Heat and Mass Transfer Model for Desiccant Solution Regeneration

Article pubs.acs.org/IECR

Heat and Mass Transfer Model for Desiccant Solution Regeneration Process in Liquid Desiccant Dehumidification System Xinli Wang,†,‡ Wenjian Cai,*,‡ Jiangang Lu,† Youxian Sun,† and Xudong Ding‡ †

State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering Zhejiang University, Hangzhou 310027, China ‡ EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 ABSTRACT: In this paper, a simple model, but with high accuracy for a packed column liquid desiccant regenerator, to describe the heat and mass transfer process is developed. By lumping fluids’ thermodynamic properties and the geometric specifications as constants, two equations related with seven identified parameters are developed to predict the heat and mass transfer rate for solution regeneration processes in the regenerator. Commissioning information and the Levenberg−Marquardt method are employed to determine the unknown parameters. Compared with previous models, the presented model is simply constructed and accurate and requires no iterative computations while applied in predicting the heat and mass transfer rate once the parameters of the proposed model are determined. Experimental results demonstrate that the current model is effective to predict the performance of desiccant regeneration in the regenerator over wide working conditions. The proposed model promises to have wide application for real-time performance monitoring, optimization, and control for liquid desiccant regeneration. Goswami14 carried out investigations on coupled heat- and mass-transfer processes of a liquid desiccant dehumidifier by experimental investigation and proposed a finite difference model. Fumo and Goawami15 and Yin et al.16 made some modifications based on the model proposed by Oberg and Goswami to discuss the performance of a random-packing LDDS with lithium chloride as desiccant solution. The analytical solution of the modified finite difference model is developed by employing some linear approximations, and outlet conditions can be estimated more accurately through this method.17 Babakhani and Soleymani18 presented a finite difference model to describe heat and mass transfer process for the packed liquid desiccant regenerator and the analytical solution of the model war also given. However, it is quite complex to develop and solve the finite difference models and iterative calculation is essential since outlet states of fluids are general unknown, therefore the finite model is not suitable to be utilized in real-time performance evaluation and optimization of the LDDS.19 For the NTU and empirical approaches, Chen et al.19 presented NTU models for both counter-flow and parallel-flow configurations in a packed-type LDDS. The solution of the proposed models has satisfactory accuracy when compared to the data available from the literature. Liu et al.20 developed a theoretical model using NTU as input parameter correlated with the corresponding experimental data to simulate the heat and mass transfer process in a cross-flow dehumidifier and regenerator. Further, the authors showed that the analytical solutions which can be utilized in optimization design of the

1. INTRODUCTION During the past several decades, the liquid desiccant dehumidification system (LDDS) has achieved a steady rise for air dehumidification in comfort conditioning of buildings. Compared with the conventional cooling-based dehumidification method by cooling air below the dew point, the LDDS shows excellent performance characteristics with the possibility of energy conservation through turning the energy usage away from electric power to low grade and renewable energyfor instance solar energy, industrial waste heat, etc.;1with flexibility in operation of independent air humidity and temperature control; and with the advantage of employing the environment-friendly hygroscopic salt solutions as working fluids which do not deplete the ozone layer.2 The study on liquid desiccant air dehumidification can be traced back to 1955 when the first open-cycle air-conditioning system operating with triethylene glycol as the liquid desiccant was designed by Lof.3 Since then a large number of studies have been made on system design,4,5 experimental investigation6,7 and performance evaluation.8−10 Among these, the development of the heat- and mass-transfer models in LDDS is essential for all of these studies. So far, three kinds of models have been developed, namely: finite difference model, effectiveness number of transfer units (NTU) model, and empirical model.11 In the finite model, the packed column is divided into small control volumes, and the energy and material balances are solved in each control volume. Wide investigation has been carried out on the finite difference model to predict the performance of LDDS due to the high accuracy. Gandhidasan et al.12 and Factor and Grossman13 proposed theoretical models for the LDDS to analyze the hea- and masstransfer processes in both dehumidifier and regenerator under various operating conditions, and good agreement was achieved between the experiments and the theoretical model. Oberg and © 2014 American Chemical Society

Received: Revised: Accepted: Published: 2820

September 18, 2013 January 11, 2014 January 29, 2014 January 29, 2014 dx.doi.org/10.1021/ie403102x | Ind. Eng. Chem. Res. 2014, 53, 2820−2829

Industrial & Engineering Chemistry Research

Article

Figure 1. Scheme of a packed liquid desiccant dehumidification system.

LDDS based on the available NTU model.21 Sensitivity analysis of the heat- and mass-transfer process were carried out by Khan and Ball22,23 conducted in a packed-type liquid desiccant system to determine the dehumidifier and regenerator performance by using methods of an empirical nature. Though the empirical models are easy to develop, some crucial parameters related to the performance of the system should be obtained in advance which is very difficult in practical applications. Furthermore, accuracy will be reduced if it is extended over a wider operating region. The finite difference models can give predictions with good accuracy, but the solving process is time-consuming and requires iterative computing. The NTU model and the empirical model are simplified but with low accuracy when they are expanded. These models are unsuitable for real-time performance monitoring and optimization and control of a liquid desiccant regenerator for which accurate operating data and heat/mass transfer prediction in real-time are required. In this report, a hybrid modeling approach based on an empirical nature and system operating data to develop simple models,24−26 for real-time applications of performance monitoring and optimization and control of the regenerator, is presented. By lumping dimensionless and thermodynamic parameters into seven characteristic parameters, the heat- and mass-transfer process in the regenerator can be described by two simple nonlinear equations. An experiment is carried out to determine the related parameters by using the Levenberg− Marquardt method, and the identified model is then varified by the operating data collected from the experiment in real-time. Also, the comparison between the presented model and previous studies are made.

