Analysis and Modeling of Wangqing Oil Shale Drying Characteristics in a Novel Fluidized Bed Dryer with Asynchronous Rotating Air Distributor

(College of Energy Resource and Power Engineering, Northeast Dianli University, Jilin 132012)

Analysis and Modeling of Wangqing Oil Shale Drying Characteristics in a Novel Fluidized Bed Dryer with Asynchronous Rotating Air Distributor

Yang Ning; Zhou Yunlong; Miao Yanan

(College of Energy Resource and Power Engineering, Northeast Dianli University, Jilin 132012)

In order to replace the conventional distributor, a novel asynchronous rotating air distributor, which can optimize the drying ability of fl uidized bed and strengthen the drying performance of oil shale particles, is creatively designed in this study. The rotating speed of the asynchronous rotating air distributor with an embedded center disk and an encircling disk is regulated to achieve the different air supply conditions. The impacts of different drying conditions on the drying characteristic of Wangqing oil shale particles are studied with the help of electronic scales. The dynamics of experimental data is analyzed with 9 common drying models. The results indicate that the particles distribution in fl uidized bed can be improved and the drying time can be reduced by decreasing the rotating speed of the embedded center disk and increasing the rotating speed of the encircling disk. The drying process of oil shale particles involves a rising drying rate period, a constant drying rate period and a falling drying rate period. Regulating the air distributor rotating speed reasonably will accelerate the shift of particles from the rising drying rate period to the falling drying rate period directly. The two-term model fi ts properly the oil shale particles drying simulation among 9 drying models at different air supply conditions. Yet the air absorbed in the particles’ pores is diffused along with the moisture evaporation, and a small amount of moisture remains on the wall of fl uidized bed in each experiment, thus, the values of drying simulation are less than the experimental values.

drying characteristic, modeling, asynchronous rotating air distributor, air supply condition

1 Introduction

Raw shale oil which is transformed by thermal decomposition of kerogen in oil shale can be further processed to produce oil products.With special composition and structure, oil shale has wide potential application in power generation, mineral exploitation, chemical engineering, and environmental protection[1-3]. As oil shale is a porous material, interior and exterior factors may lead to moisture permeation in the exploitation and storage process. If the moisture content is excessive, immediate distillation of oil shale will consume a large quantity of heat for evaporation of moisture. Meanwhile, a large quantity of vapor in the distillation furnace may increase the load of recycling and oil/water separation system, and decrease the recovery ratio of oil shale. Therefore, a dehydration process is essential prior to oil shale distillation.

Gas-solid fluidized bed dryer, as a common industrial equipment, is widely applied in production[4-8]. However, the obvious disadvantages of conventional fluidized bed, such as turbulent fl uctuation of the bed surface and nonuniform particles’ distribution, lead to unsatisfactory drying efficiency. In recent years, many scholars have done a lot of research work to improve the drying efficiency of fluidized bed. Li Fan, et al.[9]installed a stirrer inside the fluidized bed to prevent particles from adhesion, agglomeration and attachment on the wall effectively, and enhanced the heat transfer effect between the wet particles. Gong Guoqing, et al.[10]transformed the constant air supply of the conventional fluidized bed into periodic air supply, so that the air fl ow passing through the orifice plate presents periodic variation by regulating its frequency and conductivity to achieveparticles’ fluidized drying. Kuipers, et al.[11]utilized a vibration source which is appropriate for a specific requirement and is installed in the conventional fl uidized bed to create a new fl uidized bed dryer that can overcome disadvantageous channeling and slugging phenomenon, and intensify the heat and mass transfer rate to a large extent. In the year of 2006, Madhiyanon, et al.[12]developed a rotating air distributor, the central position of which was connected to the electromechanical spindle to rotate the air distributor indirectly by regulating the rotating speed of spindle, which optimized the particles distribution condition significantly to some extent. Thereafter, promoting the drying ability of the fl uidized bed achieved a milestone. Sobrino, et al.[13]further studied the in fl uence of air distributor’s rotating speed within the range of 0—100 r/min on the drying effect, and found that the uniformity of particles’ lateral distribution and drying ability of fl uidized bed improved with the increase of rotating speed. Nevertheless, it is worth considering that whether a rotating speed of air distributor maintained at 100 r/min is the optimal drying condition and is it possible to promote drying ability of fl uidized bed further by changing the rotating speed of air distributor. In this paper a novel asynchronous rotating air distributor is creatively invented. By regulating the rotating speed of the embedded center disk and the encircling disk, the optimal rotating speed of asynchronous rotating air distributor under different air supply conditions was explored after comparing the drying efficiency. The dynamics of drying experimental data were analyzed with 9 common drying mathematical models to establish the drying models that were appropriate for simulation of oil shale particles drying process under different asynchronous rotating conditions. This will provide a powerful basis for effective oil shale drying.

