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Experimental and theoretical study of adsorptionkinetics of Difluoromethane onto activated carbons

Ahmed A. Askalany a,*, Bidyut Baran Saha b,c

a Mechanical Engineering Department, Faculty of Industrial Education, Sohag University, Sohag 82524, Egyptb Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen 6-1, Kasuga-shi,

Fukuoka 816-8580, Japanc International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka,

Nishi-ku, Fukuoka 819-0395, Japan

a r t i c l e i n f o

Article history:

Received 19 June 2014

Received in revised form

28 September 2014

Accepted 7 October 2014

Available online 16 October 2014

Keywords:

Adsorption kinetics

Activated carbon

Difluoromethane

LDF

FD

* Corresponding author. Tel.: þ20862730572,E-mail address: ahmed_askalany3@yahoo

http://dx.doi.org/10.1016/j.ijrefrig.2014.10.0090140-7007/© 2014 Elsevier Ltd and IIR. All rig

a b s t r a c t

This paper presents theoretical and experimental adsorption kinetics of Difluoromethane

(HFC-32) onto activated carbon powder of type Maxsorb III and activated carbon fiber of

type A-20. The experimental runs have been conducted on an apparatus that has been

designed and built specially for this purpose. The adsorption kinetics have been deter-

mined at different adsorption temperatures ranging from 25 �C to 65 �C. The experimental

data are reduced and fitted with linear driving force (LDF) and Fickian diffusion (FD)

models. It has been found that both LDF and FD models are able to simulate the adsorption

kinetics of HFC-32 onto activated carbon powder and fiber with an error of ±5%.

© 2014 Elsevier Ltd and IIR. All rights reserved.

Etude exp�erimentale et th�eorique de la cin�etique d’adsorptionde de difluorom�ethane sur du charbon activ�e

Mots cl�es : Cin�etique d’adsorption ; Charbon activ�e ; Difluorom�ethane ; Lin�eaire force motrice ; Diffusion de Fickian

1. Introduction

According to the dramatic increase of the global energy de-

mand that has been occupied by a shortage in energy supply,

renewable energy applications becomeone of the solutions for

theenergy crisis.Oneof these applicationswhichmaybeaid in

mobile: þ201028721274..com (A.A. Askalany).

hts reserved.

solving this problem is the thermally powered adsorption

cooling system. Unremitting researches have been carried out

to bring the adsorption cooling systems to the existence (Alam

et al. 2013; Askalany et al., 2012, 2013a; Chan et al., 2012; Dabler

and Mittelbach, 2012; Gordeeva and Aristov, 2014; Khattab

et al., 2012; Sharafian and Bahrami, 2014; Tso and Chao, 2012).

Nomenclature

A surface area, m2

C adsorption uptake, kg kg�1

C0 equilibrium uptake, kg kg�1

Ds surface diffusion, m2 s�1

Ds0 pre-exponential coefficient, m2 s�1

Ea activation energy, kJ kg�1

F constant

m mass of adsorbate, kg

n constant

Rp particle radius, m

t time, s�1

V volume, m3

Subscripts

ads adsorber

eva evaporator

exp experimental

f final status

i initial

pore pore volume

sol solid

theo theoretical

tube connecting tubes

void void spaces between adsorbent particles

z measurement number

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 9 ( 2 0 1 5 ) 1 6 0e1 6 8 161

In order to build an adsorption cooling system, there are

some indispensable steps which should be followed. The

first step is studying the adsorption isotherms of the

adsorbent/refrigerant pair. The second step is studying the

adsorption kinetics of the working pair. Adsorption kinetics

could be defined simply as time-variation of the rate of

adsorption capacity for an adsorbent/adsorbate pair. For

better design of adsorption chillers, it is essential to deter-

mine accurately the kinetics of adsorption pair. Many re-

searches have been conducted to determine the adsorption

kinetics of different adsorption pairs (Atakan et al., 2013;

Dawoud, 2013; Glaznev and Aristov, 2008). These results

have been conducted to detect the most accurate theoretical

model which fits the experimental data of the studied

adsorption pair.

