31

Contact Drying Modelling of Agitated Porous Alumina Beads

A. GEVAUDAN

CETIAT. 27-29 boulevard du 11 Novembre 1918, BP 6084, 69604 Villeurbanne (France)

J. ANDRIEU

UniversitP Claude Bernard, Lyons I, Laboratoire d’Automatigue et de GCnie des Pro&d&s, URA CNRS, 0.1328, Bat. 305, 69622 Villewbanne Cidex (France)

(Received February 5, 1991: in final form April 8, 1991)

Abstract

Contact drying of porous alumina beads (hygroscopic material) was studied at atmospheric pressure in an agitated laboratory disc dryer in order to have a better understanding of the heat and mass transfer phenomena occuring during the process.

Drying kinetics and temperature profiles were determined as a function of operating parameters, namely, the initial moisture content, the plate temperature and the agitation frequency. These data (drying kinetics, temperature profile) were modelled using a contact drying model adapted to this hygroscopic material. The experimental data which are a function of two main parameters, namely, the plate temperature and the stirrer rotation speed, were in good agreement with the model prediction.

1. Introduction

Contact drying in an agitated bed is often used to dry granular materials like pharmaceutical products, mineral powders, agricultural products or foodstuffs; in this last case it can be a combined cooking-drying operation involving complex physico-chemical phe- nomena (starch gelatinization), like in gari process- ing from fresh cassava mash [ 1,2]. The contact drying of free-flowing agitated granular materials has been studied extensively by Schliinder and his colleagues in Karlsruhe [ 3-71.

Except for the works of Tsotsas [3] and Forbert and Heimann [7], most of these studies were realized with non-hygroscopic materials and under vacuum. Very few papers concerning contact drying of agi- tated beds at atmospheric pressure have been pub- lished [4]; so, on the basis of these previous studies our research work was intended to study first the case of the contact drying of material at normal atmospheric pressure (model testing) and then to extend our results to foodstuff drying, namely, to the cassava mash cooking-drying process.

After a brief presentation of the drying contact model and its theoretical aspects [ 1, 4, 51, we studied the influence of the main operating parameters (rota- tion speed, plate temperature) on the drying rate and the bed temperature profile. Finally, a comparison

between theory and experimental data is presented in terms of drying rate and bulk temperature profiles.

2. Model

This model was first proposed by Tsotsas and Schliinder [4] to analyse the contact drying of agi- tated granular materials in the presence of inert gas; it is based on the penetration theory to describe the heat transfer between a hot wall and an agitated granular bed. The steady-state mixing process is replaced by a sequence of unsteady mixing steps; a contact period of length t, is followed by an instanta- neous perfect macromixing of the bulk; during the contact period, the bulk is assumed to rest on the heating plate and to be heated by conduction. Dur- ing this contact period, the overall heat balance can be written as

4" = Jsen + JIat + JIoss (1)

where J,, is the total heat flux entering the bed, J,,,, and J,,, are the heat fluxes corresponding, respec- tively, to sensible and latent energy, and J,,,, is the heat loss flux at the surface of the bed.

The part of the entering flux not consumed as sensible energy is assumed to be transported to the surface of the bed where the evaporation takes place

0255-2701/91/$3,50 Chem. Eng. Process., 30 (1991) 31-37 c Elsevier Sequoia/Printed in The Netherlands

32

Jin

loss

Fig. 1. Temperature profiles and heat fluxes during a contact period.

(see Fig. l), so that we can write the following partial heat balances:

Ji” = Jsen + J0~, (2)

JO”1 = Jl,t + JI,,, (3)

These different fluxes can be expressed in terms of the heat transfer coefficients:

J,” = h, H (2-P-- Tn) (4)

Jin = hg, w (TH - h. ,) (5)

Jsen = (PC,),, w L TB,i+l - TB.~

Ik (6)

Jo,,=h,,wU’,.i-7’s) J loss = (k + &XT, - TA)

(8)

(9)

where T,, TH , Ts, i, T, and TA are, respectively, the temperatures of the plate, the first particle layer, the bed at the contact period i, the bed surface and the ambient air.

The contact heat transfer coefficient between the plate and the first particle layer, h,: H, was estimated by taking into account the conductton and the radia- tion in the gaseous phase [5].

The time-averaged ‘penetration’ heat transfer co- efficient, h,, w, assuming that the bulk is semi-infinite, is expressed as follows:

(10)

h, and h, are, respectively, the convective and radia- tive heat transfer coefficients between the upper sur- face of the bulk and the surrounding atmosphere.

