Abstract An innovative Diffusion Driven Desalination process was recently described where evaporation of seawater is driven by diffusion within a packed bed.
Heat Mass Transfer (2006) 42: 528–536 DOI 10.1007/s00231-005-0649-2
S P E C I A L IS SU E
James F. Klausner Æ Yi Li Æ Renwei Mei
Evaporative heat and mass transfer for the diffusion driven desalination process
Received: 14 June 2004 / Accepted: 31 January 2005 / Published online: 13 May 2005 Springer-Verlag 2005
Abstract An innovative Diffusion Driven Desalination process was recently described where evaporation of seawater is driven by diffusion within a packed bed. This work describes the evaporative heat and mass transfer analysis for the packed bed. Temperature and humidity data have been collected over a range of flow conditions at the inlet and outlet of the packed bed. The analysis agrees very well with the experimental data collected during this investigation and that which has been reported in the literature. Keywords Desalination Æ Diffusion Æ Packed bed Æ Heat/mass transfer Æ Countercurrent flow Nomenclature A Control surface area (m2) a Specific area of packing material (m2 /m3) Cp Specific heat of air (kJ/kg) dp Diameter of packing (m) D Molecular diffusion coefficient (m2/s) g Gravity (m/s2) G Air mass flux (kg/m2 s) h Enthalpy (kJ/kg) hfg Latent heat of vaporization (kJ/kg) k Mass transfer coefficient (m/s) L Water mass flux (kg/m2 s) MV Vapor molecular weight (kg/kmol) m Mass flow rate (kg/s) P Pressure (Pa) Psat Partial pressure of vapor (Pa or kPa) T Temperature (C or K) U Heat transfer coefficient (W/m2 K) U Relative humidity a Heat diffusion coefficient (m2 /s) l Dynamic viscosity (kg/m s) q Density (kg/m3) J. F. Klausner (&) Æ Y. Li Æ R. Mei Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA E-mail: klaus@ufl.edu
rL rC x
Liquid/gas interfacial surface tension (N/m) Critical surface tension of packing (N/m) Humidity ratio
Subscripts a Air evap The portion of liquid evaporated G Air/vapor mixture GA Gas side parameter based on the specific area of packing L Water in liquid phase LA Liquid side parameter based on the specific area of packing LW Liquid side parameter based on the specific wet area of packing V Water in vapor phase
1 Introduction A desalination technology that has drawn interest over the past two decades is referred to as Humidification Dehumidification (HDH). This process operates on the principle of mass diffusion and utilizes dry air to evaporate saline water, thus humidifying the air. Fresh water is produced by condensing out the water vapor, which results in dehumidification of the air. A significant advantage of this type of technology is that it provides a means for low pressure, low temperature desalination and can operate off of waste heat and is potentially cost competitive. Bourouni et al. [1], Al-Hallaj et al. [2], and Assouad and Lavan [3], respectively reported the operation of HDH units in Tunisia, Jordan, and Egypt. Muller-Holst et al. [4] fabricated an experimental Multi Effect Humidification (MEH) facility driven by solar energy and considered its performance over a wide range of operating conditions. The fresh water production varied on a seasonal basis since the process is driven by solar energy. The average fresh water production was
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about 6,000 l/month with a maximum of 10,500 l in May and 1,700 l in January. A computer simulation of the operational performance of the process was developed, and the predicted behavior agreed well with the actual behavior. An excellent comprehensive review of the HDH process is provided by Al-Hallaj and Selman [5]. It was concluded that although the HDH process operates off of low-grade energy, it is not currently cost competitive with reverse osmosis (RO) and multistage flash evaporation (MSF). There are three primary reasons for the higher costs associated with the HDH process. 1. The HDH process is typically applied to low production rates and economies of scale cannot be realized in construction. 2. Typically natural draft is relied upon, which results in low heat and mass transfer coefficients and a larger surface area humidifier. 3. Film condensation over tubes is typically used, which is extremely inefficient when non-condensable gases present. Thus a much larger condenser area is required for a given production rate, and the condenser accounts for the majority of the capital cost. Therefore, an economically feasible diffusion driven distillation process must overcome these shortcomings. Recently, Klausner et al. [6] described an innovative Diffusion Driven Desalination (DDD) process for the distillation of mineralized water. When the process is driven by waste heat derived from low pressure condensing steam within the main condenser of a steam generating power plant, there exist opportunities to produce large quantities of distilled water with lower costs than conventional desalination technologies. A simplified schematic diagram of the DDD process that indicates the flow paths and major components is shown in Fig. 1.