Figure 2. Water vapor pressure changes of desiccant solution during the cycle.

the LDDS. The cool, strong desiccant solution (state 1) is distributed into the dehumidifier on the top, and the process air is blown into the dehumidifier at the bottom, making contact with the falling desiccant solution in a counterflow configuration. Water vapor pressure in the process air is greater than that in the cool, strong desiccant solution; hence, the water vapor in the process air can be absorbed by the desiccant solution. The difference in the water vapor pressure between the process air and the desiccant solution acts as the masstransfer driving force. This process is described by lines 1−2 in Figure 2. The moisture that transfers from the process air leads to a dilution of the desiccant, resulting in a reducing of the ability to absorb water vapor. To reuse the desiccant solution, a heater is employed to heat the diluted desiccant solution (2− 3), and the heated solution will be pumped to be concentrated by regenerating the air in the regenerator. Mass transfer in the direction opposite to that which happens in the dehumidifier takes places in the regenerator since the hot, diluted desiccant solution has greater water vapor pressure than that of the regenerating air, and thus, the absorbed moisture during the dehumidification process can be transferred from the desiccant

2. THE ANALYSIS OF OPERATING LDDS The dehumidifier and the regenerator are the two main components in the liquid desiccant dehumidification system (LDDS), as shown in Figure 1. The dehumidifier dehumidifies the process air, and the regenerator regenerates the diluted desiccant solution to an acceptable concentration from the diluted solutions in the dehumidifier. Figure 2 describes water vapor pressure changes of the desiccant solution in operating 2821

dx.doi.org/10.1021/ie403102x | Ind. Eng. Chem. Res. 2014, 53, 2820−2829


Article

transfer coefficient with the heat transfer area and the temperature difference. By employing the above form, we develop the hybrid model as follows:

solution to the regenerating air, shown by 3−4. Although the desiccant solution is regenerated, the surface vapor pressure is still high due to the high temperature. Therefore, the desiccant solution should be cooled down until state 1 where the desiccant solution can be reached to complete the cycle. In the LDDS, the regenerator consumes a large amount of thermal energy. To regulate the fan and pump so that maximum energy efficiency can be obtained in the regenerator, a simple yet efficient model is necessary for real-time performance monitoring, optimization, and control. The modeling of a regenerator can be developed by a hybrid approach from physical principles of heat and mass transfer in the regenerator which is illustrated in Figure 3 schematically. In order to simplify the derivation process in the following sections, some reasonable assumptions are made:

Q = hovA(Ts , in − Ta , in)

(1)

where Q, A, Ts,in, Ta,in, and hov are the heat transfer rate, the heat transfer area, the inlet desiccant solution temperature, the inlet regenerating air temperature, and the overall heat transfer coefficient, respectively. The overall heat transfer coefficient can be expressed in terms of heat transfer resistance: 1 1 δ 1 = + + hovA hsAs λ mA m haAa

(2)

where δ, λm, hs, ha, As, Aa, and Am are the thickness of the interface, the thermal conductivity of the interface, local heat transfer coefficient regenerating air convection, the local heat transfer coefficient of desiccant solution convection, heat transfer area of desiccant solution convection, the heat transfer area of regenerating air convection, and the heat transfer area of the interface, respectively. However, the heat resistance of interface conduction is small enough to be neglected as the interface between the two fluids is very thin, and in the packed column, the heat transfer areas in different fluids and the interface are the same. Therefore, the overall heat transfer coefficient can be simplified as: hov =

1 1/hs + 1/ha

(3)

It is the characters of the interface and the moving fluid, the geometry of the packed column, and the velocity of fluid over the interface as well as the temperature differences that determine the heat transfer rate between the interface and the fluid moving over it. In the regenerator, the pump and fan are used to drive the desiccant solution and regenerating air, respectively. The type of heat transfer between the desiccant solution and the regenerating air can be considered as forced convection heat transfer. For the forced convection heat transfer, the heat transfer coefficient, h, depends on the passage diameter, D, the velocity of fluid, v, and is also influenced through the mean film temperature by the fluid’s viscosity, μ, specific heat, cp (for air humidity, humid heat is used), and thermal conductivity λ, respectively. The following equation has been developed after dimensional analysis:27

Figure 3. Schematic of a packed regenerator for desiccant solution regeneration.

1. 2. 3. 4.

Heat loss to the surroundings is negligible. Desiccant vaporization is neglected in the regenerator. There is steady state for the heat and mass transfer. Mass variations of regenerating air and desiccant solution are negligible in the regenerator. 5. The properties of the desiccant with respect to a small range of temperature variations are constant.

Nu = C(Re)e (Pr ) f

(4)

where Nu = hD/λ, Re = Dρv/μ and Pr = cpμ/λ are the wellknown dimensionless numbers in heat transfer and fluid dynamics, namely Nusselt number, Reynolds number, and Prandtl number, while C and the exponents e and f are the constant parameters that need to be determined, respectively. It can be assumed that both the volume flow rate V and the fluid density ρ remain constant for steady flow. Then the product of ρV (the mass flow rate ṁ ) is unchanged accordingly. Moreover, μ and λ are approximately unchanged if the temperature variation is not too big (less than 10% change for desiccant solution and air according to previous studies27−29). Thus, eq 4 can be expressed as follows:

