1-s2.0-s0260877401001261-main

Thin-layer modelling of black tea drying process

P.C. Panchariya a, D. Popovic b,*, A.L. Sharma c

a Central Electronics Engineering Research Institute, Pilani 333031, Indiab Institute of Automation Techniques, University of Bremen, D-28359, Bremen, Germanyc Institute of Instrumentation, D.A. University, Khandwa Road, Indore 452017, India

Received 16 March 2001; accepted 25 June 2001

Abstract

An experimental dryer was developed for determining the kinetics of black tea drying. Drying characteristics of tea were ex-

amined using heated ambient air for the temperature range 80120C and air ow velocity range 0.250.65 m/s. The data of sampleweight, dry- and wet-bulb temperatures and air velocity of the drying air were recorded continuously during each test. The drying

data were then tted to the dierent semi-theoretical models such as Lewis, Page, modied Page, two-term and Henderson and Pabis

models, based on the ratios of the dierence between the initial and nal moisture contents and the equilibrium moisture content.

The Lewis model gave better predictions than other models, and satisfactorily described the thin-layer drying characteristics of black

tea particles. The eective diusivity varied from 1:14 1011 to 2:98 1011 m2/s over the temperature range. The temperaturedependence of the diusivity coecient was described by the Arrhenius-type relationship. The activation energy for moisture dif-

fusion was found to be 406.02 kJ/mol. Temperature and air velocity dependence on drying constant was described by the Arrhenius-

type and Power-type relationships. The coecients of determination were above 0.996 for both relationships. The Arrhenius-type

model was used to predict the acceptable moisture ratios at the experimental drying conditions and to understand better the in-

uence of drying variables on drying rate constant. The results illustrate that in spite of high initial moisture content, the drying of

tea particles takes place only in the falling rate period. This single-layer drying equation can be used for the simulation of deep-bed

drying of black tea. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Thin-layer; Dhool; Moisture ratio; Non-linear regression; Predictions

1. Introduction

India is the largest producer of black cutting, tearing,and curling (CTC) tea with a distinct characteristic,taste, and avour. The tea leaves, after being pluckedfrom the tea bush, go through various processing stages,such as withering, CTC, fermentation, drying, and -nally packing. The drying operation in the tea industrydoes not merely remove the moisture content becausethere are many quality factors which can be adverselyaected by incorrect selection of drying conditions anddrying equipments. The consumer acceptability, ap-pearance and organoleptic properties are the desirableproperties of high-quality tea.

To design and control a tea dryer and to dene op-timum drying conditions, it is necessary to model the

actual process of drying in terms of mathematical rela-tions. In the actual operation, black tea is dried in var-ious types of deep-bed dryers. Due to its complexity, it isdicult to investigate the drying characteristics of anactual industrial drying bed directly. In our case theactual deep-bed drying is analysed using process statevalues such as drying air temperature, moisture content,etc. that are calculated from heat and mass balance ofthe drying process represented as a thin-layer dryingmodel. Although in the past many theoretical andempirical models were developed for various foods andagro-based products (Basunia & Abe, 2001; Can, 2000;Kiranoudis, Maroulis, Tasami, & Marinos-Kouris,1997), none of the works reported on Darjeeling blacktea.

Thus, the objective of this study was the developmentof a suitable experimental thin-layer drying apparatus,to nd out suitable model and to investigate the eect oftemperature and air velocity on the model coecientswhich can describe the drying characteristics of black teaparticles.

Journal of Food Engineering 52 (2002) 349357

www.elsevier.com/locate/jfoodeng

*Corresponding author. Tel.:+49-421-218-3580; fax: +49-421-218-

4707.

E-mail address: [email protected] (D. Popovic).

0260-8774/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0260-8774 (01 )00126-1

2. Mathematical modelling

It has been accepted that drying phenomenon ofbiological products during the falling rate period iscontrolled by the mechanism of liquid and/or vapourdiusion. Thin-layer drying models that describe thedrying phenomenon of these materials mainly fall intothree categories namely, theoretical, semi-theoretical andempirical. The rst takes into account only internal re-sistance to moisture transfer while the other two consideronly external resistance to moisture transfer resistancebetween product and air (Fortes & Okos, 1981; Hen-derson, 1974; Whitaker, Barre, & Hamdy, 1969).

