Drying of solids; estimation of the mathematical model parameters

In order to determine physical meaning of a thin‐layer mathematical model parameter, the Page model was modified and tested on numerous experimental data. Applicability of the model was tested on the drying kinetics data, X(t), of 11 different types of the porous materials and dried in a convective, vacuum and/or microwave dryers under the predetermined external process conditions. During the entire drying time the drying kinetics of all the investigated materials and heating methods were successfully correlated with the modified Page model. The evaluated values of a new parameter, t_k, corresponded to the time at which diffusion, as a governing mechanism of moisture movement through the material, started. The results were confirmed by the pore size distribution of some materials.     

Modeling the kinetics of drying of viscose fibre

The dependences for describing the kinetics of drying of viscose fibre in restriction of external and internal diffusion with consideration of the period of heating the material are examined. The kinetic dependences are compared with the experimental data for different viscose fibre drying modes and types (convection and microwave with exhaust of vapors). It was confirmed that microwave drying significantly enhances moisture removal. The experimental data on viscose fibre drying kinetics were generalized with a modified quasistationary method. These dependences describe the periods of constant and diminishing drying rates and the heating period with accuracy sufficient for practical calculations. It was shown how to determine the fibre moisture content in any drying zone with the proposed equations. __________ Translated from Khimicheskie Volokna, No. 6, pp. 54–57, November–December, 2006.     

干燥方式对红枣动力学及挥发性成分的影响

采用热风干燥、真空冷冻干燥和微波真空干燥对红枣进行干燥处理，结合顶空固相微萃取-气相色谱-质谱（headspace solid-phase microextraction-gas chromatography-mass spectrometry，HS-SPME-GC-MS）和电子鼻对枣片挥发性成分进行了分析，并对比了3种干燥方式对红枣色泽、动力学和挥发性成分的影响。结果表明，热风干燥和微波真空干燥对枣片色泽影响较大，真空冷冻干燥能够更好的保持原始色泽；对动力学方程进行拟合，发现Page 模型为预测红枣3种干燥方式干燥特性最适合的数学模型；干燥对枣片挥发性成分种类及相对含量差异显著，其中干燥前后相同的挥发性成分有19种。挥发性物质主要有酸类、酯类、醇类、醛类、酮类、烃类、杂环类和其他化合物，干燥过后枣片中酸类和烷烃类挥发性成分相对含量显著增加，醛类和杂环类物质显著降低。电子鼻结果表明干燥后枣片香气特征与新鲜红枣有较大的区别，热风干燥和微波真空干燥香味特征较为接近，微波真空干燥枣片的焦甜香特征更为明显。相较于热风干燥和真空冷冻干燥，微波真空干燥效率较高、能耗较低、周期较短，更适于制备干燥枣片。     

Color Change Kinetics of Okra Undergoing Microwave Drying

In this present study, the effect of microwave output power and sample amount on color change kinetics of Turkey okra (Hibiscus esculenta L.) were investigated by using microwave drying technique. The color parameters for the color change of the materials were quantified by Hunter L (whiteness/darkness), a (redness/greenness), and b (yellowness/blueness) values. These values were also used for calculation of the total color change (ΔE), chroma, hue angle and browning index. The microwave drying process changed color parameters of L, a, and b, causing a color shift toward the darker region. The values of L and b decreased, whereas values of a and total color change (ΔE) increased during microwave drying. The mathematical modeling study of color change kinetics showed that L and b fit a first-order kinetic model, whereas a and total color change (ΔE) followed a zero-order kinetic model. However, chroma and browning index (BI) followed a first-order kinetic model, whereas hue angle followed a zero-order kinetic model. On the other hand, the data of the total color change (ΔE), chroma, hue angle, and browning index depending on the ratio of the microwave output power to sample amount were adequately fitted to a quadratic model. For calculation of the activation energy for color change kinetics parameters, the exponential expression based on Arrhenius equation was used.     

