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Chemical Engineering and Processing 45 (2006) 1019–1028

Drying of baker’s yeast in batch fluidized bed

Mustafa Turker a, Ali Kanarya a, Ugur Yuzgec b,∗, Hamdi Kapucu a, Zafer Senalp c

a Pakmaya, P.O. Box 149, 41001, Kocaeli, Turkeyb Department of Electronics & Telecommunications Engineering Kocaeli University, 41040, Kocaeli, Turkey

c Gebze Institute of Technology, Gebze, Kocaeli, Turkey

Received 11 June 2005; received in revised form 9 December 2005; accepted 10 January 2006Available online 7 April 2006

bstract

A drying model was developed for production scale fluid bed drying of granular baker’s yeast. In the model, heat capacity of the dryer and theroduct entrained through cyclone and heat transfer from the dryer to environment were also taken into account to improve the predictive capacityf the model. Kinetic model based on the assumption that the resistances to mass transfer during drying lie not inside but liquid film around theranules was integrated into material and energy balances. Drying rate constant was determined from experimental results at constant air inlet flowate and temperature but at varying dryer loadings. Its magnitude was found as function of amount of product loaded into the dryer. Simulationsere performed for two different granule sizes and good correspondence was found between model predictions and experimental measurements

or small granule sizes. For larger granules, deviations between simulations and measurements were observed and this was attributed to diffusiveransport limitation of moisture inside granules, which requires mathematical description of spatial distribution of moisture and temperature insidehe particles. The model can be used for design, optimization and control of drying processes for various applications.

2006 Elsevier B.V. All rights reserved.

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eywords: Drying; Baker’s yeast; Modeling; Fluidized bed

. Introduction

Drying is an important unit operation widely used in chem-cal, food and pharmaceutical industries to reduce the waterontent and improve shelf life of various products. Its princi-le is based on removal of water from material by means ofvaporation [1,2]. Due to the high sensivity of biological mate-ials to high temperatures and water activities, their preservations a problem in industry and maintaining their activities over aeriod of time are required to prolong their shelve life. They mayndergo some changes during thermal drying such as destruc-ion of cell membranes, denaturation of proteins or enzymes orven death of cells [3]. Therefore, optimal operation of dryingrocess is required in order to minimize such adverse affects of

hermal drying. A large number of dryer types have been usedor drying in practice [1]. The use of fluid bed drying for granularaterials is now well established and widely used in industry. In

∗ Corresponding author. Tel.: +90 262 3351148.E-mail addresses: mustafat@pakmaya.com.tr (M. Turker),

yuzgec@kou.edu.tr (U. Yuzgec), hamdik@pakmaya.com.tr (H. Kapucu).

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255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2006.01.016

uidized bed drying process, the product to be dried is homoge-eously dispersed in the bed and isothermal operation is carriedut using fluidization of material in the dryer [4,5].

The baker’s yeast, Saccharomyces cerevisiae is a granularroduct and the drying operation reduces the moisture con-ent from 65–70% to 4–6%, with varying time between 30 and00 min to improve its shelf life [6]. Josic [7] has investigatedptimum conditions for drying of baker’s yeast. The influencef drying conditions upon the quality of baker’s yeast has beennvestigated by Zimmermann and Bauer [8] in laboratory scaleuidized bed. A mathematical model was developed to describe

he drying process and combined with deactivation kinetics.hey found good agreement between proposed model and exper-

mental results. Strumillo et al. [9] has studied drying of baker’seast with equivalent diameter of 0.85 mm in fluidized bed. Theyave taken into account dispersion in the bed and deactivationf baker’s yeast during drying. They have concluded that betteresults were obtained for plug flow of material being dried as

ar as final product quality was concerned. Grabowski et al. [10]ave compared spouted bed and fluidized bed and their combina-ions on product quality for drying of baker’s yeast. As far as theuality of final product was concerned, it was found that two step

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020 M. Turker et al. / Chemical Engineer

rying with spouted bed to reduce moisture content from 70 to5% followed by fluidized bed to achieve a final moisture contentf 6–8% appeared to be of practical importance. Bayrock andngledew [11,12] have studied effects of some operating param-ters such as temperature, drying rates and moisture levels onhe viability of baker’s yeast. Yuzgec et al. [13] have considerediffusion limited drying of cylindrical baker’s yeast granules.

