lable at ScienceDirect

Applied Thermal Engineering 66 (2014) 499e506

Contents lists avai

Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Modelling of heat and moisture transfer in desiccant packed bedutilizing spherical particles of clay impregnated with CaCl2Ahmed Ramzy*, Waleed M. ElAwady 1, Hossam AbdelMeguid 2

Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, El-Mansoura 35516, Egypt

h i g h l i g h t s

� Three models are developed for heat and mass transfer in clay þ CaCl2 packed bed.� The numerical results are compared with the experimental data from literature.� The diffusivity is estimated by comparing the numerical results with experimental data.� The adiabatic diffusion model showed the best agreement with experimental data.� Maximum absorbent ratio of 0:09kgCaCl2kg

�1clay provides a maximum adsorbed mass per kg of desiccant.

a r t i c l e i n f o

Article history:Received 22 September 2013Accepted 12 February 2014Available online 22 February 2014

Keywords:ClayCaCl2DesiccantMoist airPacked bed

* Corresponding author. Tel.: þ20 1028229032 (moE-mail addresses: ahmed_ara1979@mans.edu.eg, a

(A. Ramzy), welawady@yahoo.com (W.M. ElAw(H. AbdelMeguid).

1 Tel.: þ20 1008624370 (mobile).2 Tel.: þ20 1066464712 (mobile).

http://dx.doi.org/10.1016/j.applthermaleng.2014.02.031359-4311/� 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Desiccant packed beds of clay particles impregnated with CaCl2 (clay þ CaCl2) are employed for airdehumidification in different applications. For such beds, three mathematical models are developed forheat and moisture transfer, namely; isothermal, adiabatic and adiabatic diffusion. The models are solvednumerically by finite difference method. In order to examine the accuracy of the developed models, thenumerical results are compared with the available experimental data. The diffusivity of clay þ CaCl2particles is identified. In addition, the effect of the absorbent ratio on the bed operation is investigatednumerically.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The process of air dehumidification is shared by many practicalapplications like, air conditioning, food industry, water desalina-tion and water extraction from air. Recently, desiccant systemshave been utilized as an alternative for the commonly usedrefrigeration based dehumidification systems. The design anddevelopment of desiccant dehumidification systems have attrac-ted much of the researchers’ interest [1,2]. Investigations of heatand moisture transfer processes were conducted for differentconfigurations of desiccants (e.g., vertical packed bed [3,4], verticalfluidized bed [5], inclined fluidized bed [6], radial flow packed bed[7,8] and rotating desiccant wheel [9]). In the same context, many

bile).hmed_ara1979@hotmail.comady), hssaleh@mans.edu.eg

1

researches were carried out for new desiccant material. Heat andmass transfer in a corrugated dehumidifier matrix using fourmaterials as alternative desiccants were investigated experimen-tally [10]. The use of polyvinyl alcohol foam and polyvinyl alcohol/silica gel/molecular sieve composite as a desiccant material wasstudied numerically [11]. While, Lee and Lee [12] studied thesorption characteristics of a new polymer desiccant named superdesiccant polymer (SDP). On another hand, Aristov et al. [13] andDawoud and Aristov [14] developed desiccant material byimpregnating a host porous material with hygroscopic salt. Com-posites of CaCl2, LiBr, and different types of silica gel can adsorb upto 0.75 g H2O per 1 g of the dry sorbent [13]. The kinetics of watersorption on mesoporous silica gel and alumina in comparison withthe two composites SWSe1L and SWSe1A formed by impreg-nating these host matrices with CaCl2 was studied experimentally[14]. Moreover, Saha et al. [15] studied the thermophysical prop-erties of CaCl2esilica gel as a composite desiccant. A detailed re-view of the composite desiccants and working pairs in desiccantcooling cycles can be found in Refs. [16,17].

