GAS ABSORPTION WITH INSTANTANEOUS CHEMICAL REACTION IN A FALLING FILM FOR PARALLEL AND COUNTERCURRENT FLOWS

A theoretical analysis is presented for the absorption of a gas accompanied by instantaneous chemical reaction with a dissolved reagent in a falling liquid film of liquid. The reaction occurs on a moving front inside the liquid film separating the zones containing either of the reactants. The governing equations are solved by using a coordinate transformation to immobilize the reaction front. The effects of the different system parameters on the reaction front profile, absorption rate and enhancement factor are presented for both cocurrent and countercurrent flow of the gas. In the former case the reaction front profile shows a maximum, but in the later case it is monotonic in the axial distance along the film. The enhancement factor plots exhibit maxima in both the cases.     

ADIABATIC GAS ABSORPTION AND STRIPPING WITH CHEMICAL REACTION IN PACKED TOWERS

In the design of adiabatic gas absorption, the temperature distribution within the column is an important consideration. Temperature influences the degrees of heat and mass transfer through the thermodynamic phase equilibrium relationships and reaction rates. The capacity of an absorber is limited through the formation of a temperature plateau. Gas absorption in a chemically reactive solvent in an adiabatic packed column is modelled rationally for the first time taking into account the major heat effects. An iterative computational method for computing packed bed height is presented. The design procedure is illustrated by sample calculations for carbon dioxide (CO₂) absorption in monoethanolamine (MEA).     

COUNTERCURRENT GAS ABSORPTION WITH CHEMICAL REACTION IN A LAMINAR FALLING FILM

An analytical solution for absorption of a gas with an accompanying first order reaction in a laminar falling film is developed. The gas flow is countercurrent to that of the liquid film. Change in the gas phase concentration because of the reaction, as it happens in practical situations, has been taken into account. Some computed results are presented to show the effects of the system parameters—namely, the reaction rate parameter, the Biot number, and the absorption factor— on the mass transfer enhancement factor and on the fractional removal of the feed gas over a given non-dimensional film length.     

PERTURBATION ANALYSIS OF GAS ABSORPTION WITH CHEMICAL REACTION: A NONVOLATILE LIQUID REACTANT

Enhancement factors for gas absorption in a liquid containing a nonvolatile reactant are calculated using a regular perturbation technique. The perturbation solutions are found to be quite accurate in the slow reaction regime but lead to erroneous results for moderate and large reaction rates. To extend these solutions to the intermediate and fast reaction regimes, we have used the method of Padé approximants and Shanks transformations. The results obtained by these acceleration techniques are shown to be in excellent agreement with the direct numerical solutions for the enhancement factors in the intermediate and fast reaction regimes.     

PENETRATION THEORY ANALYSIS FOR NONISOTHERMAL GAS ABSORPTION ACCOMPANIED BY A SECOND-ORDER CHEMICAL REACTION

The penetration theory equations for nonisothermal gas absorption with second-order reaction were solved numerically using the Saul'yev method. Results for the enhancement factor and interfacial temperature rise were obtained for Hatta numbers between 1 and 10, It was found that the enhancement factor and interfacial temperature rise depend on four parameters; (i) the effective activation energy, ε_eff = (ε_R + ε_DA)/2 - ε_S, where ε_R, ε_DA, and ε_S are the activation energies for the reaction, diffusion, and solubility of the solute gas, respectively; (ii) the effective heat of generation, β_eff = (β_R + β_s)√Le, where β_R and β_s are the dimensionless heat of solution and reaction, respectively, and Le is the Lewis number; (iii) the product √rq where r is the ratio of the diffusivity of the liquid reactant to that of the solute gas and q is the ratio of the concentration of the liquid reactant in the bulk solution to that of the solute gas at the interface at the bulk temperature of the solution; and (iv) the activation energy for diffusion of the liquid reactant, ε_DB. This effectively reduces the number of parameters required to give a complete picture of the absorption from nine to four. The reduction is important since it reduces the number of van Krevelen-Hoftijzer plots and interfacial temperature-Hatta number plots required for the design of gas-liquid reactors.     