In this work, a dynamic model based on the model developedy Temple and van Boxtel [14] for continuous black tea dryings constructed to describe simultaneous mass and heat transfer,hich takes place in a completely mixed batch fluid bed. This

tudy is focused on batch drying but can easily be adapted toontinuous drying. The model was compared with experimentalata obtained from production scale fluid bed dryer for dryingf granular baker’s yeast with small and large size granules.oth types of granules fall into category A according to Geldartlassification [15].

. Process model

Model equations are constructed by combining material andnergy balances based on following assumptions [14,16] for flu-dized bed as shown in Fig. 1.

.1. Assumptions

. Fluidized bed is open to the atmosphere and therefore the topof the bed is under the atmospheric pressure. Pressure differ-ence along the bed is negligible and drying process proceedsunder constant pressure.

. Complete mixing is assumed for the product and air in the

bed.

. The resistance to mass transfers lies in the film around granu-lar particle not within the granules and this has been the basisof the assumptions in the derivation of kinetic model.

m

Ttp

Fig. 1. Layout of batch fluidiz

d Processing 45 (2006) 1019–1028

. Heat exchange between particles and air in the bed is instan-taneous; therefore air temperature and particle temperaturein bed are in equilibrium.

. Mass of air inside the bed is negligible.

. Product entrained through cyclone is accounted for in mate-rial balances.

. Mass of dryer material containing product is not negligibleand taken into account in energy balance.

.2. Model equations

The constructed model equations for all components flowingn and out of the system as follows.

.2.1. Dry solids equationIn drying process, the product is initially loaded into the dryer

nd then dried solid content of product in the system increaseshroughout the loading phase. However, some product will beost due to entrainment through the cyclones. Therefore, accu-

ulation of the product in the bed can be described by followingifferential equation:

dMb,y

dt= mi

y − moy (1)

here Mb,y is dry solid mass of product in the bed and miy is

he flow rate of the product into the bed and moy is the flow rate

f the product out of the bed. The continuous transport of theroduct out of bed can be found by following equation:

d

dt

∑mo

y(t) = m (t) (2)

oy is flow rate and

∑mo

y is total mass of entrained product.he rate of the product collected from the cyclone mo

y was con-inuously registered every minute on a balance and followingolynomial equation was obtained as a function of time during

ed bed drying process.

ing an

d

m

2

acflwflc

o

w

ww

2

s

m

2

1234

Tbda

H

E

h

h

h

h

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au

h

t

T

wtsc

h

h

Tca

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H

M. Turker et al. / Chemical Engineer

rying:

oy = 4.0 × 10−9t2 − 3.1 × 10−6t + 10−3 (3)

.2.2. Water conservation equationWater in the bed consists of water associated with the product

nd water vapor carried by air into and out of the system. Thehange of mass of water inside the bed, dWb,y/dt, relates to theow rate of water in product fed to the system, wi

y, flow rate ofater removed from product by means of evaporation, rw, andow rate of water in product entrained through cyclones wo

y. Theorresponding equations are shown below.

dWb,y

dt= wi

y − rw − woy (4)

r

ia + rw = wo

a (5)

here wia is flow rate of water as vapor in air to the system and

oa is flow rate of water as vapor in air from the dryer.

.2.3. Air conservation equationAir used for drying does not involve in any reaction (Mb,a),

ince it is neither produced nor consumed in the bed. Therefore:

dMb,a

dt= mi

a − moa

∼= 0 (6)

ia∼= mo

a (7)

.2.4. Energy balance equationThere are four components of enthalpy flow in the system:

. The energy introduced by air (hia).

. The energy introduced by yeast (hiy).

. The energy removed by air (hoa).