Assuming that the resistance to moisture ow isuniformly distributed throughout the interior of thehomogeneous isotropic material, the diusion coe-cient, D is independent of the local moisture content andif the volume shrinkage is negligible, Ficks second lawcan be derived as follows:

oMot

Dr2M : 1

Crank (1975) gave the analytical solutions of Eq. (1) forvarious regularly shaped bodies such as rectangular,cylindrical and spherical. Drying of many food productssuch as rice (Ece & Cihan, 1993), hazelnut (Demirtas,Ayhan, & Kaygusuz, 1998) and rapeseed (Crisp &Woods, 1994) has been successfully predicted usingFicks second law with Arrhenius-type temperature-dependent diusivity.

The semi-theoretical models are generally derived bysimplifying general series solutions of Ficks second lawor modication of simplied models and valid within thetemperature, relative humidity, air ow velocity andmoisture content range for which they were developed(Fortes & Okos, 1981). These models required smalltime compared to theoretical thin-layer models and donot need assumptions of geometry of a typical food, itsmass diusivity and conductivity (Parry, 1985). Amongsemi-theoretical thin-layer drying models, the two-termmodel (Eq. (2)), the Henderson and Pabis model (Eq.

(3)), the Lewis model (Eq. (5)), the Page model (Eq. (6))and the modied Page model (Eq. (7)) are used widely.

Sharaf-Eldeen, Blaisdell, and Hamdy (1980) pre-sented a two-term model to predict the drying rate ofshelled corn fully exposed to air. This model is therst two terms of general series solution to the analyti-cal solution of Eq. (1). However, it requires constantproduct temperature and assumes constant diusivity.The two-term exponential model has the form

MR M MeM0 Me A0 expk0t A1 expk1t; 2

where M , M0 and Me are the material, initial, andequilibrium moisture contents in dry basis, respectively,and A0; k0; A1; k1 are the empirical coecients.

The Henderson and Pabis model is the rst term of ageneral series solution of Ficks second law (Henderson& Pabis, 1969)

MR M MeM0 Me A0 expk0t: 3

This model was used successfully to model drying ofcorn (Henderson & Pabis, 1969), wheat (Watson &Bhargava, 1974) and peanut (Moss & Otten, 1989). Theslope of this model, coecient k0; is related to eectivediusivity when drying process takes place only in thefalling rate period and liquid diusion controls theprocess (Madamba, Driscoll, & Buckle, 1996).

The Lewis model (Lewis, 1921) is a special case of theHenderson and Pabis model where intercept is unity. Hedescribed that the moisture transfer from the foodproducts and agricultural material can be seen as anal-ogous to the ow of heat from a body immersed in cooluid. By comparing this phenomenon with Newtonslaw of cooling, the drying rate is proportional to thedierence in moisture content between the material be-ing dried and the equilibrium moisture content at thedrying air condition as:

dMdt

k0M Me 4

Notation

a; b drying constantA;A0;A1 drying constantc; c0; c1 drying constantDeff eective diusivity (m/s)D0 diusivity coecientEa activation energy (kJ/mol)k; k0; k1 drying constantM moisture contentMR moisture ratio

R2 correlation coecientR universal gas constantt time (s)T temperature

Subscriptsi ith observation0 initiale equilibrium

350 P.C. Panchariya et al. / Journal of Food Engineering 52 (2002) 349357

or after integrating yields

MR M MeM0 Me expk0t: 5

Bruce (1985) also used this model to study the dryingbehaviour of barley.

The Page model is a modication of the Lewis modelto overcome its shortcomings. This model has producedgood ts in predicting drying of grain and rough rice(Wang & Singh, 1978), white bean (Hutchinson & Ot-ten, 1983), shelled corn (Agrawal & Singh, 1977) andbarley (Bruce, 1985)

MR M MeM0 Me expk0t

n: 6

Overhults, White, Hamilton, and Ross (1973) alsomodied the Page model to describe the drying of soy-bean

