Simulation of a cross-flow continuous fluidized bed dryerfor paddy rice

M. Izadifar a, D. Mowla b,*

a Department of Chemical Engineering, Tehran University, Tehran, Iranb Department of Chemical Engineering, Shiraz University, Shiraz, Iran

Received 26 April 2002; accepted 6 October 2002

Abstract

Fluidized bed drying is an alternative drying method of paddy, which offers many advantages over other forms of drying. In this

study a mathematical model is developed to simulate the drying of moist paddy in a cross-flow continuous fluidized bed dryer

(CFCFBD). The model is based on the differential equations, which are obtained by applying the momentum, mass and energy

balances to each element of the dryer and also on the drying properties of paddy. The proposed model is solved by writing a

computer program, which takes the operating conditions as input and gives the hydrodynamic properties as well as the variation of

moisture content of paddy through the dryer as output. Different fluidizing characteristics of paddy, needed in the program, are

determined from the drying experiments in the literature. Some experimental data of CFCFBD are used to validate the predictions

of the model. The predictions of the model show good agreement with experimental results.

� 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Fluidized bed drying; Fluidized bed modeling; Paddy rice drying

1. Introduction

Drying is an important operation in the chemical,

food, metallurgical, pharmaceutical and other indus-

tries. Fluidized bed drying is considered as one of the

most successful drying techniques. The advantages offluidized bed drying can be summarized as follows:

1. High heat and mass transfer rates, because of good

contact between the particles and the drying gas.

2. Uniform temperature and bulk moisture content of

particles, because of intensive particle mixing in the

bed.

3. Excellent temperature control and operation up tothe highest temperature.

4. High drying capacity due to high ratio of mass of air

to mass of product.

Paddy is one of the grains that are needed to be dried

after harvesting. The quality characteristics of rice,

which are to be maintained during the drying process,

are the head yield, the color and the cooking qualities.

The head yield of rice is especially sensitive to the

mode of drying and is usually used in assessing the

success or failure of a rice drying system. Decreasing

head yield of rice, due to the use of inappropriate

methods in much rice growing area, especially north of

Iran, is a major problem in paddy drying. Bin dryingand thin layer drying, are the present methods that are

used for paddy drying in north of Iran. These present

methods cannot produce uniform moisture content and

temperature of paddy during the drying; and so, some

parts of paddy will be over dried and some other parts

will not be dried adequately. In addition, the drying

capacity is low and the temperature and moisture con-

tent of paddy are not under precise control in thesemethods. The use of fluidized bed dryers for paddy

drying can solve these disadvantages of the present

methods.

Research works on fluidized bed paddy drying are

still relatively limited. Sutherland and Ghaly (1990) in-

vestigated drying of paddy in a batch fluidized bed.

Their experimental results showed that head yield was

51–61%, when paddy dried from 22% to 17% (wb), butwas 15–24% when the final moisture content was 16%

wb. Tumambing and Driscol (1991) found experimen-

tally that the drying rate of paddy was affected by drying

Journal of Food Engineering 58 (2003) 325–329

www.elsevier.com/locate/jfoodeng

*Corresponding author. Fax: +98-711-6287294.

E-mail address: dmowla@shirazu.ac.ir (D. Mowla).

0260-8774/03/$ - see front matter � 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0260-8774(02)00395-3

air temperature and bed thickness. They used the drying

air temperature of 40–100 �C, bed thickness of 5–20 cm

and air velocity of 1.5–2.5 m/s in their experiments.

Prachayawarakorn and Soponronnarit (1993) developeda mathematical model for a batch-fluidized bed dryer

including drying kinetic equation and optimum ope-

rating parameters were investigated. Soponronnarit,

Yapha, and Prachayawarakorn (1995) erected a proto-

type of a cross-flow fluidized bed paddy dryer and col-

lected some experimental data. Their experimental

results showed that the system operated efficiently and

yields high product quality in terms of head yield andwhiteness. Wetchacama, Soponronnarit, and Jariya-

tontivait (2000) designed, constructed and tested a pro-

totype of vibro-fluidized bed paddy dryer with a capacity

of 2.5–5 t/h and reduced moisture content of paddy rice

from 28 to 23% d.b. at a feed rate of 4821 kg/h. Madhiy

Anon, Soponronnarit, and Tia (2000) constructed and

tested an industrial-scale prototype of spouted bed

paddy drier with a capacity of 3000 kg/h. The prototypewas shown to be a desirable feature of spouted bed as

well as capability of continuous drying and consistent

results during the testing period. Experimental results

showed that the prototype performed well on moisture

reduction and milling quality. Queiroz, Couto, and

Haghighi (2000) developed a model to simulate the mois-

ture diffusion during the drying process of rough rice by

using finite element analysis. The simulated model could

predict the temperature of the air and grain and the

moisture movement inside the rough rice kernel. Reidand Siebenmorgen (1998) explored the relationships

between rough rice surface temperature, amount of mois-

ture removed and harvest moisture content and head

rice yield reduction (HRYR) and developed a model

describing HRYR as a function of these variables.

