Examining the Suitability of the Reaction Engineering Approach (REA) to Modeling Local Evaporation/Condensation Rates of Materials with Various Thicknesses

The reaction engineering approach (REA) is examined here to investigate its suitability as the local evaporation rate to be used in multiphase drying. For this purpose, REA is first implemented to model the convective drying of materials with various thicknesses. The relative activation energy, as the fingerprint of REA, generated from one size of a material is used to model the convective drying of the same material with different thicknesses. Because the results indicate that REA parameters can model the drying of materials with various thicknesses, REA can be scaled down to describe the local evaporation rate (at the microscale as affected by local composition and temperature). The relative activation energy is used to describe the global drying rate in modeling the local evaporation rate. REA is combined with a system of equations of conservation of heat and mass transfer in order to yield the spatial reaction engineering approach (S-REA) as a nonequilibrium multiphase drying model. By using S-REA, the spatial profiles of moisture content, concentration of water vapor, temperature, and local evaporation rate can be generated, which can assist in comprehending the transport phenomena.     

Modeling of Drying of Food Materials with Thickness of Several Centimeters by the Reaction Engineering Approach (REA)

Food materials are highly perishable. Drying is necessary to restrict biological and chemical activity to extend shelf life. A good drying model is useful for design of a better dryer, evaluation of dryer performance, prediction of product quality, and optimization. The reaction engineering approach (REA) is a simple-lumped parameter model revealed to be accurate and robust to model drying of various thin layers or small objects. Modeling drying behavior of different sizes is essential for a good drying model, yet it is still very challenging, even for a traditional diffusion-based model, which requires several sets of experiments to generate the diffusivity function. The REA is implemented in this study, for the first time, to model drying of rather thick samples of food materials. An approximate spatial distribution of sample temperature is introduced and combined with the REA to model drying kinetics. Results have indicated that the REA can model both moisture content and temperature profiles. The accuracy and effectiveness of the REA to model drying of thick samples of food materials are revealed in this study. This has extended the application of REA substantially. The application of the REA is currently not restricted for thin layesr or small objects but also for thick samples.     

Reaction Engineering Approach (REA) to Modeling Drying Problems: Recent Development and Implementations

Among the drying models available in the literature, the REA model (which was first proposed in 1996) is semi-empirical. It was described based upon a basic physical chemistry principle. The “extraction of water from moist material” is signified by applying the activation energy concept. The single expression of the extraction rate represents the competition between evaporation and condensation. It also encompasses the internal specific surface area and mass transfer coefficient, and thus is linked to material characteristics. The REA can be classified into two categories—Lumped (L) REA and Spatial (S) REA—which can be used to deal with drying a material as a whole or considering the local phenomena within the material, respectively. Both models have been proven to be very effective. The REA is effective for generating parameters since only one accurate drying run is required to establish the relative activation energy function. Both internal and external resistances are modeled by the REA. In its lumped format, the REA is employed to describe the global drying rate, while in the S-REA, the REA is used to model the local evaporation rate. This article covers fundamentals of the REA which have not been fully explained, as well as the most recent development and applications. The application of the S-REA as a non-equilibrium multiphase model is highlighted.     

Multiphase modeling of intermittent drying using the spatial reaction engineering approach (S-REA)

Several schemes of energy minimization of drying process including intermittent drying have been attempted. Intermittent drying is conducted by applying different heat inputs in each drying period. An effective and physically meaningful drying model is useful for process design and product technology. The lumped reaction engineering approach (L-REA) has been shown previously to be accurate to model the intermittent drying In L-REA, the REA (reaction engineering approach) is used to describe the global drying rate. In this study, the REA is used to model the local evaporation/condensation rate and combined with the mechanistic drying models to yield the spatial reaction engineering approach (S-REA), a non-equilibrium multiphase drying model. The accuracy of the S-REA to model the intermittent drying under time-varying drying air temperature is evaluated here. In order to incorporate the effect of time-varying drying air temperature, the equilibrium activation energy and boundary condition of heat balance implement the corresponding drying settings in each drying period. The results of modeling using the S-REA match well with the experimental data. The S-REA can yield the spatial profiles of moisture content, concentration of water vapor, temperature and local evaporation/condensation rate so that better understanding of transport phenomena of intermittent drying can be obtained. It is argued here that the REA can describe the local evaporation rate under time-varying external conditions well. The S-REA is an effective non-equilibrium multiphase approach for modeling of intermittent drying process.     

