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.     

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.     

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.     

Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass‐transfer model for drying of food and biological materials

Drying is a complex process which involves simultaneous heat and mass transfer. Complicated structure and heterogeneity of food and biological materials add to the complexity of drying. Drying models are important for improving dryer design and for evaluating dryer performance. The lumped reaction engineering approach (L‐REA) has been shown to be an accurate and robust alternative for cost‐effective simulations of challenging drying systems. However, more insightful physics has to be shown spatially. In this study, the REA is coupled with the standard mechanistic drying models to yield the spatial‐REA (S‐REA) as nonequilibrium multiphase mass‐transfer model. The S‐REA consists of a system of equations of conservation with the REA representing the local evaporation and wetting rate. Results of the modeling using the S‐REA match well with the experimental data reported previously. This is the first comprehensive REA approach to model the profiles of water vapor concentration during drying of food and biological materials. This study indicates that the S‐REA can be an accurate nonequilibrium multiphase mass‐transfer model with appropriate account of the local evaporation rate. The overall REA concept is expected to contribute substantially for better and cost‐effective representation of transport phenomena of drying process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 55–67, 2013     

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.     

Multiscale Modeling of Superheated Steam Drying of Particulate Materials

A multiscale model for predicting the superheated steam drying behavior of a packed bed filled with particulate porous material is presented. By using a reaction engineering approach (REA) a semi-empirical model is developed that can describe the heat and mass transfer between a single particle and the surrounding drying agent. By analogy between superheated steam drying and hot air drying, the relative activation energy of the REA model is formulated. Next, the single-particle drying model is fed into a continuum-scale model of a packed bed. The temperature and moisture content of the solid and the vapor temperature are successfully predicted by the bed-scale model. To endow the bed-scale model with predictive capabilities, simulation results are compared with experimental literature data.     

反应工程方法在锂电池真空干燥模拟上的应用

锂离子电池注液之前的真空干燥,对于电芯的循环性能、安全性、稳定性有极其重要的影响。电芯结构设计、材料体系、烘箱尺寸等的不同会导致真空干燥过程存在差异。反应工程方法(REA)在常压、高初始水含量的对流干燥模拟预测上已有广泛应用,本研究将REA干燥理论应用于真空、低初始水含量的干燥过程仿真,发现与实验结果匹配良好。同时考虑了电芯气袋与烘箱环境湿度变化对干燥过程的影响,水含量预测偏差小于10%,利用单因子仿真实验所总结的规律能用于指导锂电池真空干燥工艺的改善。介绍了该模型在生产中的应用情况,也表明REA将在锂电池真空干燥预测上有很好的工业应用前景。     

反应工程方法在锂电池真空干燥模拟上的应用

锂离子电池注液之前的真空干燥,对于电芯的循环性能、安全性、稳定性有极其重要的影响。电芯结构设计、材料体系、烘箱尺寸等的不同会导致真空干燥过程存在差异。反应工程方法(REA)在常压、高初始水含量的对流干燥模拟预测上已有广泛应用,本研究将REA干燥理论应用于真空、低初始水含量的干燥过程仿真,发现与实验结果匹配良好。同时考虑了电芯气袋与烘箱环境湿度变化对干燥过程的影响,水含量预测偏差小于10%,利用单因子仿真实验所总结的规律能用于指导锂电池真空干燥工艺的改善。介绍了该模型在生产中的应用情况,也表明REA将在锂电池真空干燥预测上有很好的工业应用前景。     

Microwave drying at various conditions modeled using the reaction engineering approach

ABSTRACT

One of the most significant process intensification schemes in drying is microwave drying. Modeling the process of microwave drying is very useful. The lumped reaction engineering approach (REA) is now coupled with appropriate equations for modeling microwave heating. Here, a slight modification of the equilibrium activation energy is needed since the product temperature is higher than the ambient temperature. Unlike the diffusion-based approach, the REA drying parameters were generated from minimum number of drying runs. It has been found that the modifications lead to excellent agreements between the predicted and experimental data. The results of modeling match well with the experimental data. The overall model is accurate to describe the moisture content and temperature profiles. Comparisons with the diffusion-based approach indicate that the REA can achieve comparable or even better agreement toward the experimental data. This exercise has demonstrated that a simple combination of the lumped reaction engineering approach and the microwave energy absorption is versatile in predicting the microwave drying process accurately; thus, this worked example will be illustrative for future needed studies.     