. The energy removed by yeast (hoy).

he energy accumulation of the process H is assumed as adia-atic. The total energy accumulation in the bed can be written asynamic balance between energy flows to and from the systems:

= hiy + hi

a − hoy − ho

a (8)

nergy flow components of Eq. (8) can be written as:

iy = cp,ym

iyT

iy + cp,wwi

yTiy (9)

ia = cp,am

iaT

ia + cp,wvw

iaT

ia (10)

oy = cp,ym

oyT

oy + cp,wwo

yToy (11)

oa = cp,am

oaT

oa + cp,wvw

oaT

oa (12)

here T iy inlet product (yeast cake) temperature, T i

a input air tem-erature, T o

y temperature of the product that leaves the systemrom dryer cyclones, T o

a output air temperature, cp,y specific heatf product, cp,w specific heat of water, cp,a specific heat of air

d Processing 45 (2006) 1019–1028 1021

nd cp,wv specific heat of water vapor. Eq. (12) can be rewrittensing Eqs. (5) and (7):

oa = cp,am

iaT

oa + cp,wv(wi

a + rw)T oa (13)

Temperature balance equation can be obtained according tohe assumptions at Eqs. (5) and (7).

oa = Tb,a = Tb,y = T o

y = Tb,ss = T (14)

here Tb,a represents temperature of air in bed, Tb,y representsemperature of yeast in bed and Tb,ss represents temperature oftainless steel material of dryer. Therefore, Eqs. (11) and (13)an be rewritten as below,

oy = cp,ym

oyT + cp,wwo

yT (15)

oa = cp,am

iaT + cp,wv(wi

a + rw)T (16)

he total energy accumulation in the bed can be calculated byombination of energy changes of yeast-air in bed, dryer materialnd evaporation process:

= d(cp,yMb,y + cp,wWb,y)Tb,y

dt

+ d(cp,aMb,a + cp,wvWb,a)Tb,a

dt+ d(cp,ssMb,ss)Tb,ss

dt

+ rw�Hv (17)

here Mb,ss, cp,ss, �Hv and Wb,a are mass of the dryer materialhat encloses the product, specific heat of stainless steel, evapo-ation enthalpy of water and mass of water vapor, respectively.sing the assumption in Eq. (14), Eq. (17) can be written as:

= d(cp,yMb,y + cp,wWb,y)T

dt+ d(cp,aMb,a + cp,wvWb,a)T

dt

+ d(cp,ssMb,ss)T

dt+ rw�Hv (18)

ince the mass of air in bed is assumed as negligible then theerms Mb,a and Wb,a can be deleted from Eq. (18):

= d(cp,yMb,y + cp,wWb,y + cp,ssMb,ss)T

dt+ rw�Hv (19)

he main variable that the model predicts is the product temper-ture, T, used in above equation. Mb,y and Wb,y terms dependn time as Eqs. (2) and (4), respectively. Mb,ss depends on timendirectly. It varies with airflow, which is the function of time.pecific heat of yeast cp,y is a function of dry solid content. Sincery solid content varies with time during process, specific heatf yeast can be considered as a time dependent variable. Basedn this information, more open form of Eq. (19) can be obtaineds:

= (cp,yMb,y + cp,wWb,y + cp,ssMb,ss)dT + T

dt

×(

cp,ydMb,y

dt+ Mb,y

dcp,y

dt+ cp,w

dWb,y

dt+ cp,ss

dMb,ss

dt

)

+ rw�Hv (20)

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022 M. Turker et al. / Chemical Engineer

f Eqs. (8)–(10), (15) and (16) are replaced into Eq. (20), thenccumulation term becomes:

(cp,yMb,y + cp,wWb,y + cp,ssMb,ss)dT

dt+ T

×(

cp,ydMb,y

dt+ Mb,y

dcp,y

dt+ cp,wv

dWb,y

dt+ cp,ss

dMb,ss

dt

)

= cp,ymiyT

iy + cp,wwi

yTiy + cp,am

iaT

ia + cp,wvw

iaT

ia

− T (cp,ymoy+ cp,wwo

y + cp,amia + cp,wv(wi

a + rw)) − rw�Hv

(21)

Main model equation is obtained using the derivative termsn Eqs. (1) and (4):

(cp,yMb,y + cp,wWb,y + cp,ssMb,ss)dT

dt+ T

(cp,y(mi

y − moy)

+ Mb,ydcp,y

dt+ cp,w(wi

y − rw − woy) + cp,ss

dMb,ss

dt

)