MR M MeM0 Me expk0t

n: 7

The empirical models derive a direct relationship be-tween average moisture content and drying time. Theyneglect the fundamentals of the drying process andtheir parameters have no physical meaning. Therefore,they cannot give a clear accurate view of the importantprocesses occurring during drying although they maydescribe the drying curve for the conditions of the ex-periment (Keey, 1972). Among them the Thompsonmodel (Eq. (8)) was used to describe the shelled corndrying (Thompson, Peart, & Foster, 1968) and the Wangand Singh model (Eq. (9)) was applied to study the in-termittent drying of rough rice (Wang & Singh, 1978)

t a lnMR blnMR2; 8and

MR 1 at bt2: 9The inuence strength of the experimental drying vari-ables is determined by the values of themodel parameters,

A0 from the initial conditions and k0 in the form of Ar-rhenius- and Power-type equations in the following way:

In the Arrhenius type

k0 a0V a1 exp a2T

; 10

In the Power type

k0 b0T b1Vb2 : 11

Here T is the absolute temperature of the air (K), V is theair velocity (m/s), a0; a1; a2; b0; b1 and b2 are constants.

3. Materials and methods

3.1. Experiment design

Fresh macerated tea, which grows in the DarjeelingHills of India, was collected after the fermentationprocess. The macerated tea, after fermentation calledDhool, was well mixed and stored in a refrigerator in asealed container for experiments.

For drying experiments, a batch-type experimentaldryer was designed and fabricated. A schematic diagramof a laboratory dryer is illustrated in Fig. 1. The dryerconsists of three basic sections: air ow control section,heating control section, and sample platform. The con-trol air ow was circulated in the dryer by a centrifugalfan, driven by a 1.5 kW, three-phase electric motor. Theair ow rate was varied by adjusting a frequency mod-ulator that controlled the rotational speed of the fanmotor, and hence the fan speed. The air was heatedwhile owing through electric heating elements whichwere connected to a model TI series 305 controller fromTexas instruments, USA. The controller was interfacedto a PC, which used a proportional-integral control al-gorithm to adjust the drying air temperature to a givenset point.

Fig. 1. Schematic diagram of experimental laboratory dryer setup.

P.C. Panchariya et al. / Journal of Food Engineering 52 (2002) 349357 351

The drying compartment of the test chamber had aswinging door, so that the cylindrical sample tray couldbe taken out or inserted back into the chamber. Thesample tray, made entirely of stainless steel, had a per-forated plate bottom. Concentric air distribution baesxed inside both transitions to the chamber provideduniform air ow. The air ducting and the test chamberwere insulated to minimise heat losses from the system.

Air conditions throughout each drying experimentwere monitored on-line. The thermocouples and relativehumidity probes were connected to a data logger, con-verting the analogue signals to digital outputs. The dig-ital outputs were read by a personal computer throughthe data acquisition program.

3.2. Experimental procedure

Experiments were performed to determine the eectof process variables on the thin-layer drying character-istics of black tea. The variables considered were thedrying air temperature, absolute humidity, and air ve-locity. The change in absolute humidity was very lowand later on it was neglected. By considering the actualdrying range, a series of experiments were designed tocover as broad a spread of conditions as possible. Fivetemperature points were selected in the range 80120Cby 10C step. The experiments were conducted at dif-ferent air velocities in the range 0.250.65 m/s by step of0.20 m/s with constant air temperature at each. For es-timation of the experimental error, 45 drying runs wereperformed in a systematic manner, serving as threereplicates.

Prior to placing the sample in the drying chamber, thesystem was run for at least one hour to obtain steadyconditions. Once the temperature had stabilised and theair velocity was at the set value, the sample was placedon the sample holder and on-line data logging systemwas started. The ow of the heated air through thesamples was set in the upward direction. Water lossfrom the samples was determined o-line. This was doneby weighing the sample tray outside the chamber peri-odically using an electronic balance placed next to thetest chamber. The accuracy of the weighing system was0.001 g. The weighing procedure took not more than 15s after removing the sample tray out from the chamberand this method is suciently accurate for generatingreproducible drying curves. In the initial stages of eachdrying run, weights were recorded every minute, thenevery 2 min till the end point. The average moisturecontent of the samples for each weighing period wascalculated based on the net mass of the samples (100 g)and the initial moisture content was determined beforeeach experiment. The initial and nal moisture contentswere determined by a Sartorious moisture meter bydrying the sample at 100C. During the experiments, thedry- and wet-bulb temperatures of the air entering the

plenum chamber were measured on-line using thermo-couples. The air velocity was measured by a hot wireanemometer with a reading accuracy of 0:05 m=s, themeasurement location being 50 cm above the plenum ofthe test chamber.