Nomenclature

A cross section area [m2]a volumetric surface area [m�1]C air absolute humidity [kg m�3]c specific heat capacity [kJ kg�1 K�1]D diffusivity [m2 s�1]d diameter [m]dv incremental volume [m3]HA heat of adsorption [J kgw�1]h convictive heat transfer coefficient [W m�2 K�2]hm convective mass transfer coefficient [kg m�2 s�1]L height [m]_Q flow rate of air [m3 s�1]Re Reynolds numberRH relative humidityr radius [m]T temperature [�C]t time [s]W bed water content [kgw m�3]WP Intra particle water content [kgw kgd�1]

X salt concentration ½kgCaCl2 kg�1solution�

y axial position in the bed [m]

Greeka solution ratio ½kgsolution kg�1

clay�b absorbent ratio ½kgCaCl2kg�1

clay�ε porosityleff effective thermal conductivity [Wm�1 K�1]rb bed density ½kgclayþCaCl2 m

�3�v superficial velocity of air stream [m s�1]

Subscripts0 initial conditiona air side propertyb bed side propertyd desiccant (clay þ CaCl2)i inlete outletP particlev water vapourw water

Fig. 1. Physical model of clay þ CaCl2 bed during adsorption/desorption processes.

A. Ramzy et al. / Applied Thermal Engineering 66 (2014) 499e506500

Hamed [18] pioneered the use of composite desiccant ofclay þ CaCl2 particles, and investigated it performance theoreti-cally and experimentally. The theoretical model assumedisothermal processes and a uniform air humidity throughout thebed. Tretiak and Abdallah [19] proposed empirical relations ofmoisture accumulation during adsorption and desorption pro-cesses in packed bed of clay þ CaCl2 particles. In addition, Hir-emath and Kadoli [20] investigated the transient characteristics ofmoisture adsorption on clay þ CaCl2 particles in a vertical packedbed, and. presented a theoretical model based on the pseudo gasside resistance [21].

However, numerical simulation of heat and moisture in-teractions between air stream and the particles in a desiccantbed provides useful insight into the dynamics of the bed and itsperformance characteristics. To the best of our knowledge, themodelling of heat and moisture transfer in a packed bed utilizingparticles of clay þ CaCl2 considering the intra-particle moisturediffusion has not been investigated so far. Furthermore, it isstrongly believed that the intra particle moisture diffusionshould be considered for better simulation of such transportprocesses. Hence, in the current study, three differentmathematical models for heat and moisture transfer in packedbed of clay þ CaCl2 particles are presented. These models areisothermal, adiabatic and adiabatic diffusion. The isothermalmodel neglects the effect of heat of adsorption, while the adia-batic model abandons the intra-particle moisture diffusion, onanother hand, the adiabatic diffusion model considers the intra-particle moisture diffusion. Experimental data collected fromprevious work [18e20] are used to obtain the diffusivity in thedesiccant particle and to validate the theoretical models. More-over, the effect of the absorbent ratio, (i.e. the mass ratio of CaCl2to clay particles), on the performance of the bed is investigatednumerically.

2. Mathematical modelling

The physical model for the packed bed of clay þ CaCl2 is illus-trated in Fig. 1. Through such beds, the desiccant material partiallyadsorbs the moisture content of the flowing air in transient heatand moisture transfer processes. This adsorption process is

accompanied by a significant release of heat, which leads to astrong coupling between heat and moisture transfer processes. Themathematical models are developed considering the followingassumptions:

1. Pressure drop across the bed is small that it has a negligibleeffect on properties of the air stream.

2. Air velocity is uniform along the radial direction, and the flow isin the axial direction only.

3. Average bed porosity is assumed at all locations in the packedbed.

4. Water vapour is the only adsorbable species in the air stream.5. Heat and moisture transfer processes take place only by forced

convection to or from the air stream.6. Moisture diffusion in the spherical clay þ CaCl2 particle takes

place only in the radial direction.

The clay þ CaCl2 particles are prepared by immersing thespherical dry clay particles in a pool of a CaCl2 solution with aninitial concentration of 0:5 kgCaCl2kg

�1solution for 24 h [18]. Applying

the gravimetric analysis for the obtained desiccant particles, thewater content is obtained as follows,

A. Ramzy et al. / Applied Thermal Engineering 66 (2014) 499e506 501

W ¼ 1rb

mw

mclay þmCaCl2

!¼ b

ðbþ 1Þrbð1� XÞ

X(1)

Eq. (1) is used to obtain the salt concentration; X. Hence, theequilibrium vapour pressure can be calculated using thepolynomial,

pv ¼X6i¼0

aiTi (2)

The extracted data from CaCl2ewater chart presented in Ref.[22] has been used to produce the six degree polynomial (Eq. (2))by the method of least squares. Where, pv is in mmHg and tem-perature ranges between 0 and 120 �C. The values of the regressionconstants, ai, for different ranges of salt concentration are furnishedin Table 1.