2 Experimental

2.1 Experiment samples

The experiment was carried out using Wangqing oil shale particles from Jilin province. The moisture content of oil shale particles was 31.99%. Oil shale samples were crushed and sieved to 1—3 mm, then kept in a constant temperature drying oven as spare. Table 1 shows the proximate and elemental analysis of samples.

Table 1 Proximate and elemental analysis of Wangqing oil shale

2.2 Experiment device and method

Flow diagram of the experiment is presented in Figure 1. The experiment was performed in a Plexiglas fluidized bed column with a height of 1.5 m and a diameter of 0.21 m. The air supplied by a Roots blower was heated by the air heater prior to passing through a valve into the fluidized bed. The asynchronous rotating air distributor was installed at the bottom of the fluidized bed. The temperature sensor and the vortex fl owmeter were located at the entrance of fluidized bed, which could monitor the real-time temperature and airflow rate, respectively. The air fl ow velocity and temperature in this experiment were set at 1 m/s and 100±0.5 ℃, respectively. The sampling aperture was installed at the middle of fl uidized bed for the purpose of sampling at any time without suspending the experiment and eliminating influence on the continuous drying process.

Figure 1 Flow diagram of experimental system

The particles distribution in fluidized bed was investigated using the coupled technique of Electrical Capacitance Tomography (ECT) which was located at a height of 0.5 m, and the ECT device was composed of a capacitance array sensor, the data sampling frequencyof which was 2 frames/s and the driving frequency was 9.6 Hz. The multiple electrode measurement results can reflect the concentration and distribution of particles in the cross section of fluidized bed, a darker color of electrical capacitance tomography image indicated to a higher particles concentration.

Figure 2 Asynchronous rotating air distributor

As shown in Figure 2, the asynchronous rotating air distributor was composed of an embedded center disk and an encircling disk, the surface of which were uniformly arranged with 13 and 16 hemispheric caps, respectively, with a diameter of 1 cm for each cap and 8 holes (with a diameter of 1 mm) on it, and the structure diagram of hemispheric cap is shown in Figure 3. The schematic diagram of asynchronous rotating air distributor is presented in Figure 4. The converter motor A was connected with a spindle fixed at the center of air distributor to drive the embedded center disk air distributor, and the converter motor B was connected with a transmission support fi xed on the periphery of air distributor with a drive belt to drive the encircling disk air distributor indirectly. The rated speed of converter motor in the experiment was 0—1 400 r/min, and the spindles of converter motor A and B were connected to the reducer with a velocity ratio of 1:7, which with the help of coupling could realize the rotating speed of air distributor variation within 0—200 r/min, while producing different air supply conditions. Different air supply conditions are shown in Table 2, in whichN1refers to the rotating speed of the embedded center disk air distributor, whileN2refers to the rotating speed of the encircling disk air distributor. The air distributor reaches a synchronous rotating condition whenN1=N2.

