Drying kinetics of coated sodium percarbonate particles in a conical fluidized bed dryer

Powder Technology 269 (2015) 30–37

Contents lists available at ScienceDirect

Powder Technology journal homepage: www.elsevier.com/locate/powtec

Drying kinetics of coated sodium percarbonate particles in a conical fluidized bed dryer Saeideh Hematian, Faramarz Hormozi ⁎ Faculty of Petroleum, Gas and Chemical Engineering, Semnan University, P.O.Box 35131-19111, Semnan, Iran

a r t i c l e

i n f o

Article history: Received 3 August 2013 Received in revised form 20 August 2014 Accepted 21 August 2014 Available online 29 August 2014 Keywords: Coated sodium percarbonate Drying Conical fluidized bed dryer Effective diffusivity Activation energy

a b s t r a c t Sodium percarbonate is a white powder that is used as bleach in detergent industries. Because of its sensitivity to environment and tendency to maintain the strength of bleaching action, it needs to be coated. Therefore, the drying of the coated sodium percarbonate particles is the main stage of their production process. In this study, the kinetics of the drying process of coated sodium percarboanate particles is investigated using a particle fluidization method and a conical fluidized bed dryer on a laboratory scale. The experiments are conducted at the inlet air temperature of 60, 70, and 80 °C and the air flow rate of 90, 100, and 120 m3/h. Then, some of the widely used drying models are fitted to the experimental data of the moisture ratio. The fit quality of the models is determined using the coefficient of determination (R2), root mean square error (RMSE), and reduced chi – square (χ2). Among the considered models, the ʻModified Henderson & Pabisʼ model with average R2 = 0.988204 and the ʻtwo termʼ model with average R2 = 0.985082, under almost all operating conditions, and the model developed by Verma et al. with average R2 = 0.971698 at high flow rate and high temperature are selected as the best models. In the drying process of coated sodium percarbonate particles, the effective diffusivity varies from 2.2337 × 10−10 to 22.0648 × 10−10 m2/s. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Sodium percarbonate (Na2CO3.H2O2) or solid hydrogen peroxide is used as bleach in the detergent industry. Bleaches are compounds that can clean fabrics and hard surfaces and remove stains. Sodium perborate monohydrate, sodium perborate tetrahydrate, and sodium percarbonate are some of the common types of bleaches. These compounds release hydrogen peroxide by hydrolysis in the alkaline aqueous environment. Recently, sodium perborate has been replaced by sodium percarbonate because the cleaning strength of sodium perborate is poor at a low temperature and borates contain particles of certain environmental pollutants [1]. Sodium percarbonate particles are coated because of their sensitivity to environmental moisture and temperature. During the coating process in the fluidized bed, three operations are repeated continuously which are particle fluidization, spraying of coating solution on the particles and drying of wetted particles. Therefore, the drying of the coated sodium percarbonate particles is the main stage of their production process. Therefore, it is necessary to know the kinetics of the sodium percarbonate drying process in order to produce the desirable coated product. Authors have focused on the drying process of coating, in this study. Since a long time, fluidized bed technology has been used in industrial dryers for drying wet solid granular particles. Fluidized bed dryers ⁎ Corresponding author. Tel.: +98 23 33383911 E-mail address: [email protected] (F. Hormozi).

http://dx.doi.org/10.1016/j.powtec.2014.08.050 0032-5910/© 2014 Elsevier B.V. All rights reserved.

have successfully been used for drying products such as food products (maize, coconut, chillies, black tea, and soybean), Agricultural products (paddy and colza), chemical products (biosynthesis products, nylon, and baker’s yeast), and bleaching agents (sodium perborate and sodium percarbonate) [2]. In the recent years, the study of the kinetic behavior in the drying process of various materials is an issue that has attracted considerable attention. Tasirin et al. (2007) studied the drying process of bird’s chillies using an experimental fluidized bed dryer and compared this result with the results obtained from sun drying. They performed their experiments using two different bed depths (2 and 4 cm) with air velocities of 0.85, 0.97, and 1.09 m/s and at operating temperatures of 50, 60, and 70 °C. They determined the first and the second critical moisture contents and later used them in a thin layer analysis. Furthermore, they illustrated that the bird’s chillies which were dried using the fluidized bed dryer were better in quality compared to those which were dried under the sun [3]. In another research, Aghbashlo et al. (2009) investigated the thin layer drying behavior of potato slices in a semi-industrial continuous band dryer. They performed their experiments at air temperatures of 50, 60, and 70 °C; air velocities of 0.5, 1, and 1.5 m/s; and chain linear velocities of 1.85 × 10−4, 2.22 × 10−4, and 3 × 10−4 m/s. Further, they recorded the moisture content of the samples at specific time intervals. Finally, they determined the ʻpageʼ model to be the best model on the basis of the modeling results [4]. Meziane (2011) investigated the drying kinetics of olive pomace in a fluidized bed dryer. He performed his experiments at different

