A STOCHASTIC APPROACH TO THE DRYING OF SOLIDS IN A MULTI-STAGE FLUIDIZED BED

The residence times of solids flowing through a fluidized bed dryer exhibit dispersion about the mean. In this paper, expressions for the probability density functions of solids moisture content in the various stages of a multi-stage dryer are derived. A simple recurrence relationship for the moments of the distribution is also presented. The analysis is applied to the drying of cereal grains, and it is shown that the degree of drying increases with the number of stages in the dryer. Probability density functions of the moisture content are presented.     

INFLUENCE OF SOLIDS MOISTURE CONTENT ON THE AVERAGE RESIDENCE TIME IN A ROTARY DRYER

The solids mean residence time in a rotary dryer is influenced by several variables such as dryer dimensions and solids characteristics. One of these characteristics, usually not taken into account in correlations proposed to estimate the mean residence time, is the solids feed moisture content. Although it is well known that the solids moisture content has a major impact on the ability of the solids to move along the rotary dryer, it does not enter as a parameter in available correlations. In this investigation, numerous experiments were performed in a pilot-scale rotary dryer to study the influence of solids moisture content and drying gas temperature on the mean residence time. Sand employed in cement makeup was used to perform these experiments. Results show that the mean residence time for a moisture content in the range of 8% to 12% is four times higher than for dry solids. The moisture content and the drying gas temperature influence significantly the shape of the residence time distribution curve.     

Spray Drying of Tomato Pulp: Effect of Feed Concentration

The effect of feed concentration on spray drying of tomato pulp preconcentrated to 78, 82, and 86% wet basis is investigated in two spray drying systems: a pilot scale spray dryer (Buchi, B-191) with cocurrent regime and a two-fluid nozzle atomizer, and the same connected with an absorption air dryer (Ultrapac 2000). Data for the residue on the chamber and cyclone walls were gathered and two types of efficiencies were calculated as an indication of the spray dryer performance. Tomato powders were analyzed for moisture, particle size, and bulk density. In both spray drying systems, with increases in tomato pulp concentration overall thermal efficiency, evaporative efficiency, material loss in the cyclone, powder moisture content, and bulk density decreased, whereas powder particle size increased. On the contrary, the effect of feed solids content on residue formation and product recovery was dependent on the drying medium. In the standard dryer, the higher the feed concentration, the higher was the residue accumulation, and the lower the product recovery, whereas in the modified system increases in pulp concentration resulted in lower residue formations and higher product yields.     

A Method for Determination of Porosity Change from Shrinkage Curves of Deformable Materials

The novel low-cost band thermodynamic dryer equipped with a solar collector, a parabolic focusing collector, a heat exchanger, screw fan, and a drying cabinet with a band was designed and tested. The maximum temperature in the solar collector reached 85°C, which was 55°C above the ambient temperature. The required drying time was 4.5 h, much reduced from the traditional solar drying time of 48 h. The final moisture content of the Roselle calyx was 12% w.b., which is the recommended storage moisture content. Measurements of ambient temperature and humidity, air temperature, and relative humidity inside the dryer as well as solids moisture loss-in-weight data are employed as a means to study the performance of the dryer. Solar drying was compared with conventional sun drying and heated air drying, using the following evaluation criteria: drying time, dried Roselle color, texture, taste, and production cost. For evaluation, a model-based Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methodology was used. After the evaluation, the proposed continuous solar dryer was found to be better than conventional drying and heated air drying due to slower drying rate and better quality of the dried Roselle.     

Simulation of Recirculating Circular Grain Dryer with Tempering Stage

The diiffusion model describing internal diiffusion of moisture within a grain kernel during drying and tempering stages was incorporated in the cross-flow drying model to simulate the recirculating circular grain dryer with drying and tempering stages. Experiments were conducted on an experimental prototype recirculating circular grain dryer for wheat and rough rice drying. The simulated grain temperature and moisture content were compared with the experimental data of drying wheat and rough rice, the maximum deviation of the outlet grain temperature was 5°C and the maximum deviation ofthe final grain moisture content was 0.3% w.b. The simulating program for recirculating circular grain dryer was used for analyzing the effects of structure parameters and hot air parameters on the dryer performance. Recommendations for design of the recirculating circular grain dryers are drawn from the experiments and simulation.     