突出预测指标钻屑量影响因素研究

煤与瓦斯突出事故已成为当前严重的矿山灾害之一,钻屑指标法是预测该事故的常用方法。分析了煤体物理力学性质、矿山压力、瓦斯压力及测定误差对钻屑量大小的影响。总结出在钻孔半径一定的条件下,钻屑量与煤体的容重、泊松比、煤的弹性模量、矿山压力、瓦斯压力的关系。最后对影响钻屑量测定准确度的因素(钻杆的弯曲程度和连接形式,钻孔施工速度,人为因素和设备因素等)进行了归纳,提出了定期检查和检修设备、加强预测人员专业知识培训、规范操作等改进意见,以便提高预测煤与瓦斯突出的准确性和可靠性。     

A kinetic study of microwave and fluidized-bed drying of a Chinese lignite

The drying kinetics of Chinese lignite in nitrogen fluidized-bed, superheated steam fluidized-bed and microwave were investigated. The changes in the mass as a function of drying time were measured under various drying conditions. The variations of moisture ratio with time were used to test ten different thin-layer empirical drying models given in the literature. In studying the consistency of all the models, some statistical tests, such as χ², residual sum of squares (RSS) and F-value were also used as well as coefficient of determination R². In nitrogen fluidized-bed and superheated steam fluidized-bed, the Midilli–Kucuk model best described the lignite drying process. Drying data in microwave were best described by the Page model, indicative of a difference in kinetics between the two drying methods. This difference was attributed to different heat transfer mechanisms under conventional and microwave drying conditions. The effects of drying parameters in nitrogen fluidized-bed, superheated steam fluidized-bed and microwave drying on the constants and coefficients of the selected models were studied by multiple regression analysis. The apparent diffusion coefficient of moisture in samples was obtained from the kinetics data and the apparent activation energies under nitrogen fluidized-bed, superheated steam fluidized-bed and microwave drying were found to be rather similar.     

MICROWAVE VACUUM DRYING KINETICS OF SOME FRUITS

ABSTRACT

Microwave vacuum drying kinetics of three fruits (namely, apple, kiwi and pear) were studied by introducing an one-parameter empirical mass transfer model, involving a characteristic parameter (drying constant), as a function of process variables. The model was tested with data produced in a microwave oven equipped with vacuum apparatus, using non-linear regression analysis. The investigation involved a wide range of microwave power and vacuum pressure levels. The parameters of the model considered were found to be greatly affected by the microwave power level while vacuum pressure affected slightly the process.     

Solubility Calculation of Oil‐Conta‐minated Drill Cuttings in Supercritical Carbon Dioxide Using Statistical Associating Fluid Theory (PC‐SAFT)

Supercritical fluid extraction is a new technology that could be effectively used to treat oil‐contaminated drill cuttings generated during drilling for oil and gas. In this work, the solubility of oil‐contaminated drill cuttings in supercritical carbon dioxide is obtained by an experimental flow type apparatus. The solubility was measured at 200 bar pressure, over a temperature range of 55–79.5 °C. The measured solubility and experimental data for oil in drill cuttings were correlated using the PC‐SAFT, PR and SRK EOS models, without any adjustable parameters. Average absolute derivations of less than 15.1 %, 98.7 %, and 99.3 % are achieved between predicted and experimental values for the PC‐SAFT, PR and SRK EOS models, respectively, over a wide range of temperatures.     

Drying Kinetics and Energy Consumption in Vacuum Drying Process with Microwave and Radiant Heating

The general objective of this work is to analyze energy input in a vacuum process with the incorporation of microwave heating. Thus, necessary criteria for designing an efficient freeze-drying operation are considered through the analysis of strategies based on the combination of different intensities of radiant and microwave heating. The other aim of this research topic is to study the kinetics of drying in relation to mass transfer parameters. Five freeze-drying strategies using both heating systems were used. Consequently, energy input could be related to diffusivity coefficients, temperature and pressure profiles during dehydration of the product and analyzed in comparison to a conventional freeze-drying process.     

