Investigation of drying Geldart D and B particles in different fluidization regimes.

Ng, Wai Kiong ; Tan, Reginald B.H.

Drying of nylon (Geldart D) and expanded polystyrene (Geldart B) particles in fixed and fluidized beds were studied experimentally and theoretically. Fluidized bed dryers are sometimes operated at velocities beyond bubbling fluidization to mitigate against de-fluidization of surface wet particles. It was found that theoretical analysis using three different drying methods could predict the constant-drying rate at such velocities and also across the entire fluidization regimes (fixed bed, bubbling, slugging and turbulent fluidization) as long as the bed remains completely fluidized. Results also showed that the theoretical predictions were accurate beyond previously reported velocity limits in a laboratory scale dryer. During bubbling fluidization, the cross flow factor method was used effectively to predict the influence of bubble phase on drying rates. In the falling-rate period, it is demonstrated that the drying behaviour of nylon at different gas velocities can be characterised by a single normalized drying curve.

On a etudie de maniere experimentale et theorique le sechage de particules de nylon (Geldart D) et de polystyrene expanse (Geldart B) dans des lits fixes et fluidises. Les sechoirs a lits fluidises fonctionnent parfois a des vitesses qui vont au-dela de la fluidisation bullante pour attenuer la de-fluidisation des particules mouillees en surface. On a trouve que l'analyse theorique a l'aide de trois methodes de sechage differentes pouvait predire le taux de sechage constant a de telles vitesses et egalement dans tous les regimes de fluidisation (fluidisation a lit fixe, bullante, pistonnante et turbulente) tant que le lit demeure entierement fluidise. Les resultats montrent egalement que les predictions theoriques sont precises au-dela des limites de vitesse mentionnees precedemment dans un sechoir a l'echelle de laboratoire. Lors de la fluidisation bullante, on a utilise avec efficacite la methode du facteur d'ecoulement transversal afin de predire l'influence de la phase bullante sur les vitesses de sechage. Dans la periode de vitesse descendante, on demontre que le comportement de sechage du nylon a differentes vitesses de gaz peut etre caracterise par une courbe de sechage normalisee unique.

Keywords: fluidized beds, drying, de-fluidization, cross flow factor, large particles

INTRODUCTION

Fluidized beds are frequently selected as processing equipment because of their excellent heat transfer properties and the ease in controlling transfer of solids into, out of, and within the process system. In gas-solids fluidization, fluidized beds have been used most frequently in drying operations than in any other single application (Geldart, 1986). The first commercial fluidized bed dryer was installed in USA in 1948 to dry dolomite or blast furnace slag (Zahed et al., 1995). Since then, hundreds of fluidized bed dryers have operated worldwide, primarily for granular materials that can be easily fluidized, such as sand, grains, chemical crystals and fertilizers. Vanecek et al. (1966) presented an extensive survey of different materials (granular, in solutions, suspensions and pastes) that are dried using fluidized beds.

Despite extensive applications, today's process design of fluidized bed dryers still requires a laboratory bench-scale set-up to determine fluidization behaviour and batch drying tests to determine drying kinetics of a particular system before verification is carried out on a pilot-scale and/or full commercial-scale (Davidson et al., 1985; Devahastin, 2000; Kunii and Levenspiel, 1991). Bench-scale batch drying curves are typically obtained for at least one set of operating conditions and used to extrapolate drying performance for larger-scale operations and other operating conditions. To describe these batch drying curves quantitatively, drying models, such as constant-rate drying model, falling-rate drying model, liquid diffusion model or receding drying front model, are chosen and parameters are selected to fit into the model (Chandran et al., 1990; Mourad et al., 1997; Wantano et al., 1998). Two or more models are usually used to fit one drying curve, when different drying periods occur within the same curve. An alternative approach to describe these batch drying curves quantitatively is to estimate heat and mass transfer coefficients using transport equations (Ciesielczyk, 1996; Kerkhof, 1994). Recent research work has been focused on coupling the relevant theoretical drying models of the material to be dried (Coumans, 2000) with heat and mass transfer between the two or three phases inside bubbling fluidized beds (Burgschweiger et al., 1999; Zahed et al., 1995; Chen et al., 2001).