GAS ABSORPTION INTO A LIQUID FLOWING OVER A SPHERE WITH A SECOND-ORDER IRREVERSIBLE CHEMICAL REACTION

The objective of the work presented here is to theoretically investigate the absorption of a gas into a liquid flowing in laminar flow over a sphere with a second-order irreversible chemical reaction occurring between the absorbed gas and a nonvolatile solute present in the liquid. Commonly used simplifications in the diffusion-reaction equations and for the liquid velocity profile and the liquid film thickness on the sphere are investigated, and it is found that, under the experimental conditions usually encountered, these simplifications are justified. Numerical results for the absorption rate are presented graphically in two figures which may be used to estimate the second-order kinetic rate coefficient for the reaction between the absorbed gas and the nonvolatile liquid-phase solute. A criteria is developed for the conditions under which a second-order reaction may be considered to be pseudo-first-order,     

GAS ABSORPTION WITH CHEMICAL REACTION INVOLVING A VOLATILE LIQUID REACTANT: PENETRATION THEORY SOLUTION

A penetration theory analysis is presented for the problem of gas absorption, with chemical reaction involving a volatile liquid reactant. Model equations are derived and solution techniques are presented. It is shown that as long as the diffusivities of two reactants are equal, the enhancement factors predicted by film and penetration theories only mildly differ. Except for slow and instantaneous reaction regimes, the liquid reactant volatility can be markedly detrimental to enhancement of absorption rate by chemical reaction.     

石灰石固硫反应模型

在燃烧固硫试验系统和LCT－2型热天平上对石灰石固硫反应特性进行了试验研究．建立了石灰石煅烧与固硫反应同时进行时的数学模型,并通过试验结果的计算机处理,得到CO_2通过固硫剂颗粒的扩散系数D_(co_2)与传质系数a_(co_2).模型的合理性通过理论计算与试验结果的比较得到了验证．     

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。     

橡胶老化的化学应力松弛数学模型

以Maxwell数学模型为基础,从老化机理及化学流变学观点出发,并考虑到橡胶的粘度与老化时间的关系。推导出橡胶老化的化学应力松弛数学模型:σ/σ_0=Bexp[-A(1+K_ct)~a]。参数α与橡胶的粘度和老化机理有关。参数A反映了老化时发生物理松弛的能力,参数B是发生物理松弛和化学应力松弛的相对常数。通过测试未加防老剂的NBR-26硫化胶老化过程中的化学应力松弛和时数据进行计算机处理,证实此数学模型是正确的。通过时NBR-26硫化胶和BR硫化胶老化时化学应力松弛的参数分析可知,温度较低时,老化以氧化和交联为主,温度较高(200℃)时则以降解反应为主。     

TPA和EG连续生产PET的第一酯化反应器操作模拟

对乙二醇(EG)和对苯二甲酸(TPA)连续生产对苯二甲酸乙二酯(PET)的第一酯化反应器进行了数学模拟。数学模型中包括了反应动力学方程、气液平衡和气液传质方程,使模拟结果接近于工厂实践。此外对不同停留时间、不同的反应器操作温度及压力、不同的进料 EG/TPA 的 mol比,进行了模拟计算,得出了反应器出口各种产物的组成随操作参数的变化,并对各操作参数的范围和对反应的影响进行了评述。     

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.     

THE ENHANCEMENT OF GAS ABSORPTION BY A HETEROGENEOUSLY CATALYSED CHEMICAL REACTION IN A STAGNANT LIQUID: TEMPERATURE RISE AND EFFECTIVENESS OF THE CATALYST

