用Ha′la限制式结合γ~∞数据推算多元汽液平衡

提出了一种把Wilson方程参数间关系——Ha′la限制式和无限稀释活度系数相关联,用以估算三元系汽液平衡的方法。用汽液色谱测定挥发性溶质在不挥发性溶剂及混合溶剂中无限稀释活度系数,与Ha′la限制式相结合预测三元系汽液平衡,同文献位相比较:从Dortmund数据库的汽液平衡数据中选取了13组同时具有三元系和二元系汽液平衡数据的体系,用拟合和无限稀释活度系数及Ha′la限制式结合的方法求取Wilson参数,进而预测汽液平衡,与文献值相比较;又在三元系的三个二元系之间用同样办法进行相互推算;又利用两个二元系和三元系的一点数据进行预测;所得结果均较满意。为证明所用方法的可靠性,并对预测误差的置信度上限作了相应的估算。     

一个非局部组成型活度系数方程

根据前文提出的液体混合的通用Gibbs自由能模型,导得了一个两参数非局部组成型活度系数方程.它适用于各种小分子液体混合物和高分子溶液,并能由二元参数预测多元系汽液平衡.对小分子液体混合物的泡点计算结果表明,除了醇/烃系统外,计算准确度不逊于局部组成型活度系数方程.它对高分子溶液的适用性则明显地优于UNIQUAC等方程.     

应用多元粘性硬球体系比较局部组成活度系数模型

改进了Baxter粘性硬球混合物热力学性质的计算方法,求得由四种粘性硬球组成的四个三元体系的超额体积和各组份活度系数,运用这些数据,对Wilson、NRTL、UNIQUAC以及似化学局部组成模型的关联和预测性能进行了比较。结果表明,对于粘性球体系,似化学局部组成模型的关联和预测性能最佳,其次是Wilson、NRTL和UNIQUAC。     

A DIFFUSION MODEL WITH A MOISTURE DEPENDENT DIFFUSION COEFFICIENT FOR PARBOILED RICE

A mathematical model describing moisture migration by diffusion in a solid sphere with variable diffusion coefficient is proposed. An analytical expression for dependence of the diffusion coefficient with moisture content was derived based on the assumption that the activation energy for diffusion varies linearly with the desorption energy.

The expression for moisture dependence of diffusion coefficient was used to simulate drying of parboiled rice in the temperature range 50-90°C. The mathematical model shows good agreement between observed and predicted drying rate curves.     

SPRAY DRYING DYNAMIC MODELING WITH A MECHANISTIC MODEL

ABSTRACT

In this work we suggest the dynamic modeling of a spray dryer considered as a series of well-stirred dryers. That is, a series of dryers in which the output variables are equal to the state variables. The state equations were obtained from the heat and water mass balances in product and air. Additionally, heat and water mass balances in interface jointly with water equilibrium relation between product and air were considered. A pilot spray dryer was modeled assuming one, two, five and 20 well stirred steps. Low-fat milk with 10–20% of solids was dried at different inlet air temperatures (120–160°C), air flow rate of 0.19 kg dry air s^?1 and different feed rates (1.4 ? 4.2 × 10^?4 kg dry solids s^?1). Stationary result showed that the model predicts the experimental air outlet temperature, at different inlet conditions with a maximum deviation of 6°C. The dynamic simulation reproduce the experimental one with moderate accuracy. Experimental dynamic showed that the pilot plant spray dryer has a well-stirred process behavior. The model represents a method for estimate outlet product moisture as function of the outlet air temperature. This has application for automatic control because there is not an easy way to measure on-line measure the outlet product moisture content.     

SPRAY DRYING DYNAMIC MODELING WITH A MECHANISTIC MODEL

In this work we suggest the dynamic modeling of a spray dryer considered as a series of well-stirred dryers. That is, a series of dryers in which the output variables are equal to the state variables. The state equations were obtained from the heat and water mass balances in product and air. Additionally, heat and water mass balances in interface jointly with water equilibrium relation between product and air were considered. A pilot spray dryer was modeled assuming one, two, five and 20 well stirred steps. Low-fat milk with 10-20% of solids was dried at different inlet air temperatures (120-160°C), air flow rate of 0.19 kg dry air s^-1 and different feed rates (1.4 - 4.2 × 10^-4 kg dry solids s^-1). Stationary result showed that the model predicts the experimental air outlet temperature, at different inlet conditions with a maximum deviation of 6°C. The dynamic simulation reproduce the experimental one with moderate accuracy. Experimental dynamic showed that the pilot plant spray dryer has a well-stirred process behavior. The model represents a method for estimate outlet product moisture as function of the outlet air temperature. This has application for automatic control because there is not an easy way to measure on-line measure the outlet product moisture content.     