S. Hematian, F. Hormozi / Powder Technology 269 (2015) 30–37

Nomenclature A, B, a, b, c, n coefficients in models K, g, h constants in models effective moisture diffusivity (m2/s) Deff constant (m2/s) D0 activation energy (KJ/mol) Ea M moisture content (kg water/kg dry matter) initial moisture content (kg water/kg dry matter) M0 equilibrium moisture content (kg water/kg dry matter) Meq MR moisture ratio (dimensionless) MRexp,i i-th experimental moisture ratio (dimensionless) MRpre, i i-th predicted moisture ratio (dimensionless) N number of observations Z number of constants in a model R universal gas constant (KJ mol−1 K−1) RMSE root mean square error coefficient of determination R2 T drying temperature (°C) absolute temperature (K) Tabs t time (min) chi - square χ2

temperatures of drying air (50, 60, 70, and 80 °C) and different bed heights of the sample (41, 52, and 63 mm) using a constant air velocity of 1 m/s. He determined the model developed by Midilli et al. to be the best model on the basis of the recorded data of moisture and the results of fitting these data to ten widely used models [5]. In one of the latest researches, Kaleta et al. (2013) investigated the drying behavior of an apple (Var. Ligol) dried in a fluidized bed dryer and formulated three new drying models using which they satisfactorily described the drying characteristics of apple cubes [6]. In the recent years, many procedures for the production of coated sodium percarbonate have been proposed in several patents [7]. These patents have reported the fluidized bed to be the best equipment for the coating process. Notwithstanding the importance of the drying of the coated particles, there are few papers that deal with this operation in a fluidized bed [for example, 8–11]. The main purpose of this study is to investigate the effect of the inlet air temperature and the air flow rate on the drying kinetics of coated sodium percarbonate in a conical fluidized bed dryer, to fit the experimental data to the widely used mathematical models of drying, and to select a suitable drying model for the purpose of simulation. Further, the effective moisture diffusivity in the drying process of the coated sodium percarbonate particles is calculated in the current work. Neglected by a majority of the studies on the drying of chemical products in a fluidized bed dryer the drying behavior of sodium pecarbonate particles is focused upon in this study. Further, authors have modeled the drying kinetics in a conical fluidized bed because the vessel geometry affects the drying process [12] as this topic has received little research attention and little information is available on it.

2. Materials and methods 2.1. Material Sodium percarbonate particles were purchased from a local corporation. Coated sodium percarbonate is a stabilized grade of sodium carbonate peroxyhydrate, specially designed for use in bleach additive products, detergent powders and automatic machine dishwash powders. Sodium percarbonate combines the properties of hydrogen peroxide with the properties of sodium carbonate in an easy to use, free

31

flowing, white granular powder with excellent water solubility and high rate of dissolution. Sodium percarbonate particles are coated using combination of sodium sulfate solution (20% by weight), sodium carbonate solution (20% by weight) and water glass (sodium metasilicate), in this study. Sum of the weight of sodium carbonate and sodium sulfate must be approximately 10% of the Sodium percarbonate particles without coat (weight ratio of sodium sulfate to sodium carbonate is 75:25). Particles are stored in the proposed conditions. Physical/chemical properties of sodium percarbonate are given in Table 1. Their average radius was almost 490 μm. The average of the initial moisture content of the particles was determined in every stage of the experiment by sensors which were mounted in the bed. Approximately 2 kg of the prepared particles were placed in the fluidized bed dryer for the drying process. Initial bed height was 8.83 cm.

2.2. Drying equipment and experimental procedure In this study, the effects of air temperature and flow rate variations on the drying kinetics were investigated using the available batch fluidized bed dryer. Fig. 1 shows a schematic representation of the batch fluidized bed dryer that was used in the experiments. The drying chamber had a stainless steel cone having a bottom diameter of 20 cm and top diameter of 40 cm; the cone was 80 cm in height. The air distributor was a steel circle with circular holes having a diameter of 1 cm (see (4) in Fig. 1). Fluidization air was provided by a 2.5 kW fan (Greenco, 2RB NO. BN 10010826013, Zhejiang Greenco Industry Co. Ltd., China, see (2) in Fig. 1). Twelve heating elements with a power of 1000 W were mounted as the heater in the air way (see (3) in Fig. 1). During the experiments, the air flow rate was measured using a rotameter which was located in the air way. Moreover, one capacitive humidity sensor and one temperature sensor of the RTD (pt100) type were placed in the air entrance for recording the inlet air moisture and temperature. Four other humidity sensors and five other temperature sensors were mounted across the bed. The resulting data from the sensors were recorded using two data recorders; both recorders worked with the same time interval. Before each experiment, the bed was filled with 2 kg of humid coated sodium percarbonate particles. Experiments were conducted at the inlet air temperature of 60, 70, and 80 °C and the air flow rate of 90, 100, and 120 m3/h. During the experiments, the moisture content of the bed samples was recorded continuously (every 10 s) by using a recorder (The moisture content of the particles that is used in this study, was

