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

ABSTRACT

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.     

PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

ABSTRACT

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

Drying of Coarse Particles in a Vertical Pneumatic Conveyor

In the present work, one-dimensional two-phase continuum models were applied to simulate the pneumatic drying of porous alumina and solid glass particles. Pressure profiles, gas and solid temperature, and gas and solids moisture profiles were obtained in a 53.4-mm conveying tube. For both particles, maximum values of gas-to-particle heat transfer coefficients were obtained at air velocities close to the minimum pressure gradient velocity. Experimental temperature and moisture profiles of gas and solids were compared to simulated predictions, showing that models based on the two-phase flow approach fail to predict all the observed physical phenomena in simultaneous momentum, heat, and mass transfer for pneumatic drying of coarse particles. However, using adequate correlations and constitutive equations to predict interaction forces and transport parameters, it was possible to obtain good predictions of gas and solid temperature profiles and of moisture content.     

FUNDAMENTALS OF GRANULATION TECHNIQUES

In the present work, one-dimensional two-phase continuum models were applied to simulate the pneumatic drying of porous alumina and solid glass particles. Pressure profiles, gas and solid temperature, and gas and solids moisture profiles were obtained in a 53.4-mm conveying tube. For both particles, maximum values of gas-to-particle heat transfer coefficients were obtained at air velocities close to the minimum pressure gradient velocity. Experimental temperature and moisture profiles of gas and solids were compared to simulated predictions, showing that models based on the two-phase flow approach fail to predict all the observed physical phenomena in simultaneous momentum, heat, and mass transfer for pneumatic drying of coarse particles. However, using adequate correlations and constitutive equations to predict interaction forces and transport parameters, it was possible to obtain good predictions of gas and solid temperature profiles and of moisture content.     

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.     

MOISTURE PROFILES IN A MODEL FOOD GEL DURING DRYING: MEASUREMENT USING MAGNETIC RESONANCE IMAGING AND EVALUATION OF THE HCKIAN MODEL

Magnetic resonance imaging (MRI) was used to obtain moisture profiles of a model food gel during drying. A cylinder of gel, 1 cm in diameter, with an initial moisture content of 76% was imaged while drying at room temperature. Moisture profiles were obtained from the imaging data by imaging calibration samples of known moisture content. Signal intensity of the images was found to be highly proportional to solids content. The moisture profiles were compared to profiles predicted by a finite difference solution of Fickian radial diffusion in a cylinder. Actual moisture profiles obtained by MRI were much flatter near the center of the cylinder, with a steeper moisture profile near the edge, compared to the typical parabolic shape of the Fickian model. The Fickian model was found to be an inaccurate predictor of the interior moisture profile of the model food gel, since effective diffusivity was found to not be solely a function of moisture content. The moisture profiles obtained provide for a method to evaluate other mass transfer models, and the methods outlined provide a technique to explore mass transfer within actual food materials during processing.     

DRYING SIMULATION OF CORN WITH TEMPERING

This work presents a dirTusion model and experimental investigation or com drying with tempering. The model solves numerically the dirTusion equation for a hygroscopic porous solid consisting of two concentric spheres (starchy endosperm and pericarp) with different shell thickness and relative resistances to moisture flow. Multipass drying was simulated to evaluate the effect of tempering on drying process. Predicted moisture profiles within the kernel were used to evaluate the actual time for complete tempering or tempering index. The effect of the initial moisture for tempering and the number of drying passes on the net drying time were analyzed. A mathematical expression was formulated to estimate the tempering index under different tempering conditions.     

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%.     

Drying of Soybean Seeds in a Concurrent Moving Bed: Heat and Mass Transfer and Quality Analysis

The purpose of the present work is to study the simultaneous heat and mass transfer between air and soybean seeds in a concurrent moving bed dryer, based on the application of a two-phase model to the drying process. The numerical solution of the model is obtained by using a computational code based on BDF methods (Backwards Differentials Formulas). The experimental data of air humidity and temperature and of seed moisture content and temperature at the dryer outlet are compared to the simulated values, showing a good agreement. This work also analyzes the effect of the main process variables (drying air temperature, air relative humidity, air velocity and solids flow rate) on the soybean seeds quality during drying. Empirical equations fitted to the experimental data are proposed for predicting the soybean seed quality (germination, vigor and fissures) as a function of the investigated variables.     