An Evaluation of Factors Influencing the Energy-Efficient Operation of Well-Mixed Fluidized Bed Dryers

This article describes the results of calculations of specific energy consumption, E_s, performed on a well-mixed fluidized bed dryer simulator. Exhaust air temperature-humidity loci required to yield a specified outlet moisture content were also determined. Most of the calculations related to solids whose drying rate was gas-film controlled. Six model drying curves were employed to examine the effects of drying rate and hygroscopicity in addition to the normal operating parameters. The results indicated that E_s was highest for slow-drying hygroscopic solids and lowest for fast-drying, non-hygroscopic solids. Specific energy consumption increased with decreasing bed temperature and outlet moisture content and with increasing heat loss but was independent of solids loading and airflow rate. For both the aforementioned solids and a much slower drying material (wheat), there was close agreement between the zero heat loss data and a single theoretical curve approximating the performance of an ideal adiabatic dryer. Distinct differences between the behavior of well-mixed and plug flow fluidized bed dryers are reported.     

A Cross-Flow Model for Continuous Plug Flow Fluidized-Bed Cross-Flow Dryers

Plug flow fluidized bed cross-flow dryers have been used in drying of particulate solids such as paddy and other grains for many years. However, simulation of the performance of any particular design of the dryer has always been problematic due to the inadequate overall empirical models used that are too inflexible and too specific to the particular design. In addition, previous theoretical models of the plug flow fluidized bed cross-flow dryer did not model the gas cross flow properly and had difficulty in modeling the moving solid bed. A new steady-state cross-flow model of the dryer that models the gas cross-flow is proposed. The profiles for the solids and air moisture contents and temperatures were found to be dependent on the gas-solid flow ratio, G/F, the specific heat demand, C_PY(T_I - T_A)/(Y_E - Y_I), the total number of a transfer units, N_T = Gε/KφaSL and the specific drying load, (X_I - X_P)/ (Y_E - Y_I). The model was validated by comparing the simulated data with experimental data that were obtained by drying paddy in a plug flow fluidized bed cross-flow dryer pilot plant. The model was found to estimate very well the solids moisture content and temperature, the gas moisture content and temperature profiles, and the driving force profile.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Bibliography of Literature on Fundamentals and Applications of Vibration in Particle Processing

This article describes the results of calculations of specific energy consumption, E _s , performed on a well-mixed fluidized bed dryer simulator. Exhaust air temperature–humidity loci required to yield a specified outlet moisture content were also determined. Most of the calculations related to solids whose drying rate was gas-film controlled. Six model drying curves were employed to examine the effects of drying rate and hygroscopicity in addition to the normal operating parameters. The results indicated that E _s was highest for slow-drying hygroscopic solids and lowest for fast-drying, non-hygroscopic solids. Specific energy consumption increased with decreasing bed temperature and outlet moisture content and with increasing heat loss but was independent of solids loading and airflow rate. For both the aforementioned solids and a much slower drying material (wheat), there was close agreement between the zero heat loss data and a single theoretical curve approximating the performance of an ideal adiabatic dryer. Distinct differences between the behavior of well-mixed and plug flow fluidized bed dryers are reported.     

Online measurement and control of solids moisture in fluidised bed dryers

Currently, two main methods are used to take online measurement of the solids moisture in fluidised bed dryers, namely microwave resonance and near infrared spectroscopy. In this paper, a new online approach to solids moisture measurement of batch fluidised bed dryers by electrical capacitance tomography (ECT) is presented for the first time. Based on online measurement of solids moisture, it is possible to implement feedback control and process optimisation of batch fluidised bed drying processes, aiming to increase the operation efficiency and to improve product quality. A twin-plane ECT sensor with eight electrodes in each plane is mounted in the bottom of a glass fluidisation chamber. From the adjacent electrode pairs, the water content of the solids is estimated based on the correlation between the moisture content and the permittivity value. To reduce measurement error, the effect of temperature on moisture measurement is compensated. The fluidisation velocity is estimated by a semi-empirical function based on the measured water content. The acquired information is sent to a controller to adjust the air flow rate of the fluidised bed dryer. To validate the moisture measurement by ECT, a mathematical model has been developed, based on the measured temperature and relative humidity of the outlet air. The Landweber iteration method is applied to reconstruct images. The averaged solids concentration along the radial direction at different fluidisation conditions is given and compared with results by the linear back-projection (LBP) method. Results from batch drying processes with online measurement and feedback control are given and compared with no feedback control. To compare the operation efficiency, the thermal efficiency is considered and the results show the possibility of online control and optimisation of the fluidised bed drying processes, based on online measurement of solids moisture by ECT. Some challenges and future work are discussed.     