3.2.1. Equilibrium moisture contentThe equilibrium moisture content of the black tea at

dierent drying conditions used in the drying experi-ments was calculated using the following GAB equationform:

Me awMmck1 kaw1 ckaw kaw ; 12

c c0 exp c1RTab

; 13

k k0 exp k1RTab

; 14

where Me is the equilibrium moisture content (%dry basis), aw is the water activity, and Tab is the absolutetemperature (K) and R is the universal gas constant8:32 kJ mol1 K1. The values of the constants c0,k0; c1 and k1 are 0.02521, 0.99328, 14644.71 and 147.031,respectively (Panchariya, Popovic, & Sharma, 2001).

3.3. Data analysis procedure

The collected data by on-line measurement as well aso-line were analysed using non-linear regression tech-niques. There are several criteria to evaluate the ttingof a model to experimental data. According to Noom-horm and Verma (1986) a model is good when thecorrelation coecient (R2) is high and mean square error(MSE) is low. Other authors like Andriu, Stamatopo-lous, and Zaropolous (1985); Chen and Morey (1989)and Palipane and Driscoll (1994), besides, use the meanrelative deviation modulus P . In this study, the non-linear regression method was based on the LevenbergMarquardt (LM) algorithm (Marquardt, 1963) and isthe most widely used algorithm in non-linear leastsquares tting. The LM algorithm, starting from someinitial parameter values, minimises v2 by performing aseries of iterations on the parameter values and com-puting v2 at each stage. In order to do this, rst partialderivatives were calculated for all values of the inputvariables.

The empirical coecients can be estimated by ttingthe total model employed to the experimental dryingcurves. The goodness of t of the tested models to theexperimental data are the coecients of determination(COD, R2), the reduced v2 and the MSE between theexperimental and calculated values for the tested mod-els. The v2 can be described in equation form as


v2 1N n

XNi1

MRexpi MRcali 2; 15

where MRexpi is the experimental moisture ratio at ob-servation i; MRcali is the calculated moisture ratio at thisobservation, N is the number of observations, and n isthe number of constants. The lower the values of v2,higher the value of coecients of determination (R2) andlower the mean square of the MSE, which were chosenas the criteria for goodness of t.

4. Results and discussion

As the tea samples (Dhool) were collected at dierenttimes from the tea garden, it is obvious that the initialmoisture content of all the runs was not the same. Inorder to normalise the drying curves, the data involvingpercentage dry basis moisture content versus time weretransformed to dimensionless parameter called as mois-ture ratio versus time. Fig. 2 shows the typical charac-teristic drying curve (moisture ratio versus time) of blacktea particles during thin-layer drying operation at dif-ferent temperatures.

The drying data were then tted to the dierent semi-theoretical models such as Lewis, Page, modied Page,two-term and Henderson and Pabis models, based onthe ratios of the dierence between the initial and nal

moisture contents and the equilibrium moisture content.The models were evaluated based on MSE, correlationcoecient (R2), and the v2. The details of the statisticalanalysis are presented in Table 1.

The Henderson and Pabis, the two-term, the Pageand the modied Page models obtained a coecient ofdetermination (R2) greater than the acceptable R2 valueof 0.93 at all drying air temperatures (Madamba et al.,

Fig. 2. Variation of moisture ratio with time at dierent temperatures

and 0.45 m/s air velocity.