The equation of moisture balance for the gas phase flowingthrough the bed is derived by applying the species conservation lawon an incremental volume of the bed as follows,

_QaCa y; tð Þ ¼ _QaCa yþ dy; tð Þ þ εbvCavt

þ 1� εbð Þ vWvt

!dv (3)

Expanding appropriate terms, simplifying and dividing bydv ¼ Abdy, Eq. (3) can then be written as,

vCavy

¼ �εbva

vCavt

� 1� εbva

vWvt

(4)

Applying the moisture balance in the solid phase, the accumu-lation of moisture in the clay þ CaCl2 particles can be representedas the amount of mass transferred to the particles as follows,

vWvt

¼ hmarað1� εbÞ

ðCa � CPÞ (5)

where, hma(Ca � CP) is the volumetric convective moisture transferrate, a is calculated as a ¼ 6(1 � εb)/dP and CP is calculated asfollows [4];

CP ¼ ra �0:622pvðXÞ

p� 0:378pvðXÞ (6)

Eq. (5) is applicable only when a desiccant particle is modelledas a lumped system and the intra-particle diffusion resistance isabandoned. Otherwise, the moisture balance is implemented on anincremental volume of a spherical desiccant particle; hence Eq. (5)is replaced by,

vWP

vt¼ D

r2v

vr

�r2vWP

vr

�(7)

The right-hand side of Eq. (7) represents the intra-particlemoisture diffusion term, while the left-hand side represents therate of change of the water content in the incremental volume. Eq.

Table 1Regression constants (a0ea6) for Eq. (2).

X [%] a0 a1 a2

0 5.945 �4.268E-1 1.203E-120 4.236 �2.987E-1 5.155E-230 4.24 �8.309E-1 1.371E-140 1.926 1.25E-01 1.19E-0250 �213.555 2.045Eþ1 �7.42E-155 �7.707Eþ1 3.793 �2.056E-260 2.661Eþ6 �1.31Eþ5 2.68Eþ3

(7) has an initial condition of WP(r,t ¼ 0) ¼ W0 and boundaryconditions as follows:

At r ¼ 0vWP

vr¼ 0 (8)

At r ¼ dP2

DvWP

vr¼ hm

raðCP � CaÞ (9)

Substituting Eq. (5) into Eq. (4) and rearranging, the equation ofgas phase moisture balance is represented by,

vCavy

¼ �εbva

vCavt

� hmarava

ðCa � CPÞ (10)

The boundary and initial conditions for Eq. (10) areCa(y ¼ 0,t) ¼ Cai and Ca(y,t ¼ 0) ¼ CP0, respectively.

The energy equation for gas phase is derived by applying theenergy conservation law as follows,

Energy inþ liberation rateþ convection rate

¼ Energy outþ accumulation rate (11)

where the terms “Energy in” and “Energy out” are represented inFig. 1 as _haðyÞ and _haðyþ dyÞ, respectively. Replacing each term inEq. (11) with its appropriate mathematical form,

raAvcaTað Þy þ hmacvdv Ca � CPð Þ TP � Tað Þð Þy þ hadv TP � Tað Þð Þy¼ raAvcaTað Þyþdy þ raεdvca

vTavt

� �y

(12)

Dividing Eq. (12) by dv ¼ Ady and rearranging, Eq. (12) can thenbe written as,

�vTavt

�y¼��v

εb

vTavy

þ araεbca

�hmcvra

ðCa � CPÞ þ h�ðTP � TaÞ

�y

(13)

Eq. (13) has the following boundary and initial conditions,Ta(y ¼ 0,t) ¼ Tai and Ta(y,t ¼ 0) ¼ Ta0, respectively.