In industrial polymer production, fluidized bed drying is often the last but vital operation to ensure good product quality. Low moisture content in the polymer product is a prerequisite for subsequent extrusion processes. During the drying process, the fluidized bed is usually operated in the bubbling regime as the gas bubbles help to promote good solids mixing. This paper, however, aims to predict the drying rates at velocities beyond the bubbling regime because such velocities are often used to overcome process upsets in industrial practice. Modelling work on drying at such velocities has rarely been reported. For instance, in nylon production, the particles entering the fluidized bed dryer are wet and sticky as they have been treated under cooling water during pelletization. These particles often clump together and de-fluidize the bed. To mitigate against this problem, higher fluidizing gas velocities are used to breakup these clumps of particles. In this work, three theoretical methods are used to model drying rates of two particle types at a laboratory fluidized bed. The accuracy and the range of validity of the three methods are discussed. The methods are based on adiabatic heat-mass balance (Kunii and Levenspiel, 1991), Chilton-Colburn analogy of heat-mass transfer (Sherwood et al., 1975) and mass transfer coefficient by Gupta and co-workers (Gupta et al., 1974; Delvosalle and Vanderschuren, 1985). After surface water is removed, the characteristic drying curve method is used to model the drying rates during the falling-rate drying period (Keey and Suzuki, 1974).

EXPERIMENTAL

The objective of the experiments was to measure the drying rates of wetted nylon and expanded polystyrene (EPS) particles in an air-fluidized bed and to compare them against those predicted using theoretical models. These drying rates were measured at different fluidizing velocities from [u.sub.mf] to 5 x [u.sub.mf], [u.sub.mf] being the incipient fluidizing velocity of the dry particles.

Experimental Apparatus

The experiments were carried out in a batch fluidized bed dryer (Figure 1), which was a Pyrex cylindrical column with internal diameter of 0.05 m and height of 0.8 m. The air distributor was a stainless steel perforated plate. The column was topped by a conical freeboard, 0.15 m high, inclined at 45[degrees]. In all experiments, the column was filled with particles at a stationary bed height of 0.1 metre, which was similar to that in industrial dryers. Before entering the bed, the fluidizing air was measured by a mass flow meter (Brooks 5863i) and dehumidified by passing through a column containing a drying agent. In all experiments, the relative humidity of the inlet and outlet air were measured using two thermohygrometers (Testo T635) installed at the bed inlet and outlet. From these measurements, the inlet and outlet humidities were calculated. A material balance, using the measured humidities and measured airflow rates gave the drying rates. The moisture content of particles was calculated using the loss of moisture as measured by the gain in humidity between inlet and outlet air.

[FIGURE 1 OMITTED]

The set-up was designed to operate across the entire fluidization regimes from [u.sub.mf] to 5 x [u.sub.mf] ranging from fixed bed, bubbling, slugging, spouting to turbulent fluidization. For nylon particles, fluidizing velocities ranged from 0.41 m x [s.sup.-1] to 3.74 m x [s.sup.-1] and for EPS particles, they ranged from 0.26 m x s-1 to 0.76 m x [s.sup.-1]. The corresponding regimes at different velocities are shown in Table 1. The incipient fluidizing velocity of dry particles was determined from pressure drop measurements across the air distributor and fluidized bed surface. The pressure drop through the air distributor as a function of airflow rate was first measured in an empty column with no solids using a differential pressure transducer (Flotech Setra C230). Pressure drop across the fluidized bed was then obtained by subtracting from this pressure drop at each airflow rate from the total pressure drop with solids in bed. A plot of this relationship gave the incipient fluidizing velocity of the dry particles. The measured minimum fluidization velocities of nylon and both types of EPS particles were 0.74 m x [s.sup.-1] and 0.26 m x [s.sup.-1], respectively. For nylon, the measured value agreed well within 3% deviation from the theoretical predictions using Wen and Yu's correlation (Wen and Yu, 1966). For EPS, the measured value was significantly higher than both calculated values, which could possibly be due to the presence of surface charges.