Figure 3 The structure diagram of hemispheric cap

Figure 4 Schematic diagram of asynchronous rotating air distributor

Table 2 Different air supply conditions of asynchronous rotating air distributor

3 Results of Moisture Measurements and Discussion

Oil shale particles during the drying process was weighed with electronic scales (AUW320 g/0.1 mg). About 3 kg of well prepared oil shale particles were dried in the fluidized bed under a specific air supply condition. The total drying time was 60 minutes, and 10 g of particles were extracted from the sampling aperture and placed in the constant temperature drying oven every 2 minutes. The whole drying process in oven was fi nished until the weight difference was less than 0.001 g; the weight loss was equal to the moisture content (MR) of oil shale at different time.

The calculation ofMRis expressed by Equation (1):

whereMtis the moisture content of oil shale particles in dry basis (kg/kg);Mois the original moisture content of oil shale particles in air-dried basis (kg/kg);Meis the equilibrium moisture content of oil shale particles in airdried basis (kg/kg);Mtis the drying time of oil shale particles (s).

The original moisture contentMoof oil shale particles can be calculated by the following Equation (2):

wheremois the original weight of oil shale particles before drying (kg/kg);meis the fi nal weight of oil shale particles after drying in oven (kg/kg).

Figure 5 Moisture content of oil shale particles changing with time under the synchronous rotating condition of air distributor

Mecan be neglected since it is relatively small compared to the moisture contentMtandMo. Figure 5 illustrates the curve for drying of oil shale particles’ moisture content changing with time under the synchronous rotating condition of air distributor. With the increase of rotating speed, the drying time decreases constantly with drying ef fi ciency enhanced, and it is concluded that this phenomenon is attributed to the distribution of oil shale particles. Figure 6 shows the ECT measurement results of particles distribution under the synchronous rotating condition of air distributor, and particles can form the annular-core structure when the rotating speed isN1=N2=0 r/min. This phenomenon has also been confirmed in many researches[14-22], since the airflow rate is high in central region where the distribution of particles concentration is uniform. As regards the particles collision and wall blocking effect, the local gas velocity near the wall region is significantly lower than that in the central region, resulting in particles accumulation in the vicinity of the wall region. By increasing the rotating speed of air distributor appropriately, the airflow in the central and wall region can be equilibrated effectively to approach an uniform airflow distribution condition and alleviate the particles accumulation effect in the wall region. Consequently, the oil shale drying efficiency is significantly optimized with an increasing contact area of oil shale and airflow. The results shown above are consistent with those of Sobrino, et al.[13]. However, the drying efficiency does not reach the optimum value when the rotating speed of air distributor increases toN1=N2=100 r/min. The drying time reduces continuously with the increase of rotating speed and reaches an optimum value, when the rotating speed increases toN1=N2=150 r/min. And then, a further increase of rotating speed leads to a decline of drying ef fi ciency, which occurs mainly because the corresponding rotating centrifugal force is obviously higher than that of the airflow equilibration. The drying air fl ow cannot dry the particles adequately as a result of particles accumulation in the wall region again.

Figure 6 ECT measurement results of particles distribution under air distributor’s synchronous rotating condition

