Drying Kinetics of Sludge from a Wastewater Treatment Plant

Drying kinetics of sludge from a municipal sewage treatment plant were determined in a laboratory drying tunnel with parallel airflow at different temperatures and air velocities. The constant drying rate period was identified followed by two falling rate periods. Drying kinetics in these falling rate periods were then satisfactorily modeled using the modified quasi-stationary method and the Fick's second law. The two-period model was used, however, to describe drying kinetics over the entire drying process, and the equation for a generalized drying curve was proposed. The effective diffusivity was also determined from the integrated Fick's equation, and correlated with temperature by an Arrhenius type equation.     

The Drying Kinetics and Equilibrium Moisture Content of MDF Fibers

An experimental device was constructed to study the drying kinetics of wood fibers under controlled conditions. The device consisted of a drying chamber in which a net basket filled with the fiber material was connected to a load cell. The drying medium was then forced through the basket at controlled levels of humidity and temperature.

Experiments were performed with spruce fibers and the drying medium at varying temperature (50–170°C) and relative humidity (1–86%). In general, the drying rate increased with increasing temperature and decreasing relative humidity. A constant drying rate period was observed in all cases. The critical moisture content was approximately 1.25. The characteristic drying curve has a slight downward concave shape. The equilibrium moisture contents obtained at ambient temperature agree well with data in the literature.     

Drying Kinetics of Instant Asian Noodles Processed in Superheated Steam

The objective for this work was to develop a novel technique for creating instant noodles by determining the drying kinetics of noodles undergoing simultaneous drying and processing using superheated steam. The mathematical model of moisture ratio was differentiated to determine the drying rates of noodles during processing. There was a constant rate drying period for all temperatures at a steam velocity of 1.5 m/s but there was no constant rate drying period at a steam velocity of 0.5 m/s. The constant rate drying period suggested by measurement of internal noodle temperature is much longer and well defined for all processing conditions than from the drying curves. The constant drying rate period, was nearly 200 s at 110°C but decreased to 50 s at 150°C. Equilibrium moisture content isobars were determined from mass changes during superheated steam processing. It was determined that isotherm equations for equilibrium moisture content in hot air systems may be utilized to model isobars in superheated steam systems.     

Drying Kinetics of Pinus Rqdiata Boards at Elevated Temperatures

ABSTRACT

From the numerical results of a rigorous, mathematical model, the rate–o–drying curves for high–temperature seasoning of Pinus radiata board show that the drying process can be divided into three periods. Based on the mechanistic picture of moisture movement and differences in the movement in each period, this paper simplifies the model by using the concept of the haracteristic drying curve.

In heartwood drying, the first period is very short (5–15 minutes), hence it can be neglected, whereas for sapwood, the first period is substantial with the drying rate being taken as constant in the analysis. Since the physical characteristics of the second and third drying periods are different, separate characteristic drying curves have been developed for each period. It has been found that common normalised drying curves are able to describe the results generated from the earlier model for normal range of kiln conditions over the examined ranges in dry–bulb temperatures of 1 10–140°C, wet–bulb temperatures of 70–90°C and air velocity of 3–7 m s^-1. Therefore. the derived simplified model can directly be used to calculate kiln–wide variations in moisture content and drying rate.     

Microwave Heat Treatment of Spinach: Drying Kinetics and Effective Moisture Diffusivity

The effect of microwave drying technique on moisture content, moisture ratio, drying rate, drying time, effective moisture diffusivity, and porosity of spinach (Spinacia oleracea L.) were investigated. By increasing the microwave output powers (180-900 W) and the sample amounts (25-100 g), the drying time decreased from 18 to 3.5 min and increased from 7.7 to 25 min, respectively. To determine the kinetic parameters, the drying data were fitted to various models based on the ratios of the differences between the initial and final moisture contents and equilibrium moisture content versus drying time. Among of the models proposed, Page's model gave a better fit for all drying conditions applied. The activation energy was calculated using an exponential expression based on Arrhenius equation. The relationship between the drying rate constant and effective moisture diffusivity was also estimated and gave a linear relationship.     