= cp,ymiyT

iy + cp,wwi

yTiy + cp,am

iaT

ia + cp,wvw

iaT

ia

− T (cp,ymoy+ cp,wwo

y + cp,amia + cp,wv(wi

a + rw)) − rw�Hv

(22)

he Eq. (22) can be simplified as

dT

dt= A − BT

C(23)

here parameters A, B and C are:

= cp,ymiyT

iy + cp,wwi

yTiy + cp,am

iaT

ia + cp,wvw

iaT

ia − rw�Hv

(24)

= cp,ymiy + Mb,y

dcp,y

dt+ cp,w(wi

y − rw) + cp,ssdMb,ss

dt

+ cp,amia + cp,wv(wi

a + rw) (25)

= cp,yMb,y + cp,wWb,y + cp,ssMb,ss (26)

Heat transfer from the surface of the dryer to environment haslso been considered in overall energy balance using followingquation for dryer heat transfer coefficient [17]:

a = 1.37

(T − Tsurr

L

)1/4

(27)

ssuming that resistance to heat transfer lies outside the dryer.surr and L represent ambient air temperature and fluid bed

ength, respectively. However, it has not been seen any signifi-ant effect in model output when this equation has been includedn the overall energy balance. Thus, adiabatic drying has beenustified an Eq. (27) has not been included in the model at theresent work.

.3. The water releasing ability of product

The ability of drying material to release moisture depends onany factors such as material’s cellular and structural integrity,

td(b

d Processing 45 (2006) 1019–1028

aterial properties, mechanism of drying process applied, dryernd water sorption and desorption mechanisms. Drying rate isetermined by examining these parameters [18]. The ability ofroduct to release water can be found by multiplying mass ofry solid and specific drying rate. The specific drying rate ofroduct refers to J so that the water releasing ability of productan be written as:

w = Mb,yJ (28)

Specific drying rate is described as mass of water removedrom material at unit time interval:

= dX

dt(29)

A commonly used simple model to describe specific dryingate J is as follows, assuming that the resistance to mass transferies in the liquid film around the particle;

= dX

dt= k(X − Xe) (30)

here k is drying rate coefficient (h−1), X moisture contentkg water/kg dm) and Xe is equilibrium moisture content (kgater/kg dm). Using this equation, the drying time can be cal-

ulated separately for constant and falling drying periods [2].However, a new method of drying time calculation has been

eveloped to enable one to describe the total drying processncluding constant and falling drying rate periods in singleinetic expression [2]. The principle of this method is based onhe generalized mass transfer equation written in the followingorm;

= dX

dt= k(X1 − X)(X − Xe) (31)

here X1 is the initial moisture content and the expressionX1 − X)(X − Xe) represents the driving force for drying. Theimulation starts by choosing a value X(t = 0) slightly differentrom X1.

.4. Constraints on drying rate

Latent heat required for mass transfer of water from solido gas phase is supplied by hot air. Evaporation rate cannot be

ore than the evaporative capacity of the air. During the constantate period, drying rate is governed by evaporative capacity ofir. However, the rate is controlled by water releasing capacityf product during falling rate period where exhaust air is notaturated with water vapor [19].

. Solution of model equations

The mathematical model developed in previous section isased on the first order ordinary differential equation with ini-

ial and boundary conditions. Therefore, Runge–Kutta finiteifference method has been used for the solution of the Eq.23) describing product temperature [20]. The temperature haseen calculated by the following equations where k0, k1, k2 and

M. Turker et al. / Chemical Engineering and Processing 45 (2006) 1019–1028 1023

solut

ks

k

k

k

k

T

sa

4

Fig. 2. Algorithm for

3 represent the coefficients in the Runge–Kutta method, h theampling period and k is the step.

0 = A − BT(k − 1)

C(32)

1 = A − B(T (k − 1) + 0.5k0h)

C(33)

A − B(T (k − 1) + 0.5k1h)

2 =

C(34)

3 = A − B(T (k − 1) + k2h)

C(35)

iasd

ion of drying model.