Materials and Preparation

Nylon and expanded polystyrene (EPS) were selected as test materials because they belonged to different particle classes and had different fluidization behaviour when wet. The dry nylon particle was elliptical with major and minor diameters of 2.5 mm and 2 mm, respectively, and had a density of 1140 kg x [m.sup.-3]. Two types of dry spherical EPS particles were used with average diameters of 1.8 mm and 2.4 mm and they had the same density of 127 kg x [m.sup.-3]. As nylon particles were large and dense, they fell into Geldart Type D. Being smaller and less dense, EPS particles lay below Type B near the bottom of the standard Geldart diagram (Geldart, 1973). When the particles were wet, nylon was more readily fluidized as compared with EPS, which tended to clump together and de-fluidized the bed. All moisture content data were on a bone-dry basis.

Nylon and EPS samples were prepared with the following procedures. Nylon particles were soaked in water for nine d at room temperature of around 22[degrees]C before being dripped dry in a sieve. The moisture content was determined gravimetrically to be about 20 wt.%. EPS particles were prepared according to manufacturer's instructions by "expanding" their sizes from 1 mm to 3 mm in boiling water for 5 min. The EPS particles were then dried in an oven at 100[degrees]C overnight and hand-sieved using mesh sizes ASTM E-11 #14, #10 and #7 to obtain two average sizes at 1.8 mm (called EPS-1) and 2.4 mm (called EPS-2). Next, they were soaked in water at room temperature for 24 h before being dripped dry in a sieve. The moisture content measured by gravimetry ranged between 30 and 70 wt.% for EPS-1 and between 15 and 35 wt.% for EPS-2. It was difficult to prepare EPS particles with consistent moisture contents because the particles tended to clump together when wet and this led to different quantities of water being trapped inside the inter-particle voids.

THEORETICAL METHODS

To predict the drying rates of wetted nylon and expanded polystyrene (EPS) particles in an air-fluidized bed, three theoretical methods from literature were used to model the constantrate drying period while the falling-rate period was modelled using the characteristic drying curve method.

In modelling the constant-rate drying period, all three methods are based on the same concept: drying rate is determined by the maximum moisture carrying capacity of inlet air under the following assumptions:

a. Drying takes place in a well-insulated environment, i.e. there is negligible heat transfer between the fluidized bed and surroundings via the column wall.

b. As the bed temperature falls from room temperature to adiabatic saturation temperature of inlet air, the heat loss from the particles has negligible effect on the drying rate.

c. The evaporation of surface moisture is not hampered by internal resistance, such as capillary action or diffusion.

e. During bubbling fluidization, the presence of bubbles does not reduce the drying rate.

The first two assumptions are easily justified using standard heat transfer correlations. The third can also be verified by measuring the relative humidity outlet air and ensuring that the outlet air is at adiabatic saturation. However, the last assumption needs to be verified by calculating a cross-flow factor. During bubbling fluidization, a fluidized bed is divided into a bubbling phase containing gas bubbles and a dense phase containing the remaining fluidizing gas and solids. Bubbles can pose as a gas by-pass through the bed of particles and reduces the moisture transport between the particles and the fluidizing gas. The cross-flow factor [X.sub.b] is defined as the number of times a gas bubble is fl ushed by the fluidizing gas in the dense phase:

[X.sub.b] = K/[u.sub.b]/[H.sub.max] (1)

The mass transfer coefficient between bubbles and the remaining fluidizing gas K was evaluated according to the following empirical correlation for large particles by Sit and Grace (1981). The average bubble velocity [u.sub.b] and bubble diameter [d.sub.b] taken at mid-bed height were determined from correlations for Geldart Type B and D particles given in (Geldart, 1986):

[K.sub.c] = [u.sub.mf]/3 + [(4 x [D.sub.a] x [[epsilon].sub.mf] x [u.sub.b]/[pi] x [d.sub.b]).sup.0.5] (2)

Computed results showed that at velocities that bubbling fluidization occurred, the cross-flow factor for nylon was 3.2 and that for EPS-1 and EPS-2 varied between 12.6 and 3.7, respectively. As previously shown by Davidson et al. (2001), at cross-factor greater than three, there was good mixing between the bubbles and the remaining fluidizing gas and therefore, the bubble phase did not affect the drying rates. It was noted that the validity of this assumption was strongly dependent on bed diameter. In an industrial-scale fluidized bed, the bubbles could grow large enough to act as an effective bypass to reduce the drying rates.

