribution along membrane length.
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Fig. 4. Humidity distribution along membrane length.
temperature and sweep temperature. Due to small resistance of membrane material and small thickness, the temperature difference between the two sides of membrane is very small (in the order of 10−4◦ C). The small temperature difference results in a limited performance, which will be discussed later. This result is a sharp contrast to the analysis by M. Tasaka et al. [13]. The difference may be attributed to the difference of flows studied (they studied the Thermo-osmosis between two liquid flows). The humidity distributions of the fluids are shown in Fig. 4. As can be seen, the humidity pump mode is
realized throughout the membrane length. The sweep absorbs the moisture from the feed and drives them away. Humidity distribution is linear both for the feed and for the sweep. No re-mix occurs. The moisture osmosis rate along the membrane length is shown in Fig. 5. The value is very stable. The reason for this phenomenon is that a stable temperature difference between two sides of membrane can be quarantined by counter flow arrangement. Numerical results found that the counter flow arrangement is superior to concurrent flow arrangement for both the heat transfer and the mass transfer. Thus, counter-flow
Fig. 5. Vapor reverse-osmosis rate along membrane length.
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Fig. 6. Influence of thickness on vapor reverse-osmosis rate.
humidity pump performs better than concurrent flow humidity pump. The thickness of the membrane is another important factor. The influence of membrane thickness on humidity pump performance is shown in Fig. 6. As can be seen, vapor osmosis rate decreases with an increase in thickness. It should be noted that the performance of a humidity pump is determined by two resistance: thermal resistance and mass transfer resistance. The bigger the thickness, the greater the thermal resistance and the mass transfer resistance. A greater thermal resistance is beneficial for the performance since the bigger the temperature difference, the larger the osmosis rate. However, a greater mass transfer resistance is detrimental to humidity pump performance. These are two opposite effects. For the present material, the effect of mass transfer resistance is more important than that of thermal resistance. Therefore, performance decreases with an increase in thickness. Since the driving force of water osmosis is the temperature difference of the two fluids. The permeability of the membrane increases with a rise in temperature difference of two inlets, as shown in Fig. 7. The permeability can be raised 10 times higher when the temperature difference of inlets is increased from 20 to 100◦ C. In Fig. 8 are shown the effects of mass flow rate of two fluids on permeability. As can be seen, the permeability increases with an increasing mass flow
rate. This is due to a greater temperature difference and a smaller vapor partial pressure difference between the two fluids resulted from increased mass flow. When the flow rate is bigger than 0.2 kg s−1 , the step of increase tends to be smaller. Even though the permeability is increased, the dehumidification effectiveness of the humidity pump decreases, which is undesirable. From above analysis, it is clear that humidity pump can be realized by the use of waste heat. However, the performance is very limited. The water vapor transfer rate is relatively small. For practical applications, an osmosis rate in the order of 10−5 kg m−2 s−1 is required to keep the bulk and investment within the economic limits. New membrane material that has a better performance is desired. To investigate the effects of parameters of material on humidity pump performance, a new coefficient which reflects both the adsorption characters and the thermodynamic and dynamic parameters of the membrane material should be defined. In simulations, we found that the humidity pump performance is very sensitive to a factor shown as following. ψ = γ 0.2
Dwm λm
1/3 (33)
where γ is the coefficient in adsorption isotherm (Eq. (16)) of membrane material, Dwm is the diffusivity of
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Fig. 7. Effects of temperature difference on permeability.
water in membrane (m2 s−1 ), and λm is the thermal conductivity of membrane material (kW mK−1 ). We define this dimensional parameter the humidity pump factor. For the present membrane material, the value of ψ is about 0.006 mK−1/7.5 kJ1/3 . The corresponding vapor osmosis rate is in the order of 10−7 kg m−2 s−1 . The variations of humidity pump performance with different humidity pump factor are shown in Fig. 9. As can be seen, the water osmosis rate increases with a rise in ψ. When the ψ is smaller than 0.035 mK−1/7.5 kJ1/3 , the step of increase is very
large. When the ψ is bigger than 0.035 mK−1/7.5 kJ1/3 , the step of increase tends to be small. A further increase in ψ has little merit in further increasing the performance. On the other hand, when ψ is bigger than 0.02 mK−1/7.5 kJ1/3 , the water osmosis rate is bigger than 1.0−5 kg m−2 s−1 , and the humidity pump can be used in practical systems. Thus, new material with humidity pump factor ψ bigger than 0.02 mK−1/7.5 kJ1/3 is desired for the implementation of membrane-based Humidity Pump.
Fig. 8. Influence of mass flow rate of fluids on permeability.
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Fig. 9. Variation of permeability of the humidity pump with ψ.
4. Conclusions In this paper, the mathematical model for a counter flow membrane-based humidity pump is set up. The thermodynamic basis for dehumidification is presented. Using a hydrophilic porous membrane core, the performance and limitations of the Humidity Pump is analyzed. It is found that the thermally driven water reverse-osmosis can be realized when the heating and cooling fluids have a certain temperature difference. The performance of Humidity pump decreases with an increase in thickness, but increases with increasing temperature difference between two inlets. The performance of humidity pump is mainly determined by a parameter named humidity pump factor ψ. The value of ψ of present material is very small, resulting in limited performance. For practical systems, new material with ψ bigger than 0.02 mK−1/7.5 kJ1/3 is desired. It’s our future research direction.
5. Nomenclature a A b cp
Thermal diffusivity (m2 /s) Membrane area (m2 ) Width of the flow channel (m) Specific heat (kJ kg−1 K−1 )
C de D Dva Dwm ˙ G h H k L Lw m ˙ P P∗ Q R S T x, y, z yH2 O λ δ ω ν µ
Water concentration in membrane (kg m−3 ) Hydraulic diameter (m) Moisture transfer rate (kg s−1 ) Diffusivity of vapor in air (m2 s−1 ) Diffusivity of water in membrane (m2 s−1 ) Total mass flow rate of air streams (kg s−1 ) Convective heat transfer coefficient (kW m−2 K−1 ) Height of the flow channel (m) Convective mass transfer coefficient (m s−1 ) Length of the flow channel (m) Latent heat of evaporization of water (kJ kg−1 ) Mass flow-rate for unit cross-section area (kg m−2 s−1 ) Pressure (Pa) Reference pressure (Pa) Heat transfer rate (kW) Ideal gas constant (kJ kg−1 K−1 ) Entropy (kJ kg−1 K−1 ) Tempareture (K) Coordinates (m) Mole fraction of vapor in air Thermal conductivity (kW m−1 K−1 ) Thickness of membrane (m) Humidity (kg water/kg air) Dynamic viscosity (Pas) Chemical potential (kJ kg−1 )
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ρ ψ
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Density (kg m−3 ) Humidity pump factor (mK−1/7.5 kJ1/3 )
Subscripts a Air f Fluids I Inlet m Membrane s Surface v Vapor w Water 1 Feed, feed inlet 2 Sweep, sweep inlet 3 Feed outlet 4 Sweep outlet
Acknowledgements This project is funded and approved by UTRC (United Technologies Research Center of USA). References [1] G.W. Brundrett, Handbook of dehumidification technology, Butterworths, London, 1987.
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