(k) = T (k − 1) + (k0 + 2k1 + 2k2 + k3)h

6(36)

The program algorithm for solution of set of equations ishown in Fig. 2 in detail. The sampling period has been chosens one second for the solution of the model equations.

. Materials and methods

The experiments were carried out in production scale flu-

dized bed dryer. Yeast cake was extruded into the dryer through

perforated plate of different diameter to get desired granuleize. The fluid bed consisted of centrifugal fan to supply airrawn from ambient air (Fig. 1). Air inlet temperature was main-

1024 M. Turker et al. / Chemical Engineering and Processing 45 (2006) 1019–1028

F2

t

�

T

waoT

5

5

fflot

iidfichmoisture removal rates are calculated and presented in Table 1and Fig. 6 for different loadings. As can be seen from these fig-ures, the maximum specific water removal rates are inverselyproportional to the loading.

Table 1Maximum moisture removal rate as function of dryer loading at constant airinlet temperature and flow rate

Loading (kg) Maximum moisture removal rate(kg water/kg dry product h)

150 9.0

Fig. 3. Air temperature and airflow rate used for the small particle size.

tained at 100 ◦C as shown in Fig. 3 during most part of dryingprocess. The temperatures and humidities of air at inlet and out-let and its flow rate were measured on-line and registered on acomputer in order to establish continuous material and energybalances for the prediction of the moisture content and temper-ature of the product.

The mass of the structural material of the dryer in contactwith granular yeast, which is a function of air flow rate, is takeninto account in the model presented in this paper. Followingequation is derived for the mass of stainless steel in contact withthe product to be used in energy balance:

Mb,ss = 2 × 10−6f i2a + 1.505 × 10−1f i

a + 2 × 10−12 (37)

where f ia is flow rate of input air with the unit of kg/h. The

specific heat of yeast is a function of its dry solid ratio and fol-lowing equation is derived for the specific heat capacity of yeastas a function of dry solid ratio based on experimental results ofJosic [7]. Dry solid ratio at time t refers to Y(t) and specific heatcapacity of product as a function of dry solid content is givenby;

cp,y(t) = −6 × 10−6Y3(t) + 8 × 10−4Y2(t)

− 5.34 × 10−2Y (t) + 4.26 (38)

where the dry solid ratio, Y (kg dry solid/kg total) can be definedas:

Y = 100Mb,y

Mb,y + Wb,y(39)

Specific heat capacity of water vapor depends on air temper-ature and is given by following equation [21]:

cp,wv(t) = 0.2324(8.22 + 1.5 × 10−4T (t) + 1.3 × 10−6T 2(t))

(40)

234

ig. 4. Progress of moisture removal at different loadings (kg): (�) 150, (�)50, (�) 300 and (�) 400.

The evaporation enthalpy of water is a function of tempera-ure and given by following equation [21]:

Hv(T ) = �Hv1

(1 − Tr

1 − Tr1

)0.38

(41)

r = T

Tc,wand Tr1 = T1

Tc,w(42)

here �Hv1 is evaporation enthalpy of water at known temper-ture T1, Tr is reduced temperature, Tc,w is critical temperaturef water which is 647.3 K and evaporation enthalpy of water at1 = 0 ◦C �Hv1 = 2501 kJ/kg [22].

. Results and discussion

.1. Determination of drying rate constant

Determination of drying rate constant was carried out at dif-erent dryer loadings but constant air inlet temperature and airow rates. Therefore, the drying rate constant was estimatednly as a function dryer loading. The progress of drying alongime is shown in Fig. 4 for different dryer loadings.

The moisture content of product decreased slowly as the load-ng to the dryer increased from 150 to 400 kg. The drying curvesn Fig. 4 have three different slopes; loading period, constantrying period where drying rate proceeds at maximum rate andnally reduced drying period where drying rate decreases afterritical moisture content. The specific moisture removal ratesave been plotted in Fig. 5 for different loadings and maximum

50 5.100 4.500 3.6

M. Turker et al. / Chemical Engineering and Processing 45 (2006) 1019–1028 1025

loadi

ce

t

tpsbd

Z

Tr

Fa

scXle

Ψ

X

wa

Fig. 5. Specific moisture removal rates at different

Integration of Eq. (31) from the initial equilibrium moistureontent X1e to the final moisture content Xe gives the followingxpression for drying time;

