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Drying 2004 – Proceedings of the 14th International Drying Symposium (IDS 2004) São Paulo, Brazil, 22-25 August 2004, vol. A, pp. 129-136 FLUIDIZED BED DRYING: INFLUENCE OF DISPERSION AND TRANSPORT PHENOMENA Mirko Peglow¹, Stefan Heinrich¹, Evangelos Tsotsas2 and Lothar Mörl¹ Otto-von-Guericke-University, Universitätsplatz 2, 39106 Magdeburg, Germany 1. Institute of Process Equipment and Environmental Technology E-mail: stefan.heinrich@vst.uni-magdeburg.de, mirko.peglow@vst.uni-magdeburg.de 2. Institute of Process Engineering Keywords: fluidised bed drying, dispersion, sherwood number, nusselt number ABSTRACT A model for fluidised bed (FB) drying is presented. The model is based on a simple two phase approach which distinguishes between a suspension phase and a bypass phase. To investigate the influence of backmixing effects in the gas phase caused by turbulences, dispersion coefficients are used. Therewith the complete range from ideal plug flow to total backmixing behaviour can be simulated and the influence of non ideal backmixing for different simulation scenarios can be analysed. INTRODUCTION While bubbling fluidised beds provide favourable conditions for a number of separation or reactive processes, the performance of such processes is influenced and may be limited by the distribution and mixing of fluid and solids in the bed, and by transport phenomena. Particle-to-fluid heat and mass transfer coefficients which may appear to be much smaller than respective values for the single particle are one well-known expression of this influence. Indeed, it could be demonstrated by Groenewold and Tsotsas (1999) that too low transfer coefficients can be explained on the basis of suspension gas backmixing, and the performance of fluidised bed evaporators and dryers can be predicted accurately, without any fitting. However, the approach of these authors is semi-empirical, it implements – directly or in effective transfer coefficients – only limiting cases of dispersion. On the other hand, models for spray fluidised bed processes like granulation, coating or agglomeration – as those developed by Heinrich, Mörl and co- workers (2002) – use finite dispersion coefficients for the solids, and need such dispersion coefficients in order to properly describe the spatial distribution of particles with a wet surface. In the same models, plug flow is assumed for the gas. Successful fluidised bed reactor models by Artlich et al. (1998) take finite dispersion of both, the solids and the fluid, into account, but neglect fluid-to-particle mass and heat transfer resistances. 129 The aim of this study is to develop a generic model which takes into account dispersion in all phases as well as mass transfer resistance. Due to the model assumptions of normalised drying curve after van Meel, (1958) heat transfer will be neglected. MODELING Previous approaches To investigate backmixing effects in FB drying, Groenewold et al. (1999) introduced an apparent Sherwood number. From the equivalence of efficiency for perfect backmixing and ideal plug flow NTU CSTR (1) 1 − exp ( − NTU PFTR ) = 1 + NTU CSTR an apparent Sherwood number was derived Re0Sc Sh A H (2) Sh app = ln 1 + PFTR V Bed A V H Bed Re0Sc applying the definition of the number of transfer units (NTU) to equation (1) Sh A V H Bed (3) NTU = . Re0Sc The result of this transformation is that a backmixing effect is introduced into the drying kinetics. Using this Sherwood number in a plug flow model, a perfect backmixing can be obtained, which can be used to predict the first and second drying period at low Reynolds numbers (see Groenewold et al., 1997). Assumptions The new model is applied for batch drying processes. It is based on a simple two-phase-approach with an active bypass as it is shown in Figure 1 (see Groenewold et al., 1997). The assumptions for the model are: • The bypass fraction is independent of bed height. • A number of transfer units ( NTU SB ) describes the mass transfer between suspension and bypass phase. • The mass transfer between particle and gas bulk is given by the real Sherwood number, which tends to a finite value at low Reynolds numbers. This Sherwood number is calculated after Gnielinski (1980). • Backmixing effects in all phases caused by turbulences are considered by axial dispersion coefficients. The radial dispersion is neglected. • The concept of the normalized drying curve (van Meel et al., 1958) is used to describe the falling drying rate in the 2nd Figure 1. Two-phase-model. drying period. Balances To describe the drying process for the first and second drying period, three states have to be taken into account. The three following equations can be derived by balance in a differential volume element. • Air humidity in suspension phase ∂YS ∂ 2 YS m DryAir ∂Y 1 dz 1 dz (4) = DS + − S dz + NTU PS ( YSat − YS ) υ − NTUSB ( YS − YB ) ∂t ∂z 2 dm DryAir ∂z 1− ν H Bed 1 − ν H Bed 130 • Air humidity in bypass phase ∂YB ∂ 2 YB m DryAir ∂Y 1 dz (5) = DB + − B dz + NTU SB ( YS − YB ) ∂t ∂z 2 dm DryAir ∂z 1− ν H Bed • Particle moisture content ∂X ∂ 2X m 1 dz (6) = D P 2 − DryAir NTU PS ( YSat − YS ) υ ∂t ∂z dm P 1 − ν H Bed Boundary conditions of first kind at the inlet and at the outlet ∂YS ∂Y ∂YS ∂Y (7) = B =0 = B =0 ∂z z =0 ∂z z =0 ∂z z = HBed ∂z z = HBed are used. The humidity of suspension gas and bypass gas weighed with bypass fraction gives the humidity of air at the outlet Y out = (1 − ν ) YSout + νYB . out (8) The equations to calculate the fluid dynamic and mass transfer are given in the appendix. SIMULATION Numerical Solution The Method-of-Lines transforms the partial differential equations (4)-(6) into ordinary equations using finite differences in space domain. This system was embedded in a Runge-Kutta-procedure of 4th order using an adaptive step size control in form of a full/half step strategy. Due to the fact, that in the first drying period the states of suspension and bypass humidity are in a steady state, equations (4) and (5) were set to zero and the particle moisture balance was neglected. The obtained non-linear equations, used for parameter studies for the first drying period, were solved using the Levenberg-Marquardt-Method. Analytical Solution To get an analytical solution the drying efficiency is introduced defined as Y out − Y in (9) η= . YSat − Y in The total efficiency of a two-phase-model is obtained by summation of the single efficiency of suspension and bypass, weighed with bypass fraction η = (1 − ν ) ηS + νηB . (10) To obtain an analytical solution the model of inactive bypass has to be assumed, where the efficiency of the bypass is always zero. Therefore the following equations are obtained to describe ideal plug flow resp. total backmixing behaviour NTU NTU (11) ηPFTR = (1 − ν ) 1 − exp − , ηCSTR = (1 − ν ) . 1− ν 1 − ν + NTU To represent the effects of backmixing, bubble behaviour as well mass transfer from suspension to bubble gas an additional plot is used. Therefore the determined efficiency can always be applied on a simple (homogeneous) plug flow model, as it is written in equation (12) η = 1 − exp ( − NTU ) . (12) Out of this consideration a Sherwood number can be calculated, which fits the mass transfer to the previously given drying efficiency in the simple plug flow model. This Sherwood number is defined as Re0Sc (13) Sh Plug = − ln (1 − η) . A V H Bed 131 The analytical solutions for both limiting cases are plotted in Figure 2 for a bypass fraction of ν = 0 and ν = 0.2 . It is assumed, that the coefficient (AV/Hbed)/Sc in equation (13) is 20 and the “real“ Sherwood number, following the requirements mentioned above, is independent of the Reynolds number and has a constant value of Sh = 20 . The plots show that a system with total backmixing has a lower efficiency than the ideal plug flow. For plug flow the efficiency of suspensions phase achieves at high NTU numbers (>10) a value of 1, wherewith the total efficiency is decreased by bypass fraction. For high Reynolds numbers (small NTU numbers) a plug flow system and a system with total backmixing have the same efficiency. For systems with high efficiency (close to 1) the difference between different models comes out by conversion of efficiency to the Sherwood number. Figure 2. Numerical solution for PFTR and CSTR . Testing the model – Analytical solution vs. numerical solution In order to check the quality of the numerical solution, simulation Table 1: Simulation Parameter. results for a system with ideal plug flow (DS = 0) and a system with Parameter total backmixing (DS → ∞ ) were compared with the analytical mBed [ kg ] 1 solutions given in equation (11). The mass flux was changed in a range from the minimal fluidisation (Re0 = 33) up to the discharge dP [ mm ] 1 point (Re0 = 275). Further simulation parameters are given in Table ρP [ kg / m³] 2000 1. The comparison of the results is shown in Figure 3. It comes out d App [ mm ] 200 that the model can predict CSTR behaviour correctly by choosing an adequate value for the dispersion coefficient. To analyse the X0 [ kg / kg ] 0.2 influence of the dispersion coefficient in the suspension phase, X crit [ kg / kg ] 0.1 further simulations were done by changing the dispersion in a range of DS = 0 – 50 m²/s keeping the fluidisation velocity constant. The X hyg [ kg / kg ] 0 results for minimal fluidisation and discharge point are shown in Y in [ kg / kg ] 0.01 Figure 4. At low Reynolds numbers a dispersion of DS = 1 m²/s results in a total backmixing, while at high Reynolds numbers close ϑ in [°C ] 50 to the discharge point a dispersion of DS = 20 m²/s is necessary to DP m2 / s 0.5 produce ideal CSTR behaviour. Based on these results the following simulations were done with the DB [ −] 0 dispersion coefficients given in Table 2. NTU SB [ −] 0 Table 2: Variation of Dispersion. ν [ −] 0.2 mDryAir 0.02- DS m 2 / s 0 0.1 0.5 1 2 5 10 20 50 [ kg / s ] 0.16 132 Figure 3. Numerical solution vs. analytical solution for PFTR and CSTR. Figure 4. Variation of dispersion coefficient at fluidisation and discharge point. Parameter variation – Standard case Figure 5. Standard case (parameters see Table 1). The simulation results with the parameters given in Table 1 are plotted in Figure 5. For all simulations the total efficiency vs. NTU number, the Reynolds number vs. Sherwood number for simple plug flow and the Reynolds number vs. the relative change of Sherwood are shown. For low Reynolds numbers at fluidisation point the influence of backmixing on the mass transfer is low. The value of Sherwood is in a range of 2 to 4 and has a maximal relative