Applying the energy balance for the solid phase on the incre-mental volume of the bed,

Conduction inþ Sorption heat release rate ¼ Conduction outþ convection rateþ accumulation rate

(14)

where, the heat transfer by conduction is represented asQy ¼ �leffvTP/vy. The effective bed thermal conductivity, leff, iscalculated using the geometric mean relation [23] as follows,

leff ¼ lεba l1�εbP (15)

a3 a4 a5 a6

�5.438E-3 1.313E-4 �1.336E-6 5.307E-9�2.007E-3 4.9E-5 �4.597E-7 1.841E-9�5.749E-3 1.177E-4 1.032E-6 �3.533E-9�4.45E-4 1.34E-5 �1.14E-7 4.79E-101.33E-2 �1.18E-4 5.05E-7 �6.92E-10�1.582E-3 3.588E-5 �2.645E-7 7.374E-10�2.915Eþ1 1.779E-1 �5.77E-4 7.787E-7

A. Ramzy et al. / Applied Thermal Engineering 66 (2014) 499e506502

Expanding and substituting appropriate terms in Eq. (14), toproduce,

�vTPvt

�y¼ a

rPð1� εbÞcP

leffa

v2TPvy2

þHAhmra

ðCa�CPÞ�hðTP�TaÞ!

y

(16)

Eq. (16) has an initial condition of TP(y,t ¼ 0) ¼ TP, and boundarycondition as follows

vTPvy

����y¼0

¼ vTPvy

����y¼L

¼ 0 (17)

The above developed relations accomplished the required setsof equations of the considered models. The isothermal model isrepresented by Eqs. (5) and (10), while, the adiabatic model iscomprised of Eqs. (5), (10), (13) and (16). Finally, the adiabaticdiffusion model consists of Eqs. (7), (10), (13) and (16).

3. Auxiliary data and relations

In this study, the particle density is 1600 kg m�3. The relationsfor specific heat of clay þ CaCl2 particle is calculated as,

cP ¼ W � cw þ ð1�WÞb� cCaCl2 þ ð1�WÞð1� bÞ � cclay(18)

The specific heat of air is obtained by [4],

ca ¼ 1ra

ð1884� Ca þ 1004ð1� CaÞÞ (19)

The thermal conductivity of the CaCl2ewater solution is close tothat of water [24,25]. Hence, the thermal conductivity of theclay þ CaCl2 particles is assumed 1.8 Wm�1 K�1 similar to that ofmoist clay. Average heat of adsorption of the water vapour isassumed 2300 kJ kg�1.

The convective heat and mass transfer coefficients are calcu-lated using the relations presented in Ref. [21].

For adiabatic model:

h ¼ 0:683ravcaRe�0:51 (20)

hm ¼ 0:704ravRe�0:51 (21)

For adiabatic diffusion model:

h ¼ 1:6ravcaRe�0:42 (22)

hm ¼ 1:7ravRe�0:42 (23)

The root of mean square of errors (RMSE) is defined as,

RMSEðZÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1�Zth � Zexp

�2n

s(24)

where, Z refers to the investigated parameters; W, Ca and Ta.

4. Numerical procedure

The three developed models consist of different sets of couplednonlinear partial differential equations. In order to solve thesemodels, CrankeNicholson scheme is implemented to solve Eq. (7),while the explicit finite differencemethod is employed to solve Eqs.(5), (10), (13) and (16). Computer codes are developed using pro-gramming language C to obtain the results of the numerical models.It is observed that by decreasing the grid size less than 1.0 mm, thenumerical results are not depending on the grid size. Hence, a timestep of 0.5 s and a grid size of 1.0 mm are used in the numericalcalculations. The calculation procedures are explained as follows,

1. Define the operating and design parameters of adsorptiontest, namely, db, Lb, dp, εb, Xo, Tbo, v, Tai, and Cai

2. Calculate the numerical grid parameters Dt, Dy, nsteps.3. Start time stepwise calculations for t ¼ 0 to t ¼ ttotal.4. Start bed height stepwise calculations for y ¼ 0 to y ¼ Lb.5. Set new guess for Ta (yþ Dy, t), Ca (yþ Dy, t), Tb (y, tþ Dt) and

W (y, t þ Dt).6. Calculate the average thermophysical properties ca, ra, cP, rP,

XP and CP, and heat and mass transfer coefficients h and hm.7. Calculate the new prediction of Ta (y þ Dy, t), Ca (y þ Dy, t), Tb

(y, t þ Dt) and W (y, t þ Dt).8. Compare the new predictions of Ta (yþ Dy, t), Ca (yþ Dy, t), Tb

(y, t þ Dt) and W (y, t þ Dt) with the initial guess. If therelative difference is greater than 10�10, repeat steps 5e8.

9. Repeat steps 4e8 until y ¼ Lb.10. Export the calculated results at this time step to an output

data file.11. Initialize the properties of the bed, Tb and W, as numerically

predicted in the previous time step.12. Repeat steps 3e11 until t ¼ ttotal.