The evaporation flux at the bed surface, assuming the Lewis hypothesis, is

g =cz h M”Oln PT-PP,,. c M.4 P. I3 p* - pv, ,(Td

(11)

Product hygroscopicity is taken into account by modifying the water saturation pressure, P,, sat, by introducing the solid activity a,,,(X, 7’s), calculated from the desorption isotherms, and by adding the

desorption heat AHdes to the heat of vaporization AH, :

P v. s = Pv, Sat a,,(X Ts)

A& = AH, + AHder(X)

The contact time t, is expressed by

(12)

(13)

tk = Nrnixlz (14)

where Z is the rotation speed of the stirrer and Nmi, an empirical parameter, called the mixing number, depending on the dryer type, on the stirring device and on the mechanical properties of the material. The system defined by eqns. (4)-( 14) can be solved numerically if the bed initial conditions are known (i.e. temperature and solid humidity), so that we obtain, at each contact period, the drying rate and the mean temperature of the bed.

3. Materials and method

3.1. Materials

The model material was selected from the follow- ing criteria: ~ a marked hygroscopic behaviour; - well-known physical properties; - no major changes during drying (no shrinkage, chemically inert).

So, we chose active alumina, type A 2-5, manufac- tured by Rhone-Poulenc, shaped as porous spherical beads (porosity ap = 0.59) of large specific area (so = 325 m2 g-‘). The other main physical properties are listed in Table 1.

The solid-phase (Al,O,) thermal conductivity was found in the literature [l] (&,, = 30 W m-’ K-‘) as well as the specific heat correlated as a function of temperature by the relationship

c 0.3415 x 108

‘p, sol = 1124+0.1269- TZ (15)

where Cr,, so, is expressed in J kg-’ K-’ and T in K. Furthermore, the water desorption data of alu-

mina beads are strongly dependent on alumina type (texture, structure). Thus, the isotherm of our mate- rial was determined at 60 “C with the saturated salt solution method. The experimental points were fitted using the well-known GAB model [Xl:

a,,lx = Ala,,,* + -4,~ + -4, (16)

The values of the coefficients A,, A, and A,, fitted by using a non-linear least squares method, are summa- rized in Table 2.

TABLE 1. Physical properties of alumina beads

Bead mean diameter 4 Solid density PSUI Bed apparent density P.xw

2 x 10-Z m 3000 kg mm3

770 kg m-’

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TABLE 2. GAB model coeficient values

T A, A2 A3 RMS 60 “C -8.72 8.86 1.25 8.6%

3.2. Experimental equipment

A laboratory disc dryer (diameter 240 mm) was built in order to determine the drying curves and to study the influence of the operating parameters on the drying rate: stirrer speed, type of paddle, hot- plate temperature. This equipment was designed to control the plate temperature and to record the following variables: bulk temperature of the bed, temperature and relative humidity of the ambient air (Fig. 2).

The stirring device was designed to weigh the sample container at given time intervals by dissociat- ing the weighing instrument (electronic balance of range 4300 g _t 0.1 g) and the agitator.

Paddles of different shapes can be adapted to sweep the upper surface of the plate. More details concerning the experimental set-up can be found in ref. 1.

3.3. Experimental procedure

Drying runs were conducted with samples of about 200 g of wet product. The initial moisture content was determined by weighing five samples before and after complete dehydration in an oven set at 180 “C for 3 h. The same procedure was repeated

ii,

at the end of the experimental run to measure the final moisture content of the bed. The drying rate curve was obtained by smoothing the experimental drying curve m = f(t) by parabolic regression on five experimental points. The bed and the hot-plate tem- peratures were calculated by time-averaging values recorded every 5 s [ 11.

Nine drying runs were carried out at four different plate temperatures (70, 90, 110 and 130 “C) and four rotation frequencies (ranging from 0 to 42 rpm). During the experiments the temperature of the ambi- ent air was close to 30 “C and the air relative humid- ity was also quite constant around 60%-70%.

4. Results and discussion

4.1. Drying kinetics: experimental data

As shown in Fig. 3, two zones can be distinguished in the drying rate curves:

(1) a first zone of variable length where the drying rate decreases steeply-this first phase ends with moisture contents about 0.45 kg/kg (dry bed), vary- ing slightly with the plate temperature level;

(2) a second zone where the drying rate falls more slowly and tends to zero when the bed moisture content approaches the equilibrium moisture, this latter being fixed by the final product temperature and by the relative humidity of the air.