DYNAMIC ANALYSIS OF CONTINUOUS WELL-MIXED FLUIDIZED/SPOUTED BED DRYERS

A diffusion-based mathematical model is presented for the prediction of the dynamics of drying in continuous well-mixed fluidized/spouted beds. Numerical techniques are used to solve the model equations. The outlet solids moisture content, the outlet air humidity and solids temperature are predicted as a function of time for the falling rate drying period. The model is helpful in describing the drying process during the startup periods and in studying open loop behavior of drying process. The model is also useful in designing control system for fluidized/spouted bed dryers.     

DRYING SIMULATION OF CORN WITH TEMPERING

Abstract

This work presents a dirTusion model and experimental investigation or com drying with tempering. The model solves numerically the dirTusion equation for a hygroscopic porous solid consisting of two concentric spheres (starchy endosperm and pericarp) with different shell thickness and relative resistances to moisture flow. Multipass drying was simulated to evaluate the effect of tempering on drying process. Predicted moisture profiles within the kernel were used to evaluate the actual time for complete tempering or tempering index. The effect of the initial moisture for tempering and the number of drying passes on the net drying time were analyzed. A mathematical expression was formulated to estimate the tempering index under different tempering conditions.     

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.     

Experimental Investigation and Modeling of Plug-Flow Fluidized Bed Drying Under Steady-State Conditions

In this study, a model for a plug-flow fluidized bed dryer under steady-state conditions was presented. The model was based on differential equations; thus the bed of the dryer was divided horizontally and vertically into major and minor control volumes, respectively. Each control volume was composed of two thermodynamic systems: solid and gas. The mass and energy balances of the particles in the major control volume based on the axial dispersion were developed to derive the axial profiles of solid moisture content and temperature. To derive the variation of gas humidity and temperature along the bed height and hence the axial profiles of outlet gas humidity and temperature, the mass and energy balances in the gas over the minor control volume, considering the plug flow of gas through the bed, were developed. The model was validated by comparing the simulation results with the experimental data obtained by drying the long-grain rough rice under steady-state conditions in a laboratory-scale, plug-flow fluidized bed dryer. A very satisfactory agreement between the simulation and the experimental data of solid moisture content, solid temperature, and outlet gas humidity and temperature was achieved. Also, the effects of inlet gas temperature, weir height, and inlet dry solid mass flow rate on the simulated axial profiles of solid moisture content and temperature, humidity difference between inlet and outlet gas, and outlet gas temperature were investigated.     

Continuous on-line measurement of solid moisture content during fluidized bed drying using triboelectric probes

Wet granulation and drying of solids in fluidized beds are widely used in the pharmaceutical, food and fertilizers industries. Although the moisture content of fluidized solids is the key parameter for on-line process monitoring, reliable, accurate and economical moisture sensors are lacking. The aim of this work was, therefore, to develop a new technique using triboelectric probes for real-time measurement of moisture content in fluidized beds, and to validate its applicability to fluid bed drying of glass beads (Sauter-mean diameter of 171 μm) and silica sand particles (Sauter-mean diameter of 190 μm) wetted by water. Several triboelectric probes, installed at different locations throughout the bed, monitored the bed moisture content during both the liquid spraying and the following drying process. The measuring technique developed in this study makes use of inexpensive probes that do not require any maintenance. The triboelectric signals were continuously recorded by a data acquisition system and, at selected times, samples of bed solids were taken and analyzed for their moisture content using Karl Fischer titration. The triboelectric signals were correlated with the moisture contents determined by titration to calibrate the technique, which was found to be sensitive to moisture contents below 100 ppm. For most of the experiments the bed was operated in the bubbling regime with a superficial gas velocity of 0.4 m/s. The relationship between triboelectric signal and moisture content was unaffected by changes in the fluidization gas velocity of up to 25%, and could be easily automated for direct control of industrial granulation and drying processes.     