Superheated Steam Drying of Single Wood Particles: Modeling and Comparative Study with Hot Air Drying

A deterministic model is developed to describe the superheated steam drying process of single wood particles. A comparison between calculated data and experimental observations infers that the moisture‐dependent effective diffusivity is suitable to be used for beechwood material drying. To reduce the computational cost of the deterministic drying model, a semi‐empirical model is proposed within the framework of a reaction engineering approach (REA). The validity of the proposed model is checked by comparing against experimental data from literature. The experimental drying behavior may fairly be reflected by the reduced model. Due to the simplicity and predictive ability of the REA model, this semi‐empirical model can be implemented to describe heat and mass transfer between a population of single particles and a drying agent in dryer models.     

Modeling of Convective Drying of Sawdust Using a Reaction Engineering Approach

Drying as a simultaneous heat and mass transfer process can be modeled via the reaction engineering approach (REA) where the apparent activation energy of the material is established and related to its moisture content during drying. This relationship is unique as the normalized activation energies can be collapsed into a single equation irrespective of the drying conditions and dryer types. Here, REA was applied to model the drying kinetics of sawdust using convective hot air in a laboratory setup. The normalized (relative) activation energy curve generated from one drying experiment was employed to predict the drying kinetics and temperature profiles. The REA can describe well the convective drying kinetics of sawdust, and major physics of the drying process was captured well with this technique.     

Drying of a system of multiple solvents: Modeling by the reaction engineering approach

Drying is a very important industrial operation in society. In drying, solute may dissolve in an aqueous solvent, a nonaqueous solvent or a mixture of solvents. Many mathematical models have been published previously to model drying of solute in water. The reaction engineering approach (REA) is known to be an easy‐to‐use approach. It can describe well many drying cases of water removal. Currently, no simple lumped model has been attempted to describe drying of porous materials containing a mixture of solvents. In this study, for the first time, REA is constructively implemented to model drying in a mixture of one aqueous and one nonaqueous solvent. The REA is applied here to model the drying of polyvinyl alcohol/methanol/water under constant and time‐varying environmental conditions. Similar to the relative activation energy of water, that of methanol is generated through one accurate drying run. For modeling the time‐varying drying, the relative activation energies are the same as those for modeling convective drying under constant ambient conditions but combined with the equilibrium activation energies at the corresponding humidity, methanol concentration, and temperature for each drying period. The REA is accurate to model drying of a solute in nonaqueous solvent as well as in a mixture of noninteracting solvents. In the future, spatially distributed REA for nonaqueous or mixtures of both aqueous and nonaqueous solvent will be explored for fundamental understanding and for practical application. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2144–2153, 2016     

Application of the reaction engineering approach (REA) for modeling intermittent drying under time-varying humidity and temperature

A ‘good’ drying model is important for the design of dryer, evaluation of dryer performance and prediction of product quality. Among the available models, the reaction engineering approach (REA) is a lumped model, proven to be simple, robust and accurate to model drying of several materials. In this paper, the REA is implemented to model intermittent drying, which is usually practiced for saving energy consumption and maintaining product quality during drying, under time-varying drying air temperature and humidity, which is a challenging drying case to model. For this purpose, the equilibrium activation energy (ΔE_v,b) is defined according to the drying settings in each time period and combined with the relative activation energy (ΔE_v/ΔE_v,b) generated from the convective drying experimental data obtained under constant drying conditions. The mass and heat balances also implement the corresponding drying settings in each time period during the intermittent drying. The results indicate that the REA can describe both the moisture content and temperature profiles of the intermittent drying under time-varying drying air temperature and humidity well. The accuracy, simplicity and robustness of the REA for the intermittent drying under time-varying drying air temperature and humidity are proven here. This has provided a major and significant extension of the REA on modeling challenging drying cases.     