Table 1

Statistical results obtained from dierent thin-layer drying models

Model T (C) R2 MSE v2 104The Henderson and Pabis model 80 0.943 0.0048 1.2423

90 0.944 0.0030 1.2078

100 0.947 0.0026 0.9778

110 0.939 0.0039 1.4722

120 0.931 0.0184 8.3845

The Page model 80 0.938 0.0348 9.2404

90 0.944 0.0030 1.2066

100 0.947 0.0026 0.9826

110 0.939 0.0038 3.4141

120 0.929 0.0159 7.2558

The modied Page model 80 0.932 0.0047 1.2403

90 0.934 0.0031 1.2065

100 0.936 0.0024 1.9821

110 0.938 0.0038 1.4131

120 0.921 0.0159 7.2530

The two-term model 80 0.946 0.0038 2.3094

90 0.947 0.0030 1.3046

100 0.950 0.0025 1.0042

110 0.944 0.0035 1.4371

120 0.937 0.0182 9.1006

The Lewis model 80 0.941 0.0048 1.2143

90 0.944 0.0030 1.1630

100 0.947 0.0026 0.9479

110 0.949 0.0014 0.1499

120 0.948 0.0026 1.0011


1996). The MSE and v2 values were below 0.018 and9:0 104, respectively, for all drying air temperatures.Though, the MSE and coecient of determination (R2)values for all the models were quite reasonable but the v2

values were greater than the values obtained by the Lewismodel. Hence, the Lewis model gave better predictionsthan others, and satisfactorily described the thin-layerdrying characteristics of Darjeeling black tea particles.

The experimental results also illustrate the absence ofconstant drying period and drying takes place only inthe falling rate period. This indicates that diusion is themost likely physical mechanism governing moisturemovement in the tea particles. The results were consis-tent with observations made by Temple and Boxtel(1999) who reported the absence of the constant rateperiod during drying of black tea (African variety).Thus, the drying kinetic data for each experimental runwere interpreted using a Lewis model as discussed in theprevious subsection.

The variation of moisture ratio with time for each runwas used for calculating the drying constant (k0) of theLewis model using non-linear regression method. Thecoecient of determination (R2), MSE and v2 betweenthe experimental and calculated moisture ratios wereobtained. The coecient of determination (R2) was morethan 0.93 in all the cases. Tables 2 and 3 illustrate theestimated values of the parameters involved with theLewis model along with their corresponding coecientof determination (R2) and mean square of deviations(MSE) with v2 between the experimental and calculatedmoisture ratios for each drying run. The results show thereasonability of the estimated data and experimentaldata. Figs. 36 show the details of the drying runs.

4.1. Eect of drying variables

Based on the above results, the Arrhenius model wasemployed to examine the eect of other sample param-

eters like air temperature, absolute humidity, air veloc-ity, and characteristic dimension on the thin-layerdrying kinetics of black tea particles. The drying curves

Table 2

Results of non-linear regression analysis for empirical constants of the Lewis model

Model T (C) k0 R2 MSE v2 104The Lewis model 80 0.0017 0.941 0.0048 1.2143

90 0.0024 0.944 0.0030 1.1630

100 0.0030 0.947 0.0026 0.9479

110 0.0036 0.949 0.0014 0.1499

120 0.0046 0.948 0.0026 1.0011

Table 3

Results of non-linear regression analysis for empirical constants of the Arrhenius and Power equations

Equation Parameters R2 MSE v2 104a0 a1 a2

Arrhenius 0.12563 1.15202 209.12341 0.99869 0.02318 1.654

b0 b1 b2Power 0.64801 107 2.14815 1.14635 0.9975 0.03154 1.734

Fig. 3. Variation of moisture ratio with time at dierent air velocities.

Fig. 4. Variation of drying constant k with temperature at dierentair velocities.


(moisture ratio versus drying time) for a range of valuesof a given variable by keeping the other variable con-stant were drawn and compared.

Due to wetness of the Dhool, it is not possible toprecisely separate the particles of dierent characteristicdimensions so this parameter was not included intothe experimental study. For the range of experimentalstudy, the absolute humidity had a smaller value and ithad a negligible eect on the drying curve in comparisonwith other parameters.

The inuence of temperature on the thin-layer dryingcurve is shown in Fig. 2. The increase in temperaturemeans the increase in drying rate and the gure shows asexpected. Fig. 3 shows the eect of air velocity on thedrying curve at constant temperature of 100C. This canbe interpreted as at a constant temperature, increasingair velocity increases drying rate. Hence, the air ve-

locity has a signicant inuence on drying curves such astemperature. Fig. 4 illustrates the variation of dryingconstant (k0) with dierent temperatures and at dierentair velocities.

