The drying of grain in dryers of a crossflow moving bed type was theoretically and excerimentally studied. Two different duer configurations were analyzed. a.
DRYING TECHNOLOGY. 16(9& 10). 1999-2015 (1998)
MODELING AND SIMULATION OF CROSSFLOW MOVING BED GRAIN DRYERS
N. ~6rrez'. M. Gustafsson', A. Schreil' and J. Martinez' 1 Dept. of Chemical Engineering and Technology, Royal Institute of Technology S- 10044 Stockholm, Sweden 2 Facultad de Ingenieria Quimica, Universidad Nacional de Ingenieria Apartado 5595, Managua, Nicaragua
Key Words and Phrases: crop drying; dryer design ABSTRACT The drying of grain in dryers of a crossflow moving bed type was theoretically and excerimentally studied. Two different duer configurations were analyzed. a drver Gith centrdkr distribution and another wilh multl'ole air ducts. ~xoenmental in~ormallunwas obtained in p~lot-sizedryers A mathem;ticnl model lo rikulalc llx process was developed Hindered drylng u;l\ accounrerl lor by uslng the conccpl of relative drvine r a t e . - ~ adiustable n fact06 s~ecificto the drver8. wasised to account for the un~er(~>nt~es of the>ontacl area nnd'the umsfer c&ffic~ents mcountercd in the literature. Agreement between ex~rimentalrcsulls and simul.!lions WL. farly eood. Simulatiins showed that distance between inlet air and outlet devices. air to solid flow ratlo and dryer height to crurs seclion muo havc great ~nflucnceon the process The mathematicd model may be a uceful tool for process explor~tionand optimization of this type of dryers
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INTRODUCTION Crossflow moving bed dryers are frequently used to process grain in Nicaragua. These are convective dryers wilh grain falling by gravity in contact with a stream o f hot air. There are two main air supply configurations: one with central air distribution and another with multiple inlet and outlet air ducls. These dryers offer
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the advantages of a simple mechanical design, easy maintenance and flexibility to dry different grains. Unfortunately, these dryers are often old and work inefficiently, from both an energy consumption an&a product quality point of view. For these reasons, it would be desirable to optimize the drying process to achieve savings of energy, good product quality and a reduction of operational costs. Considerable work has k e n devoted to grain dryer simulation. Douglas et al. (1994) reviewed the work performed on deep-bed grain drying and developed a distributed panmeter model to simulate the process. Recently. Mom Lima et al. (1996) developed a two-phase model for grain drying in a crossflow sliding bed dryer that was used to estimate of the ovenll volumeuic transfer coefficients. Bmozo et al. (1996) modeled the drying of soybean seeds in a crossflow moving bed dryer. Sun et al. (1991, 1992) modeled air flow and heat and moisture transfer between two channels in an industrial corn dryer. They concluded that air from an inlet channel is distributed in downward and upward directions. The same was observed by Ohlsson (1994) in experiments performed with colored smoke. This fact has not been considered in previous models to describe heat and mass transfer in the dryer. Chaabouni et al. (1992) studied the flow of particles in industrial single-pass grain dryers. They found that a kinematic two-dimensional model gave a good prediction of residence time dispersion. The objective of this work was to develop and experimentally verify a model which included the effects of gas flow in crossflow moving bed dryers, as well as to examine the influence of the main design parameters on the dlying of grain in this kind of equipment.
THEORY A mathematical model lo simulate dryers must express the heat and mass transfer
between falling grain and crossflowing air. This demands development of two types of models: a material model to predict the equilibrium and kinetics of the material of interest and an equipment model that describes the flow and residence times of the solid and gas in the dryer, as well as the mass and heat transfer coefficients.