3. MODEL OF HEAT TRANSFER Packing material is often applied in the regenerator to increase the air−desiccant contact area because a thin film will form on the packing material surface when the desiccant solution falls down along channels of the packing (shown in Figure 3). The staggered arrangement of the packing can enhance the convective effect between the rising regenerating hot air and the falling desiccant solution. Sensible heat transfer occurs between the two fluids through the channels of packing material. The heat is transferred from the hot desiccant solution in convection to the interface, conducted through the interface, and then finally transferred into the regenerating air. The heat transfer rate is generally expressed by multiplying the heat

⎛ 4ṁ ⎞e ⎛ cpμ ⎞ f λ = bṁ e h = C⎜ ⎟⎜ ⎟ ⎝ πμD ⎠ ⎝ λ ⎠ D

(5)

where b = C(4/πμD)e(cpμ/λ)f λ/D. 2822



Article

where aω is the wetted specific surface area, αt is the specific surface area, and Dp is the packing material nominal size, which is determined by the packing geometry and remains constant for a certain type of packing material, Da, vH, μa, and Ds,ρs,μs are the diffusivity, humid volume or density, and viscosity of regenerating air and desiccant solution, respectively. μa, vH, DaμsρsDs can be assumed not to change when the temperature variations between regenerating air and desiccant solution are small (less than 25 °C for regenerating air and 10 °C for desiccant solution). The correlations mentioned above can therefore be simplified below:

The overall heat transfer coefficient of the packing column can be written as: e

hov =

b (R ṁ ) 1 = a bas s 1/bsṁ se + 1/bamȧ e 1 + ba (Ras)e s

(6)

where ṁ s and ṁ a are the flow rates of the desiccant solution and regenerating air, respectively. Ra,s = ṁ a/ṁ s is the ratio of the regenerating air flow rate to the desiccant solution flow rate, bs and ba are the two constant coefficients related to the desiccant solution and the regenerating air. By combining eqs 1 with eq 6, the heat transfer rate in the packing column regenerator for this hybrid model in empirical nature is derived as: Q=

c1(Ra , sṁs)c3 1 + c 2(Ra , s)c3

(Ts , in − Ta , in)

ka = b3(mȧ )e1

ks = b4(ṁ s)e2

KG =

KG =

1 Hb4(ṁ s)e2

b

1 + Ta , inH b4 (ṁs)e2 (mȧ )−e1 3

c4(ṁ s) 1 + c5Ta , in(ṁ s)c6 (mȧ )c7

(15)

where c4 = Hb4, c5 = Hb4/b3, c6 = e2,c7 = −e1. Thus, the mass transfer flux in the regenerator can be finally presented as: N=

c4(ṁ s)c6 (p* − pa , in ) 1 + c5Ta , in(ṁ s)c6 (mȧ )c7 s , in

(16)

where the regenerating air water vapor pressure at the inlet of the regenerator, pa,in, can be determined from the definition of relative humidity: pa , in = φa , inpa , sat (17) where φa,in is the relative humidity of inlet regenerating air, and pa,sat is the saturated water vapor pressure, influenced only by the air temperature, and can be fitted in terms of temperature by the data available:31 pa , sat = γ0Ta2, in + γ1Ta , in + γ2

(18)

For temperatures between 30 to 55 °C, the constants are: γ0 = 13.099, γ1 = −688.46, γ2 = 14009. For the temperature of desiccant solution ranges from 50 to 60 °C and the concentration ranges from 27% to 35% in regenerator, the thermodynamic properties of the lithium chloride solutions have been discussed by Conde,32 and the surface of the water vapor for the desiccant solution can be described by algebraic fitting:

where ka, ks, and H are the gas phase mass transfer coefficient in convection, the liquid phase mass transfer coefficient in convection, and Henry’s law constant, respectively. The correlations of the mass transfer coefficients for both gas and liquid phases in the packed column between regenerating air and desiccant solution were respectively presented by Onda29,30 as follows:

(11)

+

Hb4(ṁ s)e2 (14)

(9)

⎛ 4ṁ ⎞e2 ⎛ μ ⎞ f2 ⎛ ρ ⎞ j2 s ⎟ s s g2 ⎜ ⎟ α ks = a 2⎜⎜ ( D ) ⎟ t p ⎜⎜ ⎟⎟ 2⎟ ⎜ ρ μ D α μπ D ⎝ sg ⎠ ⎝ ωs ⎠ ⎝ s s⎠

Ta , in

=

c6

where N, KG, ps,in * , and pa,in are the mass flux, overall mass transfer coefficient in the regenerator, the equilibrium water vapor pressure of the desiccant solution, and the water vapor pressure of the inlet of regenerating air, respectively, and KG can be expressed as follows, based on Henry’s law and the mass transfer two-film theory,28

(10)

1 b3(ṁa)e1

(8)

⎛ 4ṁ ⎞e1⎛ v μ ⎞ f1 αD H a a ⎟ ka = a1⎜⎜ ⎟ (αt Dp)g1 t a 2⎟ ⎜ RTa ⎝ αt μa πD ⎠ ⎝ Da ⎠

(13)

where b3 = a1(4/αtμaπD2)e1 (vH μa/Da)f1 (αtDp)g1 αtDa/R, b4 = a2(4/αωμsπD2)e2 (μs/ ρsDs)f 2 (αtDp)g2 (ρs/μsg)j2. Substituting eqs 11 and 12 into eq 8,

4. MODEL OF MASS TRANSFER In the regenerating process, three mass transfer resistances have to be overcome for water vapor on its way from the desiccant solution to the regenerating air: the resistance in desiccant solution itself, that at the interface of the two fluids, and finally the resistance of the regenerating air. The resistance of the interface between the two fluids can be very small and can be neglected because the high solution flow rate is generally applied in the regenerator and the mass transfer between the regenerating air and the desiccant solutions at the interface is very fast when compared to the mass transfer within either the desiccant solution or the regenerating air. Moreover, an assumption can be made that an equilibrium state exists at the interface in terms of mass transfer. Consequently, mass transfer with the driving force in terms of water vapor pressure in the gas phase can be described to develop the hybrid model in empirical nature:

1 KG = 1/ka + 1/Hks

(12)

and (7)

where c1 = baA, c2 = ba/bs, c3 = e.