Difluoromethane (HFC-32) is a hydofluoroocarbon refrig-

erant that has been used either as a pure fluid for low tem-

perature refrigeration or as an ingredient of 400 series

nonazeotropic refrigerants 407a,b,c and 410a,b for packaged

air conditioning applications. HFC-32 is also present in R-504

that was used as a refrigerant but now phased out under

Montreal Protocol because of the presence of chloropenta-

fluoroethane (CFC-115) which has large ozone depletion po-

tential. Adsorption data on HFC-32 are expected to be

beneficial for two distinct applications, namely, for possible

thermal compression when used as a pure component and

separation of the mixtures at the end of the life cycle

(Askalany et al., 2013b).

Table 1 e Specifications of the adsorbents.

ACP ACF

Pore volume (cm3 g�1) 1.7 1.0

Surface area/m2 g�1 3200 2200

Mean pore diameter/nm 2 2

Amount in adsorption cell (g) 10.10 2.75

2. Working pairs and experimentalapparatus

Activated carbon fiber (ACF) of type A-20 and activated carbon

powder (ACP) of type Maxsorb III, were developed by AD0ALLCo. Ltd., Japan, and Kansai Coke & Chemicals Co. Ltd., Japan,

respectively. Table 1 summarizes the characteristics of the

studied adsorbents. A detailed description and chemical

analysis of the used adsorbents have been presented by

Askalany et al., 2013b. Samples of HFC-32 were supplied by

Daikin Co. Ltd., Japan and helium by Asahi Sanso Shokai Ltd.,

Japan, respectively with a stated purity of 99.995% for both

HFC-32 and helium.

An experimental apparatus has been designed and built to

investigate the adsorption kinetics of HFC-32 onto activated

carbonbased adsorbents. It consistsmainly of an adsorber and

an evaporator as shown in Fig. 1. The Adsorber and the evap-

orator are connected through 1/4 inch steel tube. In order to

control the flow of refrigerant, seven ball valves are installed.

The adsorber is 2500 cm3 bottle made of a stainless steel (SUS

304) and withstands a maximum loading pressure of 3 MPa.

A copper tube coil of a diameter of 1/8 inch has been

fabricated inside the adsorber to improve heating and

cooling the adsorbent as shown in Fig. 2. The copper coil is

connected to a water circulator. The circulator has a heating

and cooling capacity of 1.7 kW which used to control the

temperature of the water bath. The adsorber has a mesh

which is used to prevent the migration of the adsorbent

particles. The evaporator is made of stainless steel (SUS 304)

bottle of a volume of 3 L (3000 cm3). It has been designed to

manage a maximum pressure of 3 MPa. Each of the adsorber

and the evaporator is installed inside a water bath with

0.2 m3 volume in order to manage and regulate its temper-

ature. Each water bath is connected to a water circulator in

order to heat or cool the water and to achieve a preselected

temperature.

The apparatus has been connected to a vacuum pump

which has been used for evacuation purposes. A number of

type K thermocouples are attached at the locations in the test

rig where the temperature has to be measured.

Pressure transducers are used to measure the pressure of

the adsorber and the evaporator. A high precisionCoriolis flow

meter is installed between the evaporator and the adsorber to

measure the flow rate of the refrigerant during the adsorption

Fig. 1 e Schematic diagram of the experimental apparatus adsorption-kinetics evaluation.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 9 ( 2 0 1 5 ) 1 6 0e1 6 8162

processes. The accuracy and sensitivity of the used in-

struments have been furnished in Table 2.

3. Test procedure

Before inserting the adsorbent inside the adsorber, it has been

heated up to 150 �C for duration of 3 h to extract its moisture

then it has been weighed. After inserting the adsorbent into

the adsorber, the whole apparatus is evacuated using a vac-

uum pump with a pumping speed of 500 L min�1 and 9.3 Pa

ultimate pressure. The apparatus has been evacuated to a

pressure of 10 Pa in about 3 h in order to ensure that there are

no residual gases inside the apparatus.

Temperatureof theadsorberandevaporator isadjusted tobe

at the same value using the water circulators and water paths.