DISTRIBUTION PATTERNS DUE TO DIFFUSION IN A COAGULATION-FRAGMENTATION PROCESS WITH CLUSTER-WALL INTERACTIONS

The chemical reactivity of metal nanoclusters is determined mainly by their size and their oxidation state. The control of metal particle size is essential in order to manipulate their reactivity and interfacial behavior. Uniformity of size and spatial distribution of the metal nanoclusters is essential in the study of their properties and can be achieved primarily by conducting their synthesis in the presence of stabilizers. These materials, such as surfactants or polymers, adsorb onto the surfaces of growing clusters and create a “shielding effect,” a chemical barrier that prevents the effects of van der Waals interactions between particles, thus inhibiting particle aggregation. Polymers are frequently used as stabilizers for metal clusters because they are transparent, permeable, and nonconductive, and as such, do not interfere with and/or mask the potential optical, electrical, and catalytic properties of these clusters. When the concentration of the polymer in the reaction solution is above its critical coil overlap, entanglements occur, and hence the polymer may be viewed as a dynamically cross-linked network. Since the metal precursors can interact with the polymer via weak polar interactions, the metal cluster formation will therefore occur within the confines of these closed polymeric domains. In this work we will show, both theoretically and experimentally, the consequences of these interactions in the confines of the polymeric domains on metal particle size and particle size distribution.     

PNEUMATIC DRYING WITH SUPERHEATED STEAM: BI-DIMENSIONAL MODEL FOR HIGH SOLID CONCENTRATION

The utilization of superheated steam for pneumatic drying of solid particles makes it possible to operate with high particle concentration without the problem of phase saturation which tends to occur when hot air is utilized for drying. Normally, the operation of pneumatic dryers is analyzed through variations of unidirectional flows. For highly diluted transport conditions this is a correct assumption, but when the solid concentration is too high, the fluid dynamics is highly modified and the gas and solid velocities are distorted by solid–solid and Solid–Wall -interactions. These conditions affect the temperature distribution along the axial and the radial coordinates, which makes a bi-dimensional model analysis very important. Mathematical models have been developed for the bi-dimensional fluid dynamics of pneumatic transport. The present work applies one of these models to describe the axial and radial variation of velocities in a gas and particulate phase flow.     

A NEW INTERNAL MODEL CONTROL SCHEME WITH SIMPLIFIED DESIGN AND IMPLEMENTATION

This paper proposes a new internal model control scheme. The proposed scheme does not require an explicit transfer function model of the process. The design procedure is simple and the parameters of the controller are given in analytic formula. The resulting controller is of fixed-order form, which makes implementation easy. Simulation shows that the proposed scheme gives consistent and satisfactory performance for a large class of processes.     

MATHEMATICAL MODEL OF L-LACTIC ACID FERMENTATION IN A RDC COUPLED WITH PRODUCT SEPARATION BY ION EXCHANGE

A Rotating Disk Contactor (RDC) was designed to perform the L-lactic acid fermentation with a filamentous fungus, Rhizopus oryzae, which was immobilized on the surface of rotating disks. The bioreactor was operated in repeated batch or continuous modes. The growth rate of the fungi was about 1 mm/day perpendicular to the disks' surface. A weak-base anionic resin, D354, was selected which was high in selectivity for lactic acid separation. Even at low concentration, the ion exchange capability was about 0.5 g Lac/g dry resin. A coupled process of L-lactic acid fermentation and ion-exchange separation was evaluated experimentally. The results indicated that the pH value of the fermentation broth could be maintained at pH 3.5 without any addition of alkali. The conversion ratio of glucose to L-lactic acid was about 0.7 g/g and the fermentation rate was able to reach as high as 62.5g glucose per hour per square meter of the disk surface area. A mathematical model was proposed to describe the simultaneous process of L-lactic acid fermentation and separation by ion exchange, in which the thickness increase of mycelia as well as the substrate and product inhibitions were included. The model simulation was in good agreement with the experimental data.     

同心圆活动导流墙生化反应器混合液的分流调节特性

污水生化反应器中混合液的内回流特性是影响系统生物脱氮除磷效能的关键因素之一.探讨了同心圆活动导流墙反应器中混合液内回流分流量的计算模型,分析了反应器中活动导流墙不同开角值与循环混合液内回流量Q_缺/Q＿好的定量分配.当导流墙开角α在0～15°范围内,L_(BD)/L_(BE)=0.25～0.48时,循环流量Q_缺/Q_好的值为1.19～1.94,系统处理生活污水可获得良好的同时生物脱氮除磷效能,出水水质达到城镇污水处理厂污染物排放标准一级B标准(GB 18918-2002).冬季低温工况条件下,通过调节减小Q_缺/Q_好比值为0.97～1.07,能够在一定程度上降低低温对生化反应过程造成的负影响.     