Table 1 Physical/chemical properties of sodium percarbonate. Property

Results/Remarks

Molecular formula Physical state Synonyms

2Na2CO3 .3H2O2 White powder PCS; solid hydrogen peroxide; sodium carbonate hydrogen 15630-89-4 239-707-6 314.06 g/mol 300–900 μm

CAS number EINECS number Molecular Weight Average particle size Particle size N1600 μm or N1400 μm b150 μm Density Bulk density Available Oxygen (AvOx) Water Solubility Rate of dissolution Vapor pressure pH

≤3% ≤10% ≤2% 2.14 g/cm3 900–1100 kg/m3 ≥13 % 140 g/l at 20 °C ≥90% (after 2 min) b10−3 Pa at 25 °C About 10.5 at 1% concentration (20 °C)

32

S. Hematian, F. Hormozi / Powder Technology 269 (2015) 30–37

Fig. 1. Fluidized bed dryer. (A) Experimental set-up. (B) Schematic representation of dryer: (1) fluidization air; (2) fan; (3) heater; (4) air distributor; (5) LED; (6) filter; (7) electrical switchgear; (8) computer; (9) nozzle; (10) atomization air; (11) liquid input to nozzle; (12) exhaust air; (13) coating solution*; (14) pump; (15) liquid uniform distributor system; (16) inlet air to system and output of compressor; (17) liquid outlet; (18) temperature recorder; (19) moisture recorder. *Equipment connected to section 13 was used in the coating process.

determined inline using the lowest sensor that is in full contact with particles). The number of experimental points was high because of the continuous recording, unlike that in most of the studies in this field. The air flow rate was controlled using a rotameter that was located in the air way, and the inlet air temperature was maintained at the desired value, in each stage.

3. Mathematical modeling of drying process

Model no. Model equation

Model name

References

1 2 3 4 5 6

Newton or Lewis Page Modified Page Henderson and Pabis Logarithmic Two term

[6,21–23] [6,24–26] [27,28] [29–31] [32,33] [34,35]

Two term exponential

[6,36]

Wang and Singh Thompson Diffusion approach

[27] [37,38] [32,33]

Verma et al.

[39]

Modified Henderson and Pabis Simplified Fick's diffusion (SFFD) equation Modified Page Eq. (2) Midilli and Kucuk

[40]

7

3.1. Modeling of drying kinetics Many researches have been performed in field of drying kinetics modeling. Fifteen widely used models were used for describing the drying kinetics given in Table 2. In these models, MR represents the moisture ratio and is dimensionless; it is expressed by the following equation:
 M−Meq  MR ¼
M0 −Meq

Table 2 The most important mathematical drying models.

8 9 10 11 12 13

ð1Þ

14 15

MR = exp(−kt) MR = exp(−ktn) MR = exp(−(kt)n) MR = a exp(−kt) MR = a exp(−kt) + c MR = a exp(−bt) + c exp(−dt) MR = a exp(−kt) + (1−a) exp(−kat) MR = 1 + at + bt2 t = A Ln(MR) + B [Ln(MR)]2 MR = a exp(−kt) + (1−a) exp(−kbt) MR = a exp(−kt) + (1−a) exp(−gt) MR = a exp(−kt) + b exp(−gt) + c exp(−ht) MR = a exp[−c (t/L2)] 2 n

MR = exp[−k(t/L ) ] MR = a exp(−ktn) + bt

[41] [42] [43]

S. Hematian, F. Hormozi / Powder Technology 269 (2015) 30–37

33

Fig. 2. Effect of temperature (T = 60, 70, 80 °C) on moisture ratio at constant flow rate (Q = 90 m3/h) during drying of coated sodium percarbonate particles in batch fluidized bed dryer.

Fig. 4. Effect of temperature (T = 60, 70, 80 °C) on moisture ratio at constant flow rate (Q = 120 m3/h) during drying of coated sodium percarbonate particles in batch fluidized bed dryer.

In this equation, M denotes the moisture content of the samples; M0, the initial moisture content; and Meq, the equilibrium moisture content in each stage of the experiment. Meq or equilibrium moisture is obtained from an empirical equation, such as the relation proposed by Tia et al. (1990) and can be expressed as follows:

of the curve fitting.

   −21065 −1:25 RH ¼ exp :Meq R:T  −21065 0:8 R:T: ln ðRHÞ

M M0

χ ¼

ð3Þ

SStot ¼

ð4Þ

Therefore, in the next stage of modeling, moisture experimental data were rewritten in the MR form. As mentioned in the previous section, data were recorded every 10s continuously by sensors connected to a recorder. A non-linear regression analysis was performed using the Matlab software (Matlab R2009a, USA), and the least squares method was used for fitting the experimental data to all the considered models (fifteen models). In this study, three statistical parameters were used for evaluating the vicinity amount of the models and the experimental data. The coefficient of determination (R2), root mean square error (RMSE), and reduced chi – square (χ2) determined the suitability level

Fig. 3. Effect of temperature (T = 60, 70, 80 °C) on moisture ratio at constant flow rate (Q = 100 m3/h) during drying of coated sodium percarbonate particles in batch fluidized bed dryer.