In this paper, unlike the most research works that are

carried out on batch fluidized bed paddy drier, modeling

and design of a continuous fluidized bed paddy dryer ispresented. Unlike the previous models, the moisture

content of particle and the latent heat of desorption-

vaporization aren�t assumed to be constant, but are al-

lowed to vary with length of the bed and other conditions.

2. Mathematical model

Fig. 1 shows the schematic diagram of a continuous

fluidized bed dryer. Paddy enters to the system by a

helical feeder and is fluidized by the hot air, which comesfrom the bottom of the bed. Then, because of fluidiza-

tion and slope of the bed, paddy moves horizontally

along the system and exits from the end. Dusts and

Nomenclature

ap specific surface (m3/m3 of bed)

Cpg specific heat of dry gas (j/kg �C)Cps specific heat of paddy (j/kg �C)Cpv specific heat of vapor (j/kg �C)Deff effective diffusivity (1/s)hc heat transfer coefficient (j/m2 �C s)

K mass transfer coefficient (m/s)

m̂m evaporation rate per bed volume (kgH2O/m3 s)

P pressure (Pas)

P � vapor pressure (mmHg)

Pt total pressure (mmHg)

Pr Prandtl number

R particle radius (m)r radius (m)

RHe relative humidity in equilibrium (decimal)

Sc Schmidt number

t time (s)

Tg gas temperature (�C)Tg average gas temperature (�C)Tgi inlet gas temperature (�C)Tp particle temperature (�C)Umf minimum fluidization velocity (m/s)

Ur real velocity (m/s)

Us velocity of particles in the bed (m/s)

Wb bed width (m)

x bed height (m)

X average particle moisture content (kg H2O/kg

dry matter)

Xe equilibrium moisture content (kg H2O/kg drymatter)

Xi initial particle moisture content (kg H2O/kg

dry matter)

Y absolute humidity (kg H2O/kg dry air)

Ye equilibrium absolute humidity (kg H2O/kg

dry air)

Z bed length (m)

Greeks

emf minimum fluidization porosity (m3/m3 of

bed)

W2 constant in Eq. (11)

k latent heat (j/kg)

qg gas density (kg dry gas/m3)qs particle density (kg dry salid/m3)

h angle of inclination of the bed

sg shear stress of gas phase (Pas)

ss shear stress of solid phase (Pas)

326 M. Izadifar, D. Mowla / Journal of Food Engineering 58 (2003) 325–329

probably some paddy and other grains, which have been

transported by exit air from the bed, are separated from

the air by a cyclone.

In order to develop a mathematical model to repre-

sent this type of dryer, the bed is first divided horizon-tally into n elements of dz length and then each of these

elements is divided vertically into m subelements of dxheight. Now according to the two-phase theory of flui-

dization, each subelement is assumed to consist of two

different phases, which are called emulsion (dense) and

dispersed (dilute) phases as shown schematically in Figs.

2 and 3. Application of the momentum, material and

energy balances to each phase of these subelements willproduce the governing equations for this type of dryer.

In this case it is assumed that the system operates at

minimum fluidization conditions so the superficial andreal velocity of air in the bed are related as follows

(Kunii & Levenspil, 1991):

Ur ¼ Umf=emf ð1Þ

2.1. Momentum balance

As it is shown in Fig. 2, air enters to an element

slantwise with an angle of h and after passing througheach subelement, as shown in Fig. 3, exits from the top

of the element. Applying the momentum balance to the

emulsion and dispersed phases will result the following

differential equations of each phase respectively:

dðUsÞdz

¼ �ssWb 1� emfð ÞqsUs

þqs � qg

� �g sin h

qsUs

ð2Þ

where ss is shear stress between flow of the particles and

the wall of dryer and airflow.

dðUrÞdx

¼ �g cos hUr

� sgWbqgUremf

� dpqgUremf

� �dx

ð3Þ

where sg is shear stress between airflow and the wall of

dryer and the flow of the particles.