= 1

k(X1 − Xe)ln

(X1 − X)(X1e − Xe)

(X1 − X1e)(X − Xe)(43)

The initial equilibrium moisture content X1e corresponds tohe moisture content of the product during the initial dryingeriod where the temperature of the drying air at the producturface is equal to the wet-bulb temperature. Its value can easilye calculated from Eq. (43) on the basis of the experimentalrying curve when Z–t plot is drawn where Z is defined as;

(X − X)(X − X )

= ln 1 1e e

(X1 − X1e)(X − Xe)(44)

his graph gives straight line with the slope equal to the dryingate constant k and the intercept on the Z-axis equal to X1e as

ig. 6. Maximum moisture removal rate as function of dryer loading at constantir inlet temperature and flow rate.

usga

F(

ngs (kg): (�) 150, (�) 250, (�) 300 and (�) 400.

hown in Fig. 7. If the value of X1e is unknown the curve onoordinates Z–t can be constructed for any reasonable value ofie = X1e for X1 < X1e. Then the real value of the initial equi-

ibrium moisture content can be calculated from the followingquation;

= ez(0) lnX1e − Xe

X1 − X1e(45)

1e = X1 + Xe

1 + Ψ(46)

here Ψ represents intermediate parameter for X1e calculationnd z(0) is the value of intercept on Z-axis. If the value of Xe is

nknown it can be determined by a trial and error method sub-tituting in consecutive values of Xe until the curve on the Z–traph becomes straight line as shown in Fig. 7. In Fig. 7 reason-ble straight lines are obtained for most part of the experimental

ig. 7. Z–t plot for determination of drying rate constant for different loadingskg): (�) 150, (�) 250, (�) 300 and (�) 400.

1026 M. Turker et al. / Chemical Engineering and Processing 45 (2006) 1019–1028

Table 2Drying rate constants

Batch loading (kg) k (h−1)

150 10.97250 8.26300 7.08400 5.45

dip

S

Frl

wfoTt

k

5

F(

Fig. 8. Drying rate constants as function of loading.

rying points, rapid drying phase and most part of reduced dry-ng phase, apart from last few points at the very end of dryingrocess.

The slopes of each line in Fig. 7 are equal to

lope = k(X1 − Xe) (47)pT

ig. 10. Simulation results for 250 kg (a), 300 kg (b), and two different batches at 400�) and product temperature (�). Continuous lines are model predictions.

ig. 9. Effect of cyclone loss on the model output; symbols are experimentalesults, continuous lines are the model output with cyclone effect and dashedines are the model output without cyclone effect.

here the values of drying rate constants can be calculatedor each set of drying experiment. The values in Table 2 werebtained for different dryer loadings that are plotted in Fig. 8.he magnitudes of drying rate constants fit to following equa-

ion:

(h−1) = 14.027 − 0.0221 × (kg cake) (48)

.2. Simulation of fluid bed dryer

The drying process consists of three phases. In the firsthase dryer is loaded with granulated material to be dried.hen drying temperature is increased to initiate constant dry-

kg loadings (c) and (d) for small size granules: experimental moisture content

M. Turker et al. / Chemical Engineering an

F(

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giposafitppfmfirfidm

ftot

pa

6

eduodecbcoFqtlsmiaToawefaArAtrp[i

A

ABcCfhhHIJ

−1

ig. 11. Simulation result for larger granule: experimental moisture content, X,�) and product temperature, T, (©) and continuous lines are model predictions.

ng phase. Third phase is reduced drying phase or called fallingate period. Finally dried material discharged from the dryerhen the desired end dry matter was reached. The dryingodel with kinetic parameters determined in the previous sec-

ion was validated on two sets of experimental data obtainedrom batch fluid bed. The experiments were carried out withwo types of products dried in the dryer with different diameter:ne extruded through 0.0006 m diameter perforated holes intoryer and the second one extruded through 0.0012 m diametererforated holes to get larger granules. In the model, rate ofroduct removal from the cyclone was taken into account andts effect is shown in Fig. 9. As can be seen from this figure,he contribution of the product entrained through the cycloneuring drying does not have any significant effect on the modelutput.