Thin-layer drying of porous materials: Selection of the appropriate mathematical model and relationships between thin-layer models parameters

Experimental investigation of the drying kinetics of various types of materials was carried out in laboratory-scale dryers under different conditions of temperature, microwave heating power and pressure. Leather samples (mechanically and vacuum-dewatered bull napa and wet blue cutting), paperboards (grafopack, testliner), wood (alder, birch, willow) and two pharmaceutical powders (chlorpropamide and hydrochlorotiazide) were dried in a microwave dryer. Thin clay slabs, Al–Ni catalyst and chlorpropamide were dried in a convection dryer, while chlorpropamide and ketoprofen were dried in a vacuum dryer. In order to compare drying kinetics, experimentally obtained data, X = f(t), were correlated with the Lewis “thin-layer” equation, the modified Page equation and Fick's second law. The drying constant, effective diffusion coefficient, mass transfer coefficient and modified Page model parameters were estimated by fitting the selected mathematical models to experimental data. High levels of correlation between measured and calculated data were obtained for all materials and dryers using modified Page model. The application of the Lewis and Fick's equation is justified only for drying of clay, catalyst and leather. Mass transfer coefficient depends linearly on the drying constant. The relation between the modified Page model parameter and the drying constant can be represented by a unique power function.     

微波加热在毛条烘干中的应用研究

介绍了应用微波加热烘干毛条的基本原理,研究了微波干燥设备的烘干效率、节能效果及烘干效果,结果表明,微波加热可以应用于纺织印染行业,为微波加热在纺织印染行业的推广应用提供了研究基础。通过生产应用,在计算微波加热毛条烘干工艺参数时,微波烘干机的干燥效率可取1.1kg/kW﹒h,微波干燥后,毛条含水率均匀,颜色前后色差无变化,纤维的强度和手感得到改善,微波干燥节能效果,比射频烘干节能约20%。     

Vaporization Processes and Pressure Buildup during Dewatering of Dense Refractory Castables

This work describes an experimental investigation on the dewatering kinetics of high-alumina refractory bodies under several heating conditions. The drying stages involving the removal of unbound water have been correlated with the two consecutive thermal processes by which liquid water transforms into vapor during heating: evaporation and ebullition. Thermogravimetric data have been used as the basis for a discussion of the parameters that affect the performance of both vaporization processes and guide the design of suitable heating schedules aimed at minimizing the drying time and the risk of harmful pore pressurization.     

TEMPERATURE AND MOISTURE CHANGES DURING MICROWAVE DRYING OF SLICED FOOD

ABSTRACT

Microwave drying characteristics of sliced foods were investigated using potatoes (Solarium tuberosum) as a test model. Sliced samples were dried to 7-10% moisture content at microwave power levels between 2.2 W/g and 3.6 W/g (raw material). Moisture and temperature changes during drying were monitored. Semi-empirical models were developed that followed temperature and moisture changes during microwave drying. Sliced potatoes experienced three distinct periods: a warming-up period with little removal of moisture; a constant temperature period in which most of the drying took place; and a heating up period in which the drying rate decreased and sample temperature increased rapidly, often causing partial charring. Product temperature during the second period of microwave drying increased with sample thickness and microwave power. Drying rates were not affected by slice thickness, but increased with the microwave power/mass ratio. Product charring towards the end of drying may be avoided by reducing microwave power and increasing ambient air velocity.     

DRYING KINETICS OF A MULTICOMPONENT MIXTURE OF ORGANIC SOLVENTS

ABSTRACT

Drying kinetics of volatile organic solvents have been examined during the drying process of a pharmaceutical coating containing a multicomponent mixture of ethyl acetate, n-heptane, propanol-2, and toluene. A complete set of experiments was performed in two drying apparatuses, a laboratory air-dryer and an oven dryer, for a wide range of drying temperature, air velocity, initial coating thickness and drying time. An empirical kinetic model is used to predict the concentration of each organic solvent in the mixture during the drying process. The results show that both drying conditions and sample characteristics affect significantly the drying rate of solvents.     

COMPARISON OF CONVECTIVE, VACUUM, AND MICROWAVE DRYING CHLORPROPAMIDE

Drying kinetics of convective, vacuum, and microwave drying of a pharmaceutical product, chlorpropamide, has been investigated on a laboratory scale, in the temperature interval from 40°C to 60°C, and the range of microwave heating power from 154 W/kg_dm to 385 W/kg_dm.

The experimental data obtained were approximated with the “thin-layer” equation and a two parameter exponential model. In order to compare convective, vacuum, and microwave drying, effective diffusion coefficients and specific heat consumption were calculated for each drying method.