Heat and Mass Transfer in an Agitated Contact-Convective Heated Dryer

For the investigation of the drying process of a pharmaceutical fermentation waste and for determining specific heat and mass transfer coefficients an agitated contact-convective heated dryer was constructed. This dryer is also suitable for drying of other granular solids with high moisture content. Hence we investigated the drying of a by-product from bio-ethanol production, as well. The pilot-plant agitated dryer makes possible continuous measurement and data-acquisition. Data-acquisition of heated wall temperature, inlet and outlet air temperatures and humidity, mass reduction of the material makes possible the determination of transfer coefficients by the heat and mass balance of the dryer. The measured heat and mass transfer coefficients serve as proper input parameters for the simulation calculations.     

MATHEMATICAL MODELING OF MULTISTAGE DIFFUSION-CONTROLLED PNEUMATIC-CONVEYING DRYER TRAIN

Based on the single stage dryer model (Qi, 1996), a model for a multi-stage diffusion-controlled pneumatic-conveying dryer train was developed. The model consisted of a set of algebraic equations describing the relationship between the moisture level in solids and major process parameters (i.e., diffusivity, partition coefficient, particle size, number of stages, solids loading, residence time, etc.rpar;. The effects of these parameters on drying were studied using the model. Equilibrium and other special or asymptotical conditions (e.g., infinitesimal injection of drying gas, uniform partition coefficient and Fourier numbers, etc.rpar; were analyzed. Model calculations have been shown to compare very well with data from an actual plant HOPE drying process.     

PNEUMATIC DRYING IN DILUTED PHASE: PARAMETRIC ANALYSIS OF TUBE DIAMETER AND MEAN PARTICLE DIAMETER

In previous work on pneumatic drying presented by the authors, a mathematical model based on the conservation equations of momentum, mass and energy was proposed. This model was developed taking into account axial and radial profiles for gas and solids velocities, pressure and porosity in the drying tube. These dynamic profiles influenced the behavior of temperature in the gas and particulate phases, gas humidity and solids moisture content. In this work, this model has been used to perform a parametric analysis of the tube and panicle diameters in the pneumatic drying process. These variables were analyzed here for fixed conditions of gas and solids flowrates and initial values of temperatures, humidity and moisture content. Factorial planning was applied to the numerical solution of the mathematical model. Experimental data obtained in a pilot scale pneumatic dryer were used as the initial conditions in the simulation to specify the levels of the variables analyzed. Results on the influence of tube diameter and particle diameter on the drying process were obtained by statistical analysis of the responses generated by the factorial planning.     

MATHEMATICAL MODELING OF DIFFUSION-CONTROLLED PNEUMATIC-CONVEYING DRYERS

A mathematical model for a continuous pneumatic-conveying dryer has been developed for removing internally bound moisture from solid particulates. The dryer relies on a recirculating carrier gas stream for entrainment. Drying is carried out by injecting into the gas loop a fresh stream of conditioned drying gas while an equal amount of wet gas is vented out. Because pneumatic-conveying dryers usually employ huge gas velocities, the particulates are well dispersed in the gas. Therefore, for solids absent of surface moisture, the drying kinetics is controlled by intraparticle diffusion. The mode! developed based on the diffusion mechanism relates the moisture reduction in the solids to various process parameters (diffusiv-ity, partition coefficient, particle size, residence time, solids loading, drying gas usage, and carrier gas recirculating rate), and is fully predictive. Therefore, it can be used to study the effects of these variables. The model was compared with the plant data and found to match the data within ± 15%.     

A Novel Design of Crop Dryer for Use in Developing Countries

The dryer is required for drying of grain as well as drying of the processed products in small catchment agro processing centers in the developing world. However, due to varied material characteristics of grain and secondary processed product, two entirely different types of dryers are required. The grain is dried in a recirculatory dryer, whereas processed product is dried in a tray dryer, where it is frequently mixed and trays are also intermittently changed. To avoid the need for two dryers, a novel design of a low-cost hot air dryer was developed where just by changing the trays the dryer can be converted from an LSU grain dryer to a tray-type product dryer. The dryer was tested for drying soybean grain as well as processed soy products like blanched soybean dal and soyflakes. The capacity of the dryer was 100 kg/batch in a tray dryer with each tray accommodating 10 kg of wet material. In case of LSU mode, the capacity of the dryer was 250 kg of grain per batch. The drying time required was 5 h for 250 kg of wet soybean from 24 to 10% moisture content, whereas in a tray dryer 100 kg blanched soybean dal was dried from 60 to 10% in 5 h and 100 kg of soyflakes from 25% moisture content to 10% moisture in 1.75 h. The cost of the dryer is estimated at US$580.00 and it can be fabricated in a moderately equipped workshop in developing countries.     