Adiabatic Heat-Mass Balance--Method 1

Method 1 predicts the drying rate on the assumption that both heat and mass transfer between the fluidizing air and water on particle surface occurs at thermodynamic equilibrium (Kunii and Levenspiel, 1991). At equilibrium, the outlet air temperature would be same as the adiabatic saturation temperature of inlet air, which could be taken from psychometric charts (Keey, 1978). Using the temperature difference between inlet and outlet air, the heat given up by the inlet air was used to determine the drying rate in the following equation:

[M.sub.s] x [d.sub.X]/dt = - A x [[rho].sub.a] x u x [c.sub.pa] x ([T.sub.i] - [T.sub.e])/[DELTA][H.sub.vap] (3)

Chilton-Colburn Analogy of Heat and Mass Transfer--Method 2

Both Methods 2 and 3 were used to calculate the moisture content of the fluidizing air at bed outlet. By integrating the change in moisture content inside an infinite small volume over the fluidized bed height as shown in Equation (4), the moisture content was expressed as a function of bed height (Sherwood et al., 1975)

[p.sub.a] x u x [d.sub.Y] = [h.sub.c] x a/[c.sub.pa] x [Y.sub.e] - Y(H)] x dH (4)

Based on the Chilton-Colburn analogy between heat and mass transfer, the mass transfer coefficient of moisture was substituted with a convective heat transfer term [h.sub.c]/[c.sub.pa] given by following expressions (Keey, 1978):

[h.sub.c] = [j.sub.H] x [c.sub.pa] x [rho] x u, where (5)

[j.sub.H] = 1.0/[epsilon] x [[Re.sub.p]/(1 - [epsilon])].sup.-0.5]. (6)

By re-arranging Equation (4), the bed height needed to achieve a given moisture content in the outlet air was expressed in Equation (7):

H = [[rho].sub.a] x [c.sub.pa] x u/[h.sub.c] x a x ln[[Y.sub.e] - [Y.sub.i]/[Y.sub.e] - Y(H)] (7)

To achieve adiabatic saturation at bed outlet, the bed heights at different fluidizing velocities were determined theoretically. The moisture content at adiabatic saturation was a function of the temperature and moisture content of inlet air and could be taken from psychometric charts. As long as the bed heights observed during experiments were higher than the theoretical values, the drying rate could be calculated using the difference in moisture content between the inlet air and that at adiabatic saturation.

Mass Transfer Coefficient--Method 3

Method 3 calculates the moisture content of the fluidizing air at bed outlet using an empirical correlation for the gas-to-particle mass transfer coefficient, which was verified over a wide range of experimental data by Gupta, Delvosalle, Vanderschuren and co-workers (Gupta et al., 1974; Delvosalle and Vanderschuren, 1985). The drying rate was determined in a similar manner as Method 2, except that the convective heat transfer term was replaced with the mass transfer coefficient given by the following correlations:

[k.sub.m] = [j.sub.D] x [Re.sub.p.sup.1.0] x [Sc.sup.-0.667] x [mu]/[d.sub.p], where (8)

[j.sub.D] = 0.455/[epsilon] x [Re.sub.p.sup.-0.407] (9)

RESULTS AND DISCUSSION

Experimental

Experimental results are illustrated in Figures 2 to 4. The drying rate of nylon was plotted on the abscissa of the diagrams, and the fluidizing velocity was the parameter varied.

[FIGURES 2-4 OMITTED]

In drying nylon, Figure 2 illustrated the typical "drying curve" with an initial constant-rate period followed by a falling-rate period. Constant-rate drying is usually associated with removal of free water from particle surface and the falling-rate period with bound water inside particles. In drying EPS, as the range of initial moisture content of EPS varied and no constant-rate drying was observed, the normalized moisture content was chosen as the ordinate to present a more reflective comparison of drying rates at various fluidizing velocities.

From Figure 2, it was observed that drying rates of fluidized nylon particles fall to very low values after a short duration of less than 15 min. To verify that this observation was not due to a lack of sensitivity in the thermohygrometers in measuring small differences in relative humidity, drying of single nylon particles was studied using thermal gravimetric analysis (TGA, Biorad Universal V2.5H). TGA is highly sensitive to weight loss. Inside the TGA cell, the temperature was held constant at two different temperatures at 23[degrees]C and 35[degrees]C using purified air as carrier gas at a flow rate of 100 ml x [min.sup.-1]. The thermo analytical pattern showed an initial steep fall in drying rate followed by relatively low drying rates. This could be explained by the evaporation of free water from the particle surface followed by the slow drying of bound water inside the particles. TGA results tallied well with those in Figure 2 and verified that the steep fall in drying rate for nylon particle was not due to a lack of sensitivity in the thermohygrometers.