5. Experimental data

The experimental data for the adsorption of water vapour inpacked beds of clay þ CaCl2 particles reported in Refs. [18e20] areused to validate the results of the developed models. Table 2 liststhe specific data of these experiments. For more details on theexperimental setup, procedures and error analysis [18e20], can bereferred.

To avoid the formation of solution droplets on the particle sur-face during the adsorption process, the maximum allowable solu-tion ratio (i.e. the mass ratio of CaCl2 þ water solution to the clayparticle) imports a limitation on the particle composition. In case offorming solution droplets on the particle surface, the amount ofCaCl2 salt in clay particles decreases (washing effect). Consequently,the particles lose its adsorptive characteristics with continuousoperation of adsorption/desorption processes.

Measurements for the maximum allowable solution ratio, a,were carried out. Themass of five samples of dry clay particles weremeasured using a sensitive electronic balance with a resolution of0.1 g. These samples were immersed in a water pool for 24 h. Afterremoving the samples from the water and removing the residualwater, the mass was recorded again. Computing the difference inthe mass of each sample, the average allowable solution ratio isfound as 0:212 kgsolutionkg

�1clay.

6. Results and discussion

In the following, the diffusivity of water molecules in theclay þ CaCl2 particles is obtained by comparing the results ofthe adiabatic diffusionmodel with the experimental data. Then, the

Table 2Bed and air flow conditions for experiments [18e20].

Run Lb [m] db [mm] εb dP [mm] b W0 [kgw/m3] TP0 [ C] v [m s�1] Cai [kg/m3] Tai [ C] Ref.

1 0.545 50 0.4 10 0.124 100 33 1.5 0.02 38 [20]2 0.545 50 0.4 10 0.124 91 33 0.65 0.019 36 [20]3 0.545 50 0.4 10 0.124 101 33 1.0 0.019 37 [20]4 0.21 100 0.466 9 0.1 0.15 30 2.0 0.0138 30 [18]5 0.61 305 0.46 16.5 0.185 0.04 22.6 0.17 0.0163 22.6 [19]

A. Ramzy et al. / Applied Thermal Engineering 66 (2014) 499e506 503

results of the isothermal, adiabatic and adiabatic diffusion modelsare comparedwith the experimental data reported in Refs. [18e20].In addition, the effect of the absorbent ratio on the bed operation isinvestigated.

Fig. 3. RMSE of numerical results by adiabatic diffusion model with respect to theexperimental data at different values of diffusivity, D, for Run “1”.

6.1. Determination of diffusivity in clay þ CaCl2 particles

To estimate the diffusivity in the desiccant particle, the nu-merical results of the adiabatic diffusion model are obtained usingdifferent values of the diffusivity; D. Fig. 2a, b shows the experi-mental and numerical transient variation of exit air absolutehumidity and temperature for Run “1”. Experimenting withdifferent diffusivity values, the numerical results using diffusivity of5 � 10�10 m2 s�1 have more acceptable agreement compared to theresults obtained using diffusivity of 5 � 10�9 and 1 � 10�11 m2 s�1.Fig. 3 shows RMSE of the numerical results of exit air absolutehumidity and temperature with respect to the experimental datafor different values of diffusivity. It can be seen that when thediffusivity is 5 � 10�10 m2 s�1, the average RMSE has a minimumvalue of 11.65%, where, the RMSE for the exit air absolute humidityand temperature are 14.2% and 8.4%, respectively. The numericalresults for runs “2” and “3” using diffusivity of 5 � 10�10 m2 s�1

have RMSEs of 10.6% and 22.8%, respectively.Using the same procedure, the diffusivity values for Run “4” and

“5” are obtained as 7 � 10�9 m2 s�1 and 8 � 10�10 m2 s�1, respec-tively. The discrepancies in diffusivity values are justified by; thedifferent researchers [18e20] used different techniques andmaterial for the fabrication of clay particles.