N = KG(ps*, in − pa , in )

1 Ta , in

ps*, in = β0 + β1Ts , in + β2ωs + β3Ts2, in + β4 ωs2 + β5Ts , inωs (19)

where ωs is the desiccant solution concentration and the fitted parameters are: β0 = −2.6434273, β1 = 0.20955349, β2 = 5.2451548, β3 = 0.0054591075, β4 = 61.771904, β5 = −1.5411157. Thus, eqs 7 and 16 together with only seven parameters (c1− c7) present the heat and mass transfer process in the 2823



Article

installed in the outlet of the regenerator column (refer to 6 and 4 in Figure 4) to measure the outlet conditions of regenerating air and the air flow rate. Solution temperature and flow rate are respectively measured by a PT100 temperature sensor and a magnetic flow meter located in the desiccant conduit (refer to 7 and 5 in Figure 4). The concentration of desiccant solution is determined by the temperature and density,27 the density is measured by a glass hydrometer. Table 1 lists the specifications

regenerator. Compared with previous models, the proposed model is characterized by fewer parameters than can be identified through the Levenberg−Marquardt method by realtime operating data (see Appendix A for details).

5. MODEL VALIDATION AND DISCUSSION In order to validate the present regenerator model, the experiment is conducted on a liquid desiccant dehumidification system operating with aqueous lithium chloride as the desiccant (illustrated in Figure 4). The regeneration capacity of the experimental rig is as follows:

Table 1. Specification of the Sensors sensors

type

humidity/temperature transmitter solution temperature sensor solution flow meter

accuracy

probe PT100, 3-wire magnetic flow meter blade glass hydrometer

airflow meter density meter

range

0.5%, 0.1 °C 0.15 °C

0−100%, 0−60 °C

±0.5%

0−25L/min

±0.5% 1 kg/m3

0−600m3/h 1100−1300 kg/m3

0−100 °C

of the installed sensors. By using the sensors, the heat transfer rate and mass flux in the regenerator can be calculated by the real-time operating data based on the energy and mass balances, N = mȧ (Ya , out − Ya , in)

(20)

Q = mȧ (Ha , out − Ha , in) − λwN

(21)

where Ya,out, Ya,in, Ha,out, and Ha,in are the absolute humidity and enthalpy of regenerating air at the outlet and inlet sides, respectively. The absolute humidity and enthalpy can be determined by the temperature and relative humidity which are measured and recorded by the data acquisition system. λw is the latent heat of water vaporization. In order to show the effectiveness of the model, two error indexes, relative error (RE) and root-mean-square of relative error (RMSRE), are proposed: RE =

|Dreal − Dcalc | × 100% Dreal M

Figure 4. Photo of regenerator: 1 - regenerator (packed column); 2 heater; 3 - pump; 4 - airflow meter; 5 - solution flow meter; 6 humidity/temperature transmitter; 7 - solution temperature sensor.

RMSRE =

∑i = 1

(

Dreal − Dcalc Dreal

M

(22) 2

)

(23)

Experimental data with 100 sets from a wide operating range of the regenerator is acquired to determine the model parameters through the Levenberg−Marquardt method. Ambient air is utilized as the regenerating air, and its conditions cannot be controlled; thus, only inlet desiccant solution conditions and air flow rate are changed in the experiment. After identification, the parameters are determined as c1 = 4.9895, c2 = 4.2247, c3 = 1.0113 in eq 7 and c4 = 0.0104, c5 = 0.4660, c6 = 0.5455 and c7 = −0.5313 in eq 16. To show the effectiveness of the proposed model in system performance prediction and monitoring, 270 points which can cover 10− 90% of the designed capacity tested and the heat transfer rate from 0.6 to 1.6 kW and mass flux from 0.002 to 0.016 kg/m2s, respectively. Table 2 gives the description of the identification and validation data in the experiment, while predicted values of heat transfer rate together with the experimental values are given in Figure 5 and the RE is shown in Figure 6, accordingly. It can be deduced that for most of the data points, the RE is less

• Regenerating air flow 500 m /h • Heater capacity 3.0 kW • Regeneration rate 5 kg/h which can supply enough concentrated desiccant solution to the dehumidifier which can cover the sensible and latent load from a 100 m2 room in Singapore. The polypropylene column, which is made of anticorrosive material, is 1 m in height. Structured packing material with face dimensions 300 mm × 00 mm × 450 mm is filled in the packed column. To obtain a good distribution of desiccant solution, a distributor is installed on the top of column, and a wire mesh made of stainless steel is equipped to remove desiccant droplets carried by the highspeed regenerating air. All motors (fans, pumps) are installed with variable speed drive (VSD) to adjust the air and solution flow rates during different conditions. A humidity/temperature transmitter with probe type and a blade airflow meter are 3

2824



Article

Table 2. Data Description in the Experiment regenerating air

desiccant solution data sets

Ts (°C)

ωs (%)

ṁ s (kg/min)

ṁ a(kg/min)

identification data testing data

52.8−60.3 52.4−61.5

29.7−38.5 29.5−39.1

3.6−7.08 3.0−7.08

1.5−3.18 1.62−3.0

Figure 7. Model prediction for mass transfer.

Figure 5. Model prediction for heat transfer.