Fig. 1 Flow diagram for the DDD process
A main feed pump draws water from a large body of seawater. The surface water is pumped through the main feed water heater. (a) For the present application the heat is provided from low pressure condensing steam within a power plant. After the main heater, the feed water is sprayed into the top of a diffusion tower. (b) On the bottom of the diffusion tower, low humidity air is pumped in using a forced draft blower. The water falls countercurrently to the airflow through the diffusion tower by the action of gravity. The diffusion tower is packed with very high surface area packing material. As water flows through the diffusion tower, a thin film of water forms over the packing material and contacts the air flowing upward through the tower. As dictated by Fick’s law and the conservation of mass, momentum, and energy, liquid water will evaporate and diffuse into the air, due to concentration gradients. The diffusion tower should be designed such that the air/vapor mixture leaving the diffusion tower should be fully saturated. The water not evaporated in the diffusion tower, is collected at the bottom and removed with a brine pump. The air entering the diffusion tower will be dried in the direct contact condenser. (c) The saturated air/ vapor mixture leaving the diffusion tower is drawn into the direct contact condenser with a forced draft blower, where the water vapor is condensed into fresh liquid water that is collected in the sump of the condenser. A practical difficulty that arises is that film condensation heat transfer is tremendously degraded in the presence of non-condensable gas. In order to overcome this problem a direct contact condenser is used. For the present application the warm fresh water discharging the direct contact heat condenser will be chilled in a conventional shell- and -tube heat exchanger using saline cooling water. A portion of the chilled fresh water will be directed back to the direct contact heat exchanger to condense the water vapor from the air/vapor mixture
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discharging from the diffusion tower. The rest of the fresh water is the fresh water production. The dried air is returned to the diffusion tower. An appropriately designed DDD fresh water production plant requires a detailed heat and mass transfer analysis of the diffusion tower and direct contact condenser. This work will focus on the evaporative heat and mass transfer analyses required to design and analyze the diffusion tower.
2 Mathematical model The evaporation of mineralized water in the diffusion tower, shown in Fig. 2, is achieved by spraying heated feed water on top of a packed bed and blowing the dry air countercurrently through the bed. The falling liquid will form a thin film over the packing material while in contact with the low humidity turbulent air stream. Heat and mass transfer principles govern the evaporation of the water and the humidification of the air stream. When the system is operating at design conditions, the exit air stream humidity ratio should be as high as possible. The ideal state of the exit air/vapor stream from the diffusion tower is saturated. The most widely used model to estimate the heat and mass transfer associated with air/water evaporating systems is, that due to Merkel [7], which is used to analyze cooling towers. However Merkel’s analysis contains two restrictive assumptions,
Fig. 2 Diagram of diffusion tower
1. on the water side, the mass loss by evaporation of water is negligible and 2. the Lewis number (Le ¼ DaVV ; which is a measure of the ratio between characteristic lengths for thermal and mass diffusion) is unity. Merkel’s analysis is known to under-predict the required cooling tower volume and is not useful for the current analysis since the purpose of the diffusion tower is to maximize the evaporation of water for desalination. Baker and Shryock [8] have presented a detailed analysis of Merkel’s original work and have elucidated the error contributed from each specific assumption in Merkel’s model. Sutherland [9] developed an analysis, which includes water loss by evaporation but ignores the interfacial temperature between the liquid and air. Osterle [10] assumed that air is saturated throughout the whole process, Lewis number is unity, and air in contact with the liquid film is saturated at the water temperature. El-Dessouky