6.2. Numerical results of the theoretical models

The numerical results of the exit air absolute humidity andtemperature during the adsorption process are shown in Figs. 4 and5. The results of isothermal, adiabatic and adiabatic diffusionmodels are plotted along with the experimental data for Runs “1e

Fig. 2. Transient variation of exit air absolute humidity and temp

3”. The adsorption process is characterized by an initial sharp rise inboth absolute humidity and temperature. The exit air temperaturereaches a peak then decreases gradually as depicted in Fig. 5. Due tothe initial high rate of adsorption which is accompanied byreleasing large amount of heat, the temperature of the bedincreases which in turn heats up the flowing air. As the temperatureof the bed increases, the mass transfer potential decreases sharply.Consequently, the released heat of adsorption falls, which explainsthe peak of exit air temperature response curve as shown in Fig. 5.The exit air absolute humidity is minimal at the start of theadsorption process and followed by a rapid increase of its value. Thesharp rise in the exit air absolute humidity occurs approximatelyuntil the time of the peak of exit air temperature as depicted inFigs. 4 and 5. As time progresses, the salt concentration decreases

erature during Run “1” using different values of diffusivity.

Fig. 4. Experimental and theoretical results for transient variation of exit air absolutehumidity during adsorption processes.

Fig. 5. Experimental and theoretical results for transient variation of exit air tem-perature during adsorption processes.

A. Ramzy et al. / Applied Thermal Engineering 66 (2014) 499e506504

gradually which in turn decreases the mass transfer potential, thatexplains the gradual increase in the exit air absolute humidity asillustrated in Fig. 4. Similar behaviour can be observed in Fig. 6,which shows the transient variation of the exit air absolute hu-midity for Run “4”. From Fig. 4, large deviation is observed betweenthe numerical results of isothermal model and the experimentaldata.

As illustrated in Fig. 5, a significant variation of the transient exitair temperature is observed. The maximum differences of airtemperature through the bed are about 9, 5 and 8 K for Runs “1”, “2”and “3”, respectively. By reviewing CaCl2ewater charts, a temper-ature difference of 10 K increases the equilibrium vapour pressureby about 20 mmHg, which in turn affects significantly the masstransfer potential. Therefore, the modelling of adsorption processshould incorporate the effect of the released heat of adsorption. Foradiabatic and adiabatic diffusion models, numerical results of exitair absolute humidity agreewith the experimental data as shown inFig. 4. On the other hand, numerical results of exit air temperatureaccord with the experimental data trend, however, a difference inmagnitude is observed, which is due to the effect of the thermalinertia of the bed container and the heat losses to the ambient.

As shown in Fig. 6, numerical results for transient variation ofthe adsorbedmass are compared to the experimental data reportedin Ref. [19]. Good agreement is observed between the numericalresults of adiabatic and adiabatic diffusion models when compared

with the experimental data with RMSE of 2.7% and 3.9%, respec-tively. While, the numerical results obtained by the isothermalmodel agree with the experimental data up to time of about 1000 s(Relative time ¼ 0e0.18). During this period, the bed is stillwarming up by the released heat of adsorption. Therefore, the bedcan be assumed isothermal. For advanced time, the numericalresults deviate significantly from the experimental data. This isexplained by that, the temperature rise in the bed considerablyaffects the bed performance, which is not incorporated in theisothermal model. The RMSEs for numerical results of averagewater content for Runs “1e3” and adsorbed mass for Run “5”obtained by isothermal, adiabatic and adiabatic diffusion modelsare furnished in Table 3.

From the presented comparison between the numerical resultsand the experimental data, it can be concluded that both adiabaticand adiabatic diffusion models provide relatively acceptablepredictions of the performance of clay þ CaCl2 packed bed duringthe adsorption process.

6.3. Investigation of absorbent ratio effect

As depicted in Fig. 7, the effect of varying absorbent ratio from0.05 to 0.3 on the trajectory of exit air absolute humidity is inves-tigated. The results show that the exit air absolute humidity

Fig. 6. Experimental and theoretical results for transient variation of exit air absolutehumidity and adsorbed mass of water.

Fig. 7. Transient variation of exit air absolute humidity during adsorption process fordifferent absorbent ratios.

A. Ramzy et al. / Applied Thermal Engineering 66 (2014) 499e506 505

decreases with the increase of the absorbent ratio compared at thesame instance. This is due to that, increasing the absorbent ratioincreases the salt concentration as depicted in Fig. 8. Consequently,the potential of mass transfer increases. Moreover, Fig. 7 illustratesthat increasing the absorbent ratio from 0.05 to 0.2 affects signifi-cantly the exit air absolute humidity, while this effect is minor forthe absorbent ratio more than 0.2, which indicates the existence ofan optimal value of the absorbent ratio. Fig. 9 depicts the specificadsorbed mass for different absorbent ratios. The results of the

Table 3RMSE of the numerically predicted average bed water content using isothermal,adiabatic and adiabatic diffusion models.