CROSSFLOW MOVING BED GRAIN DRYERS Configuration of the Dryers The two types of moving-bed dryers that were studied are shown schematically in Figure 1. The main difference between the dryers is the manner in which the air is distributed. The first dryer is based on the principle of a multitude of inlet and outlet air ducts located across the column. These ducts have an inverted v-shaped cross section. Every other row of ducts is an inlet row, and every other an outlet row. The ends of the inlet ducts and the beginnings of the outlet ducts are sealed. Air flows from an inlet row into the grain and leaves the column through the rows of outlet ducts located below and above. In the second type of dryer, hot air is distributed by vents from the central pan of the dryer to the grains, which fall by gravity through two lateral compartments. After contact with the solids, air leaves the dryer by vents located at the external surfaces of the lateral compamnents. In both dryers, solids may he recycled if moisture content of the grains is not reduced to the required level in a single cycle. Mathematical Model In order to obtain a manageable model for the drying process, the complex gas and solids flow patterns can he simplified by identifying a single functional unit, such as those described in Figure 2, in the active zone of the dryers. The basic assumption is that air from an inlet device is split into two streams, one of which leaves the dryer through the outlet immediately above, while the other flows downwards and abandons the dryer through the lower outlet device. To rake into consideration minor air streams that can pass the outlet ducts placed directly in the vicinity of a given inlet duct and mix with air from ducts located far away, is not difficult. However, these effects are not important since the air main s u e a m coming from above or below will counteract distant air backmixing. In spite of the different configurations in this idealized
both dryers may be regarded as
formed by a sequence of the same basic unit (Figure 3). This unit or section is divided into two subsections: an upper one with solids falling in counter-current with respect to gas and a lower one with c o w r e n t flows
a) Multiple air ducts (MAD)
b) Cenual air distribution (CAD)
FIGURE I . Schematic description of the dryers
o =air inlet x
= air outlet
a) Multiple air ducts (MAD)
b) Central air distribution (CAD)
FIGURE 2. Schematic description of the dryers, functional units
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FIGURE 3. Idealized scheme of the dryers
between the phases. The total height of the dryer is thus comprised of n sections numbered from I at the top to n at the bottom. The section numbered 0 represents the elevator used to recycle the grain. The elevator can also be regarded as an active pan of the dryer. Because of the symmetry, in this sequence of sections only the half of the dryer with central air distribution is considered. The sections of the dryer with multiple v-shaped ducts may be defined either as the space between two successive individual ducts or as the space between two rows. Since the cross
section of the dryers is not uniform, an equivalent value can be estimated as the real volume of the dryers corrected for the volume occupied by the ducts divided by the distance between two vertical inlet ducts. The case is really three-dimensional, but the main changes occur vertically. The assumption that residence time in the active part of the dryer is the same for all grains is another important simplification of the model. It is equivalent to neglecting the longitudinal dispersion of the solids. This condition is not really satisfied if the height of the dryer is such that the required final moisture is achieved after passing through the dryer once. On the other hand, in units recycling solids, residence times of the particles will become uniform after only a few cycles. This has been demonstrated experimentally by Gustaffsson and Schreil (1996). Mass and Energy Balances A mass balance in the volume element shown in Figure 3 leads to the following expression for the transfer of humidity between the phases:
M X = - VdY
(1)
where V and L are flows of dry air and dry solids, respectively and Y and X are moisture contents of the phases expressed on a dry basis. Changes in liquid content of the solids with respect to z are also related to evaporation rate from the surface of the solids in contact with the hot air stream. as follows:
where a is specific area of the grain per volume bed, S is cross section of the volume element and N, is evaporation flux. By utilizing equation I . it is possible lo obtain a similar expression to describe the changes in moisture content of the gaseous stream, as follows:
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Temperature changes in both p h a m may be obtained from the energy balances. For the solids, it may be written as
where T, is moist solid temperature, q, is heat transferred from the air by convection, h is water heat of vaporization and C is specific heat capacity. The subscripts w and s denote water in liquid phase and dry solids, respectively. The corresponding expression for the gaseous phase is
where ql is heat dissipated into the environment from the volume element and the subscripts g and v denote gas and water vapour, respectively. As equation 5 is wrinen, all losses are assigned to the gas phase. Equations 2 to 5 are valid for cocurrent contact between the phases and where rhe total air flow is V. These equations can be used with any of the subsections of an arbitrary section j, if V is replaced by - r v i i n ) when applied to the counter-cmnt subsection and by (1 - r ) d " ) when applied to the co-current subsection. Factor r is the inlet air flow J