The rotating speed of the embedded center disk and the encircling disk air distributor are regulated respectively to investigate the drying characteristics of oil shale particles under asynchronous rotating condition. As for the excessive air supply conditions, typical air supply conditions are selected by comparing the experimental results. The curve for drying of oil shale particles showing the change of moisture content with the time under asynchronous rotating condition is presented in Figure 7, and Figure 8 exhibits the ECT measurement results of particles distribution under the asynchronous rotating condition. Compared with the drying time of the optimum synchronous rotating condition (N1=N2=150 r/min), the corresponding drying time increases, when the rotating speed is maintained atN1=150 r/min andN2=125 r/min, as well as atN1=175 r/min andN2=150 r/min. It indicates that the air supply conditions mentioned above strengthen the swirling intensity of the central region, which can result in particles accumulation in the wall region, and would destroy the effective drying ability of the fluidized bed. Therefore, reducing the rotating speed of the encircling disk and increasing the rotating speed of the embedded center disk of air distributor cannot promote the drying efficiency. In contrast, the drying time decreases when the air supply condition coversN1=125 r/min andN2=150 r/min, which implies that the drying ef fi ciency can be further promoted under asynchronous rotating condition, as compared with the optimum synchronous rotating condition. Reducing the rotating speed of embedded center disk can weaken the air fl ow intensity in the central region of the fl uidized bed, and then accelerate the particles in the wall region returning to the central region, making the particles distribution approach uniformity. With the decrease in rotating speed of embedded center disk air distributor the corresponding drying time increases suddenly under the air supply condition coveringN1=75 r/min andN2=150 r/min, the rotating speed of the embedded center disk is signi fi cantly less than that of the encircling disk at this moment. With the weakened intensity of airflow in the central region, particles from the wall region begin to accumulate in the central region, which would restrict the effective contact between drying airflow and particles. The drying time can be decreased as well when the air supply condition coveringN1=150 r/min andN2=175 r/min increases the rotating speed of the encircling disk of air distributor. However, the drying time is much longer than the time of reducing the rotating speed of embedded center disk of air distributor. With the continuous increase of the encircling disk until the air supply condition reachesN1=150 r/min andN2=200 r/min, the drying efficiency would reduce obviously, which indicates that the phenomenon of particles accumulation in the central region occurs in advance.

Figure 7 Change of moisture content of oil shale particles with time under the asynchronous rotating condition of air distributor

The drying rateRDof oil shale particles can be calculated according to Equation (3):

whereMt+dtis moisture content of air-dried basis for the time interval dt(kg/kg).

The drying rateRDof oil shale particles changing with moisture contentMRunder the air distributor synchronous rotating condition is shown in Figure 9. The drying process of particles in the fl uidized bed is mainly divided into 3 periods, viz.: the rising drying rate period, the constant drying rate period, and the falling drying rate period. The moisture on the surface of particles evaporates gradually while absorbing the heat of drying airflow in the rising drying rate period and causing the lowering of particles’ surface temperature, and the temperature difference between the particle surface and the internal region drives the diffusion of moisture to the surface. The slope of the drying curve increases gradually with the increase of rotating speed, as the particles distribution approximates uniformity in the process of rotation. The optimized contact area between particles’surface and drying air fl ow would increase the temperature gradient in the particles, which could produce a larger moisture driving force and a corresponding drying rate. The slope of the drying curve remains constant within a period of time when the drying curve reaches the peak, which is called the constant drying rate period, and the moisture evaporation rate of the particles’ surface is equal to the internal moisture diffusion rate. The falling drying rate period appears with the decrease of the curve slope, the period is mainly related with the removal of bound water. The moisture diffusion rate inside the particles islower than the moisture evaporation rate on the surface of particles, which would lead to a reduction of drying rate. The reason for the ‘slow-fast-slow’ tendency of drying rate in the falling drying rate period is owing to the phenomenon that the partially unbound water still exists in the particles at the beginning of the falling drying rate period. In the mid-falling drying rate period, the internal diffusion resistance of moisture content is significant when the particles are getting smaller in the drying process, and the drying rate reduces rapidly as there is insufficient time to ensure the diffusion of moisture to the particles’ surface. The downward tendency of curve is not obvious as the drying rate is already in a low level when the drying process reaches the later period. Particles finally will reach an equilibrium moisture content if the residence time is sufficiently long. The maximum drying rate is 0.049 gH2O/(g·min) when the rotating speed increases toN1=N2=150 r/min, which corresponds to an optimum synchronous rotating condition. Most of the particles are accumulated on the wall region by increasing the rotating speed continually (when the rotating speed exceedsN1=N2=150 r/min), so that the air supply condition would destroy the air fl ow drying ef fi ciency and reduce the drying rate.