Higher rates and shorter drying times were achieved at a higher temperature and microwave heating power. The highest drying rates and the lowest specific heat consumption were achieved with microwave drying. This leads to the conclusion that microwave heating is the most appropriate method for drying of chlorpropamide. The quality of product was not changed for all applied methods.     

Mathematical modelling of wheat drying by fractional order and assessment of transport properties

The purpose of this study is to evaluate both the temperature and the initial moisture content of the material in mathematical models of drying. For this, empirical lumped parameter models were fitted based on experimental data of moisture over time. Furthermore, a new semi-empirical drying kinetics model was applied. This model was developed using the generalization of arbitrary order of the Lewis equation obtained through the Laplace transform. After performing the fit, the fractional order model for drying wheat seeds as a temperature function was generalized. Distributed parameter models were also fitted to evaluate the influence of initial moisture content on drying kinetics and to estimate the moisture profile along the position inside the seed. It was verified that the fractional order model presented statistical results similar to models with a higher number of constants, being used to generalize the kinetic drying model for the three wheat cultivars. Generalized models showed better fits for the 3 cultivars with first-degree function, and the maximum global deviation was 10%, 15%, and 20% for the cultivars BRS–Atobá, BRS–Jacana, and BRS–Sanhaço, respectively. In addition, the distribution of moisture content inside the seed was verified by the distributed parameter model, which predicted the experimental data with an overall deviation of around 10%.     

USE OF NEW APPLICATOR DESIGN IDEAS TO IMPROVE UNIFORMITY OF PAPER DRYING VIA MICROWAVE ENERGY

Previous studies of microwave drying of paper have employed slotted waveguides having the slots along the centerlines of the waveguide broad walls. It has now been recognized that a slot height that varies with cross-machine position can be designed to achieve better heating uniformity. This configuration can compensate for the reduction in peak electric field strength due to absorption in the paper web as the waves propagate across the width of the paper machine. In this paper, we present a model that facilitates design for uniformity. We then investigate the tradeoff between efficiency and heating/drying intensity, and present preliminary model results indicating the ranges and combinations of basis weight and moisture content which are most compatible with the goals of achieving uniform microwave energy absorption, high efficiency, and high drying rate.     

USE OF NEW APPLICATOR DESIGN IDEAS TO IMPROVE UNIFORMITY OF PAPER DRYING VIA MICROWAVE ENERGY

Previous studies of microwave drying of paper have employed slotted waveguides having the slots along the centerlines of the waveguide broad walls. It has now been recognized that a slot height that varies with cross-machine position can be designed to achieve better heating uniformity. This configuration can compensate for the reduction in peak electric field strength due to absorption in the paper web as the waves propagate across the width of the paper machine. In this paper, we present a model that facilitates design for uniformity. We then investigate the tradeoff between efficiency and heating/drying intensity, and present preliminary model results indicating the ranges and combinations of basis weight and moisture content which are most compatible with the goals of achieving uniform microwave energy absorption, high efficiency, and high drying rate.     

微波干燥玉米籽粒的试验研究

针对玉米热风干燥中存在的问题。运用自制的微波干燥试验设备。采用不同的质量比功率和加热时间及配套的工艺流程。研究了玉米微波干燥特性及干燥条件对干燥品质、能耗的影响；分析了微渡干燥玉米过程中单位质量功耗、温度、平均失水速率与玉米籽粒发芽率、爆腰率和淀粉得率的关系；确定了影响微波干燥玉米的工艺参数和玉米微波干燥的合理工艺流程。研究结果表明：玉米微波干燥主要处于恒率干燥阶段，应用微波技术既能快速而经济地对玉米籽粒进行干燥，又能保持其种用价值，且有利于改善其品质。     

微波加热在纱线烘干中的应用

介绍了微波加热的基本原理、特点以及影响微波加热的因素,与蒸汽烘干、射频烘干相比,微波加热比蒸汽烘干节能40％,比射频烘干节能20％,仅每年运营维护费用比射频烘干节省4．5万元。提出应重点加强微波与物料间相互作用理论、微波场中物料的传热、传质机制,微波加热工艺与设备、微波加热技术与其它技术的有机结合等方面的研究。