Modeling and Experimental Studies of Adsorptive Dewatering of Selected Aliphatic Alcohols in Temperature Swing Adsorption System

Based on experimental work, closely coupled with mathematical modeling, an analysis was performed of the adsorptive drying of selected water-aliphatic alcohol solutions. The experimental work involved ethanol, n-propanol, and n-butanol dehydration using two adsorbents, 3A and 4A zeolite molecular sieves. The isothermal model developed in this paper incorporates an overall linear mass driving force, including liquid film mass transfer and intraparticle diffusion coefficients, a variable axial diffusivity, and experimentally determined Langmuir-Freundlich isotherms. Breakthrough curves generated by the model were compared with those obtained experimentally, giving a fairly good fit. The model simulations enabled determination of the water content profiles in adsorbent beds.     

Foam-Mat Freeze Drying of Egg White—Mathematical Modeling Part II: Freeze Drying and Modeling

Foam-mat freeze drying is one of the promising methods of drying, which utilizes advantages of both freeze drying and foam-mat drying. Egg white with its excellent foaming properties makes a suitable candidate for foam-mat freeze drying. Experiments were conducted to study foam-mat freeze drying of egg white, in an effort to determine the suitability of this method. Xanthan gum (XG) at 0.125% concentration was used as stabilizer for foaming. The results showed that the addition of xanthan gum during foaming has a positive impact in reducing the total drying time and also produces excellent quality egg white powder. The addition of stabilizer also plays an important role in improving drying. Simple models were applied for determining drying time and diffusion coefficients during freeze drying.     

Spray Drying of Lactobacillus plantarum WCFS1 Guided by Predictive Modeling

Shelf life of probiotic microorganisms can be retained by drying. Spray drying is an economically interesting alternative to freeze drying with that respect. However, the viability can decrease due to the drying process and testing it is laborious and expensive. This research shows that the viability of Lactobacillus plantarum WCFS1 during pilot scale drying can be predicted with kinetics gathered at a single droplet level. Using this approach, it could be demonstrated that the viability of L. plantarum WCFS1 during spray drying is mainly determined by the combination of temperature and moisture content during the first 0.5 seconds after atomization. The combination of a high moisture content and a high temperature appeared most detrimental to the residual viability. Moreover, it was found to be important to take into account the particle size distribution during atomization when predicting viability, since this has a large effect on the moisture content during this first 0.5 seconds. Finally, it was observed that shelf life during storage was mainly determined by the moisture content of the powder. A lower moisture content resulted in a higher viability. Above a moisture content of 6%, shelf life stability rapidly decreased in the applied maltodextrin (DE = 16) matrix.     

Mathematical Modeling of the Coupled Transport Phenomena and Color Development: Finish Drying of Trellis-Dried Sultanas

A mathematical model for simulation of simultaneous heat and mass transport was developed to describe the drying kinetics during finish drying of trellis-dried sultanas. In this model, the governing partial differential equations for heat and mass transfer for a solid spherical body were numerically solved using a finite difference technique. In addition, a kinetic model was coupled to the heat and mass transfer calculations to simultaneously predict the evolution of product color during the drying process. This allows predictions of moisture content, temperature, and color profiles of the product in a space–time domain during the drying process as a function of various operating conditions.

Predictions compared well with the experimental values, implying that the proposed numerical model can be used with confidence for the simulation of the important transport phenomena in optimizing the design and operation of a drying system for sultanas that maximizes the retention of the desired product color. The work has demonstrated the importance of establishing optimal and closely controlled drying conditions because significant effects of the key operational parameters on drying kinetics and the associated changes of product color were found. The modeling approach proposed here can be extended to other products and for incorporation of other product quality indices.     

A Review on Paste Drying with Inert Particles as Support Medium

An overview of the contributions of the literature in the field of drying with inert particles is presented. Recent experimental studies developed in conventional spouted and fluidized beds aimed at describing and understanding the effects of the presence of a liquid or paste on the global behavior of these types of dryers are approached. Advances in numerical simulation of drying with inert particles are discussed. Several open research issues and future perspectives are addressed.     

Modeling of Drying of Gaseous Mixtures in TSA System with Fixed Bed of Solid Desiccants

A nonisothermal, nonequilibrium mathematical model was developed to theoretically analyze adsorptive drying of gaseous mixtures containing water and volatile organic compounds (VOCs). The analysis concerns a four-bed cyclic temperature swing adsorption (TSA) system. The two fixed beds are formed of silica gel primarily as the water vapor adsorbent. The other two consist of activated carbon as the adsorbent of the organic component (e.g., benzene, isopropanol). In the model, possible insignificant interactions among the VOCs and water during adsorption and desorption were neglected. The following parameters were considered to study their effect on the process efficiency: relative humidity of the inlet gas, temperature of the purge gas, and height of the adsorbent beds. Simulation results showed that both the shape of the adsorption isotherm and heat effects played an important role in the breakthrough behavior of water vapor adsorption on silica gel. The model accurately simulated experimental data taken from literature.     