Figure 8 ECT measurement results of particles distribution under asynchronous rotating condition of air distributor

Figure 9 Drying rateRDof oil shale particles changing with moisture contentMRunder synchronous rotating condition of air distributor

As presented in Figure 10, the maximum drying rate is 0.085 gH2O/(g·min) when the air supply condition coversN1=100 r/min andN2=150 r/min under the optimum asynchronous rotating condition, which is 1.73 times higher than the optimum synchronous rotating condition. The curve shapes of the asynchronous and synchronous rotating condition of air distributor, as presented in Figure 9 and Figure 10, are obviously different. The drying curve from the rising drying rate period goes to the falling drying rate period directly, which barely has a constant drying rate period under asynchronous rotating condition, which demonstrates that the asynchronous rotating drying style will improve the particles distribution by reasonably regulating the rotating speed of the embedded center disk and the encircling disk respectively, and the accumulated particles in the wall region will return to the central region of the fluidized bed , the drying efficiency is promoted and the unbound water inside the particles is completely evaporated in the rising drying rate period. Then the falling drying rate period emerges, which is characterized by diffusion of bound water in the particles. Upon further reducing the rotating speed of embedded center disk of air distributor, the constant drying rate period begins to appear with a rapidly decreasing drying ability of the fl uidized bed.

Figure 10 Change in drying rateRDof oil shale particles with moisture contentMRunder asynchronous rotating condition of air distributor

4 Analysis of Experimental Drying Dynamics Data

In order to explore an optimal drying mathematical model suitable for simulating the drying process of Wangqing oil shale particles under different asynchronous rotating conditions, nine common drying mathematical models are summarized in existing drying experimentsas shown in Table 3. The experimental data of particles drying dynamics are analyzed with 9 common drying models[23-29]. Correlation coefficientR2and chi square error χ2are used as the indices to evaluate the goodnessof-fit comparison results. The model is equipped with better goodness-of- fi t whenR2is close to 1 and χ2is close to 0. Correlation coef fi cientR2and chi square error χ2can be calculated by applying the following Equations (4) and (5),

Table 3 Drying mathematical models

The model fi tting results are presented in Table 4. As the rotating speed of the embedded center disk is reduced, the speed difference between the encircling disk and the embedded center disk is increased continuously, with its correlation coefficientR2at first increasing and then decreasing, while the chi square error χ2at fi rst decreases then increases. ThoughR2is close to 0.9 and χ2is close to 0 in most model fi tting results, the two-term drying model performs an optimal fi tting results for oil shale particles drying simulation under the condition of asynchronous rotating of air distributor, as the correlation coef fi cientR2is above 0.997, which is larger than other 8 models, and the chi square error χ2is closest to 0, which is less than other 8 models.

Table 4 Fitting results of mathematical models for drying

As shown in Figure 11, the experimental values and fi tting values of particles’ moisture content are compared under the asynchronous rotating condition. Experimental data scatter around the straight line with a slope of 45°, which implies that the two-term model fits properly the oil shale particles drying simulation among 9 drying models in another way. The average relative error of moisture content between experimental values and fi tting values is 6.58%. The overall fi tting effect gradually worsens with a decreasing rotating speed of embedded center disk in air distributor. This phenomenon can be attributed to two reasons, one is that the drying ability of fl uidized bed is strengthened under the speci fi c air supply condition, and the air absorbed in particles pores can diffuse along with the evaporation of moisture. The other reason is that a small amount of moisture remains on the wall of fl uidized bed in each experiment, thus the weight loss of particles includes the weight of air absorption, the moisture evaporation and the moisture remaining on the wall, whereas the weight loss of model fitting results coversthe moisture evaporation only. Therefore, the results of drying fi tting values are less than the experimental values. With a further reducing rotating speed of the embedded center disk (with the air supply condition equating toN1=75 r/min andN2=150 r/min), the fitting effect is improved as the drying ability of fl uidized bed has been destroyed.