et al. [11] have presented improved analyses for counter flow cooling towers, yet he assumed the available interfacial area for heat transfer is the same as that of mass transfer, which is only true when the packing is thoroughly wetted and is rare. An empirical enthalpy equation is used for the air/vapor mixture and is only valid for temperatures between 10C and 50C. The present model does not require any of the assumptions used in prior works. The current model includes the evaporation of water, the interfacial heat resistance between water and air, and the different interfacial areas for heat transfer and mass transfer. The current formulation is based on a two-fluid film model for a packed bed in which conservation equations for mass and energy are applied to a differential control volume shown in Fig. 3. In this figure, there is a clear interface between the liquid film and air/vapor mixture. Because the air is blown from bottom to top of the packed bed, the z-axis denotes the axial direction through the packed bed. The conservation of mass applied to the liquid phase of the control volume results in,
Fig. 3 Differential control volume for liquid/vapor heat and mass transfer within diffusion tower
531
d d ðmL;z Þ ¼ ðmV;evap Þ dz dz
ð1Þ
where m is the mass flow rate, the subscript L denotes the liquid, V denotes the vapor, and evap denotes the portion of liquid evaporated. Likewise, the conservation of mass applied to the gas (air/vapor mixture) side is expressed as, d d ðmV;z Þ ¼ ðmV;evap Þ: dz dz
ð2Þ
For an air/water–vapor mixture the humidity ratio, x, is related to the relative humidity, U, through, x¼
mV 0:622UPsat ðTa Þ ¼ P UPsat ðTa Þ ma
ð3Þ
Ti ¼
TL þ ðUG =UL ÞTa 1 þ ðUG =UL Þ
ð8Þ
In general the liquid side heat transfer coefficient is much greater than that on the gas side, thus the interfacial temperature is only slightly less than that of the liquid. The conservation of energy applied to the liquid phase of the control volume yields, d dðmV;evap Þ ðmL hL Þ ¼ hFg þ UaðTL Ta ÞA dz dz
ð9Þ
where U is the overall heat transfer coefficient, h is the enthalpy, and hFg is the latent heat. Noting that dhL L dhL ¼ CpL dTL ; dzd ðmL hL Þ ¼ hL dm dz þ mL dz and combining with Eqs. 9 and 1 results in an expression for the gradient of water temperature in the diffusion tower,
where P is the total system pressure and Psat (Ta) is the water saturation pressure corresponding to the air temperature Ta. It is assumed the total system pressure is constant. It is noted that the pressure drop is on the order of 100 Pa, which is a fraction of a percent of the absolute pressure. Using the definition of the mass transfer coefficient applied to the differential control volume and considering the interfacial area for mass transfer may differ from that of heat transfer, then,
where L = mLA is the water mass flux. Eq. 10 is also a first order ordinary differential equation with TL being the dependent variable and when solved yields the water temperature distribution through the diffusion tower. The conservation of energy applied to the air/water– vapor phase of the control volume yields,
d ðmV;evap Þ ¼ kG aw ½qv;sat ðTL Þ qv;1 ðTa ÞA dz
ð4Þ
Applying the perfect gas law [12] to the vapor, the gradient of the evaporation rate is expressed as, d MV Psat ðTi Þ UPsat ðTa Þ ðmV;evap Þ ¼ kG aw A ð5Þ dz Ti Ta R where kG is the mass transfer coefficient on gas side, a is the specific area of packing, which is defined as the total surface area of the packing per unit volume of space occupied, aw is the wetted specific area, Mv is the vapor molecular weight, R is the universal gas constant, Ti is the liquid/vapor interfacial temperature and A is the cross sectional area of the diffusion tower. Combining Eqs. 2, 3, and 5 the gradient of the humidity ratio in the diffusion tower is expressed as, dx kG aw MV Psat ðTi Þ x P ¼ ð6Þ dz Ti 0:622 þ x Ta G R where G=maA is the air mass flux. Eq. 6 is a first order ordinary differential equation with dependent variable, x, and when solved yields the variation of humidity ratio along the height of the diffusion tower. In order to evaluate the liquid/vapor interfacial temperature, it is recognized that the energy convected from the liquid is the same as that convected to the gas, UL ðTL Ti Þ ¼ UG ðTi Ta Þ
ð7Þ
where UL and UG are the respective liquid and gas heat transfer coefficients, and the interfacial temperature is evaluated from,