Run RMSE (W) [%]

Isothermal model Adiabatic model Adiabatic diffusion model

1 33.23 3.1 2.332 21.04 2.83 2.453 42.03 1.79 4.145a 30.2 2.7 3.9

a The RMSE’s for numerical results of adsorbed mass.

studied case reveal that, the optimal absorbent ratio, that achievesthe maximum specific adsorbed mass of water, is about0:185 kgCaCl2 kg

�1clay. In addition, Fig. 9 shows the solution ratio of

the bed for different absorbent ratios after 1 h of the bed operation.The obtained numerical results illustrate that, increasing theabsorbent ratio increases the bed solution ratio. Also, the resultsdepict that, the solution ratio has a value of 0:4 kgsolution kg�1

claywhen the bed is operated for 1 h based on optimal absorbent.However, the maximum allowable solution ratio is obtainedexperimentally for the burned clay as 0:212 kgsolutionkg

�1clay, which

sets a practical limitation on the absorbent ratio of the bed. Whenthe solution ratio exceeds its measured allowable value, the excesssolution of CaCl2 þ water forms droplets on the surface of the clayparticles. Progressing in time, the formed droplets accumulate atthe bottom of the bed container. Consequently, the particle contentof CaCl2 decreases, which is considered as a washing process.Hence, it can be stated that the absorbent ratio of the bed is limitedby the ability of the clay particles to hold the CaCl2 þ water solu-tion. Therefore, to maintain the solution ratio less than itsmeasured allowable value, the absorbent ratio of the bed should beless than 0:09 kgCaCl2 kg

�1clay for the studied case as depicted in Fig. 9.

Hence, it concludes that, to operate the bed of clayþ CaCl2 particles

Fig. 8. Transient variation of average bed salt concentration during adsorption processfor different absorbent ratios.

Fig. 9. Variation of specific adsorbed mass and solution ratio during 1 h adsorptionprocess for different bed absorbent ratios.

A. Ramzy et al. / Applied Thermal Engineering 66 (2014) 499e506506

under the optimal absorbent ratio, a specific research is required todevelop clay particles with a higher allowable solution ratio.

7. Conclusions

In this study, both adiabatic and adiabatic diffusion modelsprovide acceptable predictions for the operation of clay þ CaCl2packed bed during adsorption process. The intra particle waterdiffusivity is identified as 5 � 10�10, 8 � 10�10 and 7 � 10�9 m2 s�1

for the considered experimental data. For the studied cases, anoptimal absorbent ratio that achieves maximum specific adsorbedmass is obtained as 0:185 kgCaCl2 kg

�1clay. However, the allowable

solution ratio is identified experimentally as 0:212 kgsolution kg�1clay.

Therefore, to keep the solution ratio within its allowable limits, amaximum absorbent ratio of 0:09 kgCaCl2kg

�1clay is recommended.

Development of clay particles with a higher allowable solution ratiois crucial to increase the bed adsorptivity.

References

[1] K. Daou, R.Z. Wang, Z.Z. Xia, Desiccant cooling air conditioning: a review,Renew. Sustain. Energy Rev. 10 (2006) 55e77.

[2] A.A. Kinsara, M.M. Elsayed, O.M. Al-Rabghi, Proposed energy-efficient air-conditioning system using liquid desiccant, Appl. Therm. Eng. 16 (1996) 791e806.

[3] K.D. Kafui, Transient heat and moisture transfer in thin silica gel beds, J. Heat.Transfer 116 (1994) 946e953.

[4] A.A. Pesaran, A.F. Mills, Moisture transport in silica gel packed bedsdI.Theoretical study, Int. J. Heat Mass Transfer 30 (1987) 1037e1049.

[5] A.M. Hamed, W.R. Abd El Rahman, S.H. El-Emam, Experimental study of thetransient adsorption/desorption characteristics of silica gel particles in fluid-ized bed, Energy 35 (2010) 2468e2483.

[6] A.M. Hamed, Experimental investigation on the adsorption/desorption pro-cesses using solid desiccant in an inclined-fluidized bed, Renew. Energy 30(2005) 1913e1921.