Otherwise, the mean bed temperature curves (see Fig. 4) can be divided into different periods, whose limits correspond approximately to the limits ob- served in the drying rate curves.

In the first period, the mean bed temperature T, exhibits a peak at X 2 0.45 kg/kg (d.b.) and then remains nearly constant. At the drying end, TB in- creases again when the moisture content approaches the equilibrium moisture.

The first period, characterized by a steep rise in bed temperature, corresponds to a transient heating of the bed during which the bed reaches thermal

Fig. 3. Experimental drying kinetics: influence of plate tempera- ture for z = 14 rpm. Fig. 2. Experimental set-up

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T Bed

(“C)

60 -

0

A

x

m

I 0

40 0

30 4

0 0.1 0.2 0.3 0.4 0.6 0.6

X (kg/kg d.b.)

Fig. 4. Mean bed temperature variation: influence of plate tem- perature for Z = 14 rpm.

equilibrium. Nevertheless, the bed temperature curves measured by Tsotsas [3] do not exhibit such a high peak but present a quick increase followed by a plateau.

This difference could be explained in our case by a higher amount of superficial water which increases the stickiness of the bed. The efficiency of the stirrer is thus reduced, leading to the formation of big particle clusters having higher moisture content, so that the net heat transfer from the wall to the bed is increased. Furthermore, the decrease in the moisture content improves the mixing conditions but strongly reduces the apparent thermal conductivity of the bed; thus the heat flux entering the bed decreases, consequently inducing the temperature of the bed to fall.

Also, the drying rate is very high at the beginning of drying (high heat flux entering the bed and large amount of free water); it then falls steeply due to the decrease in the heat penetration coefficient.

The second period starts when all the superficial water at the external surface of the particles has been evaporated. As observed by Tsotsas [3] in vacuum drying, the decrease of the drying rate is quasi-linear for X < 0.15 kg/kg (d.b.). This strong decrease in the drying rate has to be related to the lower value of the heat penetration coefficient and to the hygroscopicity of the product. The bed temperature curves are similar to those obtained by Tsotsas [3], who ob- served a steady increase in the bed temperature over the same period.

4.2. Plate temperature

As shown by Fig. 3, the drying rate increases strongly with the plate temperature over the whole moisture content range, as indicated in the literature [3-61.

There are two main reasons for this effect: (1) an increase in the heat flux entering the bed

due, on the one hand, to higher values of the heat

transfer coefficients and, on the other, to higher temperature differences ( TP - r,) ;

(2) an increase in the water vapour partial pres- sure inside the bed which increases the vapour diffu- sion flux.

4.3. Agitation speed

The effect of the agitation speed can be observed in Figs. 5 and 6 concerning, respectively, the drying rate and the evolution of the bed temperature for four different rotation frequencies (r, = 90 “C).

For fixed bed drying (Z = 0), the drying rate falls very rapidly during the drying process and is always lower than in an agitated bed.

For an agitated bed (Z Z 0), after a short steep decreasing period (0.40 < X < 0.57 kg/kg), the dry- ing rate diminishes classically, as explained before. Moreover, we observe that the different drying rate curves are not significantly different in the range defined by 14 < Z < 42 rpm.

0.6

X (kg/kg d.b.)

Fig. 5. Experimental drying kinetics: influence of stirrer speed for TP = 90 “C.

76

70

z (wn) 66

60 x0

T&d A 11

(“C)

66 0 28

60

t 0 42

46

40 1 36

t

u

OA

30 m ,

0 0.1 0.2 0.3 0.4 0.6 - 0.6

X [kg/kg d.b.)

Fig. 6. Mean bed temperature evolution: influence of stirred speed for r, = 90 “C.

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Qualitatively, these results can easily be inter- preted by the heat penetration theory [3-61.

Indeed, for large particles, such as the alumina beads used in this study, the heat transfer from the wall to the bed is probably controlled by the contact resistance [3, 61. Thus, when the bed is agitated, increasing the rotation speed will only contribute to reducing the contact time t, and therefore the heat penetration transfer coefficient will improve, but not the contact heat transfer coefficient h, “.

Inversely, when no agitation is carried out (fixed bed), the drying is controlled by the heat penetration resistance, which increases with time. Moreover, very soon after the beginning of the drying process, the first particle layers are dry, limiting the heat flux penetration to the bulk, because of the low thermal conductivity of the dry particle layers. Schematically, a moving evaporation front will then progress to- wards the free surface of the bed.

The mean bed temperature evolution can be ex- plained in a similar way [ 11.