A Learning Process Simulator for Fluidized Bed Dryers Application to Bentonite Drying

A fluid bed dryer simulator was developed under Excel 5 wlth Visual Basic for Applications environment The simulator iS based on a mathematical model describing heat and mass transfer in the dryer. The total model incorporates empirical models for the Drying Constant and the Residence Time. These empirical models are crucial in the total model efficiency. Thus a procedure for updating the parameters of the empirical models is provided. This procedure constitutes the 'learnhg' property of the simulator. Two databases are Supplied. The first contains laboratory drying data and it is used for tuning the Drying Constant empirical model. The second contains industrial drying data from the real operation of the dryer, and it is used for tuning the Residence Time empirical model. The experience from the industrial application of the simulator proved that the simulator is a powerful tool for flexible operation of an industrial dryer. This paper is presents the total mathematical model of the dryer, the learning concept, and the databases, including useful information concerning the drying kinetics of bentonite. A simulator outline is presented and typical capabilities and uses are briefly described. A case study for flexible operation of an industrial dryer is discussed.     

Heat and Mass Transfer in Unsaturated Porous Cake with Heated Walls

The mineral granules in the industrial drying units such as rotary dryer or fluidized dryer or the membrane in the PEMFC experience transient multiphase heat and mass transfer with transient heating mode. In particular, the transport process within mineral granules in the dryer is difficult to model owing to effects of complicated granule-granule collision and granule-heated surface. This article presents a comprehensive model consisting of continuity and heat and mass balances of three phases in an unsteady state. Numerical results revealed the flow patterns and temperature distributions of gas and liquid phases in mineral granule over time. The thermal response of the heated medium will be very different under low and high mixing intensities. The development of a recirculation liquid zone to balance the yielded capillary suction gradient enhances local evaporation and vapor accumulation rates, thus determining the overall evaporation rate form medium.     

A Learning Process Simulator for Fluidized Bed Dryers Application to Bentonite Drying

ABSTRACT

A fluid bed dryer simulator was developed under Excel 5 wlth Visual Basic for Applications environment The simulator iS based on a mathematical model describing heat and mass transfer in the dryer. The total model incorporates empirical models for the Drying Constant and the Residence Time. These empirical models are crucial in the total model efficiency. Thus a procedure for updating the parameters of the empirical models is provided. This procedure constitutes the ‘learnhg’ property of the simulator. Two databases are Supplied. The first contains laboratory drying data and it is used for tuning the Drying Constant empirical model. The second contains industrial drying data from the real operation of the dryer, and it is used for tuning the Residence Time empirical model. The experience from the industrial application of the simulator proved that the simulator is a powerful tool for flexible operation of an industrial dryer. This paper is presents the total mathematical model of the dryer, the learning concept, and the databases, including useful information concerning the drying kinetics of bentonite. A simulator outline is presented and typical capabilities and uses are briefly described. A case study for flexible operation of an industrial dryer is discussed.     

A Model for Drying of an Aqueous Lactose Droplet Using the Reaction Engineering Approach

Spray drying is the primary method for manufacturing of food powders from liquids. Optimal design and optimization of spray drying operations at the fundamental level require both modeling of the drying characteristics of a single droplet and dryer wide simulations using computational fluid dynamics (CFD). An accurate yet simple model for drying of a single droplet, which does not require solution of partial differential equation, is ideal input for CFD simulations. The reaction engineering approach (REA) is shown to be appropriate in this regard. It has been successfully used for prediction of skim and whole milk droplet drying behavior under various drying conditions. In this study, an aqueous lactose solution was dried in droplet form and the appropriate REA model parameters obtained. The change of diameter of the droplet during drying was measured experimentally and compared with the model results.     

A Model for Drying of an Aqueous Lactose Droplet Using the Reaction Engineering Approach

Spray drying is the primary method for manufacturing of food powders from liquids. Optimal design and optimization of spray drying operations at the fundamental level require both modeling of the drying characteristics of a single droplet and dryer wide simulations using computational fluid dynamics (CFD). An accurate yet simple model for drying of a single droplet, which does not require solution of partial differential equation, is ideal input for CFD simulations. The reaction engineering approach (REA) is shown to be appropriate in this regard. It has been successfully used for prediction of skim and whole milk droplet drying behavior under various drying conditions. In this study, an aqueous lactose solution was dried in droplet form and the appropriate REA model parameters obtained. The change of diameter of the droplet during drying was measured experimentally and compared with the model results.     