dTL G dx ðhFg hL Þ UaðTL Ta Þ ¼ þ L dz CpL CpL L dz
dðmV,evap Þ d ðma ha þ mV hV Þ þ hFg dz dz ¼ UaðTL Ta ÞA
ð10Þ
ð11Þ
Noting that the specific heat of the air/vapor mixture is evaluated as, ma mV Cpmix ¼ CPa þ Cpv ð12Þ ma þ mV ma þ mV and the latent heat of vaporization is evaluated as, hFg ðTa Þ ¼ hV ðTa Þ hL ðTa Þ
ð13Þ
combining with Eqs. 11 and 2 yields the gradient of air temperature in the diffusion tower, dTa 1 dx hL ðTa Þ UaðTL Ta Þ ¼ þ 1 þ x dz Cpmix Cpmix Gð1 þ xÞ dz
ð14Þ
Eq. 14 is also a first order ordinary differential equation with Ta being the dependent variable and when solved yields the air/vapor mixture temperature distribution along the height of the diffusion tower. Eqs. 6, 10, and 14 comprise a set of coupled ordinary differential equations that are used to solve for the humidity ratio, water temperature, and air/vapor mixture temperature distributions along the height of the diffusion tower. However, since a one-dimensional formulation is used, these equations require closure relationships. Specifically, the overall heat transfer coefficient and the gas side mass transfer coefficient are required. A significant difficulty that has been encountered in this analysis is that correlations for the water and air/vapor heat transfer
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coefficients for film flow though a packed bed, available in the open literature (McAdams et al. [13] and Huang and Fair [14]), are presented in dimensional form. Such correlations are not useful for the present analysis since a structured matrix type packing material is utilized, and the assumption employed to evaluate those heat transfer coefficients are questionable. In order to overcome this difficulty the mass transfer coefficients are evaluated for the liquid and gas flow using a widely tested correlation, and a heat and mass transfer analogy is used to evaluate the heat transfer coefficients. This overcomes the difficulty that gas and liquid heat transfer coefficients cannot be directly measured because the interfacial film temperature is not known. The mass transfer coefficients associated with film flow in packed beds have been widely investigated. The most widely used and perhaps most reliable correlation is that proposed by Onda et al. [15]. Onda’s correlation, shown in the Appendix, is used to calculate the mass transfer coefficients in the diffusion tower, kG and kL. However, it was found that Onda’s correlation underpredicted the wetted specific area of the packing material. Therefore, a correction was made as follows, ( " #) 3=4 rc 1=2 1=5 0:05 aw ¼ a 1 exp 2:2 ReLA FrL WeL rL ð15Þ see Appendix for details. As mentioned previously, the heat and mass transfer analogy [16] is used to compute the heat transfer coefficients for the liquid side and the gas side. Therefore the heat transfer coefficients are computed as follows, Heat transfer coefficient on the liquid side NuL 1=2 PrL
¼
ShL
ð16Þ
1=2
ScL
KL 1=2 UL ¼ kL qL CPL DL
ð17Þ
Heat transfer coefficient on the gas side NuG 1=3 PrG
¼
ShG 1=3
ð18Þ
;
ScG
UG ¼ kG ðqG CPG Þ1=3
KG DG
2=3 ð19Þ
Overall heat transfer coefficient U ¼ ðUL1 þ UG1 Þ1
ð20Þ
where K denotes thermal conductivity and D denotes the molecular diffusion coefficient. In order to test the proposed heat and mass transfer model, consideration is first given to the cooling data of Huang and Fair [17]. Using the analysis presented above, the exit water temperature, exit air temperature
and exit humidity ratio are computed using the following procedure. 1. Specify the water mass flux, air mass flux, water inlet temperature, air inlet temperature and inlet humidity ratio. 2. Guess the exit water temperature. 3. Compute the temperature and humidity distributions through the packed bed using Eqs. 6, 10, and 14 until z reaches the height of the packed bed. 4. Check whether the predicted inlet water temperature agrees with the specified inlet water temperature, and stop the computation if agreement is found, otherwise repeat the procedure from step 2. A comparison between the measured exit water temperature, exit air temperature and exit humidity ratio reported by Huang [17] with those computed using the current model are shown in Fig. 4a, b for 2.54 cm pall ring packing. As seen in the figures the comparison is generally good. The exit air temperature and exit water temperature are slightly over-predicted. The exit humidity ratio prediction is excellent.
