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Food Control 12 (2001) 77±83

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Steady state modelling and simulation of an indirect rotary dryer rquez, Dio genes L. Melo Edgardo R. Canales *, Rodrigo M. Bo Department of Chemical Engineering, University of Concepci on, P.O. Box 160 ± C, Correo 3, Concepci on, Chile Received 2 February 1998; received in revised form 20 June 2000; accepted 20 June 2000

Abstract A steady state model for a ®sh meal indirect pilot plant rotary dryer with steam tubes is developed. The model is based on mass and energy balances and heat transfer constitutive equations. Simulated and experimental results are presented. The moisture condition of ®sh meal predicted by the model agrees satisfactorily with experimental values obtained in the pilot plant dryer within the range of operating conditions explored. Ó 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction Over the years, Chile has consolidated its position in the international market as one of the main ®shing countries. A large part of the ®sh harvest is destined to the production of ®sh meal. During this process, great care is required since the material is submitted to severe thermal conditions that could induce a series of unfavorable deterioration reactions. Then the importance of the drying operation in the quality of the product and in the economic aspect of the elaboration of ®sh meal. Conventional direct rotary dryers have been used in ®sh meal factories, because heat and mass transfer rates are accomplished very e€ectively. However, extended exposure of the product to combustion gases at high temperature (800°C) induced a series of deterioration reactions that a€ected the ®nal quality of the meal. Adsorption of such toxic substances in the gases as NOx can cause the formation of nitrosamines with cancerous properties. Some countries are restricting the use of drying with combustion gases for certain nutritional products (Wilkes, Ponlsen & Green, 1991). Indirect rotary dryers with steam-heated surfaces (tubes, coil, jackets) at low temperature have been introduced in almost all ®sh meal plants in the last 10 years. The drying process occurs in an atmosphere of slightly superheated steam provided from the vapourisation of the water content of the wet solid particles, and some little entrainment of air. Typical drying temperatures are about 96±98°C, and surface temperature of

*

Corresponding author. Tel.: +56-41-204534; fax: +56-41-247491.

heating devices are below 170°C (saturated steam at 6 bar gage as heating medium). In this way, ®sh meal deterioration is avoided and its quality is improved. The objective of the present work is to develop the mass and energy balances for an indirect pilot plant rotary dryer with steam tubes, as well as to quantify the mechanisms of heat and mass transfer, in order to obtain a steady state model for the dryer.

2. Steady state modelling The dryer of the pilot plant is of the indirect type; its main characteristic is the use of both jacket and tubes as heat transfer areas with high pressure saturated steam as the heat source. The dryer is made of stainless steel, with a total length of 3.050 (m), internal diameter of the jacket of 0.497 (m) and 36 tubes of 0.019 (m) of diameter each. See Fig. 1. By means of steady state heat and mass balances within and element of the dryer, a mathematical model is developed assuming that there are no radial temperature and moisture pro®les. The steady state model of the indirect dryer is based on the following assumptions: solids and vapours ¯ow through the dryer in plug ¯ow. Thus the axial displacement velocity of the solid is constant. Solid particles are of uniform size. There are no heat losses to the surroundings. There are negligible temperature gradients in the tubes and jacket walls. There is negligible axial dispersion of solids in the dryer. In order to simplify the modelling of the drying process, the operation is divided in two zones, as can be

0956-7135/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 6 - 7 1 3 5 ( 0 0 ) 0 0 0 2 7 - X

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Nomenclature Aj area of heat transfer of the jacket (m2 ) super®cial area of the solids by volume of Asv dryer (m2 /m3 ) area of heat transfer of the tubes (m2 ) At drag coecient CD heat capacity of vapours (J/kg K) cv cl heat capacity of the liquid water (J/kg K) heat capacity of the solid (J/kg K) cs D dryer internal diameter (m) particle diameter (mm) dp F feed ¯ow of ®sh press cake (kg/s) ¯ow of dry solids (kg/s) Fs f volumetric fraction of solids in the dryer coecient of heat transfer vapour±solid hsv (W/m2 K) coecient of heat transfer jacket±vapour hjv (W/m2 K) htv coecient of heat transfer tubes±vapour (W/m2 K) thermal conductivity of vapours (W/m K) kv L total length of dryer (m) N rotation speed of the dryer (rpm) Nu Nusselt number P ambient pressure of drying (atm) p partial pressure of the steam in vapour phase (atm) Pr Prandtl number saturation pressure of liquid water (atm) psat Psteam pressure of the saturated steam of tubes and jacket (kgf /cm2 )