Microwave Heat Treatment of Spinach: Drying Kinetics and Effective Moisture Diffusivity

The effect of microwave drying technique on moisture content, moisture ratio, drying rate, drying time, effective moisture diffusivity, and porosity of spinach (Spinacia oleracea L.) were investigated. By increasing the microwave output powers (180–900 W) and the sample amounts (25–100 g), the drying time decreased from 18 to 3.5 min and increased from 7.7 to 25 min, respectively. To determine the kinetic parameters, the drying data were fitted to various models based on the ratios of the differences between the initial and final moisture contents and equilibrium moisture content versus drying time. Among of the models proposed, Page's model gave a better fit for all drying conditions applied. The activation energy was calculated using an exponential expression based on Arrhenius equation. The relationship between the drying rate constant and effective moisture diffusivity was also estimated and gave a linear relationship.     

A New Variable Diffusion Drying Model for the Second Falling Rate Period of Paddy Dried in a Rapid Bin Dryer

The objectives of this article is to propose a new drying model for the second falling rate period known as the variable diffusion controlled period that follows after the first falling rate period and to propose a new method to determine the second critical moisture content that separates these two periods. Experimental work on paddy drying at minimum fluidization velocity was carried out in a rapid bin dryer. The effects of operating temperatures (60-120°C) and bed depths (2-6 cm) on the paddy drying characteristics were investigated. It was found that the normalized drying rate of paddy was proportional to the normalized moisture content in the first falling rate period but in the second falling rate period, the normalized drying rate of the material varies exponentially with the normalized moisture content. The different relationship between the normalized drying rate and the normalized moisture content in the first and second falling rate periods indicate that two different mechanism of moisture transport are at work. The new exponential model of the second falling rate period and the linear model of the first falling rate period were found to fit the experimental data very well. Derivation from variable diffusion equation shows that the linear model is the result of constant diffusion coefficient whereas the new exponential model is the result of linear diffusion coefficient. This also implies that the first falling rate period is a constant diffusion controlled period and the second falling rate period is a variable diffusion controlled period. In addition, drying kinetics data of a drying process that fits the exponential model over a very slow drying period will show that the drying process is under the effect of a linear diffusion coefficient. It was also found that the proposed new method to determine the second critical moisture content that distinguishes between the first and second falling rate periods by using a sudden change in the value of the drying rate gradient to a much lower value at that point is more rigorous and yet simpler than the method of determining the specific location of the receding drying boundary since it is based on the behavior of the actual drying kinetic data.     

A Simple Data Processing Approach for Drying Kinetics Experiments

A simple mathematical approach is proposed to be applied to drying kinetics raw data processing. The data collected in a drying experiment of powder cork under constant air drying conditions served as case study to present the methodology. Two functions (linear and third-degree polynomial) were used to fit solid moisture content in the constant drying rate and the falling rate periods. The drying rate curve was obtained by differentiation and the time at which the drying rate period's transition occurs was determined iteratively until virtually continuous functions were achieved. The critical moisture content was easily identified and two falling drying rate periods were detected.

The powder cork moisture decrease was also used to test several semiempirical models available in the literature. The Logarithmic, Midilli, and Page Modified I models were the ones that revealed the best correlations performance. When the methodology proposed was applied using these models, the critical moisture content was underpredicted.

The effective moisture diffusivity and the activation energy were also obtained for powder cork after the proposed mathematical approach has been applied on the raw data obtained in experiments performed at different air drying temperatures.     

确定碱式氯化镁纳米棒干燥动力学参数的新方法

根据碱式氯化镁纳米棒干燥动力学实验数据,拟合得到的干燥方程为MR=exp[-(kt)n],干燥时间指数为n=1.8114,式中的干燥速率常数,k=Aexp(-CT/T)exp(-CLL)=Aexp[-(EV+RTCLL)/RT]=Aexp[-(EV+Ed)/RT]=Aexp(-E/RT),扩散活化能Ed=RTCLL,表观活化能E=EV+RTCLL。采用一种确定干燥动力学参数的新方法—等湿分比法,得到界面蒸发活化能为EV=15.399kJ·mol-1,长度常数CL=161.380m-1,温度常数CT=1852.177K,频率因子A=8.997min-1。     