Figure 8. Relative error for mass transfer.

transfer rate, and regeneration rate. Flow rate and temperature of the desiccant solution are the two variables that have the most significant effect on the performance of the regenerator. Figures 9−12 show the experimental data for regeneration together with the model predicting results with the liquid desiccant flow rate varying from 2.86 to 7.12 kg/min and liquid desiccant temperature from 53.6 to 61 °C. Uncertainties of the Figure 6. Relative error for heat transfer.

than 10% with the average RE of 3.84% and RMSRE of 0.0473. While the comparison results of the mass flux in the regenerator predicted by the proposed model with the collected experimental data and the RE are shown in Figure 7 and Figure 8, respectively, 94% of the 270 data points are within the RE of ±10% with the average RE of 5.02% and RMSRE of 0.0623. The conclusion can be drawn from the results that the proposed model shows satifactory agreements with the experimental data (RE < 10%) and that validating the modeling approach is effective and accurate enough for real-time applications in performance monitoring, optimization, and control for the regenerator in the liquid desiccant dehumidification system. Some experimental data sets have been selected to study the influence of the variables on regenerator performance, heat

Figure 9. Experimental data and predicted results by the proposed model for influence of the desiccant flow rate on the heat transfer rate. 2825



Article

rate can enhance the heat transfer process by increasing the convective heat transfer coefficient and a higher inlet desiccant temperature can give bigger convective heat transfer coefficient and temperature difference and consequently gives the increase of heat transfer. For the regeneration rate is enhanced with the increase of the desiccant flow rate and desiccant inlet temperature, as shown in Figure 11 and Figure 12. It happens because a higher desiccant flow rate will maintain a higher regeneration rate with less desiccant temperature reduction, and a higher desiccant inlet temperature means a higher water vapor pressure and higher potential for heat and mass transfer since the vapor pressure of the desiccant is highly dependent on the temperature. Moreover, in order to illustrate the effectiveness of the proposed model in different systems, reliable sets of experimental data in the study of Fumo and Goswami15 are used to identify the model, and comparisons are made between the predicting values from the proposed model and that from the study of Babakhani and Soleymani18 which also refers to the same data. The regeneration rate is taken as the predicting variable to be compared because it is the key factor to show the performance of the regenerator. Figure 13 gives the comparison

Figure 10. Experimental data and predicted results by the proposed model for influence of the desiccant inlet temperature on the heat transfer rate.

Figure 11. Experimental data and predicted results by the proposed model for influence of the desiccant flow rate on the regeneration rate.

Figure 13. Comparison between the predicted regeneration rates in different models and the experimental data from Fumo and Goswami.16

of predicting regeneration rates presented in the current study and those obtained by Fumo and Goswami15 and Babakhani and Soleymani.18 The relative error comparison between the proposed model and models presented in refs 15 and 18 is shown in Figure 14. It should be pointed out that the regeneration rates predicted by Fumo and Goswami15 are consistently a little smaller than the experiment data and with higher relative errors, as shown in Figure 13 and Figure 14. Babakhani and Soleymani18 and the proposed model can obtain more accurate predictions of the regeneration rates, and the relative errors are less than 10%. However, complex parameters such as thermodynamic properties of the fluids, geometric specifications of the packing materials, and the heat and mass transfer coefficients are needed in both the models of Fumo and Goswami15 and Babakhani and Soleymani.18 These parameters can hardly be obtained in practical applications which limit its applications in real-time performance monitoring, optimization, and control. While only the input variables of the regenerator such as desiccant solution temperature, flow rate, concentration, and the air temperature, flow rate, relative

Figure 12. Experimental data and predicted results by the proposed model for influence of the desiccant inlet temperature on the regeneration rate.

experimental data are calculated, and the error bars are also given in the figures. It turns out once again that the current model has good accuracy and the calculated heat and mass transfer rates show good agreement with the experimental data. From Figure 9 and Figure 10, the heat transfer rate increases with the increase of desiccant flow rate and inlet desiccant temperature. It can be explained that a higher desiccant flow 2826



Article

variables with the regenerator are involved in this model so that iterative computation can be avoided when the proposed model is applied in performance prediction for the liquid desiccant regenerator. Furthermore, complex parameters such as the thermodynamic properties of the fluids, packing geometric specifications, and thermodynamic numbers (Reynolds, Nusselt, and Prandtl) are considered as lumped parameters and can be identified by operating data. According to the validation results, the current regenerator model is accurate enough for performance prediction and monitoring over a wide operating range: heat transfer rate from 0.6 to 1.6 kW and mass flux from 0.002 to 0.016 kg/m2s. The present model, with only seven parameters involved, is simple, flexible, relatively accurate, and easy for engineering applications compared with the previous models of the regenerator. After identification of the operating data collected from a specific system, the proposed model can be used to monitor, optimize, and control the performance of the regenerator by predicting the heat- and mass-transfer processes with the inlet conditions, such as flow rate, concentration, and temperature of the desiccant solution and flow rate, relative humidity, and temperature of regenerating air. It should be pointed out, however, that the model parameters may vary after a long period of operating time and should be updated periodically to predict the regenerator performance accurately. The performance optimization by using the proposed model is under study currently, and the results will be discussed later.

Figure 14. Comparison of relative errors for predicting the regeneration rate in different models.

humidity are involved in the current model which is developed based on a hybrid method. Real-time predicting can be obtained because of all the input variables involved in the model can be measured directly by the sensors and transducers installed in the system. Moreover, in the studies of Fumo and Goswami15 and Babakhani and Soleymani,18 the heat and mass transfer process was described by basic differential equations, and solving these equations is time-consuming and complex because the outlet conditions of the regenerator must be initially guessed, and iterative computations are required until the results converge to the known inlet conditions. In the current model, the complex parameters are processed by lumping parameters and the lumped parameters can be determined by the operating data; no iterative computing is needed while the identified model is applied in real-time performance monitoring, optimization, and control for the regenerator. Therefore, in comparison with the existing models, the present model is simple, accurate, able to be expanded, and suitable for real-time performance monitoring, optimization, and control. Table 3 illustrates the comparison between the existing regenerator models and the current model.

