A molecular approach to the calculation of gas adsorption isotherms on molecular sieves: Noble gases on type 4A and 5A zeolites

A general equation for gas adsorption isotherms in microporous adsorbents is derived on the basis of the molecular chemical potentials of the gas and adsorbed phases and the theory of volume filling of the adsorption space by adsorbate molecules. Both adsorbate-absorbate and adsorbate-adsorbent interactions are considered in computing the molecular free energy of adsorption. The equation is applied to the calculation of isotherms of noble gases on molecular sieves type 4A and 5A in the range 77.4°K to 333°K, 0.001 mm Hg to 40 atmospheres. Comparison of the calculated isotherms and experimental data shows that the adsorption equation can be used over a wide range, but requires interpolation over a short intermediate region of adsorbate concentrations. An important feature of this equation is that it reduces to Henry's law at low adsorption concentrations.     

MULTICOMPONENT ADSORPTION EQUILIBRIUM OF GASES IN ZEOLITE: EFFECT OF PORE SIZE DISTRIBUTION

The effect of pore size distribution of zeolite on the multicomponent adsorption equilibrium is studied. All species compete locally for a given pore and this can be described by the extended multicomponent Langmuir isotherm. The size exclusion effect is taken into account in the competition of different species for a given pore so large molecules have less degree of accessing available pores. The pore size is related to the adsorbate-adsorbent interaction energy by the Lennard-Jones potential. The isotherm parameters extracted from single-component data fitting are used to predict multicomponent adsorption equilibrium. When validated with binary experimental data of CO₂, H₂S and propane in H-mordenite, collected by Talu and Zwiebel (1986), this model provides better results than a previously proposed heterogeneous model based on a uniform energy distribution and a local IAST (Hu and Do, 1995).     

固液相变数学模型中有效热导率

在一维固液相变数学模型中有效热导率计算公式的研究基础上,根据理论分析和实验数据,对一维有效热导率进行了修正,并把有效热导率计算公式应用到二维相变问题中.通过对等热通量和等壁温边界条件的仿真计算结果与实验数据相比较,说明了本文的有效热导率计算方法的合理性.     

Physical adsorption of gases on graphitized carbon black

The Percus-Yevick equation of state is applied to a two-dimensional adsorbed fluid. Calculation of the adsorption isotherm is divided into two parts: the Henry's constant for gas-solid interactions, and the configurational contribution of the two-dimensional film. The theory is compared with experimental data for adsorption of argon and krypton on graphitized carbon black and agreement is excellent. This is the first successful calculation of adsorption isotherms over a wide range of temperature and surface density for which no adjustable parameters are used for the two-dimensional equation of state.     

缔合体系汽-液相平衡的研究(Ⅱ)——三元缔合体系汽-液相平衡的研究

本文提出了多元缔合体系汽-液相平衡的热力学模型,并用其计算了缔合体系水-甲酸-乙酸、水-乙酸-丙酸、水-甲酸-丙酸及甲酸-乙酸-丙酸在760mmHg下的实验液相活度系数。活度系数的计算值由Wilson方程或McCann方程给出。由相应二元体系的汽-液相平衡数据对三元体系的沸点及汽相组成进行了预测。结果表明,预测值能较好地同实验数据相吻合。     

PREDICTION OF THE ASYMMETRIC PEAK PROFILE USING A MATHEMATICAL METHOD WITH A COMPETITIVE LANGMUIR ISOTHERM

The adsorption characteristics of a single component and a binary component in the stationary phase using preparative chromatography were investigated with a six-adsorption isotherm model. These analyses were based on the Langmuir model. Each parameter of the adsorption isotherm was obtained with the adsorption raw data that was calculated by frontal analysis (FA). The experimental data and the values calculated using the adsorption isotherm model were compared. The bi-Langmuir model showed good agreement for phenol while the tri-Langmuir model showed good agreement for caffeine. Each characteristic of adsorption was obtained from these results. The effect of competitive adsorption was investigated using the parameters of the adsorption isotherm model with a single component. There was good agreement between the experimental data and the calculated values.     

PREDICTION OF THE ASYMMETRIC PEAK PROFILE USING A MATHEMATICAL METHOD WITH A COMPETITIVE LANGMUIR ISOTHERM

The adsorption characteristics of a single component and a binary component in the stationary phase using preparative chromatography were investigated with a six-adsorption isotherm model. These analyses were based on the Langmuir model. Each parameter of the adsorption isotherm was obtained with the adsorption raw data that was calculated by frontal analysis (FA). The experimental data and the values calculated using the adsorption isotherm model were compared. The bi-Langmuir model showed good agreement for phenol while the tri-Langmuir model showed good agreement for caffeine. Each characteristic of adsorption was obtained from these results. The effect of competitive adsorption was investigated using the parameters of the adsorption isotherm model with a single component. There was good agreement between the experimental data and the calculated values.     

