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.     

IMPROVEMENT OF DEEP-BED CROSSFLOW MODEL BY A DIFFUSION COMPONENT FOR THE GRAIN PARTICLE AND LOG MODEL FOR EVALUATION OF RECIRCULATING CROSSFLOW DRYER

This paper presents the improved versions of -bed cross now and log simulation models. A diffusion model descries ibing internal diffusion of moisture within a grain kernel to compute moisture removal rate is developed and incur porsted in crossflow model to improve its flexlbillty and versetility. The lag model is suilably modified and employed to evaluate its accuracy and applicability compared to crossflow drying model for evaluating recirculating crossflow drying operation. Experiments were conducted on large scale recirculating crossflow dryer for corn drying. Simulation results are compared with experimental results to test the validity of drying models.     

IMPROVEMENT OF DEEP-BED CROSSFLOW MODEL BY A DIFFUSION COMPONENT FOR THE GRAIN PARTICLE AND LOG MODEL FOR EVALUATION OF RECIRCULATING CROSSFLOW DRYER

This paper presents the improved versions of -bed cross now and log simulation models. A diffusion model descries ibing internal diffusion of moisture within a grain kernel to compute moisture removal rate is developed and incur porsted in crossflow model to improve its flexlbillty and versetility. The lag model is suilably modified and employed to evaluate its accuracy and applicability compared to crossflow drying model for evaluating recirculating crossflow drying operation. Experiments were conducted on large scale recirculating crossflow dryer for corn drying. Simulation results are compared with experimental results to test the validity of drying models.     

Application of Markov Chain Analysis and Tanks-in-Series Model in Mathematical Modeling of Impinging Stream Dryers

In spite of the fact that the principles of impinging stream reactors have been developed for more than half a century, the performance analysis of such devices, from a viewpoint of the mathematical modeling, has not been investigated extensively. In this study two models are proposed to describe the drying performance of particulate materials in two-impinging stream dryers. The models are developed based on the Markov chain analysis and the tanks-in-series model. The required parameters for each model are determined by using RTD data obtained in a two-impinging stream dryer and the governing equations are solved numerically. Comparison of the results of the models with available experimental data shows that the stirred tanks-in-series model successfully explains the drying behavior in impinging stream dryers. Nevertheless, the results of the model that is developed based on the Markov chain analysis are not in exact agreement with corresponding experimental data because of the extremely short residence time of the particles inside the dryer. Also, the effects of some operating parameters on the performance of such dryers are investigated. The results indicate that the drying efficiency of the dryer increases when solid-to-gas flow rate ratio, initial moisture content, and diameter of the particles decrease and when the temperature of the carrier gas increases.     

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.     

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.     

PNEUMATIC DRYING OF MEALS: APPLICATION OF THE VARIABLE DIFFUSIV1TY MODEL

The superficial and bound moisture removal from soya meal was studied in a pneumatic dryer. The effect of external condition over the effective diffusivity in drying kinetics prediction has been demonstrated and a model that considers time variable diffusion coefficient was developed and correlated with gas temperature and velocities. A simple experimental technique using a pulse injection of humected solid was utilized to determine real drying kinetics under steady state operation with solids recycling. The model fitted the experimental data well over a gas temperature range between 100° C and 300° C and gas velocities of 3.5 m/ s and 20 m/ s.     

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.     

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.     

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.     

PNEUMATIC DRYING OF MEALS: APPLICATION OF THE VARIABLE DIFFUSIV1TY MODEL

ABSTRACT

The superficial and bound moisture removal from soya meal was studied in a pneumatic dryer. The effect of external condition over the effective diffusivity in drying kinetics prediction has been demonstrated and a model that considers time variable diffusion coefficient was developed and correlated with gas temperature and velocities. A simple experimental technique using a pulse injection of humected solid was utilized to determine real drying kinetics under steady state operation with solids recycling. The model fitted the experimental data well over a gas temperature range between 100° C and 300° C and gas velocities of 3.5 m/ s and 20 m/ s.     

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.     

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.     

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.     

Drying in a new two impinging streams reactor

A new gas-solid reactor, employing two impinging streams with oscillatory motion of the solid particles, was developed and successfully tested in evaporation experiments. Comparisons of the performance of the reactor with other commonly used devices, namely, spray dryer, spouted bed, stream dryer and a fluidized bed, indicated a most high efficiency in carrying out drying of moistened particles by a hot stream of gas. In addition, the pumping work per kg of solids transported by air through the reactor is considerably lower in comparison to a fluidized bed.     

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.     

Experiments on Hot-Air Drying of Wheat in a Semi-Technical Mixed-Flow Dryer

Although mixed-flow grain dryers are widely used, there is still a need to optimize the process control as well as the dryer apparatus. Fluctuations of the grain moisture content at the dryer entrance are still a major problem resulting in quality and economic losses due to under- or overdrying. Therefore, a mathematical model for heat and mass transfer in a mixed-flow dryer has been developed. Practical drying experiments were carried out at a semi-technical dryer test station that was operated quasi-continuous. The measurements reveal the complexity of the mixed-flow drying process. First predicted results are in satisfactory agreement with data.     

Experiments on Hot-Air Drying of Wheat in a Semi-Technical Mixed-Flow Dryer

Although mixed-flow grain dryers are widely used, there is still a need to optimize the process control as well as the dryer apparatus. Fluctuations of the grain moisture content at the dryer entrance are still a major problem resulting in quality and economic losses due to under- or overdrying. Therefore, a mathematical model for heat and mass transfer in a mixed-flow dryer has been developed. Practical drying experiments were carried out at a semi-technical dryer test station that was operated quasi-continuous. The measurements reveal the complexity of the mixed-flow drying process. First predicted results are in satisfactory agreement with data.     

DEVELOPMENT AND VALIDATION OF A PROCESS SIMULATOR FOR DRYING SUBBITUMINOUS COAL

Drying subbituminous coal has never been practiced commercially. The commercial dryers built to date have been designed for drying surface moisture in conjunction with upstream coal preparation facilities. This type of drying is mainly controlled by input energy and the basis of the design is an energy balance. In drying inherent moisture from subbituminous coal, the thermal conductivity of the coal and the diffusion of molecular water within coal particles impose limitations on the process conditions. Energy input and solids residence time in the dryer have to be controlled properly for simultaneously balancing the heat and mass transfer within the coal particles. Improper control of either parameter can cause fires and explosions during the key steps of the drying process—drying and cooling

In parallel to the Anaconda coal drying pilot plant program, a cross-flow, fluid-bed coal drying/cooling process simulator was developed for: (1) understanding the drying phenomena on an individual particle basis; (2) analyzing potential risks and safety limits, and (3) designing the Anaconda pilot plant program

The development of the process simulator was based on both first principles and laboratory data and can be divided into two phases:

1 Development of a semi-mechanistic drying model for Powder River Basin subbituminous coal employing an analytical solution of the diffusion equation

2.Formulation of a fluid-bed cross-bed cross-flow dryer/cooler simulator employing simultaneous heat and mass transfer

This model was validated against process variables data taken on a 4 tph pilot plant. An operable range, or process envelope, has been developed through the pilot plant experience and the process simulation study. Based on the model predictions, an uncertainly range was defined in the design recommendations of a pioneer coal drying plant in scale-up.