煤炭优化组合的数学模型

本文提出了一种可以使低质煤炭通过优化组合代替优质煤在某些生产部门应用的数学模型，并根据部分数据给出了计算结果。     

A MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

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.     

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.     

填料萃取塔的数学模型

对描述萃取塔传质性能的几种数学模型进行分析和比较,针对填料萃取塔的特点对其中有发展前途的复合模型进行了详细讨论。总结出模型参数的计算方法。编制了用数值方法进行模型求解的计算机软件。利用文献数据对模型进行检验,结果显示了很好的一致性。     

A NEW MATHEMATICAL MODEL FOR MASS TRANSFER IN A PACKED COLUMN

A new mathematical model,designated as stochastic state pool model,is proposed for simulating the liquid flow andmass transfer behaviour,including the concentration profiles of liquid and gas phascs in a packed column.Application ofthe new model is demonstrated by an example of the desorption of CO_2 in a packed column.     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

A COMPREHENSIVE MATHEMATICAL MODEL FOR A MULTIZONE TUBULAR HIGH PRESSURE LDPE REACTOR

In this study a comprehensive mathematical model of high pressure tubular ethylene polymerization reactors is presented. A fairly general reaction mechanism is employed to describe the complex kinetics of ethylene polymerization. To determine the variation of molecular properties along the reactor length the method of moments is applied to the infinite set of species balance equations to transform it into a low order system of differential equations in terms of the leading moments of the number chain length distribution. Detailed algebraic equations are given describing the variation of kinetic rate constants, thermodynamic and transport properties of the reaction mixture with temperature, pressure and composition. A new correlation is derived to describe the change of reaction viscosity with reactor operating conditions. The model permits a realistic calculation of temperature and pressure profiles, monomer and initiator concentrations, molecular properties of LDPE (i.e. M_n, M_m, LCB and SCB) as well as the variation of inside film heat transfer coefficient with respect to the reactor length. Simulation results are presented illustrating the effects of initiator concentration, inlet pressure, chain transfer concentration and wall fouling on the polymer quality and reactor operation. The present model predictions are in good agreement with experimental observations in industrial high pressure tubular LDPE reactors.     

A MATHEMATICAL MODEL OF A BUBBLE COLUMN REACTOR FOR THE CUMENE OXIDATION

The liquid flow field over a bubble-cap tray or a perforated plate in distillation columns was determined numerically using the upwind difference method. The results of the numerical calculations indicate that with flow over such a plate there exists a stagnant region along the side of the plate, which expands with the increase in the Reynolds number. Furthermore, the size of the stagnant region depends upon the inlet liquid velocity distribution and is at a minimum when the distribution is uniform. It was also found that by installing baffles, the size of the stagnant region may be significantly reduced.     

水泥石结构强度数学模型

波特兰水泥石的结构是一个多相、多组分、多孔结构体系，且其结构随水化硬化的时间、空间和环境面演变。     

A MATHEMATICAL MODEL FOR OXYGEN TRANSFER IN FLAT PLATE MEMBRANE OXYGENATOR

Mass transfer in a flat plate membrane oxygenator was studied and a convective mass transfer modelfor instantaeous reversible oxygenation of Cassonian fluid was presented. Numerical solution of the model canbe obtained with finite difference method. When a     

并流下行快速流态化气-固两相流动模型的研究

在直径为φ140mm,高为5.8m 的冷模实验装置内,采用四种颗粒,在气速为1.3～10m/s,颗粒循环速率为30～180kg/m~2·s 的操作范围内,测定了气-固并流顺重力场流动系统压力梯度的轴向分布,并且建立了描述该过程的一维两相数学模型。模型对该过程的予测结果与实验结果一致。     

中空纤维膜气体分离器的数学模型

本文建立了中空纤维膜气体分离器的微分数学模型,对其数值解进行了实验验证,又将其简化的代数模型同文献上的模型进行了比较,指出了各种模型适宜的使用条件,并研究确定了气体膜分离过程中较适宜的丝内径、丝长度和操作压力的范围。     

A MATHEMATICAL MODEL FOR CONTINUOUS DRYING OF GRAINS IN A SPOUTED BED DRYER

A mathematical model for a continuous spouted bed dryer has been presented to predict moisture content, air and grain temperatures as well as energy consumption. To better understand the interactive influence of processes in each region of the spouted bed, solution schemes for the spout and downcomer were treated separately. The behavior of dryer was investigated experimentally and found that the dryer behaved differently from an ideal plug flow. The drying rate as simulated by the model is almost constant during grain movement in the dryer. Absence of airflow in the downcomer leads to a tempering process that takes place in the downcomer while intense heat and mass transfer occurs mainly in the spout due to the high airflow rate there. Furthermore, by considering the predicted grain temperature history as one of the indicators of product quality, one can, in principle, design appropriate successive processes in a continuous spouted bed dryer to minimize product damage.     