Figure 11 Moisture content veri fi cation results of two-term drying model under asynchronous rotating condition of air distributor

5 Conclusions

(1) The contact area between particles surface and drying airflow is optimized and the drying time decreases constantly with the increase of rotating speed appropriately under the synchronous rotating condition of air distributor. The drying ef fi ciency reaches an optimum value when the rotating speed of air distributor increases toN1=N2=150 r/min. The particles accumulation effect in the wall region will destroy the air fl ow drying ef fi ciency with a further increase in rotating speed.

(2) The decrease of air fl ow intensity in the central region of fluidized bed and the uniform particles distribution can be achieved with a reducing rotating speed of the embedded center disk under the asynchronous rotating condition of air distributor. The drying efficiency can be promoted further when the air supply condition coversN1=100 r/min andN2=150 r/min under the optimum asynchronous rotating condition. The particles accumulation in the central region will restrict the effective contact between drying airflow and particles when the rotating speed of the embedded center disk decreases further.

(3) The drying process of oil shale particles in the fluidized bed is mainly divided into 3 periods, viz.: the rising drying rate period, the constant drying rate period, and the falling drying rate period. The drying rate under the optimum asynchronous rotating condition is 1.38 times higher than the optimum synchronous rotating condition. The unbound water in particles is completely evaporated in the rising drying rate period by reasonably regulating the rotating speed of the embedded center disk and the encircling disk, respectively, and the drying curve shifts directly from the rising drying rate period to the falling drying rate period.

(4) The two-term drying model performs the optimal fitting results for oil shale particles drying simulation under the asynchronous rotating condition of air distributor. With the optimized drying ability of fluidized bed, air absorbed in particles pores would diffuse along with the moisture evaporation and the weight loss of particles including the weight of air absorption, the moisture evaporation and the moisture remaining on the wall, which can result in higher experimental values than fi tting values.

Acknowledgements: This work is supported by the National Natural Science Foundation of China (Grant No. 51276033, No. 51541608).

[1] Li W H, Lu S F, Xue H T, et al. Oil content in argillaceous dolomite from the Jianghan Basin, China: Application of new grading evaluation criteria to study shale oil potential[J]. Fuel, 2015, 143(3): 424-429

[2] Bao W W, Liu L, Zou H F, et al. Removal of Cu2+from aqueous solutions using Na-A zeolite from oil shale ash[J]. Chinese Journal of Chemical Engineering, 2013, 21(9): 974-982

[3] Jiang X M, Han X X, Cui Z G. Progress and recent utilization trends in combustion of Chinese oil shale[J]. Progress in Energy & Combustion Science, 2007, 33(6): 552-579

[4] Law C L, Siti M T, Wan R W D. The effect of vertical internal baffles on fluidization hydrodynamics and grain drying characteristics[J]. Chinese Journal of ChemicalEngineering, 2004, 12(6): 801-808

[5] Inge J, Tobias K, Roland W. Volatile organic compound emissions when drying wood particles at high dew points[J]. Chinese Journal of Chemical Engineering, 2004, 12(6): 767-772

[6] Ingvald S, Odilio A F, Trygve M E, et al. Physical properties in drying of food products with combined sublimation and evaporation[J]. Chinese Journal of Chemical Engineering, 2004, 12(6): 814-817

[7] Zhao P, Zhao Y, Luo Z, et al. Effect of operating conditions on drying of Chinese lignite in a vibration fl uidized bed[J]. Fuel Processing Technology, 2014, 128(12): 257-264

[8] Moraveji M K, Kazemi S A, Davarnejad R. CFD modeling of heat and mass transfer in the fluidized bed dryer[J]. Trends in Applied Sciences Research, 2011, 6(6): 595-605

[9] Li F, Feng L F, Gu X P, et al. Press drop in the gas-solid stirred fl uidized bed[J]. Journal of Chemical Engineering of Chinese Universities, 2002, 16(4): 384-388 (in Chinese)

[10] Gong G Q, Lv Y Q, Yu H R, et al. A study on operation characteristics of pulse fluidized bed dryer[J]. Journal of Nanjing Forestry University. 1997, 21(S1): 43-45 (in Chinese)