3 Experimental facility In order to further test the model, an experimental diffusion tower has been fabricated. Figure 5 shows a schematic diagram of the experimental facility. The main feed water is drawn from the municipal water line. The feed water initially passes through a vane type flow meter and then enters a preheater. The vane-type flow meter, constructed by Erdco Corporation, has a range from 1.5 to 15.1 L/min with an uncertainty of ±1% of full scale. The preheater is capable of raising the feed water temperature to 50C. The feedwater then flows through the main heater, which can raise the temperature to saturated conditions. The main heater consists of two 3 kW electric coil heaters wrapped around a copper pipe, through which the feed water flows. The power to the heaters is controlled with two PID feedback temperature controllers with a 240 V output. The feed water is then sent to the top of the diffusion tower, where it is sprayed over the top of the packing material. The diffusion tower consists of three individual parts: a top chamber containing the air plenum and spray distributor; the main body containing the packing material; and the bottom chamber containing the air distributor and water drain. The top and bottom chambers are constructed from 25.4 cm (10¢ nominal) ID PVC pipe and the main body is constructed from 24.1 cm ID acrylic tubing with wall thickness of 0.635 cm. The three sections are connected via PVC bolted flanges. The transparent main body accommodates up to 1 m of packing material along the length. The packing material used for the experiments is HD Q-PAC manufactured by Lantec. The HD Q-PAC, constructed from polyethylene, was specially cut using a hotwire so that it snugly fits into the main body of the diffusion tower. The specific area of
533 Fig. 4 a Comparison of predicted exit conditions with the data of Huang and Fair [17], L=2.0 kg/m2 s. b Comparison of predicted exit conditions with the data of Huang and Fair [17], L=4.1 kg/m2 s
the packing is 267 m2/m3 and its effective diameter is 1.8 cm. Dry air is drawn into a centrifugal blower. The discharge air from the blower flows through a 10.16 cm duct in which a thermal mass flow meter is inserted. The meter range is 0–0.53 m3/s of air at 25C and atmospheric pressure. The uncertainty of the flow meter is ±1% of full scale +0.5% of the reading. The airflow rate is controlled by varying the speed of the blower. A three-phase autotransformer is used to control the voltage to the motor and regulate the speed. Downstream of the thermal mass flow meter the temperature and inlet relative humidity of the air are measured with a thermocouple and a resistance
type humidity gauge. The relative humidity is measured with two duct-mounted HMD70Y resistance-type humidity and temperature transmitters manufactured by Vaisala Corp. The humidity and temperature transmitters have a 0–10 V output signal and have been factory calibrated. The air is forced through the packing material in the diffusion tower and discharges through a plenum and vent at the top of the diffusion tower. Just above the spray nozzle within the diffusion tower, the temperature and humidity of the discharge air are measured in the same manner as at the inlet. The water sprayed on top of the packing material gravitates toward the bottom. The portion of water not
534 Fig. 5 Schematic diagram of the experimental facility
evaporated is collected at the bottom of the diffusion tower in a sump. The temperature of the discharge water is measured with a thermocouple. The static pressure at the inlet and exit of the diffusion tower are measured with two Validyne P2 strain gauge-type pressure transducers. All of the wetted parts are constructed with stainless steel. The transducers have an operating range from 0 to 36 kPa and have an uncertainty of ±0.25% of full scale. A Validyne magnetic reluctance pressure transducer measures the pressure drop across the length of the packing material. It has been calibrated for a range of 0–3 cm H2O with an uncertainty of ±0.25%. All system temperature measurements are made with type E thermocouples and have an estimated uncertainty of ±0.2C. A digital data acquisition facility has been developed for measuring the output of the instrumentation on the experimental facility. The data acquisition system consists of a 16-bit analog to digital converter and a multiplexer card with programmable gain manufactured by Computer Boards. A software package, SoftWIRE, which operates in conjunction with MS Visual Basic, allows a user defined graphical interface to be developed for the specific experiment. SoftWIRE facilitates data analysis by transferring the data to an Excel spreadsheet.