■

APPENDIX A In order to identify the seven unknown parameters, the nonlinear least-squares method is employed as follows: take M samples for the variables Ta,in, Ts,in, ṁ a, ṁ s, ϕa,in, ωs, Q, and N, and define two objective functions as the sum of the residual squares between the evaluated data and experimental data in order to determine the empirical parameters.

M

∑ r2,2 i(u2) i=1

⎞2 * − p ) − Ni⎟⎟ ( p c6 c 7 s , in , i a , in , i ⎠ i = 1 ⎝ 1 + c5Ta , in , i(ṁ s , i ) (mȧ , i ) M

model

geometric

finite difference empirical model NTU

yes

yes

present model

physical

no

no

empirical

yes

yes

physical

no

no

hybrid

⎛ c1(Ra , s , iṁ s , in)c3

(A.1)

Table 3. Comparison of Different Regenerator Models modeling technique

M

∑ r1,2i(u1) = ∑ ⎜⎜ i=1

f2 (u 2) = iterative computation

⎞2 ⎟ ( ) T T Q − − s , in , i a , in , i i⎟ 1 + c 2(Ra , s , i)c3 ⎠ i=1 ⎝

M

f1 (u1) =

=

model application design and simulation design and control design and control control and optimization

⎛

∑ ⎜⎜

c4(ṁ s , i)c6

(A.2) T

where f1(u1),f 2(u2),r1(u1),r2(u2), u1 = [c1 c2 c3] and u2 = [c4 c5 c6 c7]T are the heat transfer objective function, mass transfer objective function, residuals between the evaluated data and experimental data for heat transfer objective function, residuals between the evaluated data and experimental data for mass transfer objective function, parameter vector in heat transfer equation and parameter vector in mass transfer equation, respectively. Employing the Levenberg−Marquardt method to find the nonlinear unconstraint optimization solution, its search direction of between the steepest descent and the Gauss− Newton can be obtained by solving the following equations:

6. CONCLUSIONS A simple hybrid model which is suitable for performance monitoring, optimization, and control of operating liquid desiccant regenerators was presented in this paper. The performance of the heat and mass transfer processes in the liquid desiccant regenerator can be predicted by the developed hybrid model with only seven characteristic parameters. Different from other previous models, only inlet-related 2827

(J1(k)(u1)T J1(k)(u1) + λ1(k)I )d1(k) = −J1(k)(u1)R1(u1)

(A.3)

(J2(k)(u 2)T J2(k)(u 2) + λ 2(k)I )d 2(k) = −J2(k)(u 2)R 2(u 2)

(A.4)



■

where λ(k) ≥ 0 is a scalar, and I is the 3rd order identity matrix for the particular heat transfer model with three parameters and of order 4 for the particular mass transfer model which has four parameters, R1(u1) = [ r1,1(u1) r1,2(u1) ··· r1, M(u1)]T and

⎡ ∂r2,1 ⎢ ⎢ ∂c4 ⎢ ⎢ ∂r2,2 J2 (u 2) = ⎢ ∂c4 ⎢ ⎢ ⋮ ⎢ ⎢ ∂r2, M ⎢ ∂c ⎣ 4

∂c 2

∂r1,1 ⎤ ⎥ ∂c3 ⎥ ⎥ ∂r1,2 ⎥ ∂c3 ⎥ ⎥ ⋮ ⎥ ⎥ ∂r1, M ⎥ ∂c3 ⎥⎦

∂r2,1

∂r2,1

∂c5

∂c6

∂r2,2

∂r2,2

∂c5

∂c6

⋮

⋮

∂r2, M

∂r2, M

∂c5

∂c6

∂r1,1 ∂c 2 ∂r1,2 ∂c 2 ⋮ ∂r1, M

■

MODEL NOMENCLATURE A heat transfer area (m2) Aa heat transfer area of regenerating air convection (m2) Am heat transfer area of the interface (m2) As heat transfer area of desiccant solution convection (m2) b constant [W/m2 °C(kg/s)−e] b1−b4 constant [W/m2 °C(kg/s)−e] C constant (dimensionless) c1−c3 heat transfer model parameters c4−c7 mass transfer model parameters cp specific heat capacity of fluids [J/(kg °C)] D the structured packing diameter (m) Da regenerating air diffusivity (m2/s) Dcalc calculated data Dp packing material nominal size (m) Dreal experimental data Ds desiccant solution diffusivity (m2/s) g gravitational acceleration (m/s2) h heat transfer coefficient [W/(m2 °C)] H Henry’s law constant (Pa) Ha,in enthalpy of inlet regenerating air (kJ/kgdray air) Ha,out enthalpy of outlet regenerating air (kJ/kgdray air) ha air convection heat transfer coefficient [W/(m2 °C)] hov overall heat transfer coefficient in the regenerator [W/ (m2 °C)] hs desiccant solution convection heat transfer coefficient [W/(m2 °C)] k convection mass transfer coefficient [kg/(m2 s Pa)] ka gas phase convection mass transfer coefficient in the regenerator [kg/(m2 s Pa)] KG overall mass transfer coefficient in the regenerator [kg/ (m2 s Pa)] ks liquid phase convection mass transfer coefficient in the regenerator [kg/(m2sPa)] ṁ fluid mass flow rate (kg/s) ṁ a regenerating air mass flow rate (kg/s) ṁ s desiccant solution mass flow rate (kg/s) N mass flux in the regenerator (kg/m2 s) pa,in regenerating air water vapor pressure at inlet of the regenerator (Pa) pa,sat saturated water vapor pressure (Pa) ps,in * equilibrium water vapor pressure of desiccant solution at inlet of the regenerator (Pa) Q heat transfer rate in the regenerator (W) R ideal gas constant [J/(mol °C)] Ras mass flow rate ratio between the regenerating air and the desiccant solution (dimensionless) Ta,in regenerating air temperature at inlet of the regenerator (°C) Ts,in desiccant solution temperature at inlet of the regenerator (°C) uk1 value of c1−c3in the kth iteration uk2 value of c4−c7in the kth iteration V fluid volume flow rate (m3/s) v fluid velocity (m/s)