In the present paper a model has been developed to calculate the enhancement efficiency e of the gas absorption and the effectiveness factor η of the catalyst for a chemically reacting system consisting of a sedimented catalyst particles-containing layer of thickness γ_k adhering to the surface of a gas bubble situated in a stagnant liquid. This model predicts that for a heterogeneously catalysed first-order chemical reaction an increase in the thickness γ_k of the catalyst particles-containing layer will result in an increase of ε and a decrease of η. It has been shown that the optimum value (γ_k)_opt of this layer can be obtained from the relation (γ_k) = (D_AB/k₁₃). Further, a model is derived to calculate the steady-state temperature profile in the catalyst particles-containing layer adhering to the gas bubble surface. Both models have been applied to experimental results published in some of our previous papers. These experimental results concern the enhancement of the gas-absorption rate from a single hydrogen-containing gas bubble to a stagnant aqueous hydroxylaminephosphate-containing solution when a layer of sedimented Pd/C catalyst particles was adhered to the surface of the gas bubble. The model and the experimental results mentioned may approximately be considered as representative of slurry reactors in which finely divided catalyst particles show considerable adhesion to rising gas bubbles.     

MATHEMATICAL MODEL DEVELOPMENT AND SIMULATION OF HEAT PUMP FRUIT DRYER

ABSTRACT

A mathematical model of a heat pump fruit dryer was developed to study the performance of heat pump dryers. Using the moisture content of papaya glace' drying, the refrigerant temperature at the evaporator and condenser and the performance, was verified. It was found that the simulated results using closed loop heat pump dryer were close to the experimental results. The criteria for evaluating the performance were specific moisture extraction rate and drying rate. The results showed that ambient conditions affected significantly on the performance of the open loop dryer and the partially closed loop dryer. Also, the fraction of evaporator bypass air affected markedly on the performance of all heat pump dryers. In addition, it was found that specific air flow rate and drying air temperature affected significantly the performance of all heat pump dryers.     

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。     

DEVELOPMENT OF A NEW REACTOR FOR COMBINED COMMINUTION AND CHEMICAL REACTION

The combining of the two process steps comminution and chemical reaction is realized in a newly developed apparatus, the so-called reaction-mill. It is an up to 450°C heatable vibration-mill, that is resistant to pressures up to 2 MPa and that has a gas inlet and outlet for running heterogeneous chemical reactions during the process of comminution. The possible accelerations of the vibration-mill exceed up to 65 g and relative amplitudes of maximum 0.14 are adjustable. The advantage of the combination of the two process steps is the utilization of the effects of comminution exceeding the changes in the dispersity of the solid. The examined heterogeneous non-catalytic gas-solid reaction is the conversion of metallurgical grade (MG) silicon with gaseous hydrogen chloride to give trichlorosilane and silicontetrachloride. The examinations of the combined hydrochlorination and comminution have shown, that the induction periods in the starting phase of the reaction, carried out singularly, can be reduced to a minimum. Furthermore it could be noticed, that the lower temperature limit, which is necessary to start the reaction, could be lowered from 300°C to 100°C and that the selectivity of the reaction products is influenced by the mechanical energy. On one hand the effects are explained by the changes in the dispersity of the solid during comminution and on the other hand by a mechanical activation of the MG silicon.     

A MATHEMATICAL MODEL FOR A YANKEE HOOD

Drying of thin paper sheet on a Yankee cylinder equipped with a steam heated high velocity hood is examined. When possible infiltration of air from the surroundings is considered, then the process is fully determined by twelve variables. One of these can be chosen as an independent variable. An equation group of eleven equations is derived. The method of solution is iterative. Finally, a numerical demonstration example is presented.     

碳/碳复合材料等温化学气相渗透工艺模糊系统建模

等温化学气相渗透(chemical vapor infiltration，CVI)是制备陶瓷基和碳基复合材料重要的传统工艺，该工艺主要的不足之处是周期极长，因此，优化工艺参数、提高沉积效率是目前等温CVI工艺研究的重点。在实验样本的基础上，利用遗传算法来自动获取和优化模糊规则，从而建立了碳／碳复合材料等温CVI工艺模糊系统。通过系统对训练样本和测试样本的输出，可以看出：系统具有较高的精度和泛化能力。利用该系统，得到了沉积温度、纤维体积分数和沉积室压强等参数对等温CVI工艺的影响规律，对实际生产中CVI工艺的制定有指导意义。