4 Experimental and computational results Heat and mass transfer experiments were carried out in the diffusion tower with a packing bed height of 20 cm.
The liquid mass flux was fixed at 1.75, 1.3, and 0.9 kg/m2 s and the air mass flux was varied from 0.6 to 2.2 kg/m2 s. The inlet air temperature was about 23C while the inlet water temperature was 60C. The experiments were repeated to verify the repeatability of the results. The measured exit humidity, exit air temperature, and exit water temperature are compared with those predicted with the model for all three different liquid mass fluxes in Fig. 6a–c. It is observed that the repeatability of the experiments is excellent. The exit water temperature, exit air temperature and exit humidity ratio all decrease with increasing air mass flux for a certain water mass flux. The comparison between the predicted and measured exit water temperature and exit humidity ratio agreed very well, and the exit air temperature is slightly over predicted.
5 Conclusion In general, the analytical model proves to be quite satisfactory in predicting the thermal performance of counter flow packed beds. The excellent agreement of the model with the measured exit water temperature and exit humidity ratio is most important for desalination and water-cooling applications. A rigorous set of conservation equations have been developed for a two-fluid model applied to a packed bed, and mass transfer closure has been achieved by using a widely tested empirical correlation, while heat transfer closure has been achieved by
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Fig. 6 a Comparison of predicted exit conditions with the experimental data for different liquid mass fluxes, L=1.75 kg/m2 s. b Comparison of predicted exit conditions with the experimental
data for different liquid mass fluxes, L=1.3 kg/m2 s. c Comparison of predicted exit conditions with the experimental data for different liquid mass fluxes, L=0.9 kg/m2 s
recognizing the analogous behavior between heat and mass transfer. As previously mentioned, prior analyses, which predict the heat and mass transfer phenomenon for a specific packed bed used questionable assumptions. The current model provides a general approach, which considers the evaporation of water, the interfacial heat resistance between water and air, and the different interfacial areas available for heat and mass transfer. Due to its generality, it is believed that the current model will be very useful to both designers of diffusion towers for desalination applications as well as designers of cooling towers for heat transfer applications.
02NT41537. However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE.
Acknowledgements This paper was prepared with the support of the U.S. Department of Energy under Award No. DE-FG26-
2 kG ¼ 5:23Re0:7 GA ScG ðadp Þ aDG
Appendix A Onda’s Correlation Onda’s correlation 2=3
0:4 kL ¼ 0:0051ReLw Sc0:5 L ðadp Þ 1=3
lL g 1=3 qL
536
(
"
#) 3=4 rc 1=2 1=5 0:05 aw ¼ a 1 exp 2:2 ReLA FrL WeL rL ð21Þ ReLW ¼
L ; aw lL
ReGA ¼
G ; alG
lL lG ; ScG ¼ ; qL DL qG DG L2 WeL ¼ qL rL a
ScL ¼
ReLA ¼ FrL ¼
L alL
L2 a ; qL g
This equation 21 has been modified from the Onda’s original correlation.
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