change of less then 15 %, while the efficiency differs about 5 %. At high Reynolds numbers (low NTU) the difference between ideal backmixing and plug flow is evident. Small dispersion coefficients have no effect on Sherwood. Only for a dispersion coefficient 133 higher than 2 m²/s the behaviour changes articulately from ideal plug flow, while the mass transfer worsens about 40 %. Parameter variation – Influence of bed mass Figure 6. Variation of bed mass ( mBed = 2 kg, parameters see Table 1). In this simulation the bed mass was increased to mBed = 2 kg. Therefore a two times higher NTU number was obtained. The results are plotted in Figure 6. The results show, that for low Reynolds numbers and large values for NTU the backmixing has a low influence on Sherwood. In this range the relative change of Sherwood is less than 10 %. This is caused by the large mass transfer surface, which leads to a total saturation of suspension gas for plug flow as well as total backmixing. The variation of dispersion has a low effect on Sherwood, which has a value of about 2. Finally the abatement of Sherwood is caused by the inactive bypass, which dominates the total efficiency of the system. For high Reynolds numbers an evident effect of non-ideal backmixing exists analogue to the results of standard simulation. Parameter variation – Influence of NTU suspension – bypass Figure 7. Variation of NTU suspension – bypass ( NTU SB = 1 , parameters see Table 1). In this simulation the model of inactive bypass was transformed into an active bypass model by setting NTU for mass transport between suspension gas and bubbles to 1. For high NTU numbers the total efficiency of the system is almost 100 %, which means, that the influence of bypass is neglect able or in both phases the humidity of air is equal. It is obvious, that a small value of the backmixing coefficient decreases the Sherwood number for plug flow at 40 %. Parameter variation – Influence of bypass fraction In this simulation the bypass fraction was decreased from 20 % to 10 %. In consequence the efficiency rises for ideal plug flow and high NTU numbers to 90 %. These results are very similar to the standard simulation, however Sherwood values are a bit higher. 134 Figure 8. Variation of bypass fraction ( ν = 0.1 , parameters see Table 1) Simulation of first and second drying period For the set of parameters given in Table 1 under variation of dispersion coefficients the complete drying process was simulated. Mass flux of dry fluidisation gas was set to m DryAir = 0.1 kg/s. The second drying period is characterised by a constant falling normalized drying rate. The results of this simulation are plotted in two different manners. At first the simulated drying curve vs. process time and in a second diagram the specific evaporation rate vs. particle moisture content is plotted. Increasing backmixing causes a decreasing of drying rate. For the complete drying process no further simulations were done. Figure 9. First and second drying period ( mDryAir = 0.1 kg/s, parameters see Table 1). CONCLUSIONS Based on previous approaches a generic model was derived to investigate the influence of backmixing effects in gas phase on fluidised bed drying. With the help of the model, regarding the simplifying model assumptions mentioned above, the limiting cases of ideal plug flow and total backmixing can be reproduced as well as simulation scenarios of non-ideal backmixing. Especially the influence of backmixing effects in suspension phase were investigated in the framework of this study. For active bypass the influence of backmixing becomes more important due to the higher efficiencies achieved. Experimental data has to be compared of the simulation results to check the model. NOTATION A surface area m² D dispersion coefficient m2 / s 135 dm differential mass kg H height m m mass flux kg / s Re Reynolds number − Sc Schmidt number − Sh Sherwood number − t time s X particle moisture content kg / kg Y air humidity kg / kg z length coordinate m Greek Symbols ϑ temperature °C ν bubble fraction − υ normalized drying rate of single particle − Subscripts Superscripts app apparent in inlet B bypass phase out outlet Bed fluidized bed Crit critical CSTR continuous stirred tank reactor hyg hygroscopic P particle PFTR plug flow tubular reactor PS particle-suspension S suspension phase Sat saturation SB suspension-bypass V Volume 0 superficial LITERATURE Artlich, S., Hartge, E.-U., Werther, J. 1998. Simulation of 2-D Temperature Distributions in Fluidized Bed Reactors for Highly Exothermic Reactions, Ind. Eng. Chem. Res. no. 37, pp. 782-792. Groenewold, H., Tsotsas, E. 1998. Predicting apparent Sherwood numbers for fluidised beds, IDS 98, Vol. A, pp. 192-199. Groenewold, H., Tsotsas, E. 1997. A new model for fluid bed drying, Drying Technology, Vol. 15, pp. 1687-1698. Gnielinski, V. 1980. Wärme- und Stoffübergang in Festbetten, Chemie-Ingenieur-Technik, no. 52, pp. 228-236. Heinrich, S., Peglow, M., Ihlow, M., Henneberg, M., Mörl, L. 2002. Analysis of the start-up process in continuous fluidized bed spray granulation by population balance modelling, Chemical Engineering Science, Vol. 57 no. 20, pp. 4369-4390. van Meel, D. 1958. Adiabatic convection batch drying with re-circulation of air, Chemical Engineering Science, No. 9, pp. 36-44. 136