(A.5)

∂r2,1 ⎤ ⎥ ∂c 7 ⎥ ⎥ ∂r2,2 ⎥ ∂c 7 ⎥ ⎥ ⋮ ⎥ ⎥ ∂r2, M ⎥ ∂c 7 ⎥⎦

(A.6)

(k) (k) For sufficiently large values of λ(k) 1 and λ2 , the matrixes of J1 T (k) T (k) (k) (k) (k) (u1) J1 (u1) + λ1 I and J2 (u2) J2 (u2) + λ2 I are positive definite matrixes, and thus, d(k) and d(k) are in a descent 1 2 direction. Therefore, proper values should be assigned to λ(k) 1 (0) (0) and λ(k) 2 during the process of iteration. For λ1 = 0.01, λ2 = 0.01 and v = 10, it is specific as:

λ1(k + 1)

λ 2(k + 1)

⎧ λ (k)/v iff (k + 1) (c ) < f (k) (c ) ⎪ 1 1 1 1 1 =⎨ k k + k ( ) ( 1) ( ) ⎪ λ1 v iff (c1) > f1 (c1) ⎩ 1

(A.7)

⎧ λ (k)/v iff (k + 1) (c ) < f (k) (c ) ⎪ 2 2 2 2 2 =⎨ ⎪ λ 2(k)v iff (k + 1) (c 2) > f (k) (c 2) ⎩ 2 2

(A.8)

and u1(k + 1) = u1(k) + d1(k)

(A.9)

u 2(k + 1) = u 2(k) + d 2(k)

(A.10)

where is the value of c1−c3 in the kth iteration and is the + 1) value of c4−c7 in the kth iteration. The iteration ends if |u(k 1 k (k + 1) k − u1| < δ1, |u2 − u2| < δ2, where δ1 and δ2 are predetermined positive numbers (generally from the range of 1 × 10−6−1 × 10−5). uk1

■

ACKNOWLEDGMENTS

This work was supported by National Research Foundation of Singapore under the grant NRF2011 NRF-CRP001-090, the National Natural Science Foundation of China (NSFC) (No. 21076179), and the National Basic Research Program of China (973 Program: 2012CB720500).

R 2(u 2) = [ r2,1(u 2) r2,2(u 2) ··· r2, M(u 2)]T , and the Jacobian matrixes are defined as: ⎡ ∂r ⎢ 1,1 ⎢ ∂c1 ⎢ ⎢ ∂r1,2 J1(u1) = ⎢ ∂c1 ⎢ ⎢ ⋮ ⎢ ⎢ ∂r1, M ⎢ ∂c ⎣ 1

Article

u2k

AUTHOR INFORMATION

Corresponding Author

*Tel: +65 6790 6862. Fax: +65 6793 3318. E-mail: ewjcai@ntu. edu.sg. Notes

The authors declare no competing financial interest. 2828


Industrial & Engineering Chemistry Research vH Ya,in Ya,out αt αω δ λ λm λw μ μa μs ρs ϕa ωs