2

 X
2 12 1 n Mpre;i −M exp;i i¼1 N

ð5Þ

ð6Þ

2 Xn
M exp;i −M exp;mean i¼1

ð7Þ

2 Xn
M exp;i −Mpre;i i¼1

ð8Þ

SSerror SStot

ð9Þ

SSerror ¼

2

M exp;i −Mpre;i N−n

RMSE ¼

where RH denotes the relative humidity of air which is measurable. Thus, Meq is calculated using Eq. (3). However, Meq is usually relatively small as compared to M and M0 [5]. Thus, MR can be simplified as follows: MR ¼

i¼1

ð2Þ

 Meq ¼

Xn
2

R ¼ 1−

The best model was determined on the basis of the higher value of R2 and the lower values of RMSE and χ 2 [4–6]. 3.2. Effective moisture diffusivity calculation High energy consumption in drying industry has distinguished drying as an energy demanding function with immense industrial importance [13]. Physical and thermal properties of different matter such as heat and mass transfer, moisture diffusion, energy of activation, and energy consumption are required for ideal dryer design or improving the existing system.

Fig. 5. Effect of flow rate (Q = 90, 100, 120 m3/h) on moisture ratio at constant temperature (T = 60 °C) during drying of coated sodium percarbonate particles in batch fluidized bed dryer.

34

S. Hematian, F. Hormozi / Powder Technology 269 (2015) 30–37

Fig. 6. Effect of flow rate (Q = 90, 100, 120 m3/h) on moisture ratio at constant temperature (T = 70 °C) during drying of coated sodium percarbonate particles in batch fluidized bed dryer.

Diffusivity is a property of matter and its value depends on internal material conditions, therefore many experiments have been conducted for predicting it. Effective moisture diffusivity is defined as a property of matter as intrinsic moisture mass transfer and includes molecular diffusion, liquid diffusion, vapor diffusion, hydrodynamic flow and other possible mass transfer mechanisms [14]. Fick's second law of diffusion for spherical objects is used for calculating the effective diffusion coefficient [44,45]. MR ¼

" # Mt −Me 6 π2 Deff t ¼ 2 exp − M0 −Me π r2

ð10Þ

Where Deff denotes the effective diffusivity; r, the spherical radius; and t, the time. Eq. (10) can be rewritten in the logarithmic form as follows: 2

ln ðMRÞ ¼ ln

6 D π t − eff 2 π2 r

ð11Þ

Therefore, Deff can be estimated by plotting the ln(MR) versus t. The slope of this straight line is −Deff π2 /r2, and Deff is calculated by using the values of pi and r. Further, the activation energy is calculated using the Arrhenius equation [4,14–20]. Deff ¼ D0 exp

−Ea R Tabs

ð12Þ

D0 and Ea can be calculated using linear regression (lnDeff versus 1/ Tabs) as well. 4. Results and discussions Experiments were conducted in the available fluidized bed dryer. The drying curves are shown in Figs. 2–7 for the investigation of the

Fig. 7. Effect of flow rate (Q = 90, 100, 120 m3/h) on moisture ratio at constant temperature (T = 80 °C) during drying of coated sodium percarbonate particles in batch fluidized bed dryer.

effect of air temperature and flow rate increase on the drying rate. The moisture ratio decreased continuously with time. Moisture removal from this matter was rapid at the initial stages of drying process but later its rate decreased with time. This event occurred because the surface moisture evaporates quickly due to high heat and mass transfer coefficients in drying process. It can be pointed out that the drying rate was high at the initial stage of the drying process, but it decreased when all the surface moisture evaporated and the drying front diffuses inside the material. The drying rate increased with an increase in the air temperature at a constant flow rate (slope increase of the curve) and with an increase in the flow rate at a constant temperature (slope increase of the curve); thus, the drying time was reduced in the abovementioned cases. These results could be attributed to an increasing convective heat and the mass transfer with an increase in the air temperature and flow rate. It was noted that because of the considerable amount of experimental data, only 16 data elements were selected for comparison. According to the previous section, modeling was conducted for the falling rate zone by using the Matlab software. The falling rate zone had the highest share of the drying process. In this zone, the internal mass transfer took place by diffusion; thus, the diffusivity coefficient was important. The falling rate is shown in Fig. 8, at inlet air temperature of 80 and air flow rate of 120 m3/hr. Similar trends were observed for other operating condition. Then, the best models and the coefficients of the models were determined. The results are given in Table 3. An Investigation and pluralization of the results revealed that the modified Henderson & Pabis (12) model, Verma et al.(11) model, and two term (6) model adapted well with the experimental data under all conditions (see Fig. 9). In other words, the results revealed that the modified Henderson and Pabis model with the average value of R2 equal to 0.988204 and the two term model with the average value of R2 equal to 0.985082 under almost all operating conditions, and the Verma et al. model with the average value of R2 equal to 0.971698 at a high flow rate and temperature, fitted very well with the experimental data (see Fig. 10). The equation coefficients of the modified Henderson and Pabis model, the two term model, and the Verma et al. model are given in Tables 4–6 for all experiments. These models can be expressed by Eqs. (13–15), respectively: MR ¼ a expð−ktÞ þ b expð−gtÞ þ c expð−htÞ