split ratio. Equations 2 to 5 represent a set of ordinary non-linear differential equations that pennit calculation of changes in moisture content and temperature for both phases along a dryer section. To integrate these equations, inlet conditions must be specified. For a counrer-current subsection, they can be written as follows:
Since the outlet solids conditions for the upper subsection are the same as the inlet solids conditions for the subsequent co-current subsection, equations 2 to 5 are integrated on the lower subsection with the following inlet conditions:
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Owing to the non-linearity of the equations, they must be solved numerically. At every integration step, expressions for heat flux and evaporation rate must be provided. Mass and Heat Transfer Rates Description of drying when the mechanisms of intemal transport control the process is complex. A simple method that takes into account internal transfer within the solid is the relative drying curve. See Keey (1978) for'details. According to this method, the rate of moisture loss per unit of exposed surface may be written as
where f is a dimensionless empirical function of moisture content, M, is molecular weight of the water, k is the mass transfer coefficient, and y, and yp are the molar fractions of the vapour in the gaseous mixture at the saturated interphase and in the bulk of the gas. In the active section of the dryer, heat flux is primarily transmitted by convection with temperature differences between the hot air and the bed of solids as the driving force as shown below:
where h is the heat transfer coefficient. In addition to that dominant transfer mechanism, there may be a secondary contribution to heat transfer by conduction from the intemal hot wall to the moving bed of solids in the dryer with central air distribution as well as losses from the external faces of both dryen. Mass and Heat Transfer Coefficients According lo Gupta and Thodos (1963), experimental results in packed beds can be satisfactorily correlated by using the j-factor for heat transfer. 'Ihe following
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relationship adequately describes the heat transfer coefficient as a function of the Reynolds number under a wide range of conditions:
where the characteristic dimension in the Reynolds number is particle diameter, u is velocity and p is density of the gaseous stream. A value of 2.06 is suggested for constant b. The mass transfer coefficient may be obtained by using analogies between heat and mass transfer. Numerical Solution Solution of the differential equations described above permits the calculation of changes in moisture content and temperature of the grain and the air in every section. The equations describe an initial-value problem where location of the solids is related to residence time in the dryer by the solid linear velocity, and inlet conditions correspond to initial values. Outlet conditions after a drying cycle are obtained by successive integration of all the sections in the dryer, starting with the inlet conditions of the top section. If several drying cycles are required to reduce the moisture content of the solids to the desired level, the inlet conditions of a new cycle will be the outlet conditions of the previous cycle or of the elevator if it is considered to be an active part of the dryer. Although the differential equations that describe the counter-cumnt and co-current subsections are similar, calculations in the counter-current case require an iterative procedure since the inlet conditions of solids and gas are known for different sides of the subsection. A convenient iterative procedure is to guess the outlet conditions of the air and proceed to integrate the equations downward in the subsection. The consistency of the guess can then be controlled by comparison between calculated air temperature and moisture content and the known values of the incoming air. Calculations must be repeated until a satisfactory accuracy is reached. The secant method or another suitable one may be used to accelerate the convergence.
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EXPERIMENTAL SECTION In the experimental section, drying experiments with two medium-sized column dryers of the same type as those used by farmers in Nicaragua were performed. The grains dried were corn and rice. The dryers consist of four main parts: the active part of the dryer, a bucket elevator, a fan and a heater. Grain is transported by an elevator to the top from where it is poured into the active pan of the dryer. From there, the grain flows downward as a moving bed and
is exposed to stream of hot air, introduced by means of a fan blowing air through a heater. After the contact with the solids, the exhaust gas is released into the atmosphere. Procedure An amount of grain corresponding to the capacity of the dryers was soaked in water for several hours and the excess water was then evaporated by drying the grain in the sun. The dryer was loaded and the grain flow was started, but air was supplied only after the flow became stable and constant. Air was then supplied, and air velocity, air humidity and grain flow were measured. Heat was applied, and when the inlet temperature had stabilized, the time was set at zero and initial grain humidity and temperature, a? well as ambient temperature and humidity, were measured. During the experiment, samples of grain were taken to determine moisture content. Moisture content and velocity of the outlet air were also measured at different locations in the dryer.