Modelling of Experimental Results

Drying of surface water

During the drying of surface water, Methods 1 to 3 were used to predict the drying rates as a function of the fluidizing velocity and the results were compared with experimental data as shown in Figures 5 and 6.

[FIGURES 5-6 OMITTED]

Methods 2 and 3 were used to predict the minimum bed heights for the outlet air to achieve adiabatic saturation at the different fluidizing velocities. The results of Method 2 showed that the minimum bed heights range from 0.009 m to 0.410 m for nylon and 0.003 m to 0.052 m for EPS-1 and EPS-2. Method 3 gave values ranging from 0.008 m to 0.151 m for nylon and 0.004 m to 0.032 m for EPS-1 and EPS-2. As all measured bed heights were higher than these values, the assumption of adiabatic saturation of the outlet air stream was verified. However, it should be noted that at very low Reynolds numbers, these kinetic calculations are prone to over predict drying rates. This well-known effect of low apparent Sherwood numbers has been resolved by a two-phase model which incorporated the effect of bypassing and backmixing (Burgschweiger et al., 1999).

As expected and shown in Figure 5, the drying rates of nylon particles increased linearly with fluidizing velocity during the constant-rate period in accordance to Equation (3). All three theoretical methods were fairly accurate in predicting the drying rates across the entire fluidization regimes at velocities ranging from [u.sub.mf] to 5 x [u.sub.mf]. Even though significant changes in hydrodynamics occurred when the bed changed from fixed bed, bubbling, slugging, spouting to turbulent fluidization, these changes seemed to have little effect on accuracy of these three methods. Experimental results showed that adiabatic saturation was attained at outlet. At equilibrium conditions, all three methods should lead to identical results. However, the calculated results for Method 1 were higher by about 12% as compared to 2.5% deviations from Methods 2 and 3. This was likely due to inaccuracies arising from reading values off psychometric charts.

In drying of EPS, the absence of a constant-rate drying period was likely due to the high sorptivity of porous EPS. The drying rate in the first period depended not only on the fluidizing conditions but also on the solid moisture content (Burgschweiger et al., 1999). As a constant-rate drying period was not observed, the results from Methods 1 to 3 were compared with the initial drying rates measured. As shown in Figure 6, the experimental results were close to the theoretical values except at fluidizing velocities of 2.0 x [u.sub.mf] and 2.6 x [u.sub.mf]. During the first few minutes of the drying process, it was observed that wet EPS particles clumped together and de-fluidized the bed. This did not occur for nylon particles. This led to vapour channelling and spouting, whereby part of the fluidizing air could bypass the bed. The contact surface area between the fluidizing air and wet particle surface was therefore lower than that of a well-fluidized bed. The presence of vapour channelling and lower contact surface area might have resulted in the lower drying rates measured. Below 2.0 x [u.sub.mf], it was speculated that the effect of de-fluidization might not be significant enough to reduce the drying rate as there was more contact time between fluidizing air and particles. At higher velocity of 2.9 x [u.sub.mf], wet EPS particle clump broke up and the bed entered the turbulent regime within one to two min. The breaking up of particle clumps could explain the short dip in drying rates shown in Figures 3 and 4 as the drying process proceeded (normalized moisture content from 1 to 0.7). In the turbulent regime, the drying rate could be predicted using the three methods.

Experimental results showed that Methods 2 and 3 were accurate beyond previously reported limits of fluidizing velocities at 1.5 x [u.sub.mf] and 3 x [u.sub.mf], respectively (Keey, 1978; Gupta et al., 1974). A good agreement between predicted and measured drying rates can be seen up to fluidizing velocities of 5.1 x [u.sub.mf] and 2.9 x [u.sub.mf] for nylon and EPS, respectively.