The experimental results together with model predictions forranule sizes extruded from 0.0006 m perforated disc are shownn Fig. 10 for three different loadings. The product bed tem-erature decreases during loading phase due to rapid loadingf cold yeast cake. The model closely predicts the actual mea-urements. Only slight deviation between model predictions andctual measurements is observed in the final phase of drying ofrst two graphs of Fig. 10. However, in the final two graphs

he product temperature is well predicted for reduced dryinghase. In all experiments the accuracy of predictions for therogress of moisture content is quite acceptable. The simulationsor small particles give good correspondence to actual measure-ents. Temperature and moisture predictions are quite good andt well to simulation results during most part of drying. Theesult obtained with particles extruded through 0.0012 m per-orated plate is shown in Fig. 11. In this case, the particle sizes doubled compared to previous experiments. During constantrying rate period, the model predicts product temperature andoisture content quite well.However, major deviation is observed in predictions for

alling rate period where no moisture and temperature distribu-ion inside particles are assumed and therefore the assumptionsf the kinetic model may be invalid. As the particle size increaseshe spatial distribution of moisture and temperature inside the

k

kL

d Processing 45 (2006) 1019–1028 1027

article should be taken into account in order to improve theccuracy of the prediction.

. Conclusions

A drying model has been developed, based on material andnergy balances around production scale fluidized bed for therying of granular baker’s yeast. The model accounted for prod-ct entrained through cyclone and energy loss through the bodyf the dryer, to improve the predictions of the model on pro-uction scale. It has been observed that the amount of productntrained from cyclones did not change much the predictiveapacity of the model. In addition, the energy loss through theody of dryer was insignificant and the assumption of adiabaticonditions was justified. The model was applied to batch dryingf granular baker’s yeast with different granular dimensions.or smaller granules (0.0006 m), the model predictions wereuite reasonable and progress of product moisture content andemperature were estimated with reasonable accuracy duringoading, rapid drying and reduced drying phases. When granuleize increased to 0.0012 m, the simulations deviated from actualeasurements especially during reduced drying phase. This may

ndicate that diffusive transport of moisture inside particles playsn important role on the overall drying performance of granules.his also affects energy balance and as a result the predictionf bed temperature deviates from actual measurements. Templend van Boxtel [14] have shown that thin layer drying modelas used for simulating the fluid bed drying of black tea. How-

ver, they had to multiply the drying rate with an efficiencyactor of 0.6 to get good correspondence between model andctual measurements, indicating the limitations of the model.s a result, the model presented here may be used for drying of

elatively small particles where diffusion is not the limiting step.s the granule size increases, spatial distribution of moisture and

emperature need to be taken into account to improve the accu-acy and predictions of the model. The extended version of theresent model was previously presented for cylindrical granules13] and more complete version of distributed parameter models in preparation together with deactivation kinetic [23].

ppendix A. Nomenclature

parameter defined in Eq. (24)parameter defined in Eq. (25)

p specific heat (kJ/kg K)parameter defined in Eq. (26)flow rate (kg/h)enthalpy (J/h)heat transfer coefficientenergy accumulation term (J/h)energydrying rate (kg water/kg dry solid h)

drying rate coefficient (h ) and step in Runge–Kuttamethod

i Runge–Kutta coefficientslength

1 ing an

mMrtTw

WXY

G�

Ψ

Sabcersswwy

Sio

R

[

[

[

[

[

[[

[

[

[

[

[Hill, 1984.

028 M. Turker et al. / Chemical Engineer

mass flow rate (kg/h)mass of dry solid (kg)

w evaporation (kg/h)timetemperature (K)water flow rate (kg/h)mass of water (kg)moisture content (kg water/kg dry solid)dry solid ratio (kg dry solid/kg total)

reek lettersHv evaporation enthalpy of water (kJ/kg)

intermediate parameter for X1e

ubscriptsairbedcriticalequilibriumreduced

s stainless stealurr surround

waterv water vapor

yeast

uperscriptsinputoutput

eferences

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[

[

d Processing 45 (2006) 1019–1028

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