R Re S s Tv tR Ts Tw Vdryer vv vs vt W Wf wf Wi wi Y z DHvap lv qv qs w

rate of drying (kg water/kg meal s) Reynolds number cross-sectional area of the dryer (m2 ) slope of the dryer (m/m) temperature of the vapour (K) residence time of solids in the dryer (s) temperature of the solid (K) tubes and jacket temperature (K) volume of the dryer (m3 ) axial velocity of vapours (m/s) linear speed of solids (m/s) terminal velocity of particles (m/s) moisture of the ®sh meal (kg water/kg dry solid) ®nal moisture of the ®sh meal (kg water/ kg dry solid) ®nal moisture the ®sh meal (kg water/ kg wet solid) initial moisture of the ®sh press cake (kg water/kg dry solid) initial moisture of the press cake (kg water/ kg wet press cake) molar fraction of the steam in vapour phase (mol steam/mol vapour) local length of dryer (m) enthalpy of vaporization of water at the temperature of the solid (J/kg) viscosity of vapours (kg/m s) density of vapours (kg/m3 ) density of solid particles (kg/m3 ) sphericity of particles

seen in Fig. 2. In the ®rst zone occurs the heating of the ®sh press cake, up to the temperature of drying. It is assumed that during this stage there is no water evaporation from the solids, thus the moisture content of the solids remains constant. In the second zone, the drying of the ®sh press cake occurs. Here, water is evaporated at constant temperature. In this part of the dryer, the water content of the solids reduces until it reaches the required level.

The pressure of the generated vapour due to water evaporation from the solids is considered homogeneous throughout the dryer, thus the temperature of the vapour is uniform along the dryer. Since the dryer is open to the atmosphere at the load and exhaust zones, there is a small quantity of air

Fig. 1. Schematic of the indirect rotatory pilot dryer.

Fig. 2. Temperature and moisture pro®les along the dryer.

E.R. Canales et al. / Food Control 12 (2001) 77±83

79

Fig. 3. Solids movement inside the dryer.

present in the interior of the dryer. Drying occurs in an environment almost entirely composed of slightly superheated steam at ambient pressure. 2.1. Movement of solids The axis of the dryer is inclined at a small angle with respect to the horizontal. The particles advance through the dryer in a series of solid falls and, between falls, sliding at the bottom of the dryer, see Fig. 3. The solids fall is formed in the following way: the particles are captured by longitudinal ®ns in the low part of the dryer and carried to the upper part. The solids fall vertically from the edge of the ®n and descend through the vapour to the bottom of the dryer. In the fall the vapour may drag the particles. The dryer is inclined with respect to the horizontal, so the radial ascend and the vertical fall of the particles produces the advance of the solids along the dryer. Marshall and Friedman (1949) proposed the following correlation for estimating the solids residence time in a rotary dryer: tR ˆ

kL 0:9 N Ds

from which the axial displacement of solids is calculated as vs ˆ L=tR . Constant k is determined experimentally for each particular dryer arrangement. 2.2. Mass and energy balances Consider the schematic presented in Figs. 1, 2 and 4. The model will be developed for the heating and drying zones separately. 2.2.1. Zone I: Heating of solids In this zone, the mass balance is not needed, since there is no variation in the moisture of the solids. The energy balance establishes that heating of the solid along the dryer is caused by the rate of heat transfer from the vapour

Fig. 4. Schematic of heat transfer in the dryer.