From the above analyses, the external parameters(temperature and air velocity) have a great inuence ondrying rate and total drying takes place in the fallingrate period only. The main cause behind this can beinterpreted as the Dhool is nothing but the ruptured andcut portion of tea leaf, so the drying takes place not onlyby the epidermis of leaf but also from the cut portion ofleaf as reported by Samejima and Yano (1985) in thecase of shredded tobacco leaves.

4.2. Calculation of eective diusivity and activationenergy

As described in previous subsections that the dryingof black tea occurs in the falling rate period only andliquid diusion controls the process. Ficks second lawcan be used to describe the drying of black tea particles.General series solution of Ficks second law in sphericalcoordinates is given below (Eq. (16)) in which constantdiusivity and spherical tea particle with a diameter of0.0005 m were assumed

M MeM0 Me

6

p2X1n1

1

n2exp

n

2Deffp2

R2t

; 16

where D is the eective diusivity (m2/s) and R is theradius of the tea particles (m). The rst term of Eq. (16)is also known as the Henderson and Pabis model. Theslope, coecient, k, of this model is related to the ef-fective diusivity

k Deffp2

R2: 17

The eective diusivity was calculated by Eq. (17), usingslopes derived from the linear regression of lnMRagainst time data shown in Fig. 5. Generally, an eectivediusivity is used due to limited information on themechanism of moisture movement during drying andcomplexity of the process. The eective diusivities(Deff ) during drying of tea particles varied from 1:1411011 to 2:985 1011 (m/s) in the temperature rangefrom 80C to 120C.

Rizvi (1986) stated that eective diusivities dependon the drying air temperature besides variety and com-position of the material. The heat of sorption which is ameasure of moisture mobility within the food is anotherfactor that aects eective diusivity (Madamba et al.,1996). Eect of temperature on eective diusivity isgenerally described using Arrhenius-type relationship toobtain better agreement of the predicted curve with ex-perimental data (Crisp & Woods, 1994; Henderson,1974; Madamba et al., 1996). Crisp and Woods (1994)

Fig. 5. Experimental and predicted logarithmic moisture ratio at dif-

ferent drying times.

Fig. 6. Arrhenius-type relationship between eective diusivity and

temperature.


reasoned that temperature is not a function of radialposition in the grain under normally experienced dryingconditions, and diusivity varies more with temperaturethan moisture content

Deff D0 exp EaRTa

; 18

where D0 is a diusivity constant equivalent to the dif-fusivity at innitely high temperature and Ea is the ac-tivation energy (kJ/kg). The logarithm of Deff as afunction of the reciprocal of absolute temperature (Ta) isplotted in Fig. 6. The results show a linear relationshipbetween (logDeff ) and 1=Ta or an Arrhenius-type re-lationship (Eq. (18)). The diusivity constant (D0) andactivation energy (Ea) calculated from the linear re-gression are 1:68 107 m2=s and 406.028 (kJ/mol),respectively. It is higher than the activation energy ofvegetable waste drying (19.8 kJ/mol) (Lopez, Iguaz,Esnoz, & Virseda, 2000) and lower than the activa-tion energies of onion drying (1200 kJ/kg) (Mazza &Le Maguer, 1980) and paprika drying (2036 kJ/kg)(Carbonell, Pinaga, Yusa, & Pena, 1986).

5. Conclusions

An experimental dryer system was designed andconstructed, and operated well when used to establishthin-layer drying curves on black tea under a wide rangeof drying conditions similar to those in actual industrialblack tea drying operations. The Lewis model adequatelydescribed the single-layer drying behaviour of blacktea particles. Temperature dependence of the diusivitycoecients was described by an Arrhenius-type rela-tionship. The activation energy for moisture diusionwas found to be 406.02 kJ/mol. The drying rate constantwas correlated well with the experimental drying vari-ables like hot air velocity and hot air temperature usingthe non-linear polynomial regression model. The dryingrate constant was greatly inuenced by the air velocityand the air temperature. Further research about the ef-fect of initial moisture content, air relative humidity andlayer thickness on drying characteristics is necessary forthe optimisation of black tea drying process.

Acknowledgements

The authors gratefully acknowledge DAAD, Bonn,Germany for their nancial support to carry out thisstudy.

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