[11] Kuipers N J M, Stamhuis E J, Beenackers A A C M. Fluidization of potato starch in a stirred vibrating fl uidized bed[J]. Chemical Engineering Science, 1996, 51(11): 2727-2732

[12] Madhiyanon T, Lapirattanakun A, Sathitruangsak P, et al. A novel cyclonic fl uidized bed combustor: combustion and thermal ef fi ciency, temperature distributions, combustion intensity, and emission of pollutants[J]. Combust & Flame, 2006, 146(1/2): 232-245

[13] Sobrino C, Almendros-Ibanez J A, Santana D, et al. Fluidization of group B particles with rotating distributor[J]. Powder Technology, 2008, 181(3): 273-280

[14] Promvonge P, Boonloi A, Pimsarn M, et al. Drying characteristics of peppercorns in a rectangular fluidized bed with triangular wavy walls[J]. International Communications in Heat & Mass Transfer, 2011, 38(9): 1239-1246

[15] Saeideh H, Faramarz H. Drying kinetics of coated sodium percarbonate particles in a conical fl uidized bed dryer[J]. Powder Technology, 2015, 269(8): 30-37

[16] Srinivas G, Setty Y P. Drying behavior of uniform and binary mixture of solids in a batch fl uidized bed dryer[J]. Powder Technology, 2013, 241(3): 181-197

[17] Tasirin S M, Kamarudin S K, Jaafar K, et al. The drying kinetics of bird’s chillies in a fluidized bed dryer[J]. Journal of Food Engineering, 2007, 79(2): 695-705

[18] Srinivasakannan C, Balasubramanian N. An investigation on drying of millet in fl uidized bed[J]. Advanced Powder Technology, 2009, 20(4): 298-302

[19] Xu B, Dong Y, Wu Y B, et al. Technology and equipment for stabilized storage of wheat germ by on-line multistage fl uidization drying[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(8): 127-131 (in Chinese)

[20] Bai D, Shibuya E, Masuda Y, et al. Flow structure in a fast fluidized bed[J]. Chemical Engineering Science, 1996, 51(6): 957-966

[21] Hou B, Li H. Relationship between flow structure and transfer coefficients in fast fluidized bed[J]. Chemical Engineering Journal, 2010, 157(2/3): 509-519

[22] Teplitsky Y S, Borodulya V A, Nogotov E F. Axial solids mixing in a circulating fluidized bed[J]. International Journal of Heat & Mass Transfer, 2003, 46(22): 4335-4343

[23] Doymaz I, Tugrul N, Pala M. Drying characteristics of dill and parsley leaves[J]. Journal of Food Engineering, 2006, 77(3): 559-565

[24] Ayensu A. Dehydration of food crops using a solar dryer with convective heat fl ow[J]. Solar Energy, 1997, 59(4/6): 121-126

[25] Midilli A, Kucuk H, Yapar Z. A new model for single layer drying[J]. Drying Technology, 1997, 20(7): 1503-1513

[26] Giri, S K, Prasad S. Drying kinetics and rehydration characteristics of microwave-vacuum and convective hotair dried mushroom[J]. Journal of Food Engineering, 2007, 78(2): 512-521

[27] Overhules D G, White G M, Hamiltion M E, et al. Drying soybeans with heated air[J]. Amer Soc Agr Eng Trans Asae, 1973, 16(1): 112-113

[28] Henderson S M. Progress in developing the thin layer drying equation[J]. Transactions of the ASAE, 1974, 17(6): 1167-1168

[29] Babalis S J, Papanicolaou E, Kyriakis N, et al. Evaluation of thin-layer drying models for describing drying kinetics of figs (Ficus carica)[J]. Journal of Food Engineering, 2006, 75(2): 205-214

Received date: 2015-07-16; Accepted date: 2016-02-18.

Professor Zhou Yunlong, E-mail: neduzyl@163.com.