Article

(14) Ö berg, V.; Goswami, D. Y. Experimental study of the heat and mass transfer in a packed bed liquid desiccant air dehumidifier. Trans. ASME: J. Sol. Energy Eng. 1998, 120, 289−297. (15) Fumo, N.; Goswami, D. Y. Study of an aqueous lithium chloride desiccant system: Air dehumidification and desiccant regeneration. Sol. Energy 2002, 72, 351−361. (16) Yin, Y.; Zhang, X.; Chen, Z. Experimental study on dehumidifier and regenerator of liquid desiccant cooling air conditioning system. Build. Environ. 2007, 42, 2505−2511. (17) Ren, C. Q.; Jiang, Y.; Zhang, Y. P. Simplified analysis of coupled heat and mass transfer processes in packed bed liquid desiccant-air contact system. Solar Energy 2006, 80, 121−131. (18) Babakhani, D.; Soleymani, M. Simplified analysis of heat and mass transfer model in liquid desiccant regeneration process. J. Taiwan Inst. Chem. Eng. 2010, 41, 259−267. (19) Chen, X. Y.; Li, Z.; Jiang, Y.; Qu, K. Y. Analytical solution of adiabatic heat and mass transfer process in packed-type liquid desiccant equipment and its application. Sol. Energy 2006, 80, 1509− 1516. (20) Liu, X. H.; Jiang, Y.; Qu, K. Y. Heat and mass transfer model of cross flow liquid desiccant air dehumidifier/regenerator. Energy Conversion and Management 2007, 48, 546−554. (21) Liu, X.; Jiang, Y.; Xia, J.; Chang, X. Analytical solutions of coupled heat and mass transfer processes in liquid desiccant air dehumidifier/regenerator. Energy Convers. Manage. 2007, 48, 2221− 2232. (22) Khan, A. Y. Sensitivity analysis and component modelling of a packed-type liquid desiccant system at partial load operating conditions. Int. J. Energy Res. 1994, 18, 643−655. (23) Khan, A. Y.; Ball, H. Development of a generalized model for performance evaluation of packed-type liquid sorbent dehumidifiers and regenerators. In ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers) Winter Meeting, Anaheim, CA, U.S.A., January 25−29, 1992; pp 525−533. (24) Wang, Y. W.; Cai, W. J.; Soh, Y. C.; Li, S. J.; Lu, L.; Xie, L. H. A simplified modeling of cooling coils for control and optimization of HVAC systems. Energy Convers. Manage. 2004, 45, 2915−2930. (25) Jin, G. Y.; Cai, W. J.; Lu, L.; Lee, E. L.; Chiang, A. A simplified modeling of mechanical cooling tower for control and optimization of HVAC systems. Energy Convers. Manage. 2007, 48, 355−365. (26) Ding, X. D.; Cai, W. J.; Jia, L.; Wen, C. Y. Evaporator modeling: A hybrid approach. Appl. Energy 2009, 86, 81−88. (27) Waldram, J. R. The Theory of Thermodynamics. Cambridge University Press: Cambridge: 1985. (28) Benitez, J. Principles and Modern Applications of Mass Transfer Operations. Wiley-Interscience: New York, 2009. (29) Onda, K.; Takeuchi, H.; Okumoto, Y. Mass transfer coefficients between gas and liquid phases in packed columns. J. Chem. Eng. Jpn. 1968, 1, 56−62. (30) Kim, S.; Deshusses, M. A. Determination of mass transfer coefficients for packing materials used in biofilters and biotrickling filters for air pollution control - 2: Development of mass transfer coefficients correlations. Chem. Eng. Sci. 2008, 63, 856−861. (31) Dean, J. A., Ed. Lange’s Handbook of Chemistry; McGraw-Hill: New York, 1985. (32) Conde, M. R. Properties of aqueous solutions of lithium and calcium chlorides: formulations for use in air conditioning equipment design. Int. J. Therm. Sci. 2004, 43, 367−382.

humid volume of regenerating air (m3/kg) absolute humidity of inlet regenerating air (kgwater/ kgdry air) absolute humidity of outlet regenerating air (kgwater/ kgdry air) specific surface area (m2/m3) wetted specific surface area (m2/m3) thickness of the interface (m) thermal conductivity [W/(m°C)] thermal conductivity of the interface [W/(m°C) ] latent heat of water vaporization (kJ/kg) fluid viscosity (Pa) regenerating air viscosity (Pa) desiccant solution viscosity (Pa) desiccant solution density (kg/m3) regenerating air relative humidity (%) desiccant solution concentration (%)

Subscripts

a G in m out s sat

■

regenerating air gas phase inlet interface outlet desiccant solution saturated

REFERENCES

(1) Yin, Y.; Li, S.; Zhang, X.; Peng, D. Feasibility and performance analysis of a desiccant solution regenerator using hot air. Energy Build. 2011, 43, 1097−1104. (2) Tu, M.; Ren, C. Q.; Zhang, L. A.; Shao, J. W. Simulation and analysis of a novel liquid desiccant air-conditioning system. Appl. Therm. Eng. 2009, 29, 2417−2425. (3) Lof, G. O. Cooling with Solar Energy. In Proceedings of the World Symposium on Applied Solar Energy; Stanford Research Institute: Menlo Park, CA, 1956; p 171. (4) Xiong, Z. Q.; Dai, Y. J.; Wang, R. Z. Development of a novel twostage liquid desiccant dehumidification system assisted by CaCl2 solution using exergy analysis method. Appl. Energy 2010, 87, 1495− 1504. (5) Zhang, T.; Liu, X.; Jiang, Y. Performance optimization of heat pump driven liquid desiccant dehumidification systems. Energy Build. 2012, 52, 132−144. (6) Al-Sharqawi, H. S.; Lior, N. Effect of flow-duct geometry on solid desiccant dehumidification. Ind. Eng. Chem. Res. 2008, 47, 1569−1585. (7) Elsarrag, E.; Magzoub, E. E.; Jain, S. Mass-transfer correlations for dehumidification of air by triethylene glycol in a structured packed column. Ind. Eng. Chem. Res. 2004, 43, 7676−7681. (8) Niu, X.; Xiao, F.; Ge, G. Performance analysis of liquid desiccant based air-conditioning system under variable fresh air ratios. Energy Build. 2010, 42, 2457−2464. (9) Ma, Q.; Wang, R.; Dai, Y.; Zhai, X. Performance analysis on a hybrid air-conditioning system of a green building. Energy Build. 2006, 38, 447−453. (10) Liu, X. H.; Jiang, Y.; Yi, X. Q. Effect of regeneration mode on the performance of liquid desiccant packed bed regenerator. Renewable Energy 2009, 34, 209−216. (11) Mei, L.; Dai, Y. A technical review on use of liquid-desiccant dehumidification for air-conditioning application. Renewable Sustainable Energy Rev. 2008, 12, 662−689. (12) Gandhidasan, P.; Ullah, M. R.; Kettleborough, C. Analysis of heat and mass transfer between a desiccant-air system in a packed tower. J. Sol. Energy Eng. 1987, 109, 89. (13) Factor, H. M.; Grossman, G. A packed bed dehumidifier/ regenerator for solar air conditioning with liquid desiccants. Solar Energy 1980, 24, 541−550. 2829


Heat and Mass Transfer Model for Desiccant Solution Regeneration

Recommend Documents