[7] M.M. Awad, A. Ramzy K, A.M. Hamed, M.M. Bekheit, Theoretical and experi-mental investigation on the radial flow desiccant dehumidification bed, Appl.Therm. Eng. 28 (2008) 75e85.

[8] A.K. Ramzy, A.M. Hamed, M.M. Awad, M.M. Bekheit, Theoretical investigationon the cyclic operation of radial flow desiccant bed dehumidifier, J. Eng.Technol. Res. 2 (2010) 96e110.

[9] N. Subramanyam, M.P. Maiya, S.S. Murthy, Application of desiccant wheel tocontrol humidity in air-conditioning systems, Appl. Therm. Eng. 24 (2004)2777e2788.

[10] A.A. Pesaran, C.E. Bingham, Testing of novel desiccant materials and dehu-midifier matrices for desiccant cooling applications, in: ASHRAE SummerAnnual Meeting Vancouver, Solar Energy Research Institute, British Columbia,June 25-28, 1989.

[11] S.J. Christen, Heat and Mass Transfer Characteristics of Desiccant Polymers(M.Sc. thesis), Virginia Polytechnic Institute and State University, USA., 1998.

[12] J. Lee, D.-Y. Lee, Sorption characteristics of a novel polymeric desiccant, Int. J.Refrig. 35 (2012) 1940e1949.

[13] Y.I. Aristov, G. Restuccia, G. Cacciola, V.N. Parmon, A family of new workingmaterials for solid sorption air conditioning systems, Appl. Therm. Eng. 22(2002) 191e204.

[14] B. Dawoud, Y. Aristov, Experimental study on the kinetics of water vaporsorption on selective water sorbents, silica gel and alumina under typicaloperating conditions of sorption heat pumps, Int. J. Heat Mass Transfer 46(2003) 273e281.

[15] B.B. Saha, A. Chakraborty, S. Koyama, Y.I. Aristov, A new generation coolingdevice employing CaCl2-in-silica gelewater system, Int. J. Heat Mass Transfer52 (2009) 516e524.

[16] A.A. Askalany, M. Salem, I.M. Ismael, A.H.H. Ali, M.G. Morsy, B.B. Saha, Anoverview on adsorption pairs for cooling, Renew. Sustain. Energy Rev. 19(2013) 565e572.

[17] B. Choudhury, B.B. Saha, P.K. Chatterjee, J.P. Sarkar, An overview of de-velopments in adsorption refrigeration systems towards a sustainable way ofcooling, Appl. Energy 104 (2013) 554e567.

[18] A.M. Hamed, Theoretical and experimental study on the transient adsorptioncharacteristics of a vertical packed porous bed, Renew. Energy 27 (2002) 525e541.

[19] C.S. Tretiak, N.B. Abdallah, Sorption and desorption characteristics of a packedbed of clayeCaCl2 desiccant particles, Sol. Energy 83 (2009) 1861e1870.

[20] C.R. Hiremath, R. Kadoli, Experimental studies on heat and mass transfer in apacked bed of burnt clay impregnated with CaCl2 liquid desiccant andexploring the use of gas side resistance model, Appl. Therm. Eng. 50 (2013)1299e1310.

[21] R.S. Barlow, Analysis of the Adsorption Process and of Desiccant CoolingSystems e a Pseudo-steady-state Model for Coupled Heat and Mass Transfer,Solar Energy Research Institute, Golden, Colo, 1982.

[22] DOA, Calcium Chloride Hand Book e a Guide to Properties, Forms, Storage andHandling (Form No. 173-01534-803XQRP e USA), DOA Chemical Company,2003, http://www.prog-univers.com/IMG/pdf/CalciumChloridHandbook.pdf.

[23] H. Bjurström, E. Karawacki, B. Carlsson, Thermal conductivity of a micropo-rous particulate medium: moist silica gel, Int. J. Heat Mass Transfer 27 (1984)2025e2036.

[24] M. Ake, Thermophysical Properties of Aqueous Solutions Used as SecondaryWorking Fluids (PhD thesis), Royal Institute of Technology, KTH Stockholm,Sweden, 2007.

[25] V.S. El’darov, Thermal conductivity of aqueous solutions of KCleNaCleCaCl2system at high temperatures and pressures, High Temp. 41 (2003) 327e331.