The evaporator is then charged by refrigerant to a certain

pressure. After reaching to almost steady state conditions of

pressure and temperatureof the evaporator, thevalvesbetween

the evaporator and the adsorber are suddenly opened. Hence

the refrigerant vapor flows from the evaporator to the adsorber

through the flowmeter. The valves are closed after 100 s where

most of the adsorption process occurs at that time as shown in

Fig. 3. The refrigerant is then charged again to the evaporator.

The filling and transient period of the evaporator has been

shown in Fig. 4 for a representative temperature of 35 �C. Zone Ishows thefillingperiod andzone II shows the transientuntil the

stable conditions.Thisprocesshasbeenrepeated six timesuntil

reached to the maximum uptake of the refrigerant by the

adsorbent. The maximum pressure of the evaporator is not

allowed to exceed the saturation pressure in order to avoid

liquid transfer to the adsorber. Thepressure and temperature of

the evaporator and the adsorber has been recorded every 1 s. At

the end of measurements for an assigned adsorption-

temperature the whole system has to be evacuated. The evac-

uation process using vacuum pump continue for 24 h, during

which the system was heated up to 100 �C to eliminate any re-

sidual gases from the system.

In order to investigate the effect of the temperature on the

adsorption kinetics, the adsorption process has been repeated

at different temperatures in the range of 25 �Ce65 �C. Theadsorbed amount of the refrigerant has been measured by

high sensitive flow meter and also determined by using the

volumetric method. An example for the raw data of the flow

meter has been shown in Fig. 5 at adsorption temperature of

35 �C. In order to determine the adsorbed amount of the

refrigerant in grams at a certain adsorption temperature,

equations from 1 to 4 have been used. All densities are

determined by REFPROP9 software at the equilibrium

conditions.

Fig. 2 e Adsorber construction.

Table 2 e Characteristics of the utilized instruments.

Instrument Type Accuracy Sensitivity

Thermocouple K ±0.05 �C 0.01 �CPressure

transducer

Digital ±0.25% of reading 1 Pa

Flow meter Coriolis ±0.5% of reading 4 g min�1

Balance Digital ±0.05 g 0.1 g

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 9 ( 2 0 1 5 ) 1 6 0e1 6 8 163

mz ¼ mz�1 þ Dmload;z � Dmvoid;z (1)

Dmeva;z ¼�rads;i � rads;f

�eva

ðVeva þ VtubeÞ (2)

Dmvoid;z ¼�rads;z � rads;z�1

�ads cell

ðVvoidÞ (3)

Vvoid ¼ Vads ��madsorbent

rsolþ Vpore

�(4)

Fig. 3 e Pressure and temperature records at 35 �C of ACP/

HFC-32.

Fig. 5 e An example for flow meter readings at adsorption

temperature of 35 �C of ACP/HFC-32.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 9 ( 2 0 1 5 ) 1 6 0e1 6 8164

Here adsorbent refers to the used activated carbon. The

experimental data of ACP/HFC-32 and ACF/HFC-32 have been

presented in Table 3 and Table 4, respectively.

Table 3 e Experimental data of ACP/HFC-32.

t, sec Tevaa, �C Tads

b, �C P, MPa C, kg kg�1

130 25.2 26.1 0.44 0.48

250 23.2 23.9 0.66 0.80

370 25.2 26.3 1.05 1.02

490 25.1 26.1 1.36 1.25

600 24.8 24.9 1.36 1.27

130 34.2 35.5 0.44 0.36

250 34.1 35.3 0.75 0.66

370 34.4 36.0 0.97 0.92

490 34.5 35.5 1.18 1.05

610 34.5 34.8 1.40 1.18

710 34.7 34.9 1.39 1.20

130 45.7 46.7 0.23 0.33

250 43.9 44.1 0.41 0.60

370 44.2 44.6 0.64 0.80

490 44.2 45.4 0.96 0.99

600 44.6 44.9 0.94 1.10

4. Theoretical models

4.1. Semi-infinite model

Ruthven (1984) reported that during the initial phase of

adsorption, surface diffusion coefficient follows the uptake

behavior of a semi-infinite medium of any particle shape and

can be expressed as:

CC0

¼ 2AV

ffiffiffiffiffiffiffiDstp

r(5)

A plot of the relative uptake and square root of time for

each isotherm yields with a slope of 2A=VffiffiffiffiffiffiffiffiffiffiffiDs=p

p. So that the

values of Ds could be extracted which are expressed as:

Ds ¼ Ds0 exp

��Ea

RT

�(6)

Which can be rearranged as.