ASYMPTOTIC MEAN SQUARE PREDICTION ERROR FOR A MULTIVARIATE AUTOREGRESSIVE MODEL WITH RANDOM COEFFICIENTS

In this paper, an expression for the asymptotic mean square error in predicting more than one step ahead from a p-variate autoregressive model with random coefficients is derived. Two cases are investigated: (i) when the parameters are known, and (ii) when the parameters are estimated.     

DRYING MODEL WITH NON-ISOTROPIC SHRINKAGE DEFORMATION UNDERGOING SIMULTANEOUS HEAT AND MASS TRANSFER

A model of simultaneous heat and moisture transfer in a cylindrical sample was coupled with the virtual work principle applicable to a body undergoing shrinkage deformation in two dimensions. Non-constant physical and thermal properties were also incorporated in the model. Governing equations and boundary conditions were solved numerically using Galerkin's finite element method. To check the mathematical model drying experiments were carried out. A cylindrical potato was used as a drying sample. Experimental conditions were as follows: a drying temperature of 333 K, relative humidity of 5.4%, and air velocity of 1.6 m/s. We obtained the central temperature of the sample, average moisture content, and the shrinkage change in the axial and radial directions during drying. It was observed that the shrinkage coefficients in the axial and the radial directions were significantly different during air-drying. Comparison between predicted and experimental results provides satisfactory agreement.     

A MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

ABSTRACT

A mathematical model has been developed to describe heat and mass transfer within materials undergoing shrinkage during drying. Both heat and mass transfer equations are solved simultaneously using a numerical technique A beat pump dryer has been used to conduct experiments to validate the model. Several samples were placed in the drver and after the commencement of each drying test one sample was taken oat at rceular time interval: The bone-dry mass of each piece was also determined. This enables to determine moisture distribution within the materials. Temperatures at different locations of the material were measured with thermocouples. The predicted temperature and moisture distribution within the material agreed fairly well with the experimental results.     

AN ANALYTICAL SOLUTION FOR A TUBULAR REACTOR MODEL WITH DISPERSION IN BOTH RADIAL AND AXIAL DIRECTIONS

An analytical solution for an unsteady-state tubular reactor model with dispersion in the radial as well as in the axial direction is presented. An arbitrary initial concentration profile and an arbitrary time-varying feed concentration are allowed; and the reaction occurs also on the interior surface wall of the reactor. The problem is recast into a more tractable form by an exponential transformation and then the method of Green's function combined with the orthonormal eigenfunction expansions based on the solution of the associated Helmholtz equation is used to arrive at the solution.     

SOLIDS DISTRIBUTION IN STIRRED SLURRY REACTORS: INFLUENCE OF SOME MIXER CONFIGURATIONS AND LIMITS TO THE APPLICABILITY OF A SIMPLE MODEL FOR PREDICTIONS

The features of solids concentration distribution were investigated in baffled and unbaffled tanks of high aspect ratio, stirred with multiple radial, mixed-flow or axial impellers. In the baffled tanks the average profiles can be predicted with the sedimentation-dispersion model regardless of impeller type - in spite of slight systematic departures from the average trend at the impeller plane and/or midway between the impellers. This is hardly possible for the unbaffled tanks due to lack of physical foundation of this simple model. When the unbaffled tank is stirred with hydrofoil impellers, an inverted profile is even obtained. The mentioned departures and this last anomalous behaviour are qualitatively discussed with reference to particle-turbulence interaction.     

SOLIDS DISTRIBUTION IN STIRRED SLURRY REACTORS: INFLUENCE OF SOME MIXER CONFIGURATIONS AND LIMITS TO THE APPLICABILITY OF A SIMPLE MODEL FOR PREDICTIONS

The features of solids concentration distribution were investigated in baffled and unbaffled tanks of high aspect ratio, stirred with multiple radial, mixed-flow or axial impellers. In the baffled tanks the average profiles can be predicted with the sedimentation-dispersion model regardless of impeller type - in spite of slight systematic departures from the average trend at the impeller plane and/or midway between the impellers. This is hardly possible for the unbaffled tanks due to lack of physical foundation of this simple model. When the unbaffled tank is stirred with hydrofoil impellers, an inverted profile is even obtained. The mentioned departures and this last anomalous behaviour are qualitatively discussed with reference to particle-turbulence interaction.