Estimation of Effective Moisture Diffusivity of Okra for Microwave Drying

The effect of microwave output power and sample amount on effective moisture diffusivity were investigated using microwave drying technique on round okra (Hibiscus esculentus L.). The various microwave output powers ranging from 180 to 900 W were used for the determination of effective moisture diffusivity for constant sample amount of 100 g okra. To examine the effect of sample amount on effective moisture diffusivity, the samples in the range of 25–100 g were dried at constant microwave output power of 360 W. By increasing the microwave output powers and decreasing the sample amounts, the effective moisture diffusivity values ranged from 20.52 × 10^?10 to 86.17 × 10^?10 and 34.87 × 10^?10 to 11.91 × 10^?9 m²/s^?1, respectively. The modeling studies were performed to illustrate the relationship between the ratio of the microwave output power to sample amount and effective moisture diffusivity. The relationship between drying constant and effective moisture diffusivity was also estimated.     

Estimation of Effective Moisture Diffusivity of Okra for Microwave Drying

The effect of microwave output power and sample amount on effective moisture diffusivity were investigated using microwave drying technique on round okra (Hibiscus esculentus L.). The various microwave output powers ranging from 180 to 900 W were used for the determination of effective moisture diffusivity for constant sample amount of 100 g okra. To examine the effect of sample amount on effective moisture diffusivity, the samples in the range of 25-100 g were dried at constant microwave output power of 360 W. By increasing the microwave output powers and decreasing the sample amounts, the effective moisture diffusivity values ranged from 20.52 × 10^-10 to 86.17 × 10^-10 and 34.87 × 10^-10 to 11.91 × 10^-9 m²/s^-1, respectively. The modeling studies were performed to illustrate the relationship between the ratio of the microwave output power to sample amount and effective moisture diffusivity. The relationship between drying constant and effective moisture diffusivity was also estimated.     

Moisture Diffusion Coefficients for Modeling the First and Second Drying Sections of Green Bricks

A model has been developed that describes the dependence of the moisture diffusion coefficient on the water fraction. Until the end of shrinkage has been achieved, the moisture diffusion coefficient is proportional to the second power of the water fraction. Due to shrinkage, the relevant capillary spaces available for water transport become smaller. Consequently, the moisture diffusion coefficient decreases continually. After the end of shrinkage, the flow resistance to the water moving toward the surface increases sharply due to penetrating air. This leads to a steep drop of the moisture diffusion coefficient by several powers of ten. Measurements were carried out with specimens of defined geometry to determine the moisture diffusion coefficient. On the basis of a specified limiting value, the model is capable of calculating the moisture diffusion for all initially specified raw materials moistures. The moisture can also be determined if the degree of drying shrinkage is known. Using the determined moisture diffusion coefficient, the first and the second drying section can be located. Drying tests were carried out in a laboratory dryer and the experimental results obtained were compared to the simulation results. The simulation results are in good agreement with the experimental results.     

微波干燥法测定过磷酸钙中的水分

提出用微波干燥法测定过磷酸钙中水分的含量,测定的精密度较高,操作简便,条件容易控制,分析速度快,RSD=(n=6)为1.23%。经多次试验证明,采用本法测定结果满意。     

铜基催化剂孔隙率对气体有效扩散系数的影响

研究了18种具有不同孔结构参数的粒状铜基甲醇合成催化剂孔隙率对有效扩散系数的影响。结果发现，催化剂微孔孔隙率增大，曲节因子亦增大，扩散阻力增加。将孔隙率与催化剂曲节因子关联，得到了半经验方程，用它可估算催化剂的曲节因子。     

On the Analysis of Drying Process

Drying plays an important role in processing agricultural grains/seeds, chemicals, and other materials. In the present work, drying process has been analyzed taking published data on different grains and seeds such as rapeseed, sunflower, soybean, corn, paddy, and wheat. Mathematical expressions have been established for important drying parameters such as critical moisture content, drying rates, time required to reach critical moisture content, total drying time, and diffusivity as function of drying air temperature. The expressions involve a coefficient parameter and an exponential function of drying air temperature, Aexp(- E/RT_g),and interestingly it is shown that the same functional form with same Es can correlate the different relevant drying parameters. The coefficient parameters As and Es are decided by drying materials and drying process, and the values have been derived for different grains/seeds. The correlations are useful in analyzing the drying process.     