4.4. Model prediction

The modelling was carried out on the basis of eqns. (4))( 14). For this purpose, the main difficulty is to evaluate the rugosity of the alumina particles, this parameter appearing in the calculation of h,, H; no data were found for an estimation, so the rugos- ity was considered as a supplementary parameter. Moreover, the temperature dependence of the des- orption data and the desorption enthalpy were ne- glected. In spite of these simplifications, Fig. 7 and 9 demonstrate that the calculated drying kinetics are in satisfactory agreement with experimental data.

The model prediction concerning the temperature profiles is less accurate (see Figs. 8 and lo), but nevertheless the deviation remains within a satisfac- tory range (mean deviation about 10%).

Furthermore, we observe that the initial drying period characterized by a bed temperature peak and high drying rates cannot be predicted correctly since

0

0 0.2 x.3 0.4 0.5 0.6

X (kg/kg d.b.)

40 --

30 T

0

jj --I

0.2 0.3 0.4 0.5 0.6

X (kg/kg d.b.)

Fig. 7. Comparison between experimental and theoretical drying Fig. 10. Comparison between experimental and calculated bed kinetics: influence of plate temperature for Z = 14 rpm. temperature curve: influence of plate temperature for Z = 42 ‘pm.

Fig. 8. Comparison between experimental and calculated bed temperature curves: influence of plate temperature for Z = 14 t-pm.

0 0.1 0.2 0.3 0.4 0.5 0.6

X (kg/kg d.b.)

Fig. 9. Comparison between experimental and theoretical drying kinetics: influence of plate temperature for Z = 42 rpm.

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TABLE 3. Optimal values of A’_ as a function of stirring speed

Z (rpm) h’ “Ill Nrw [61

14 5 10.5 28 10 13.9 42 I5 16.3

the model applies only to free-flowing materials; owing to bed stickiness, this condition is not satisfied at the beginning of the drying. The major deviation between the calculated and measured drying rate curves appears at low moisture contents and for plate temperatures above 90 “C. This deviation could certainly be reduced by evaluating the desorption data more precisely over the whole temperature range concerned.

The optimal values for N,,,i,, listed in Table 3 as a function of the agitation frequency 2, are in agree- ment with the data obtained by Tsotsas and Schhin- der for normal pressure drying [4], but are lower than those calculated from the correlation proposed by Mollekopf [6].

The calculated curves were obtained with a rugos- ity value of 50 pm. The effective thermal conductiv- ity of the bed was evaluated using the model of Zehner and Bauer [9, lo] with the parameters pro- posed by these authors for a spherical particle. The calculation took into account an additional term due to the evaporation-condensation phenomenon (‘heat pipe effect’). The contact heat transfer co- efficient was calculated with a value of 0.80 for the plate covering factor and 0.80 for the accommoda- tion coefficient [5].

5. Conclusions

Contact drying kinetics of porous alumina beads were measured in an agitated laboratory disc dryer, as a function of operating parameters (plate temper- ature and agitation frequency). For this hygroscopic inorganic material, a drying model based on heat penetration theory-a single adjustable parameter model-is able to predict with reasonable agreement the drying rate curves and the temperature profiles of an agitated granular bed. The optimal parameter values obtained are in accordance with the few liter- ature data published for this dryer type.

Finally, we believe that this model could be ex- tended to other products like foodstuffs for which the rheological changes induced by the drying are more drastic than in the present case.

Acknowledgements

The present study was realized at CEEMAT/CIRAD 34000 Montpellier (France) and supported by an operating grant from M.R.T. and A.N.R.T. (con-

vention CIFRE No. 249/X5). The authors are grate- ful to G. Chuzel for his valuable comments.

Nomenclature

water activity of solid particle specific heat, J kg-’ Km’ diameter, m desorption heat, J kg-’ total heat of vaporization of bounded wa- ter, J kg-’ latent heat of vaporization, J kg-’ heat transfer coefficient, W m-* K-’ heat flux, W me2 bed height, m molar mass, kg mol-’ drying rate, kg mm2 h-’ mixing number pressure, Pa specific area of solid, m2 g- ’ temperature, K or “C time, s moisture content of dry bed (d.b.), (kg moisture) /( kg dry matter) stirrer rotation speed, rpm

porosity thermal conductivity, W m-’ K-i density, kg mm3

Subscripts

A air app apparent B bed C convection g H i. i + in k lat loss mix P P

gas first particle layer

1 contact period entering bed contact latent losses mixing plate particle radiation surface saturation sensible solid total vapour wet initial

S sat sen sol T V

:

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