固定床吸附数学模型现状及应用

主要综述了固定床反应器数学模型的发展现状，并对其在黄磷尾气的净化应用中做出一定的分析，对其提出了一些见解。     

Influence of osmotic drying with an aqueous poly(ethylene glycol) liquid desiccant on alumina objects gelcast with gelatin

Gelcasting and liquid desiccant drying are novel forming and drying methods used to mitigate common issues associated with the fabrication of complex advanced ceramic objects. In this study, the molecular weight and osmotic pressure of aqueous poly(ethylene glycol) (PEG) desiccant solutions were simultaneously varied to understand their influence on the net mass loss rates of gelcast alumina samples prepared using gelatin as a gelling agent. Additionally, the amount of PEG diffusion and water diffusion to and from the ceramic samples after 150 min of immersion in the liquid desiccant was correlated to the solution properties as was the final bulk density of the sintered samples. Solutions with high molecular weight and low osmotic pressure resulted in low PEG gain and low water loss, while solutions with low molecular weight and high osmotic pressure resulted in high PEG gain and high water loss. In some cases, more than 40 wt% of the total water per sample was removed through the liquid desiccant drying process.     

Modeling of Seed Coating in a Spouted Bed

In this work, a model based on population balance equations applied to perfect mixture domains has been employed to represent the coating of soybeans with fertilizer in a conical–cylindrical spouted bed. The results of the present model provided explicit equations for the coating mean and variance. The coating mass distribution function was validated against experimental data. The effect of operational time on the distributions was analyzed, showing that the coating uniformity can be improved by increasing the operating time.     

Fluidized Bed Air Drying: Experimental Study and Model Development

The presented study describes the processes and mechanisms of batch fluidized bed drying. The influencing factors of hot air drying are theoretically and experimentally examined, in order to present the relations between temperature and humidity profiles and all other drying parameters. A physical model is presented to facilitate the calculation of the drying processes under defined conditions. Three succeeding drying stages are therefore modeled. Mass and energy balances including all components taking part in the process are formulated. The model clarities the drying process under the assumption of pure heat transfer mechanisms. It does not contain adaptive parameters and takes into account an inactive bypass fraction of the fluidization and drying medium. The evaluation of the model was successful for two fluidized bed plants with nominal widths of 100 mm and 400 mm. The experiments showed sufficient accuracy and transferability of the model to equipment of application‐oriented dimensions.     

Modeling and Numerical Simulation of Clays Cracking During Drying

During drying or desiccation of clay-type materials, some stresses appear. Usually they are compressional inside of the material and tensional close to the surface. If the tensional stresses exceed the material strength, the clay cracks. This article is devoted to the modeling and numerical simulation of this phenomenon. The proposed model consists of two parts. The mass transfer is described by a simple diffusion equation together with convective boundary conditions. In the mechanical part it is assumed that the clay is composed of small particles linked together by cohesive forces. These forces are described with the use of mesh models. Two models are proposed: elastic (mesh consists of springs) and viscoelastic one (mesh consists of Maxwell elements). Four types of clays were tested experimentally to obtain the model parameters. The tested materials were selected with respect to different mineralogical compositions that determine the water-bonding ability. Simulations of the convective drying of bricks made of these clays were performed. It was shown that the degree of cracking depends on the quartz content of the clay. The obtained results were compared with experimental ones and good agreement between simulations and experiment was obtained. Additionally, the inner forces caused by drying are analyzed and discussed in this work.     

Experimental Study and Modeling of Crystalline Powders Vacuum Contact Drying with Intermittent Stirring

Modified literature models were successfully applied to simulate the evolution of the average solvent content (ethanol) of potassium chloride bed during vacuum contact drying with intermittent stirring. Our new modeling approach incorporated the following modifications: the introduction of a jacketed vessel heat transfer coefficient and an accumulation term for the heating wall temperature; the application of alternate static bed and stirred bed conditions; and modeling of all the three drying phases, namely the constant rate phase, the transition phase, and the falling rate phase. Moreover, several validation experiments were carried out with different operating conditions to identify the values of the unknown model parameter. The optimal stirring conditions were investigated by calculating total drying times for different sequences of stirring and no stirring periods.     

Modeling of Drying Curves for Some Foodstuffs Using a Kinetic Equation of High Order

Non-linear regression was used to fit a high order kinetic model to drying curves for mango and cassava. For comparison purposes, the same experimental data were also adjusted by non-lines regression to a model based on exponential series, and to another exponential model by simple linear regression. The high order model fit the experimental data with higher precision (r2 Al.98) than the other exponential series models. The proposed higher order model is mathematically simple as compared to the exponential series, and could be used for simulation of drying processes.     