RESULTS AND DISCUSSION The set of differential equations 2 to 5 was solved by using a fifth-order RungeKutta method with adaptive step-size control of local truncation error, and the secant method was applied to accelerate the convergence of the iterative integration in the counter-current subsections. The characteristic drying curves for rice and corn obtained by CarlCn (1994) and Ohlsson (1994) were used in the simulations. Another value of constant b was employed in equation 10 to account for the
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FIGURE 4. Pilot scale grain dryers
uncertainties in the contact area and transfer coefficients. The value was adjusted by fitting a simulation result to the result of one experiment. The same value was then applied in all the simulations. Heat loss to the surroundings was neglected in the simulations, due to the small difference between experimental tempentures and the ambient temperature. Comparison between results of drying experiments and results predicted by the model are shown in Figure 5 for the MAD and C A D dryers. Factor b was determined by using one of the experiments and the corresponding simulation at the intermediate air flowrate. Slightly better agreement was observed at the other air velocities in the MAD dryer. However, the evidence was too weak to conclude that dependency on air velocity, in the case of the C A D dryer, was not the same as that of the correlations applied to calculate the transfer coefficients and that agreement could be improved with a different exponent of the Reynolds number. The results of the simulations were strongly influenced by the initial value of the solids moisture content. An error in measuring initial moisture content or a nonrepresentative sample could seriously affect the deviation of simulation results from experimental values. The main problem was not related to the accuracy of moisture content measurements but to the practical difficulties of obtaining a grain of uniform initial moisture content. This was due to the relatively large amount of material required by each experiment. For the same reason, it was not possible to prepare
5 M
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2 Time [hr] a) F@= 0.23 kg/s
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2 Time [hr] b) F, = 0.40 kg/s
x -
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........I........
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0 0
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2 Time [hr]
2 Time [hr] 0 F$ = 0.68 kg/s
3
FIGURE 5. Comparison between experiments and simulations. MAD dryer (corn, a. b, c). Dryer volume = 0.39 m', Z = 2.2 m, r = 0.2, number of sections = 10, b = 0.05. CAD dryer (rice, d.e.0. Dryer volume = 0.19 m3, Z = 1.23111, r = 0.2, number of sections = 10, b = 0.075.
201 1
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0.16
..
$ 5 0.12
.-
0
* 0.14
.........;.........
... .........:......
0.5 Split ratio
yQ= 0.015 x,=,o:30 Z = 1.23
~. . .
0
1
a) MAD dryer, 10 cycles. 10 sections
0.5 Split ratio
1
b) CAD dryer, 30 cycles. 10 sections
FIGURE 6. Final moisture content as a function of the split ratio
solids with the same initial moisture content in the various experiments. Comparisons between experiments conducted under different conditions were also
made difficult by limitated control over drying conditions. This was partly due to drastic changes in environmental conditions that could occur during an experiment and panly to the characteristics of the equipment. To analyze the influence of the split ratio on the results, simulations with different degrees of counter-current flow were performed. (See Figure 6.) As expected, total counter-current flow leads to a lower final liquid content than total co-current flow. However, maximum efficiency is achieved at some intermediate value. Since the extreme values mean that there is no gas flow in half of the dryer, this pan of the dryer is not effective. As shown in Figure 6, the curves are rather flat at intermediate values of the split ratio. Consequently, the absence of accurate experimental values for the split ratio will not necessarily lead to unreliable simulation results unless this factor is close to the values of pure counter-current or pure co-current contact. Simulations of the MAD dryer show that at a given dryer capacity, drying efficiency is improved by increasing the height of the dryer (Figure 7a). A reduction of the number of openings or rows of ducts maintainning dryer height constant results in an improvement in drying efficiency, as shown in Figure 7h. In both
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.
. .
.......
j...
. . ..
.. ...........
.
.. ..
0
b
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a) ZIS ratio
4
0
.. ..
.. ..
2 Time [h]
.
4
b) Number of rows
0 0
"
..
..
2 Time [h]
4
c) V R ratio
FIGURE 7. Influence of some parameters on the MAD dryer. 20 cycles. F,, = 0.5 kgls. split ratio = 0.5. See additional data in Figure 6a.
cases, increased efficiency is due to a higher air velocity through the bed of grain since the total gas flow remains constant. However, an increase in the ZJS ratio or a reduction of openings or ducts cannot be unlimited since it would lead to large pressure drops and the saturation of air between openings. In the case of the ZJS ratio, there are also mechanical restrictions in choosing a high and narrow dryer. In addition, it would increase the costs of the elevator. As expected, increasing the V R ratio has a positive effect on drying.