dTs hsv  Asv  S ˆ  …Tv ÿ Ts †: dz Fs  …cs ‡ cl  Wi † The mass ¯ow-rate of dry solids is determined from the feed of press cake and its initial moisture, Fs ˆ F =…1 ‡ Wi †. The speci®c surface of solid particles is determined from its diameter and the volumetric fraction of solids within the dryer, which is experimentally measured Asv ˆ

6
f: wdp

From data published by B orquez (1996), the sphericity factor is correlated as wˆ

1 : 1:101 ‡ 414dp

The heat balance is integrated from the initial solid temperature as boundary condition at z ˆ 0, and up to the length at which the solids reach the saturation temperature, as will be next explained, point at which drying begins. The boundary between the heating zone and the drying zone is so determined. 2.2.2. Zone II: Drying of the ®sh press cake 2.2.2.1. Energy balance in the solid (Parodi, 1992). When stating the energy balance, it is considered that the vapour gives sensible heat to the solids. It receives sensible heat from the tubes and jacket, and latent heat by vapourisation of the water at the solids temperature, see Fig. 4. The heat transfer from the steam to the vapour is accomplished in parallel form through tubes and jacket walls, while the heat transferred to solids is accomplished by means of the vapour only. Interactions between solids and heating walls are neglected as heat transfer mechanism.

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It is assumed that the wall temperature of the heating surfaces corresponds to the saturation temperature of the condensing steam within tubes and jacket, Psteam ˆ psat …Tw †, because the heat transfer coecient by steam condensation is very high as compared to the tubes±vapour heat transfer coecient. This energy balance in di€erential form also holds in Zone I, heating of solids, but with the last term excluded. As mentioned before, drying occurs at ambient pressure in a vapour phase with a small fraction of air. The super®cial temperature reached by the solid particles corresponds to the saturation temperature of water vapourising at its partial pressure

where the drag coecient CD is found from well-known relationships. Tubes±vapour heat transfer coecient: Heat transfer occurs between tubes that rotate around the axis of the dryer and vapours that move slowly along the dryer. For ¯ow against circular cylinders, the heat transfer coecient is calculated from correlations presented by Bejan (1993). Characteristic length is the outside diameter of tubes, and characteristic velocity is the linear speed of rotation of tubes. Heat transfer coecient between vapours and jacket is calculated from the correlation of Seider and Tate (1936) for internal ¯ow along a circular cylinder, and the characteristic parameters are the internal diameter of the dryer and the axial velocity of vapour calculated from the ¯ow of vapourised water

p ˆ P  Y ˆ psat …Ts †:

v v ˆ Fs

hsv  Asv  Vdryer  …Tv ÿ Ts † ˆ …htv  At ‡ hjv  Aj †  …Tw ÿ Tv † ‡ Fs  DHvap  …Wi ÿ Wf †:

(a) Heat transfer by conduction. The heat transferred to solids by conduction is assumed to be negligible as compared to convective transfer, on the grounds that the surface area available for conductive transfer, namely particle contact with tubes, ®ns, and jacket, and also particle-to-particle collisions, is small. Convective transfer is assumed to occur over the entire surface area of solid particles. For a particle size of 1 mm, the estimated exposed surface area of all particles is about 75 m2 . Heating surface areas of all tubes and jacket account for 11.7 m2 . E€ective surface area for conductive heat transfer should even be less than this last ®gure. (b) Heat transfer by convection Vapour±solids heat transfer coecient: The heat transfer coecient between an isothermal surface of a falling sphere and a free isothermal ¯ow of ¯uid, as proposed by Whitaker (1972), is used. Nu ˆ 2 ‡ …0:4Re1=2 ‡ 0:06Re2=3 †Pr0:4 ; where dp ; kv q Re ˆ dp vt v ; lv lv Pr ˆ cv : kv

Nu ˆ hsv

This correlation applies in a wide range of operative conditions (3:5 < Re < 76; 000 and 0:71 < Pr < 380). The terminal velocity of falling particles is found from the force balance between the apparent weight of particles and the drag force exerted by the vapour on its surface v2t ˆ