ð13Þ

MR ¼ a expð−btÞ þ c expð−dtÞ

ð14Þ

MR ¼ a expð−ktÞ þ ð1−aÞ expð−gtÞ

ð15Þ

In the final stage, according to the previous section, the effective diffusivity was calculated for all experiments by using the linear

Fig. 8. Drying rate versus drying time (Q = 120 m3/h and T = 80 °C) during drying of coated sodium percarbonate particles in batch fluidized bed dryer.

S. Hematian, F. Hormozi / Powder Technology 269 (2015) 30–37

35

Table 3 Statistical results of considered models at different drying conditions. M.no.

T (οC) Flow rate (m3/hr) 90

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80 60 70 80

100

120

R2

χ2

RMSE

R2

χ2

RMSE

R2

χ2

RMSE

0.748631 0.977729 0.316410 0.887326 0.978711 0.938953 0.693456 0.449117 0.641050 0.838203 0.979468 0.756060 0.935380 0.982358 0.951956 0.981306 0.979734 0.972138 0.856376 0.978316 0.531129 0.814914 0.986949 0.448746 0.971817 0.960695 0.903668 0.748631 0.979465 0.316410 0.921054 0.979469 0.972108 0.981292 0.979760 0.983455 0.838203 0.979468 0.756060 0.887326 0.978711 0.938954 0.945293 0.429126 0.782019

0.006518 0.000622 0.014403 0.002955 0.000601 0.001293 0.537843 0.018804 0.002017 0.004244 0.000695 0.005168 0.001715 0.000503 0.001023 0.000501 0.000584 0.000597 0.003767 0.000612 0.009934 0.004854 0.000368 0.022139 0.528573 0.928306 0.305805 0.006669 0.000596 0.014566 0.002095 0.000585 0.000594 0.000514 0.000595 0.000358 0.004293 0.000685 0.005198 0.002989 0.000607 0.001300 0.001468 0.088593 0.004671

0.080280 0.024823 0.119681 0.053748 0.024269 0.035764 0.0673610 0.139003 0.006967 0.064407 0.023834 0.071493 0.040704 0.022093 0.031728 0.021893 0.023679 0.024162 0.060682 0.024494 0.099118 0.068887 0.019001 0.147965 0.718814 0.095380 0.687867 0.080279 0.023836 0.119681 0.044989 0.023834 0.024175 0.021901 0.023664 0.0.01861 0.064407 0.023833 0.071494 0.053748 0.024269 0.035765 0.037452 0.291633 0.067583

0.805743 0.937135 0.954476 0.893108 0.977849 0.960241 0.648900 0.935312 0.179334 0.956886 0.959563 0.954912 0.983088 0.987275 0.977305 0.990851 0.987865 0.978850 0.932554 0.973777 0.965519 0.844258 0.965974 0.976778 0.839855 0.970271 0.962422 0.956885 0.937136 0.971001 0.956886 0.987343 0.975089 0.990055 0.987910 0.986853 0.956885 0.959563 0.954912 0.893108 0.977849 0.960241 0.463219 0.809972 0.918042

0.011988 0.002779 0.002267 0.006664 0.000984 0.002000 0.062755 0.006228 0.051223 0.002688 0.001798 0.002269 0.001065 0.000568 0.001154 0.000582 0.000545 0.001087 0.004205 0.001166 0.001735 0.009710 0.001512 0.001168 0.707831 0.380940 0.870037 0.002716 0.002810 0.001474 0.002716 0.000566 0.001266 0.000646 0.000549 0.000690 0.002716 0.001807 0.002292 0.006734 0.000990 0.002021 0.156816 0.008541 0.004211

0.108937 0.052580 0.047376 0.080809 0.031211 0.044275 0.247966 0.108343 0.224027 0.051321 0.042170 0.047149 0.032143 0.023656 0.033450 0.023641 0.023101 0.032292 0.064189 0.033959 0.041231 0.097541 0.038683 0.033863 0.906023 0.534666 0.923288 0.051321 0.052579 0.037811 0.051321 0.023593 0.035045 0.024648 0.023058 0.025460 0.051321 0.042170 0.047149 0.080809 0.031211 0.044275 0.387918 0.091417 0.063568