A MATHEMATICAL MODEL FOR CONTINUOUS DRYING OF GRAINS IN A SPOUTED BED DRYER

ABSTRACT

A mathematical model for a continuous spouted bed dryer has been presented to predict moisture content, air and grain temperatures as well as energy consumption. To better understand the interactive influence of processes in each region of the spouted bed, solution schemes for the spout and downcomer were treated separately. The behavior of dryer was investigated experimentally and found that the dryer behaved differently from an ideal plug flow. The drying rate as simulated by the model is almost constant during grain movement in the dryer. Absence of airflow in the downcomer leads to a tempering process that takes place in the downcomer while intense heat and mass transfer occurs mainly in the spout due to the high airflow rate there. Furthermore, by considering the predicted grain temperature history as one of the indicators of product quality, one can, in principle, design appropriate successive processes in a continuous spouted bed dryer to minimize product damage.     

A MATHEMATICAL MODEL FOR THE CONTINUOUS VACUUM DRYING OF HIGHLY VISCOUS FOODSTUFFS

An improved mathematical model for the continuous vacuum drying of highly viscous and heat-sensitive food-stuffs was proposed. The process of continuous vacuum drying was presented as a moving boundary problem of moisture evaporation in cylindrical coordinates. Boundary condition of the first kind for the known functional dependence of the drying body surface temperature on time was considered. Finally, the appropriate system of differential equations was solved numerically and the values of drying rate, integral moisture content of the material, moving boundary position as well as temperature in any point of the material and at any moment of time were obtained. This procedure was applied to continuous vacuum drying of foods such as natural cheese and fresh fish meat paste.     

三相流态化结晶系统的数学模型

<正>要实现工业结晶过程新工艺和设备的开发以及过程操作的优化,就必须建立涉及结晶过程特性并反映结晶器流动、混合和传递规律及其相互作用关系的结晶器总体数学模型。过去几十年中已有许多研究者进行了这方面的探索,提出了各种各样的模型。特别是70年代初由Randolph和Larson提出的粒数衡算模型,将产品的粒度分布与结晶器的结构参数和操作参数联系起来,成为结晶器设计、放大和优化从经验上升到科学的重要标志。 针对不同结晶系统提出的多种数学模型中,最具典型代表性的数学模型是由Mullin等提     

A MATHEMATICAL MODEL FOR THE CATALYST DEACTIVATION IN A COMMERCIAL RESIDUE HYDRODESULFURIZATION REACTOR SYSTEM

A mathematical model that describes catalyst deactivation in a commercial Residue Hydrodesulfurization (RDS) system is proposed. In this model, coking, metal deposition and the decrease of effective diffusivities are all considered, so that it can predict the dynamics of catalyst activity during a long run of an RDS system. The RDS system under consideration here is a complex trickle bed reactor system with four adiabatic reactors in series, between which the oil is quenched by hydrogen to prevent the catalysts in the next reactor from being damaged by high temperature. This article shows that by incorporating a catalyst deactivation model into the overall reactor system model, the predicted catalyst aging curve assumes the “S” shape, characteristic of real RDS system. The model prediction are compared with data from an operating refinery and the agreement is pleasing. KEYWORDS Residue Hydrodesulfurization(RDS) Apparent activity Catalyst deactivation curve Pore radius.     

A MATHEMATICAL MODEL FOR THE CATALYST DEACTIVATION IN A COMMERCIAL RESIDUE HYDRODESULFURIZATION REACTOR SYSTEM

A mathematical model that describes catalyst deactivation in a commercial Residue Hydrodesulfurization (RDS) system is proposed. In this model, coking, metal deposition and the decrease of effective diffusivities are all considered, so that it can predict the dynamics of catalyst activity during a long run of an RDS system. The RDS system under consideration here is a complex trickle bed reactor system with four adiabatic reactors in series, between which the oil is quenched by hydrogen to prevent the catalysts in the next reactor from being damaged by high temperature. This article shows that by incorporating a catalyst deactivation model into the overall reactor system model, the predicted catalyst aging curve assumes the “S” shape, characteristic of real RDS system. The model prediction are compared with data from an operating refinery and the agreement is pleasing. KEYWORDS Residue Hydrodesulfurization(RDS) Apparent activity Catalyst deactivation curve Pore radius.