Experimental Study of the Heat and Mass Transfer During Drying in a Fluidized Bed Dryer

Drying curves obtained in a pilot-scale fluidized bed dryer using biological source solids (sawdust, soya and fish meal) were used to estimate the parameters involved in heat and mass transfer phenomenas: heat transfer coefficient and moisture diffusivity coefficient. Parameters involved in mass transfer were estimated from drying models based on diffusional mechanisms and others that in addition consider internal and external resistance to the mass transfer. The estimate ef ective diffusivity coefficient was between 2x10-11 to lx10 (m2/s) for the considered products. Heat transfer coefficient was estimated from drying data points in the constant drying rate period when the external resistance to the mass transfer controls the process.     

Experimental Study of the Heat and Mass Transfer During Drying in a Fluidized Bed Dryer

ABSTRACT

Drying curves obtained in a pilot-scale fluidized bed dryer using biological source solids (sawdust, soya and fish meal) were used to estimate the parameters involved in heat and mass transfer phenomenas: heat transfer coefficient and moisture diffusivity coefficient. Parameters involved in mass transfer were estimated from drying models based on diffusional mechanisms and others that in addition consider internal and external resistance to the mass transfer. The estimate ef ective diffusivity coefficient was between 2x10-11 to lx10 (m2/s) for the considered products. Heat transfer coefficient was estimated from drying data points in the constant drying rate period when the external resistance to the mass transfer controls the process.     

Two-Fluid, Two-Dimensional Model for Pneumatic Drying

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

Two-Fluid,Two-Dimensional Model for Pneumatic Drying

Abstract

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

流化床在生物物料热力干燥中的应用

干燥是许多生物制品的最后一道工艺操作过程。由于大多数生物制品均具有热敏和湿敏的特性,干燥方法和操作参数的选择对于生物制品活性的保存非常重要。本文通过光合菌液和复合生物饲料干燥的研究表明,流化床干燥器适用于光合菌液和复合生物饲料的干燥,干燥后产品可保持较高活性。     

Some Considerations in Modeling of Moisture Transport in Heating of Hygroscopic Materials

Hygroscopic materials are those in which the equilibrium pressure of water vapor changes with moisture content and temperature, such as food, soil or wood, etc. Heat and moisture transports are coupled in heating of hygroscopic materials. One of the major links between temperature and moisture changes is water evaporation. There have been different formulations on modeling of evaporation in the past. A typical approach (Model 1 in this article) is to equate the evaporation rate to the rate of local moisture loss. The first part of this paper illustrates that such an approach is physically incorrect based on fundamental conservation relationships. A conservation-based coupled heat and moisture transfer model (Model 2) is presented here based on previous multiphase transport models. It shows that total evaporation rate over the entire material is included in Model 1 while the local evaporation rate is not. The situations when Model 1 may or may not generate large errors are discussed. The second part of this article completes the modeling of evaporation using Model 2. Two types of formulations are given depending on the phase equilibrium of moisture in the hygroscopic materials. When phase equilibrium between water and vapor is assumed for any location at any time, vapor pressure is provided as known variables. In a nonequilibrium approach, evaporation rate needs to be provided. The latter poses numerical difficulties near the material surface, which arises from the possibility that equilibrium state may have a large change near the surface. Further discussions were made on the physical and numerical considerations in using both approaches.     

Simulating Industrial Spray-Drying Operations Using a Reaction Engineering Approach and a Modified Desorption Method

A predictive tool using a thermodynamic approach has recently been developed to determine several important gas-feed parameters for industrial spray-drying processes. In this approach, a desorption behavior of materials was evaluated and the behavior was linked with overall heat and mass balances over the dryer. Using the desorption behavior of materials and the overall heat and mass balances, a spray-drying software SD²P® was designed at the Institut National de la Recherche Agronomique (INRA) in France. The SD²P® software allows the prediction of optimal inlet drying air temperatures with acceptable accuracy (95–99% accuracy) for spray drying of dairy products. In order to predict detailed quality parameters and stickiness behavior of a product during processing, the reaction engineering approach (REA) was combined with a modified desorption method. A traditional experimental setup is replaced with a new setup, which is described in this article. Drying kinetics parameters were predicted using this new setup. Important gas-feed parameters were predicted using the 1D simulation-based software and compared with SD²P® predictions and are reported here.