CONCLUSIONS Agreement between experimental and simulation results was reasonably good. It can be improved, provided that more reliable values for contact area and transfer
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coefficients axe determined for this type of dryer. According to the simulations, the degree of countercurrent flow that maximizes drying is about half of the gas flow, and the results do not vary considerably unless the flow approximates complete countercurrent flow or complete co-current flow. For a given dryer capacity and gas-to-solids flow ratio, the most effective geometry for the dryer is that yielding the highest gas velocity. Particularly, the number of openings or inlet ducts should be minimized. An increase in pressure drop and probably in saturation of the air between two distanced outlet ducts would set the limits for a reduction of openings or ducts. The mathematical model may be a useful tool for process exploration and optimization of this type of dryer.
Specific area Constant in equation (13) Total concentration Specific heat capacity Total flow Relative drying velocity Heat transfer coefficient Mass uansfer coefficient Flow of dry solid Molecular weight Evaporation flux Prandtl number Heat flux Particle Revnolds number Split facto; Equivalent cross section ~~m~rature Gas velocity Flow of dry gas moisture content (dry basis) Air humidity (dry basis) Molar fraction of the vapour Space coordinate Dryer height
Greek lener e Bed porosity 2. Heat of vaporization p Density of the gas
m2/m3 kmollm' kJ1kg.K kg/s W/m2,K kmol /m2,s kg/s kglkmol kglm', s
kl/ m', s m2 K mk kds kg/kg kg/kg kmovkmol m m m1/m1 kJk kg/m3
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Superscripts and Subscripts: c Convection g Gas 1 Losses L Humid solid m Mixture s Solid Vapour v Liquid water w 0 Inlet or initial I Outlet or final
ACKNOWLEDGMENTS The financial support recieved from the Swedish Agency for Research Cooperation with Developing Counuies (SAREC) to cany out this study is gratefully acknowledged.
LITERATURE CITED Barrozo. M.A.S., Sartori, D.J.M.: Freire, J.T.. 1996, Simultaneous Heat and Mass Transfer during the Drying of the Soybean Seeds in a Crossflow Moving Bed. Proc. 10th International Drying Symposium IDS'96, Krakow, Poland. 30 luly-2 Aug., Vol. B, pp. 873-880. C a r l h , M., 1994, Drying Rice in a Moving Bed Dryer with Central Air Distribution, MSc Thesis. Royal Institute of Technology, Sweden, 57 p. Chaahouni, M., Flick, D., Techasena, 0.. 1992, Particles Flow in Industrial Grain Dryers. Drying 92, part B, Elsevier Science Publishers B.V., pp. 1409-1418. Douglas, P. L.. Jones, 1. A. T., Mallik. S. K., 1994, Modeling and Simulation of Crossflow Grain Dryers. Parts I, n, 111, Trans IChemE, Vol. 72, part A, pp. 325 349. Gupta, A. S. and Thodos, G.,1963, Direct Analogy between Mass and Heat to Beds of Spheres, AIChE J., 9, p. 751. Gustaffsson M. and Schreil, A,, 1996, Dispersion ans Transfer Coefficients in Moving Bed Grain Dryers. MSc Thesis. Royal Institute of Technology, Sweden. 52 p. Keey, R. B., 1978, Introduction to Indusuial Drying Operations, pp. 154-156, Pergamon Press. Oxford.
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Motta Lima, 0.C., Pinto, J. C., and Massarani, G., 1996. Parameter Estimation in Cross-Flow Sliding Bed Drying. Proc. 10th International Drying Symposium IDS'96, Krakow, Poland, 30 July-2 Aug., Vol. A, pp. 283-290. Ohlsson Y., 1994, The Drying of Corn in a Moving Bed Column Dryer. MSc Thesis, Royal Institute of Technology, Sweden. 65 p. Sun, L., Amaud, G. and Fohr, J-P., 1991, Air Flow in a Corn Dryer. Drying' 90, Part B, Elsevier Science Publishers B.V., pp. 447-454. Sun, L., Amaud, G. and Fohr. J-P., 1992, Heat and Moisture Transfer between Ducts in an Industrial Cereal Drier, Drying' 92, Part B, Elsevier Science Publishers B.V., pp. 1399-1407