4 d p g q s ÿ qv
; qv 3 CD

Wi ÿ Wf : qv S

2.2.2.2. Mass balance in the solid. The decrease of solid moisture along the dryer is due to the rate of drying of the particles dW R ˆÿ : dz vs This equation is solved beyond Zone I, from the initial solid moisture and up to the end of the dryer. (a) Rate of drying. Period of constant drying rate (Perry, 1988; Treybal, 1988). The press cake that enters the dryer is previously cooked and pressed, presenting a ®brous structure with free water entrained that would permit an extended period of constant rate of drying, that can be represented as Rˆÿ

hvs  Asv  …Tv ÿ Ts †: qv  DHvap

Drying occurs at constant saturation temperature Ts , and the rate of water vapourisation corresponds to the rate of heat transfer from vapour to solid particles. 3. Results and discussion The simulation of the indirect rotary dryer is accomplished for di€erent operating conditions, a base case is taken and the output variables (®nal moisture of ®sh meal, temperature of solids and vapours, heat transfer coecients) are plotted against the operation variables (¯ow and moisture of ®sh press cake, particle diameter, pressure of the saturated steam, speed of rotation, slope of the dryer). The simulation is carried out for the following conditions as base case: speed of rotation of dryer, N ˆ 38 (rpm); initial moisture of ®sh press cake, Wi ˆ 0:48

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Table 1 Comparison between experimental and simulated ®nal moistures in the drying of ®sh press cake Run

A B

Experimental values

Model wf (%)

F (kg/s)

Psteam (kg/cm2 )

wi (%)

wf (%)

0.02 0.03

5.0 3.0

49.0 48.0

17.5 32.0

(kg water/kg wet solid); molar fraction of steam in vapour phase, Y ˆ 0:95 (mol steam/mol vapour); slope of the dryer, s ˆ 0:02 (m/m); volumetric fraction of solids in the dryer, f ˆ 0:02; particle diameter, dp ˆ 1 mm; feed of press cake, F ˆ 0:023 kg=s; saturated steam pressure, Psteam ˆ 3:5 kgf =cm2 . Upon comparing ®nal moistures predicted by the model with experimental values obtained in the pilot dryer, it is seen in Table 1 that observed moistures are higher than predicted ones. These di€erences can be partially explained because an important fraction of the material fed to the pilot dryer is in the form of lumps with a diameter that greatly exceeds the diameter of uniformly sized particles as considered in the model. This leads to a decrease in the overall rate of drying in the actual process, because of the smaller super®cial exposed area, and also a longer water di€usion path from the interior of the lumps. The results is a ®nal product with greater water content in its interior, as was experimentally proven. Additionally, fouling produced in tubes and jacket of the dryer by the wet material decrease the coecients of heat transfer between the heating surfaces and the vapour, and as a consequence in the rate of drying. The model did not consider fouling e€ects at this stage. Discrepancies between model predictions and experimental results may also be attributed to phenomenological simpli®cation of the model that overestimate the rate of drying. First, the actual dryer certainly presents a degree of axial mixing of solids as the particles fall from the tip of the ®ns and slide along the dryer. This behaviour was observed during start-up and shut-down of the equipment. Unfortunately, there is no available information for e€ective dispersion coecients of ®sh meal in rotary dryers, and the dispersion mechanisms of heat and mass transfer were not considered in the model. As pointed out by Himmelblau and Bischo€ (1968), the plug ¯ow model predicts the best performance, whereas dispersion reduces process eciency. Secondly, it is assumed that particles fall at its terminal velocity, while in fact they must accelerate their motion from rest until they reach settling equilibrium, and in the average their velocity of falling becomes less than that of free sedimentation. As a consequence the vapour±solids heat transfer coecient becomes somewhat overestimated and so the rate of drying.