2.2. Material balance

As it is shown in Figs. 2 and 3, hot air passes througheach subelement while paddy particles pass horizontally

through it. As drying air passes through each subele-

ment, some humidity is transferred from the paddy

particles to the hot air. It is assumed in this case that the

air exiting from each subelement is in thermal equili-

brium with the paddy present in that element (Zahed,

Zhu, & Grace, 1995).

Applying the mass balance and mass transfer equa-tions to the paddy particles will result the following

governmental differential equation:

qsð1� emfÞ�ss

Wbð1� emfÞqsUs

��þðqs � qgÞg sin h

qsUs

�X

þ dXdz

Us

�þ m̂m ¼ 0 ð4Þ

and if mass balance and mass transfer equations are

applied to the hot air, a governing differential equationis obtained as follows:

qgemf

g cos hUr

"(þ sgWbqgUremf

þ dPdx

1

qgUremf

!#Y

þ dYdx

Ur

)� m̂m ¼ 0 ð5Þ

where m̂m is drying rate per unit volume of the bed and is

obtained as follows:

Fig. 2. Division of the bed into n elements and m subelements and a

schema of two-phase theory of fluidization.

Fig. 3. Flow direction of material, mass and heat transfer between air

and particles in a subelement of height of the bed.

Fig. 1. Schematic diagram of a continuous fluidized bed dryer.

M. Izadifar, D. Mowla / Journal of Food Engineering 58 (2003) 325–329 327

m̂m ¼ Kapqg½Ye � Y jx ð6Þ

where Ye is the air equilibrium moisture content and is

obtained by the following expression:

Ye ¼ RHeP �=ðPt � RHeP �Þ ð7Þwhere RHe, the equilibrium relative humidity of air incontact with paddy is given by Henderson�s equation

(Soponronnarit & Prachayawarakorn, 1994) as follows:

1� RHe ¼ exp½�0:0000078ð1:8Tgi þ 491:7Þð100XeÞ2:088ð8Þ

Eqs. (4) and (5) are governing equations of mass

transfer in the constant rate stage of drying that there is

some water as a film on the particles surface. After water

film transferring to the drying air, pattern of the drying

will be changed from constant to the falling. Therefore

governmental equations of mass transfer will be changed

as well as the drying pattern. By dividing a paddy par-ticle into the some elements along the particle radius and

applying the mass balance and mass transfer equations

to each element; the governmental differential equation

of mass transfer in the falling stage of drying is obtained

as follows:

Deff

o2Xor2

þ 2

roXor

�¼ oX

otð9Þ

where initial value and boundary conditions are as fol-

lows:

Initial value: at 06 r6R X ð0; rÞ ¼ Xi

Boundary conditions:at t > 0 ðoX ðt; 0Þ=orÞ ¼ 0

at t > 0 X ðt;RÞ ¼ Xe

����ð10Þ

2.3. Energy balance

As it is shown in Fig. 3, as drying air goes up through

a subelement, some energy is transferred from the hot

air to the paddy particles in that element. A part of this

energy is consumed as latent heat of evaporation and

some other part causes the increase of temperature of

paddy particles as they pass through that element. As it

was said, the exit air is assumed to be in thermal equi-librium with the paddy particles in each element. It

should be noted that, even though the temperature of

entered air in all of the elements along the bed is the

same, but, because of increasing the temperature of the

particles from an element to the next, the temperature of

the exit air, which is in equilibrium with the particles, is

varied from an element to the next (Ciesielczyk, 1996;

Temple & Van Boxtel, 1999). If the emulsion phase isconsidered as the system and energy balance and heat

transfer equations are applied to the system, a governing

differential equation is obtained as follows:

ðqsð1� emfÞð1þ X ÞCpsUsÞdTpdz

� CpsTpm̂m

� W2ð1þ X ÞTpm̂mþ ð1þ X ÞCpsTpssWbUs

�ð1� emfÞð1þ X ÞCpsTpðqs � qgÞg sin h

Us

þ m̂mk � hcapðT g � TpÞ ¼ 0 ð11Þ

If energy balance and heat transfer equations are ap-

plied to the dispersed phase as the system, the governing

differential equation is as follows:

qgemfð1þ Y ÞCpgUr

dTgdx

þ CpgTgm̂mþ Cpvð1þ Y ÞTgm̂m

þqgemfg cos hð1þ Y ÞCpgTg

Ur

þ sgð1þ Y ÞCpgTgWbUr

þ ð1þ Y ÞCpgTgUr

dPdx

þ hcapðTg � TpÞ ¼ 0 ð12Þ

where hc is the heat transfer coefficient between a gas

and solid particles in a fluidized bed and is given as

follows (Kunii & Levenspil, 1991):