Experimental Estimation of Effective Transport Coefficients in Freeze Drying for Simulaton and Optimization Purposes

ABSTRACT

In this work a quasi-steady-state analysis is used to describe the evolution of the sublimation front temperature in freeze-drying of a food model (aqueous solution of Tylose. 3%). From the water loss data obtained in a freeze-drying experiment, in which the upper dried surface temperature and that of the frozen zone of the food model are conmlled to a cenain heating sttategy, several values of the transport coefficients in the dried layer are calculated under different operational conditions (i.e. chamber pressure and average product temperature). These values are correlated by non linear regression and expressions for the effective thermal conductivity and water vapour diffusivity in the dried layer of the material are     

Experimental Estimation of Effective Transport Coefficients in Freeze Drying for Simulaton and Optimization Purposes

In this work a quasi-steady-state analysis is used to describe the evolution of the sublimation front temperature in freeze-drying of a food model (aqueous solution of Tylose. 3%). From the water loss data obtained in a freeze-drying experiment, in which the upper dried surface temperature and that of the frozen zone of the food model are conmlled to a cenain heating sttategy, several values of the transport coefficients in the dried layer are calculated under different operational conditions (i.e. chamber pressure and average product temperature). These values are correlated by non linear regression and expressions for the effective thermal conductivity and water vapour diffusivity in the dried layer of the material are     

A Simulation Tool for the Optimization of Lumber Drying Schedules

Abstract

A two-dimensional wood drying model based on the water potential concept is used to simulate the convection batch drying of lumber at conventional temperature. The model computes the average drying curve, the internal temperature and moisture content profiles, and the maximum effective moisture content gradient through board thickness. Various scenarios of conventional kiln-drying schedules are tested and their effects on drying time, maximum effective moisture content gradient, final moisture content distribution within and between boards, and energy consumption are analyzed. Simulations are performed for two softwood species, black spruce (Picea mariana (Mill.) B.S.P.) and balsam fir (Abies balsamea (L.) Mill.). The simulation results indicate that the predictive model can be a very useful tool to optimize kiln schedules in terms of drying time, energy consumption, and wood quality. Such a model could be readily combined with intelligent adaptive kiln controllers for on-line optimization of the drying schedules.     

Calculation of the Effective Diffusion Coefficient in Drying of Polymers,Fibres, and Composite Materials with a Quasistationary Method

Based on an analysis of the solutions of the diffusion equation for flat, spherical, and cylindrical bodies in the form of the average moisture content, an equation that approximates these solutions in the form of an exponential function is proposed. The dependence of the effective diffusion coefficient as a function of the drying time for fibre, polymeric, and composite materials is obtained based on the approximating equation for the average moisture content. Using the modified quasistationary method that describes the kinetics of drying and equations for the average moisture content, the calculated dependence for the effective diffusion coefficient is obtained. This dependence has obvious advantages in comparison to the zonal method of calculation. The proposed dependences are verified in comparison to the experimental data from a number of investigators. Good agreement of the calculated and experimental data is obtained. The dependences for the diffusion coefficients can be used to identify zones of high-intensity drying and to automate and regulate the process.__________Translated from Khimicheskie Volokna, No. 1, pp. 59–62, January–February, 2005.     

A Simulation Tool for the Optimization of Lumber Drying Schedules

A two-dimensional wood drying model based on the water potential concept is used to simulate the convection batch drying of lumber at conventional temperature. The model computes the average drying curve, the internal temperature and moisture content profiles, and the maximum effective moisture content gradient through board thickness. Various scenarios of conventional kiln-drying schedules are tested and their effects on drying time, maximum effective moisture content gradient, final moisture content distribution within and between boards, and energy consumption are analyzed. Simulations are performed for two softwood species, black spruce (Picea mariana (Mill.) B.S.P.) and balsam fir (Abies balsamea (L.) Mill.). The simulation results indicate that the predictive model can be a very useful tool to optimize kiln schedules in terms of drying time, energy consumption, and wood quality. Such a model could be readily combined with intelligent adaptive kiln controllers for on-line optimization of the drying schedules.