Fig. 4 e An example of filling and transient period of the

evaporator.

lnðDsÞ ¼ lnðDs0Þ � Ea

RT(7)

By plotting ln(Ds) against T�1, one can get the numerical

values of activation energy and the pre-exponential coeffi-

cient. This plot is known as the Arrhenius plot. The slope

yields -Ea/R and the intercept provides the constant, Ds0.

130 54.8 54.1 0.55 0.33

250 54.6 55.6 0.76 0.55

370 54.3 55.5 0.97 0.74

490 54.1 54.5 1.37 0.92

600 54.4 54.8 1.35 0.97

100 63.7 63.9 0.42 0.23

210 64.1 64.6 0.74 0.42

320 64.2 65.1 0.71 0.60

450 64.2 65.0 1.18 0.77

570 64.2 64.8 1.37 0.88

680 64.3 64.8 1.37 0.94

130 74.0 74.0 0.47 0.20

250 74.0 75.1 0.77 0.42

370 74.2 75.2 0.96 0.56

490 73.9 74.0 1.37 0.72

600 74.2 75.2 1.36 0.76

a ads: adsorber.b eva: evaporator.

Table 4 e Experimental data of ACF/HFC-32.

t, sec Teva, �C Tads, �C P, MPa C, kg kg�1

130 24.9 25.2 0.31 0.33

250 24.9 25.1 0.53 0.50

370 24.9 24.7 0.76 0.69

490 24.9 24.9 1.00 0.81

567 24.3 25.1 0.99 0.88

630 24.3 25.2 1.30 0.93

688 24.8 24.4 1.30 0.94

128 33.9 33.9 0.10 0.30

246 34.3 34.8 0.26 0.44

366 34.0 35.0 0.45 0.60

485 34.6 34.8 0.66 0.75

606 34.3 34.4 0.95 0.83

722 34.7 35.3 0.94 0.86

124 44.0 44.4 0.25 0.22

243 44.1 44.3 0.45 0.39

364 43.7 44.2 0.66 0.56

484 43.4 44.0 0.88 0.67

602 44.1 44.6 1.10 0.75

719 44.8 45.5 1.08 0.80

130 52.5 53.4 0.40 0.25

250 52.8 53.8 0.64 0.40

370 53.2 54.6 0.87 0.51

490 53.6 54.5 1.10 0.60

610 53.8 54.4 1.31 0.67

710 54.7 55.3 1.30 0.69

130 62.5 63.1 0.40 0.23

250 62.7 63.1 0.65 0.36

370 63.1 64.0 0.88 0.46

490 63.4 63.3 1.10 0.54

610 63.5 63.9 1.31 0.61

710 64.5 65.5 1.30 0.63

130 72.3 73.4 0.42 0.15

250 72.6 73.8 0.65 0.23

370 72.7 73.3 0.89 0.30

490 73.1 74.0 1.11 0.35

610 73.3 74.3 1.32 0.37

710 74.1 75.3 1.31 0.39

Fig. 6 e Time variation of rate of change of adsorbate

concentration for ACP/HFC-32.

Fig. 7 e Arrhenius plot of ACP/HFC-32.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 9 ( 2 0 1 5 ) 1 6 0e1 6 8 165

4.2. Linear Driving Force model (LDF)

The Linear Driving Force (LDF) model for gas adsorption ki-

netics is frequently and successfully used for analysis of

adsorption column dynamic data and for adsorptive process

designs because it is simple, analytic, and physically consis-

tent (Sircar and Hufton, 2000). The LDF model is shown in Eq.

(8) (Ng et al., 2013).

vcvt

¼ FDs

R2p

ðc0 � cÞ (8)

Where the values of the constant F is 15 for spherical shape

and 8 for cylinderical shape (El-Sharkawy et al., 2006).

Fig. 8 e Fitting of LDF (solid lines) and FD (dashed lines)

models with experimental adsorption kinetics for ACP/

HFC-32.