Falling-rate drying

Beyond the drying of surface water, a characteristic drying curve method was used to describe the drying rate as a function of moisture content. The drying rate was normalized with respect to the constant-rate drying N/[N.sub.c] and was plotted as a function of normalized moisture content [X.sub.f] given in Equation (10):

[X.sub.f] = X - [X.sub.eq]/[X.sub.cr] - [X.sub.eq] whereby N/[N.sub.c] = 1 for all [X.sub.f] > 1 (10)

The demarcation point between the constant- and falling-rate period was used to determine the critical moisture content [X.sub.cr] of nylon as shown in Geldart (1986). As constant-rate drying was not observed for EPS, [X.sub.cr] was substituted with the initial moisture content to calculate the normalized moisture content. The equilibrium moisture content [X.sub.eq] of nylon was taken as 0.5% according to sorption isotherm data reported in Kohan (1995). Without known sorption data for EPS, the equilibrium moisture content was assumed to be zero.

As shown in Figure 7, similar characteristic curves of nylon particles were obtained across the entire fluidization regimes. Shortly after reaching the normalized critical moisture content, i.e. [X.sub.f] between 0.95 and 1, the normalized drying rates fell steeply to very low values compared to the initial drying rates during the constant-rate drying period. After the steep fall, these drying rates remained almost unchanged. The steep fall could be explained by a change in drying mechanism from evaporation of free surface water to removal of bound water by diffusion from inside the particles. As nylon has a low water diffusion coefficient of about [10.sup.-12] to [10.sup.-13] [m.sup.2] x [s.sup.-1], desorption of bound water was typically governed by Fickian diffusion (Snaar et al., 1998; Hunt, 1980) and took place very slowly compared to evaporation of free surface water.

[FIGURE 7 OMITTED]

Unlike nylon particles, the drying behaviour of EPS could not be predicted accurately with one single characteristic drying curve for all fluidizing velocities as shown in Figures 3 and 4. This was probably due to the much lower resistance against the transport of bounded water inside the EPS to the particle surface. With low internal resistance, the drying rate depended not only on moisture content but also on the initial drying rate, the temperature and internal structure of the material (Keey, 1978). The internal resistance of nylon was so high that the drying process was largely diffusion-controlled and the rate depended mainly on the moisture content inside the particles. EPS particles are porous and have no sharp transition between constant-rate, capillary- and diffusion-controlled drying periods. In general, it is difficult to predict the falling-rate period of such porous solids as considerations have to be given to the internal distribution of moisture as well as the continual change in temperature of the particles from wet-bulb temperature to dry-bulb temperature (Keey, 1972). By normalizing the drying curve of the single particle instead of the entire bed, Burgschweiger et al. (1999) incorporated the influence of material hygroscopicity in modelling the first drying period.

CONCLUSION

In the drying of non-porous and large Geldart D nylon particles, three theoretical methods were used effectively to predict the constant-rate drying in the complete range of fluidization regimes (fixed bed, bubbling, slugging and turbulent fluidization) in a laboratory scale dryer. Results of Methods 2 and 3 were less sensitive to the accuracy of input parameters as compared with Method 1. In the drying of porous and sticky Geldart B EPS particles, the theoretical methods were able to predict the initial drying rates as long as the bed was completely fluidized. At low fluidizing velocities, the sticky nature of EPS led to bed de-fluidization, which reduced the drying rate probably due to vapour channelling and lower contact surface area. Experimental results showed that both Methods 2 and 3 were able to predict drying rates up to 5.1 x [u.sub.mf] for nylon and 2.9 x [u.sub.mf] for EPS, which were higher than previously reported values of 1.5 x [u.sub.mf] for Method 2 and 3 x [u.sub.mf] for Method 3, respectively. The significance lies in the applicability of these methods to predict drying rates when fluidizing velocities higher than those at bubbling fluidization are used to mitigate against de-fluidization of wet particles.

Using the cross-flow method, it was shown that the bubble phase would not reduce the drying rate predicted by the three theoretical methods in a laboratory fluidized bed. Experimental results agreed well with this prediction.

Using the characteristic drying curve method, a single drying curve obtained experimentally for nylon particles at one fluidizing gas velocity was sufficient to predict qualitatively the falling-rate drying behaviour in different fluidization regimes.

ACKNOWLEDGMENT

The authors are grateful to Seikisui (SEA) Pte Ltd. for providing the industrial polymer samples.