0.549298 0.499651 0.857936 0.862380 0.975804 0.954369 0.542507 0.843206 0.409892 0.704558 0.887590 0.898434 0.989474 0.951598 0.997581 0.989818 0.987260 0.997918 0.712460 0.706357 0.928815 0.732959 0.438032 0.928374 0.860889 0.981111 0.927035 0.972675 0.499652 0.857936 0.973524 0.983251 0.996562 0.997074 0.989120 0.998319 0.704558 0.887590 0.898434 0.862380 0.975805 0.954369 0.976431 0.988869 0.955119

0.015110 0.012157 0.005869 0.004640 0.000594 0.001899 0.019524 0.004133 0.028197 0.009961 0.002759 0.004228 0.000357 0.001200 0.000101 0.000347 0.000319 0.000088 0.009694 0.007208 0.002964 0.009003 0.013796 0.002982 0.550222 0.428621 0.943261 0.000926 0.012412 0.005960 0.000897 0.000415 0.000144 0.000101 0.000278 0.000072 0.010017 0.002788 0.004261 0.004666 0.000600 0.001914 0.000804 0.000279 0.001898

0.122584 0.109693 0.076317 0.067738 0.024122 0.043252 0.144457 0.068193 0.169414 0.099249 0.051993 0.064528 0.018733 0.034117 0.009958 0.018424 0.017503 0.009238 0.097912 0.084034 0.054022 0.094358 0.116252 0.054189 0.230015 0.647976 0.702447 0.030183 0.109694 0.076317 0.029711 0.020069 0.011872 0.009878 0.016176 0.008299 0.099249 0.051993 0.064529 0.067738 0.024121 0.043252 0.028032 0.016361 0.042895

regression; the average values are listed in Table 7. The average radius of the particles was 490 micrometer. The effective diffusivity changed between 2.2337 × 10−10 and 22.0648 × 10−10 m2/s. Effective diffusivity increased with an increase in the air temperature and flow rate. This

result could be attributed to surface wetting of particles and importance of convective heat transfer in this process. D0 and Ea were calculated using Eq. (12) and the linear regression of ln (Deff) versus 1/Tabs. The activation energy was an indication of the amount of energy required for removing moisture from a solid matrix. The activation energy for coated sodium percarbonate varied from 46.0402 to 104.930 KJ/mol. The results are presented in Table 7.

Fig. 9. Average values of R2, RMSE, and χ2 for all considered models.

Fig. 10. Average values of R2, RMSE, and χ2 for the best models.

36

S. Hematian, F. Hormozi / Powder Technology 269 (2015) 30–37

5. Table 4

Table 7 Effective diffusivity and energy activation for the different operating conditions.

The equation coefficients of the modified Henderson and Pabis model. Flow rate T (οC) Coefficients of parameter equation (m3/hr)

90

100

120

60 70 80 60 70 80 60 70 80

Parameter

Operating conditions

a

b

c

k

g

h

1.6784 1.2627 1.2779 2.0550 0.2298 −2.2220 0.0821 0.2512 −4.1257

1.3405 1.2012 0.4216 2.0527 0.5365 1.6708 0.0521 −0.4459 4.7663

0.5872 1.0181 −0.4307 0.0486 0.8537 1.6937 0.8898 1.1224 0.3398

1.2826 2.8229 0.1061 0.1840 0.0187 0.9297 −0.0217 0.0008 0.7462

1.4744 1.0242 4.7847 1.2249 0.3165 0.1261 2.6515 0.8697 0.6167

0.0651 0.0928 0.1064 −0.0654 5.2965 1.6146 0.0938 0.2548 0.0119

T (οC)

90

60 70 80 60 70 80 60 70 80

100

120

Coefficients of parameter equation

Parameter

a

c

b

d

2.8606 1.6132 0.6634 2.1011 0.3244 0.3325 0.9277 0.9951 0.8723

0.5839 1.0178 0.4034 0.0642 0.6865 0.8776 0.0494 0.0689 0.2773

1.3096 1.0902 0.3656 0.1908 0.0351 0.0927 0.0894 0.1501 0.3035

0.0646 0.0928 0.0375 −0.0519 0.6464 0.0927 −0.0374 −0.0564 0.0034

Conclusions In this study, the drying behavior of coated sodium percarbonate particles was investigated using a batch fluidized bed dryer. The drying process was investigated at the drying air temperature of 60, 70, and 80 °C and the air flow rate of 90, 100, and 120 m3/h. During the experiments, the moisture ratio of this matter decreased continuously with time (exponential form). The curves of the moisture ratio were fitted to 15 widely used mathematical models of the drying process. Suitable models were selected on the basis of the calculated R2, RMSE and χ2 values. The modified Henderson and Pabis model and the two term model adapted well with the experimental data under almost all operating conditions and the Verma et al. model adapted well at a high air temperature and flow rate. Therefore, these models were selected as the most adequate models for the drying of coated sodium percarbonate particles. The effective diffusivity was obtained using Fick's law because drying took place in the falling rate zone. The effective diffusivity changed between 2.2337 × 10−10 and 22.0648 × 10−10 m2/s.