11.0 26.0

Even when the model could be corrected considering some of the aspects discussed above ± particle size distribution, fouling factors, dispersion mechanisms, and average falling velocity of particles ± so to approximate predicted results to experimental values in Table 1, the purpose of this work was to develop a simple model that would help to explain the e€ect of di€erent conditions of operation on dryer responses (Cartes, 1996). These are next discussed. Fig. 5 shows the e€ect of feed rate of press cake that enters the dryer on the ®nal moisture of the meal. The moisture trend is to increase with the increase of the ¯ow of press cake. As the ¯ow of press cake becomes larger, the quantity of solids circulating in the dryer is augmented, provoking an inecient drying. And a decrease in the ¯ow of press cake reduces the quantity of wet solids inside the dryer, producing a better drying. This can be explained considering the drying capacity of the dryer, i.e., the heat transfer surface of the equipment is designed to evaporate a prescribed amount of water, and a higher feed of wet solids would result in a higher moisture content in the exit meal. Fig. 6 shows the e€ect of particle diameter on the ®nal moisture of meal. A clear trend to reduce the moisture when the diameter decreases is observed, for example, for a diameter of 1 (mm), the moisture is 0.14 (kg water/kg dry solid), while for a particle diameter of 2 (mm), the moisture reaches 0.23 (kg water/kg dry

Fig. 5. Simulated ®nal moisture of ®sh meal with respect to feed of ®sh press cake.

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Fig. 6. Simulated ®nal moisture of ®sh meal with respect to particle diameter.

solid), representing a variation of 64% in the quantity of water content in the meal. The increase in particle diameter beyond 3 (mm) does not provoke a drastic increase in moisture, and approaches an asymptotic value of 0.32 (kg water/kg dry solid). This is due to the fact that the exposed evaporating surface decreases with larger particle diameter. Calculation results show that the super®cial area of solids changes from 130 (m2 /m3 of dryer) for a particle diameter of 0.5 mm, to 40 (m2 /m3 of dryer) for a particle diameter of 4 mm, and remains almost unchanged for larger particles. Furthermore, the vapour±solid heat transfer coecient also decreases with particle size, from about 105 (W/m2 K) to a constant value of 40 (W/m2 K), when the particle diameter increases to 4 mm. As a consequence, the reduction of transferred heat originates an augmented moisture of ®nal product as the particle size becomes larger. The e€ect of pressure of the saturated steam through tubes and jacket on the ®nal moisture of meal is presented in Fig. 7. As expected, an increase in the pressure of the saturated steam decreases the moisture of the meal. This increase in pressure of the steam rises the temperature of tubes and jacket, enlarges the temperature di€erence available for heat transfer and generates a boost in the rate of drying. For example, for a pressure of the saturated steam of 3.0 (kgf /cm2 ), the meal reaches a ®nal moisture of 0.17 (kg water/kg dry solid), while for a pressure of the saturated steam of 4.0(kgf /cm2 ), a moisture of 0.12 (kg water/kg dry solid) is reached, representing a decrease of water content of 29% in the meal. The heat transfer coecient between tubes and vapours ranges from 23 to 30 W/m2 K, and is much less than the heat transfer coecient of condensing steam inside the tubes ± typical values are 3000±10,000 W/m2 K ± so the assumption that heating surfaces are at the saturation temperature of the steam becomes very realistic. The e€ect of air content in the vapour on the moisture of meal is not meaningful, due to the fact that the rate of

Fig. 7. Simulated ®nal moisture of ®sh meal with respect to steam gage pressure.

drying remains almost constant. In spite of the fact that temperatures of solids and vapour do not stay constant, and its temperature di€erence increases mildly with the increase of air (see Fig. 9), the vapour±solid coecient of heat transfer decreases also mildly with the increase of air content, and therefore the rate of drying stay constant. Fig. 8 presents the e€ect of the saturated steam pressure in tubes and jacket on the exit temperature of solids and vapour. The temperature of solids is independent of pressure of the saturated steam, and corresponds to the saturation temperature at the system pressure. On the other hand, the temperature of the vapour is established from a heat balance between the heating surfaces and the hot solids. The model predicts well the behaviour of this variable, since upon increasing the pressure of the saturated steam the temperature of vapours increases.