NOMENCLATURE

a exposed surface of solids per unit volume
 [[m.sup.2]/[m.sup.3]]

[c.sub.pa] specific heat capacity of air at constant pressure
 [J/(kg x K)]
[d.sub.b] bubble diameter [m]

[d.sub.p] particle volume diameter (diameter of a sphere having
 the same volume as the particle) [m]

[h.sub.c] convective heat transfer coefficient between particle
 and air stream [J/([m.sup.2] x K x s)]

[j.sub.D] mass transfer j-factor [dimensionless]

[j.sub.H] heat transfer j-factor [dimensionless]

[k.sub.m] true mass transfer coefficient in the dense phase
 [kg/([m.sup.2] x s)]

t time taken [s]

u superficial gas velocity (velocity in empty column)
 [m/s]

[u.sub.b] bubble velocity [m/s]

[u.sub.mf] minimum fluidization velocity [m/s]

A cross-sectional area of fluidized bed [[m.sub.2]]

[D.sub.a] molecular diffusivity of air [[m.sub.2]/s]

H bed height [m]

[H.sub.max] maximum bed height during fluidization [m]

K overall mass transfer coefficient [1/s]

[K.sub.c] mass transfer coefficient between dense phase
 and bubble phase [m/s]

[M.sub.s] dry mass of particles [kg]

N drying rate [kg [H.sub.2]O/(kg solids x s)]

[N.sub.c] drying rate during constant-rate drying period
 [kg [H.sub.2]O/(kg solids x s)]

[Re.sub.p] Reynolds number of flow around particle
 [dimensionless]

[S.sub.c] Schmidt number [dimensionless]

[T.sub.i] temperature of entering air stream [K]

[T.sub.e] temperature of exit air stream [K]

X moisture content [kg [H.sub.2]O/kg solids]

[X.sub.b] cross flow factor [dimensionless]

[X.sub.cr] critical moisture content [kg [H.sub.2]O/kg solids]

[X.sub.eq] moisture content at equilibrium conditions
 [kg [H.sub.2]O/kg solids]

[X.sub.f] normalized moisture content [dimensionless]

Y absolute humidity of air [kg [H.sub.2]O/kg dry air]

[Y.sub.e] absolute humidity of air stream based on adiabatic
 saturation of entry air stream [kg [H.sub.2]O/kg dry air]

[Y.sub.i] absolute humidity of entry air stream [kg [H.sub.2]O/kg
 dry air]

Y(H) absolute humidity of air stream at height
 H [kg [H.sub.2]O/kg solids]

Greek Symbols

[DELTA] [H.sub.vap] heat of vaporization of water [J/kg]

[epsilon] fixed bed porosity [dimensionless]

[[epsilon].sub.mf] bed porosity at minimum fluidization
 [dimensionless]

[[rho].sub.a] air density [kg/[m.sup.3]]

[micro] air dynamic viscosity [Pa x s]

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Wai Kiong Ng (1) * and Reginald B. H. Tan (1,2)

* Author to whom correspondence may be addressed. E-mail address: [email protected]

(1.) Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833

(2.) Department of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

Manuscript received January 27, 2006; revised manuscript received May 31, 2006; accepted for publication August 28, 2006.

Table 1. Fluidization regimes at different velocities
(a) nylon particles

Fluidization velocity Fluidization regime
[m x [s.sup.-1]]

0.41 (0.6 x [u.sub.mf]) Fixed bed

1.70 (2.3 x [u.sub.mf]) Spouting

2.04 (2.8 x [u.sub.mf]) Transition to bubbling

2.55 (3.4 x [u.sub.mf]) Transition from bubbling to turbulent

2.97 (4.0 x [u.sub.mf]) Turbulent

3.40 (4.6 x [u.sub.mf]) Turbulent

3.74 (5.1 x [u.sub.mf]) Turbulent

(b) EPS particles

Fluidization velocity Fluidization regime
[m x [s.sup.-1]]

0.26 ([u.sub.mf]) Fixed bed

0.38 (1.5 x [u.sub.mf]) Bubbling

0.51 (2.0 x [u.sub.mf]) Transition from slugging to turbulent

0.68 (2.6 x [u.sub.mf]) Transition from slugging to turbulent

0.76 (2.9 x [u.sub.mf]) Turbulent