Table 6 The equation coefficients of the Verma et al. model. Flow rate (m3/hr) T (οC) Coefficients of parameter equation Parameter

90

100

120

60 70 80 60 70 80 60 70 80

= = = = = = = = =

90 m3/h, T = 60οC 90 m3/h, T = 70 οC 90 m3/h, T = 80 οC 100 m3/h, T = 60 οC 100 m3/h, T = 70 οC 100 m3/h, T = 80 οC 120 m3/h, T = 60 οC 120 m3/h, T = 70 οC 120 m3/h, T = 80 οC

Energy Activation (KJ/mol)

2.2337 7.6377 12.5042 2.4865 12.3582 21.0430 8.5675 16.1533 22.0648

84.564

104.930

46.402

References

Table 5 The equation coefficients of the two term model. Flow rate (m3/hr)

Q Q Q Q Q Q Q Q Q

Effective diffusivity values (m2/s) × 1010

a

k

g

0.3387 1.0408 0.326 1.6297 0.3209 1.7226 0.1014 0.0063 0.2254

0.0272 0.0946 0.0250 0.1256 0.0345 0.1259 −0.0169 −0.1820 −0.0046

0.2954 3.8373 0.2878 8.9002 0.6271 0.4408 0.1008 0.1178 0.2267

[1] H. Jakob, S. Leininger, T. Lehmann, S. Jacobi, S. Gutewort, Peroxo Compounds Inorganic, Ullmann's encyclopedia of industrial chemistry, Wiley-VCH, 2007, ISBN 9783527306732. [2] W. Ramli, W. Daud, Fluidized bed dryers — recent advances, Adv. Powder Technol. 19 (2008) 403–418. [3] S.M. Tasirin, S.K. Kamarudin, K. Jaafar, K.F. Lee, The drying kinetics of bird’s chillies in a fluidized bed dryer, J. Food Eng. 79 (2007) 695–705. [4] M. Aghbashlo, M.H. Kianmehr, A. Arabhosseini, Modeling of thin-layer drying of potato slices in length of continuous band dryer, Energy Convers. Manag. 50 (2009) 1348–1355. [5] S. Meziane, Drying kinetics of olive pomace in a fluidized bed dryer, Energy Convers. Manag. 52 (2011) 1644–1649. [6] A. Kaleta, K. Gornicki, R. Winiczenko, A. Chojnacka, Evaluation of drying models of apple (var. Ligol) dried in a fluidized bed dryer, Energy Convers. Manag. 67 (2013) 179–185. [7] S. Leininger, H. Jakob, U. Kottke, Coated sodium percarbonate particles, United states patent (2010), patent No.2010/0035060 A1. [8] F. Ronsse, J.G. Pieters, K. Dewettinck, Modelling side-effect spray drying in top-spray fluidisedbed coating processes, J. Food Eng. 86 (2008) 529–541. [9] F. Ronsse, J.G. Pieters, K. Dewettinck, Modelling heat and mass transfer in batch topspray fluidised bed coating processes, Powder Technol. 190 (2009) 170–175. [10] F. Ronsse, J.G. Pieters, K. Dewettinck, Numerical spray model of the fluidised bed coating process, Dry. Technol. 25 (2007) 1487–1510. [11] M. Hemati, R. Cherif, K. Saleh, V. Pont, Fluidized bed coating and granulation: influence of process-related variables and physicochemical properties on the growth kinetics, Powder Technol. 130 (2003) 18–34. [12] M. Wormsbecker, R.V. Ommen, J. Nijenhuis, H. Tanfara, T. Pugsley, The influence of vessel geometry on fluidized bed dryer hydrodynamics, Powder Technol. 194 (2009) 115–125. [13] R.E. Treybal, Mass Transfer Operation, McGRAW-HILL Book Company, Singapore, 1981. (ISB N 0-07-065 J 76-0). [14] A. Abbaszadeh, A. Motevali, B. Ghobadian, M.H. Khoshtaghaza, S. Minaei, Effect of Air velocity and temperature on energy and effective moisture diffusivity for Russian olive (Elaeagnusan gastifolial L.) in thin-layer drying, J. Chem. Chem. Eng. 31 (1) (2012). [15] M. Aghbashlo, M.H. Kianmehr, H. Samimi-Akhijahani, Influence of drying conditions on the effective moisture diffusivity, energy of activation and energy consumption during the thin-layer drying of berberis fruit (Berberidaceae), Energy Convers. Manag. 49 (2008) 2865–2871. [16] S.J. Babalis, V.G. Belessiotis, Influence of drying conditions on the drying constants and moisture diffusivity during the thin-layer drying of figs, J. Food Eng. 65 (2004) 449–458. [17] I. Doymaz, Air-drying characteristics of tomatoes, J. Food Eng. 78 (2007) 1291–1297. [18] M. Kashaninejad, A. Mortazavi, A. Safekordi, L.G. Tabil, Thin-layer drying characteristics and modeling of pistachio nuts, J. Food Eng. 78 (2007) 98–108. [19] H.O. Menges, C. Ertekin, Mathematical modeling of thin layer drying of golden apples, J. Food Eng. 77 (2006) 119–125. [20] K. Sacilik, R. Keskin, A.K. Elicin, Mathematical modeling of solar tunnel drying of thin layer organic tomato, J. Food Eng. 73 (2006) 231–238. [21] P.W. Westerman, G.M. White, I.J. Ross, Relative humidity effect on the high temperature drying of shelled corn, Trans. ASAE 16 (1973) 1136–1139. [22] J.R. O'Callaghan, D.J. Menzies, P.H. Bailey, Digital simulation of agricultural dryer performance, J. Agric. Eng. Res. 16 (1971) 223–244. [23] W.K. Lewis, The rate of drying of solid materials, Ind. Eng. Chem. 13 (1921) 427–432. [24] Y. Agrawal, R.P. Singh, Thin layer drying studies on short grain rough rice, ASAE Paper No. 35311997. [25] A. Kader, J.M. Labivitch, F.G. Mitchell, N.F. Sommer, Quality and safety of pistachio nuts as influenced by post harvest handling procedure, The pistachio association Anuual Report1979. 45–50. [26] G.E. Page, Factors influencing the maximum rates of air drying shelled corn in thin layers, MSc Thesis Purdue University, 1949. [27] D.D. Overhults, G.M. White, M.E. Hamilton, I.J. Ross, Drying soybeans with heated air, Trans. ASAE 16 (1973) 195–200. [28] Q. Zhang, J.B. Litchfield, An optimization of intermittent corn drying in a laboratory scale thin layer dryer, Dryer Technol. 9 (1991) 383–395.