Fig. 11 e Arrhenius plot of ACF/HFC-32.

Fig. 9 e Difference between calculated and measured

adsorption uptakes for LDF and FD models against time for

ACP/HFC-32.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 9 ( 2 0 1 5 ) 1 6 0e1 6 8166

4.3. Fickian diffusion (FD)

The Fickian diffusion model is used to evaluate adsorption

kinetics of various types of adsorbate pairs. The Fickianmodel

is valid when the diffusivity is independent of adsorbate

concentration (Habib et al., 2010). The diffusion equation

which expresses the adsorption rate considering a constant

diffusivity is given by Eq. (9) (Sircar and Hufton, 2000).

cc0

¼ 1� 6p2

X∞n¼1

1n2

exp

� n2p2Dst

R2p

!(9)

where n is an integer number.

Fig. 10 e Time variation of rate of change of adsorbate

concentration for ACF/HFC-32.

5. Results

5.1. ACP/HFC-32

Fig. 6 shows the rate of change of adsorption capacity for ACP/

HFC-32 adsorption pair. The adsorption capacity rate de-

creases with the increase in time of adsorption. Fig. 7 shows

the Arrhenius plot of ACP/R32 which is essential to determine

the numerical values of Ds0 and Ea. Fig. 8 shows fitting of LDF

and FD models with the experimental data of adsorption ki-

netics for ACP/R HFC-32. This figure indicates that the both

models have a good fitting with the experimental data of

adsorption kinetics of ACP/HFC-32 adsorption pair. Fig. 9

shows the difference between the calculated and experi-

mental adsorption kinetics of ACP/HFC-32 and the difference

Fig. 12 e Fitting of LDF (solid lines) and FD (dashed lines)

models with experimental adsorption kinetics for ACF/

HFC-32.

Fig. 13 e Difference between calculated and measured

adsorption uptakes for LDF and FD models against time for

ACF/HFC-32.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 9 ( 2 0 1 5 ) 1 6 0e1 6 8 167

has been calculated employing the following equation, Eq.

(10).

DC ¼ Ctheo � Cexp

Cexp*100 (10)

According to the statistical error analysis the maximum

error percentage is 9.2% and the mean error is 4.6% for FD and

6.1% for LDF. It is clear from this figure that most of the

calculated values have error within ±5% which is acceptable

from the engineering point of view.

5.2. ACF/HFC-32

Fig. 10 shows rate of change of adsorption capacity of ACF/

HFC-32 with time at different adsorption temperatures.

Fig. 11 shows the Arrhenius plot of ACF/HFC-32.

Fig. 12 shows the fitting of LDF and FD models with the

experimental data of ACF/HFC-32. These figures indicate

that the two different theoretical models fit well with the

experimental data of the adsorption kinetics of ACF/HFC-32

pair.

Fig. 13 shows the difference between theoretical and

experimental adsorption kinetics for both LDF and FD

models. According to the statistical error analysis the

maximum error is �10% and the mean error is 6.7% for FD

and 4.2% for LDF.

Table 5 shows the activation energy and pre-exponential

coefficient for ACP/HFC-32 and ACF/HFC-32.

Table 5 e Activation energy and pre-exponentialcoefficient for ACP/HFC-32 and ACF/HFC-32.

Parameter ACP/HFC-32 ACF/HFC-32

Ds0, m2 s�1 1.2 � 10�13 1.3 � 10�13

Ea, kJ kg�1 23.8 84

6. Conclusions

The adsorption kinetics of ACP/HFC-32 and ACF/HFC-32

adsorbent/adsorbate pairs have been investigated experi-

mentally and theoretically. An experimental apparatus has

been designed and built to conduct the experimental runs.

The experimental data have been fitted with two commonly

used theoretical models (LDF and FD). The fitting has been

carried out at various adsorption temperatures ranging from

25 �C to 65 �C. The numerical values of the activation energy

and pre-exponential coefficient for ACP/HFC-32 and ACF/HFC-

32 have been estimated.

The fitting shows that both LDF and FD models could be

effectively used to simulate the adsorption kinetics of ACP/

HFC-32 and ACF/HFC-32 where the differences between

calculated and measured values are within ±5%.

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