Modelling of batch fluidised bed drying of pharmaceutical granules

This paper presents a mathematical model based on a three-phase theory, which is used to describe the mass and heat transfer between the gas and solids phases in a batch fluidised bed dryer. In the model, it is assumed that the dilute phase (i.e., bubble) is plug flow while the interstitial gas and the solid particles are considered as being perfectly mixed. The thermal conductivity of wet particles is modelled using a serial and parallel circuit. The moisture diffusion in wet particles was simulated using a numerical finite volume method. Applying a simplified lumped model to a single solid particle, the heat and mass transfer between the interstitial gas and solid phase is taken into account during the whole drying process as three drying rate periods: warming-up, constant rate and falling-rate. The effects of the process parameters, such as particle size, gas velocity, inlet gas temperature and relative humidity, on the moisture content of solids in the bed have been studied by numerical computation using this model. The results are in good agreement with experimental data of heat and mass transfer in fluidised bed dryers. The model will be employed for online simulation of a fluidised bed dryer and for online control.     

Simulation Study for Pneumatic Conveying Drying of Sawdust for Pellet Production

Pneumatic conveying drying (PCD) is a combination of heat and mass transfer and pneumatic handling technology. This technology has been extensively used in chemical, pharmaceutical, and food industries, as well as many others. The PCD technique is beneficial for agricultural products, because it can achieve high-quality drying with reduced heat damage in a very short time. In this study, one-dimensional and three-dimensional mathematical models for the drying of sawdust particles in a pneumatic dryer were developed and verified with experiments. The three-dimensional modeling was done with a computational fluid dynamics (CFD) package (ANSYS FLUENT, Ver. 13.0, Ansys, Inc.), in which the gas phase is modeled as a continuum using the Euler approach, and the droplet/particle phase is modeled by a discrete phase model with a Lagrange approach. One-dimensional analysis was performed in MATLAB (Ver. 7.0). The experiments were carried out to validate the model in a pneumatic dryer with a horizontal length of 1 m, vertical height of 1.1 m, and diameter of 0.14 m. Sawdust, a raw material used for producing pellets, was prepared from well-seasoned pinewood timber. The initial moisture content of the sawdust was 22% (wb). The hot air inlet temperature in the dryer was fixed at 100°C. The variations in air pressure, air velocity, air temperature, and particle moisture content were investigated along the length of the dryer. The final moisture contents of sawdust and air temperature were reduced by 2% (wb) and 5°C, respectively. The simulated values were in good agreement with the experimental values. The developed model was then employed for the design of a pilot-scale pneumatic dryer (length 7 m and diameter 0.14 m). The final moisture content of the sawdust particles was reduced to 14% (wb) when the dryer length was increased from 1 to 7 m. In addition, the modeling was performed using buffers in the pilot-scale dryers. The use of a buffer noticeably increased the drying efficiency.     

Modelling and Simulation of a Direct Contact Rotary Dryer

A mathematical model able to predict solid and drying gas temperature and moisture content axial profiles along a direct contact rotary dryer was developed. The study was focused on the drying kinetics based on phenomenological models. Two different drying mechanisms in the decreasing drying rate period were tested: proponional to the unbound moisture content and moisture diffusion inside the particle. Experimental data collected in a pilot-scale direct contact rotary dryer was used to validate the model. Soya and fish meals were used as drying material.     

Modelling and Simulation of a Direct Contact Rotary Dryer

ABSTRACT

A mathematical model able to predict solid and drying gas temperature and moisture content axial profiles along a direct contact rotary dryer was developed. The study was focused on the drying kinetics based on phenomenological models. Two different drying mechanisms in the decreasing drying rate period were tested: proponional to the unbound moisture content and moisture diffusion inside the particle. Experimental data collected in a pilot-scale direct contact rotary dryer was used to validate the model. Soya and fish meals were used as drying material.