S. Hematian, F. Hormozi / Powder Technology 269 (2015) 30–37 [29] M. Chhinnan, Evaluation of few selected mathematical models for describing thin layer drying of in-shell pecans, Trans. ASAE 27 (2) (1984) 610–615. [30] G.M. White, I.J. Ross, R. Ponelert, Fully exposed drying of popcorn, Trans. ASAE 24 (1981) 466–468. [31] S.M. Henderson, S. Pabis, Grain drying theory temperature effect on drying coefficient, J. Agric. Eng. Res. 6 (1961) 169–174. [32] A. Kassem, Comparative studies on thin layer drying model for wheat, 13th international congress on agricultural engineering, vol. 6, February 2–6, Morocco, 1998. [33] A. Yagcioglu, A. Degirmencioglu, F. Cagatay, Drying characteristics of laurel leaves under different drying conditions, Proceedings of the 7th International congress on agricultural mechanization and energy, May 26–27, Adana, Turkey, 1999, pp. 565–569. [34] S. Henderson, Progress in developing the thin layer drying equation, Trans. ASAE 17 (1974) 1167–1168. [35] C.Y. Wang, R.P. Singh, A single layer drying equation for rough rice, ASAE Paper No. 3001, 1978. [36] Y.I. Sharaf Elden, J.L. Blaisdell, M.Y. Hamdy, A model for ear corn drying, Trans. ASAE 23 (1980) 1261–1265.

37

[37] M.R. Paulsen, T.L. Thomson, Drying endysus of grain sorghum, Trans. ASAE 16 (1973) 537–540. [38] T.L. Thomson, P.M. Peart, G.H. Foster, Mathematical simulation of corn drying: A new model, Trans. ASAE 11 (1968) 582–586. [39] L.R. Verma, R.A. Bucklin, J.B. Endan, F.T. Wratten, Effect of drying air parameters on rice drying models, Trans. ASAE 28 (1985) 296–301. [40] V. Karathanos, Determination of water content of dried fruits by drying kinetics, J. Food Eng. 39 (1999) 337–344. [41] L. Diamente, P. Munro, Mathematical modeling of hot air drying of sweet potato slices, Int. J. Food Sci. Technol. 26 (1991) 99. [42] L. Diamente, P. Munro, Mathematical modeling of the thin layer solar drying of sweet potato slices, Sol. Energy 51 (1993) 271–276. [43] A. Midilli, H. Kucuk, Z. Yapar, A new model for single drying, Drying Technol. 20 (7) (2002) 1503–1513. [44] K.O. Falad, E. Abbo, Air drying rehydration characteristics of data palm (Phoenix dactylifera L.) fruits, J. Food Eng. 79 (2007) 724–730. [45] S. Mujumdar, Drying Technology in Agriculture and Food Sciences, Science Publisher Inc., Enfield (NH), USA, 2000.