A composite reaction engineering approach to drying of aqueous droplets containing sucrose,maltodextrin (DE6) and their mixtures

Recently, several studies have been published on the spray drying of sucrose and other low‐molecular‐weight sugars which are typically sticky materials. Sticky materials can not be processed under normal drying conditions and may require addition of high‐molecular‐weight carbohydrates such as maltodextrin. Predicting appropriate drying conditions are however difficult due to the unavailability of drying kinetics. In this article, we have formulated the drying kinetics model using the reaction engineering approach (REA) for the drying of aqueous sucrose and aqueous maltodextrin (DE6) droplets. The relative activation energy was empirically obtained based on experimental measurements. To model the drying of droplets containing both solutes (sucrose and maltodextrin), a new “composite” REA has been established and presented here for the first time. Results demonstrated that the composite REA forms a reliable framework to model the drying of aqueous solutions of pure carbohydrates and their mixtures. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

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 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.     

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.     

SIMPLIFIED MODELLING FOR THE DRYING OF A NON HYGROSCOPIC CAPILLARY POROUS BODY USING A COMBINATION OF DIELECTRIC AND CONVECTIVE HEATING

The drying of non-hygroscopic, capillary porous materials with dielectric and convective heating is considered. Simplified models are used to examine the effect of a partially wetted surface or receding evaporation front on the temperature of the wet material. Physical mechanisms which can enhance the internal moisture flow, as compared with convective heating alone, are examined ualitatively.     

SIMPLIFIED MODELLING FOR THE DRYING OF A NON HYGROSCOPIC CAPILLARY POROUS BODY USING A COMBINATION OF DIELECTRIC AND CONVECTIVE HEATING

The drying of non-hygroscopic, capillary porous materials with dielectric and convective heating is considered. Simplified models are used to examine the effect of a partially wetted surface or receding evaporation front on the temperature of the wet material. Physical mechanisms which can enhance the internal moisture flow, as compared with convective heating alone, are examined ualitatively.     

Microwave combination heating: Coupled electromagnetics‐ multiphase porous media modeling and MRI experimentation

The work includes development of a multiphase porous media model and magnetic resonance imaging (MRI) experiments to study microwave combination heating. Combination of electromagnetic, convective and radiant heating was considered. The material being heated was modeled as a hygroscopic porous medium with different phases: solid matrix, water and gas, and included pressure driven flow, binary diffusion and phase change. The three‐dimensional transport model was fully coupled with electromagnetics to include the effect of variable properties. MRI was used to obtain spatial temperature and moisture distributions to validate the model. The model demonstrated that high and low moisture materials behave differently under different combinations of heating and general guidelines for combining heating modes were obtained. Low moisture materials can be heated effectively using higher microwave power which is not possible in high moisture material. Cycling of microwave was found to be useful in distribution of excessive volumetric heat generated by microwaves. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Optimal control of convective drying of saturated porous materials

Numerical simulations of optimal control applied to saturated capillary‐porous materials subjected to convective drying are presented. The optimization process is concerned with such drying parameters as drying rate, energy consumption, and product quality. The thermo‐hydro‐mechanical model of drying is developed to describe the kinetics of drying and to determine the drying‐induced stresses which are responsible for damage of dried products. The effective and the admissible stresses are defined and used to formulate the Huber‐von Mises–Hencky strength criterion enabling assessment of possible material damage. The method of genetic algorithm is used for operation with drying conditions in such a way as to ensure minimum energy consumption and to get the effective stress less than the strength of dried material, and thus, to preserve a good quality of dried products at possibly high drying rate. Numerically simulated optimal drying processes are illustrated on the examples of finite dimensions of kaolin‐clay cylinders subjected to convective drying. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4846–4857, 2013     

Modeling Intermittent Drying of Wood under Rapidly Varying Temperature and Humidity Conditions with the Lumped Reaction Engineering Approach (L-REA)

For improving product quality and minimizing energy consumption during drying, intermittent drying is often recommended. The mathematical models that are used to describe intermittent drying are usually transport phenomena based, complex models. In this study, the lumped reaction engineering approach (L-REA) is implemented to model wood drying under rapid periodically changed drying air temperature and humidity with high number of cycles of intermittency. The equilibrium activation energy (ΔE _v,b ), an important parameter for REA approach, is evaluated according to the corresponding drying air temperature and humidity in each drying section. The results of modeling suggest the L-REA works well with the experimental data. The simplicity of the L-REA is obvious and is hoped to be used in an industrial setting more readily. The L-REA can be used for sustainable processing in industries to assist in energy audit and management.