hc ¼ qgCpgðSc=PrÞ2=3K ð13Þ

3. Solution of the model for continuous fluidized bed dryer

In order to obtain the variation of the temperatureand moisture content of the particles during drying, the

obtained governing differential equations (2)–(5), (9), (11)

and (12) must be solved simultaneously. Numerical

methods included modified Euler�s and finite differences

are applied to the ordinary and partial differential equa-

tion with giving boundary conditions, respectively. The

governing differential equations are solved and simu-

lated with performing a turbo Pascal 7 program. Forsolution of the model, the bed needs to be divided into

some elements and each element is divided into some

subelements (Maroulis, Kremalis, & Kritikos, 1995).

Governing equations (2) and (3) of momentum transfer

are solved for all of the subelements and elements. In

order to obtain the variation of temperature and hu-

midity of the drying air passing through subelements,

governing equations (5) and (12) are solved for eachsubelement and it is continued to reach the last subele-

ment in the top. If the absolute value of the difference

between the humidity of the outlet air from the last

subelement and the same air humidity in the saturated

condition, is less than a distinguished tolerance, drying

is in the constant rate and differential equations (4) and

(11) are solved to be obtained the variation of the par-

ticles moisture content, otherwise drying is in the fallingrate and differential equations (9) and (11) should be

solved. This way is continued for each element until the

bed is passed thoroughly.

328 M. Izadifar, D. Mowla / Journal of Food Engineering 58 (2003) 325–329

4. Discussion and conclusion

The mathematical model developed for a cross-flow

continuous fluidized bed dryer can be used for simula-

tion and design of this type of dryer. The complete

program which is performed for solving the proposed

model, takes as input the relative humidity and tem-

perature of using air, the initial moisture content as wellas the temperature and feed rate of entering paddy and

gives the final moisture content and temperature of

dried paddy and also the temperature and relative hu-

midity of exit air as the output. r2 of outputs data is

99.6%. As an example, the variation of paddy moisture

content and temperature with the bed length, predicted

by the proposed model for a given operating condition,

is shown on Figs. 4 and 5. On the same figures, the ex-perimental results obtained for the same operating

conditions (feed rate of 1000 kg paddy/h and drying airtemperature of 60 �C) are represented. As it is observed,

there is a good agreement between the model prediction

and experimental results. As the validity of the proposed

model is checked, it could be used for prediction of the

other variables.

References

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Madhiy Anon, T., Soponronnarit, S., & Tia, W. (2000). Continuous

drying of paddy in two-dimensional spouted bed. Kasetsart-J.-

Nat.-Sci., 34(2), 308–314.

Maroulis, Z. B., Kremalis, C., & Kritikos, T. (1995). A learning

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and moisture content to describe head rice yield reduction during

thin-layer drying of rough rice. ASAE-Annual-International-Meet-

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for fluidized bed paddy drying. Dry. Technol., 12(7), 1667–1686.

Sutherland, J. W., & Ghaly, T. F. (1990). Rapid fluid-bed drying of

paddy rice in the humid tropics. Presented at the 13th ASEAN

Seminar on Grain Postharvest Technology, Brunei Darussalam.

Temple, S. J., & Van Boxtel, A. J. B. (1999). Modeling of fluidized bed

drying of black tea. J. Agri. Engng. Res., 74, 203–212.

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Technology, Philippines.

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Technol., 13(1&2), 1–28.

15

1719

2123

2527

2931

33

0 0.5 1 1.5 2

Bed length (m)

Moi

stu

re c

onte

nt

(db

) , Model Results , Experimental Results

Bed length 1.77 m Bed width 30 cm Bed height 4 cm Drying air temperature 60 ˚C Initial moisture content 31% & 28%

Fig. 4. Variation of moisture content of paddy with bed length at

60 �C.

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8Bed length ( m )

Par

ticl

e te

mpe

ratu

re (

˚C)

, Model Results

, Experimental Results

Bed length 1.77 m Bed width 30 cm Bed height 4 cm Drying air temperature 60 ˚C Initial particle temperature 21 & 25 ˚C

Fig. 5. Variation of particle temperature of paddy with bed length at

60 �C.

M. Izadifar, D. Mowla / Journal of Food Engineering 58 (2003) 325–329 329