Fig. 8. Simulated solids and vapour temperature with respect to steam pressure.

E.R. Canales et al. / Food Control 12 (2001) 77±83

Fig. 9. Simulated solids and vapour temperature with respect to the molar fraction of steam in the vapour.

Fig. 9 shows the behaviour of the temperature of solids and vapours with respect to the molar fraction of steam in the vapour. The temperature that reaches the solids, as was already mentioned, corresponds to the saturation temperature of water at its partial pressure, and only depends of the quantity of air present in the vapour. It can be observed in Fig. 9 that as the solids are inmersed in an atmosphere thoroughly of steam, their temperature approaches the boiling temperature. The temperature of vapours also increases with an increase in the steam content, because of the increase of the coecients of heat transfer, generated by higher values of the physical properties. Also from Fig. 9 it can be said that the model predicts vapour temperatures which are higher to measured values observed in this type of dryers. This discrepancy may be explained as follows: the heat transfer coecient has been estimated from correlations for ¯ow around a sphere, but for particles of irregular shape, the heat transfer coecient increases by a factor of 1.6±2.3 due to a higher degree of turbulence around the particle (VDI-Warmeatlas, 1991). Consequently, the temperature of vapours should drop in order to maintain the heat balance. As an additional result, the model predicts a mild decrease of temperature of vapours with the increase in the ¯ow of press cake, explained by the increase of the quantity of solids circulating inside the dryer. 4. Conclusions A simple mathematical model of a pilot plant indirect rotary dryer has been developed, based on fundamental

83

principles such as plug ¯ow of both solid particles and water vapours, and drying occurring at constant rate. The model neglects axial dispersion of solids, temperature and moisture gradients within the solid particles, and particle size distribution. Steady state heat and mass balances are written ®rst for a heating zone of solids, and next for a drying zone. Predicted values of ®nal moisture of ®sh meal given by the model agree fairly well with measured experimental values, but observed ®nal moistures are higher than model predictions. The discrepancies are attributed to the simplifying assumptions, and a corrected model should include more realistic phenomena, namely: size distribution of solids, fouling resistance to heat transfer in heating surfaces, unsteady settling velocity of falling particles, and increased solid±vapour heat transfer coecient for particles of irregular shape. The model proves to be a useful tool to predict dryer behaviour. Final moisture of ®sh meal is the main response of interest, and decreases strongly with smaller particle diameter, with lower feed of press cake to the dryer, and with higher temperature of the heating medium. The model can even be improved if axial dispersion of solids is taken into account. This parameter must be determined performing appropriate experiments in the pilot dryer.

References Bejan, A. (1993). Heat transfer (1st. ed.). New York: Wiley. B orquez, R. (1996). Modeling of protein ®sh nutrient retention during drying and storage. Ph.D. Thesis, University of Concepci on. Cartes, H. (1996). Steady state modeling and simulation of a pilot plant indirect rotary dryer. Chemical Engineer Thesis, University of Concepci on. Himmelblau, D., & Bischo€, R. (1968). Process analysis and simulation. Deterministic systems. New York: Wiley. Marshall, Jr., & Friedman, S. (1949). Chemical Engineering Progress, 45, 482±573. Parodi, C. (1992). Steady state modelling of an indirect rotary dryer. Chemical Engineer Thesis, University of Santiago. Perry, R. (1988). Chemical engineers' handbook (5th. ed.). Mexico: Mc Graw-Hill, 5(20), 10±15. Treybal, R. (1988). Mass transfer operations. Mexico: Mc Graw-Hill. VDI-Warmeatlas (1991). VDI-Verlag, Sechste Au¯age, Gh1 1, Dusseldorf. Whitaker, S. (1972). AIChE Journal, (18), 361±371. Wilkes, K., Ponlsen, K. P., & Green, E., (1991). Direct drying of foods with natural gas as fuel. Institution of Chemical Engineers, Trans. I. Chem. E., 69(C), 182±188.