A Novel Design of Crop Dryer for Use in Developing Countries

The dryer is required for drying of grain as well as drying of the processed products in small catchment agro processing centers in the developing world. However, due to varied material characteristics of grain and secondary processed product, two entirely different types of dryers are required. The grain is dried in a recirculatory dryer, whereas processed product is dried in a tray dryer, where it is frequently mixed and trays are also intermittently changed. To avoid the need for two dryers, a novel design of a low-cost hot air dryer was developed where just by changing the trays the dryer can be converted from an LSU grain dryer to a tray-type product dryer. The dryer was tested for drying soybean grain as well as processed soy products like blanched soybean dal and soyflakes. The capacity of the dryer was 100 kg/batch in a tray dryer with each tray accommodating 10 kg of wet material. In case of LSU mode, the capacity of the dryer was 250 kg of grain per batch. The drying time required was 5 h for 250 kg of wet soybean from 24 to 10% moisture content, whereas in a tray dryer 100 kg blanched soybean dal was dried from 60 to 10% in 5 h and 100 kg of soyflakes from 25% moisture content to 10% moisture in 1.75 h. The cost of the dryer is estimated at US$580.00 and it can be fabricated in a moderately equipped workshop in developing countries.     

IMPROVING MDF FIBRE DRYING OPERATION BY APPLICATION OF A MATHEMATICAL MODEL

Fibre drying is an important process in production of medium density fibreboard (MDF) which consumes a large amount of energy, affects product quality and, without appropriate control, causes environmental concerns. Based on fundamental knowledge of wood fibre-water relationships and heat/mass transfer, a mathematical model has been developed to simulate the MDF fibre drying processes. The model is able to predict fibre moisture content, air temperature and air humidity along the dryer length. After validation against the measured air temperature and humidity, the model has been extended to include both fibre drying and fibre conditioning, the latter occurring in the dry fibre conveyers. Due to potential benefits in reducing emissions of volatile organic compounds (VOCs) and in improving panel quality, lower drying temperatures are more desirable than higher temperatures. However, in order to achieve the target moisture content after drying, a higher air velocity is needed or a second-stage dryer is added. The model was employed to determine the air velocity required and to assist in designing a second dryer for further drying and recovery of moist vapour and heat. A further study was undertaken to investigate fibre drying or fibre conditioning in the fibre conveyers and, once again, the fibre drying model was used to determine the air conditions.     

IMPROVING MDF FIBRE DRYING OPERATION BY APPLICATION OF A MATHEMATICAL MODEL

Fibre drying is an important process in production of medium density fibreboard (MDF) which consumes a large amount of energy, affects product quality and, without appropriate control, causes environmental concerns. Based on fundamental knowledge of wood fibre-water relationships and heat/mass transfer, a mathematical model has been developed to simulate the MDF fibre drying processes. The model is able to predict fibre moisture content, air temperature and air humidity along the dryer length. After validation against the measured air temperature and humidity, the model has been extended to include both fibre drying and fibre conditioning, the latter occurring in the dry fibre conveyers. Due to potential benefits in reducing emissions of volatile organic compounds (VOCs) and in improving panel quality, lower drying temperatures are more desirable than higher temperatures. However, in order to achieve the target moisture content after drying, a higher air velocity is needed or a second-stage dryer is added. The model was employed to determine the air velocity required and to assist in designing a second dryer for further drying and recovery of moist vapour and heat. A further study was undertaken to investigate fibre drying or fibre conditioning in the fibre conveyers and, once again, the fibre drying model was used to determine the air conditions.     

CFD Modeling of Microwave-Assisted Fluidized Bed Drying of Moist Particles Using Two-Fluid Model

The drying behavior of moist spherical particles in a microwave-assisted fluidized bed dryer was simulated. The two-fluid Eulerian model incorporating the kinetic theory of granular flow was applied to simulate the gas–solid flow. The simulations were carried out using the commercial computational fluid dynamics (CFD) package Fluent 6.3.26. The effects of different levels of microwave power densities as well as initial gas temperature on the prediction of solids moisture content, gas temperature, and gas absolute humidity were investigated. The effect of microwaves was incorporated into calculations using a concatenated user-defined function (UDF). The simulation results were compared with experimental data obtained from drying of soybeans in a pilot-scale microwave-assisted fluidized bed dryer and reasonable agreement was found. The mean relative deviation for prediction of solids moisture content, gas temperature, and gas absolute humidity were less than 3, 10, and 5%, respectively. Further work is needed to validate the proposed model for large-scale plants.