Experimental Study and Modeling of Crystalline Powders Vacuum Contact Drying with Intermittent Stirring

Modified literature models were successfully applied to simulate the evolution of the average solvent content (ethanol) of potassium chloride bed during vacuum contact drying with intermittent stirring. Our new modeling approach incorporated the following modifications: the introduction of a jacketed vessel heat transfer coefficient and an accumulation term for the heating wall temperature; the application of alternate static bed and stirred bed conditions; and modeling of all the three drying phases, namely the constant rate phase, the transition phase, and the falling rate phase. Moreover, several validation experiments were carried out with different operating conditions to identify the values of the unknown model parameter. The optimal stirring conditions were investigated by calculating total drying times for different sequences of stirring and no stirring periods.     

Fixed‐Bed Heat Storage – Mathematical Modeling Approaches

While renewable heat makes up only 13 % of overall German heat consumption, the share of renewable electricity produced from wind, solar, water, and geothermal power already reached 36 % of overall electricity consumption in 2017. One measure to support the integration of renewable heat in the German energy system is the use of heat storage systems. Although water‐based heat storage systems for temperatures up to 100 °C are state of the art, systems for temperatures up to several hundred degrees Celsius are still under investigation or in the demonstration phase. Therefore, this work focuses on the development of a simulation model for analyzing and engineering fixed‐bed thermal storage systems that are filled with an inert bulk material such as stone fragments.     

Effect of Geometry of Rice Kernels on Drying Modeling Results

Geometry of rice grain is commonly represented by sphere, spheroid, or ellipsoid shapes in the drying models. Models using simpler shapes are easy to solve mathematically; however, deviation from the true grain shape might lead to large errors in predictions of drying characteristics such as moisture content (MC) and moisture gradients (MG). This research was undertaken to determine the impact of such shape considerations on prediction of drying characteristics. Impact of shrinkage of grains caused by drying was also investigated. Three separate mathematical models, each representing rice grain by sphere, spheroid, and ellipsoid shapes, were developed to describe the drying process. These models were solved by the finite element method using Comsol Multiphysics® simulation program. Drying simulations showed important differences in predictions of MC and MG in these three models. The sphere-shaped model predicted a slower drying than the spheroid- and ellipsoid-shaped models, whose MC predictions were similar. In all three models, maximum moisture gradients (MMG) were observed along the shortest axis in the bran region. During drying, MMG increases, reaches a peak, and then decreases. Magnitude and onset of peak of MMG were different in the three models. These differences in drying predictions among the three models make it important to use the appropriate shape to represent the rice grain in mathematical models. Ellipsoid shape, which closely resembles geometry of the rice grain, was found to be the most suitable. Reliable MG predictions from such ellipsoid-shaped models could be correlated to grain fissuring, which thereafter can be employed to optimize the drying process. The impact of shrinkage of rice grains during drying on model predictions is very small. In any drying simulation, maximum error due to neglecting shrinkage would be less than 5% of total moisture loss value.     

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.     

Drying Kinetics of Apple Tissue Treated by Pulsed Electric Field

The aim of this work was to study the influence of pulsed electric field (PEF) on the drying kinetics of apple tissue. Therefore, mathematical models that are commonly used in the literature were applied to describe the process. PEF treatment of the samples was carried out at an intensity of E = 5–10 kV/cm and 10–50 pulse numbers. Subsequently, the apples were convectively dried at 70°C and air velocity of 2 m/s. Based on electrical conductivity measurement, the cell disintegration index Z _p was computed. Midilli et al.'s(Drying Technology, Vol. 20, pp. 1503–1513, 2001) model was evaluated as the most adequate to describe the moisture transfer in PEF-treated and intact samples. PEF pretreatment induced a reduction in drying time of up to 12% when 10 kV/cm and 50 pulses were applied. For instance, after 60 min of drying, the dimensionless moisture ratio for PEF-treated (10 kV/cm, 50 pulses) samples was 0.18 compared to 0.26 for the untreated apples. The effective moisture diffusivity, calculated on the basis of the Fick's second law, was 1.04 × 10^?9 m/s for intact samples and from 1.09 × 10^?9 to 1.25 × 10^?9 m²/s for PEF-treated samples at 10 pulses at 5 kV/cm and 50 pulses at 10 kV/cm, respectively.     

Modeling of Drying Curves for Some Foodstuffs Using a Kinetic Equation of High Order

ABSTRACT

Non-linear regression was used to fit a high order kinetic model to drying curves for mango and cassava. For comparison purposes, the same experimental data were also adjusted by non-lines regression to a model based on exponential series, and to another exponential model by simple linear regression. The high order model fit the experimental data with higher precision (r2 Al.98) than the other exponential series models. The proposed higher order model is mathematically simple as compared to the exponential series, and could be used for simulation of drying processes.     

Modeling and simulation of a beet pulp dryer for a training simulator

This paper deals with the modeling of a high-temperature rotatory sugar beet pulp dryer for training simulators. This model adds some aspects to traditional drum dryer models; particle size distribution, detailed modeling of the solid phase, and the inclusion of malfunctions in the model. An object-oriented simulation package is selected to implement this model in a library, together with models of other components of a drying plant. Using this library, the complete plant and its control system are built and simulated. Finally, the simulation of the plant integrated together with a SCADA makes up the training simulator.