THE TWO-THIRDS POWER MODEL FOR PREDICTING DIFFUSION COEFFICIENTS IN LIQUIDS

Most of the models found in the literature for predicting diffusion coefficients in liquids take the viscosity of the solution as inversely proportional to the diffusivity. A model (previously derived for sucrose-water system)which considers the viscosity raised to the two-third power, is evaluated here using published data for the Benzene—Cylohexane, Ethanol-Water and Acetone-Chloroform systems. These results, and results for the sucrose-water system are compared with the experimental values, and with those obtained using the Hartley—Crank equation. Better agreement with the experimental values at low and in the middle of the concentration range was found when diffusivities were calculated using the model proposed than when using the Hartley-Crank equation.     

油茶果壳活性炭对苯酚的吸附动力学研究

以油茶果壳制备的活性炭为吸附剂,探讨了温度、苯酚初始浓度对油茶果壳活性炭吸附苯酚性能的影响,并用两种动力学模型进行了拟合。结果表明:油茶壳活性炭对苯酚的吸附是一个较为快速的过程,60 min就可接近吸附平衡。油茶壳活性炭对苯酚的吸附动力学过程可以用准一级与准二级模型进行很好的描述,相关系数达到0.96以上。     

Scale-up effects due to near-wall channelling in isothermal adsorption columns: on the limitations in the use of plug flow models

The influence of the near-wall channelling phenomenon on the scale-up effects of adsorption column is analysed numerically. The radial fluid velocity profile is approximated by using the extended Brinkman model. The broadening of breakthrough curves during a change in adsorption column diameter is predicted either from the two-dimensional model of non-linear, favorable adsorption with local fluid velocity included directly in the differential mass balance equation or from the plug flow model with the influence of the flow distribution involved in the value of the effective axial dispersion coefficient. The predicted scale-up parameters are compared with available experimental data. Under discussion are the operating conditions which make the scale-up effects due to near-wall channelling significant and possible improper application of the dispersed plug flow model.     

Generalization of thermodynamic Langmuir isotherm for mixed-gas adsorption equilibria

This work presents a comprehensive thermodynamic model for both pure component isotherms and mixed-gas adsorption equilibria. A generalization of thermodynamic Langmuir isotherm, the proposed model assumes competitive adsorption of multiple adsorbates on adsorbent surface for mixed-gas adsorption equilibria, and it applies an area-based adsorption nonrandom two-liquid activity coefficient model in the activity coefficient calculations for the adsorbate phase. The resulting generalized Langmuir isotherm properly captures both surface loading dependence and adsorbate phase composition dependence for mixed-gas adsorption equilibria. The model is validated with accurate representations of gas adsorption equilibrium data for varieties of unary, binary, and ternary gas systems. The model results are further compared with those calculated from extended Langmuir isotherm and Ideal Adsorbed Solution Theory.     

负载氧化铁树脂吸附巴戟天多糖热力学动力学参数辨识

在建立巴戟天多糖在负载氧化铁树脂上吸附数学模型的基础上,采用多参数优化的非线性拟合方法,估算巴戟天多糖在负载氧化铁树脂上吸附热力学、动力学参数,并将优化计算所得到的流出曲线与实验流出曲线进行比较。结果表明：多参数优化拟合得到的巴戟天多糖理论流出曲线与实验流出曲线比较吻合。采用该方法测定不同pH值和离子强度下巴戟天多糖的吸附热力学、动力学参数结果表明：弱碱性条件下巴戟天多糖的平衡吸附容量高于酸性环境,在pH值为8．0时达到最大;随着离子强度的增大,巴戟天多糖在负载氧化铁树脂上的吸附量略有增加。     

碳酸二甲酯-碳酸二乙酯-甲醇三元体系相平衡数据的推算

采用双循环汽液平衡釜测定了常压下碳酸二甲酯-碳酸二乙酯、碳酸二甲酯-甲醇、碳酸二乙酯-甲醇三组二元体系的汽液平衡数据,实验数据经Herington面积积分法检验符合热力学一致性。用Wilson模型分别对实验数据进行了关联,利用关联出的模型参数计算相应的汽相组成,并与实验值比较,二者符合良好。利用二元体系的汽液平衡数据,由Wilson方程推算了碳酸二甲酯-碳酸二乙酯-甲醇三元体系的汽液平衡数据。为建立碳酸二乙酯和碳酸二甲酯、甲醇的精馏分离数学模型提供了基础数据。     

Modeling hydrogen fluoride adsorption by sodium fluoride

In the current study, hydrogen fluoride (HF) adsorption onto the sodium fluoride pellets is modeled. For this purpose a two-dimensional, non-isothermal model was developed and the governing equations were solved numerically. The contributions of diffusion transport in axial and radial directions also were considered in mathematical formulations. The model results of effluent concentration and breakthrough curves of HF were compared with the experimental data obtained in a lab-scale adsorption unit, reported in our previous work [1]. The results indicate while the feed gas velocity decreases, the HF adsorption capacity on NaF is significantly enhanced and there is a delay in breakthrough time. The adsorption capacity of HF on NaF decreases slightly when inlet HF concentration increases. Moreover, the model results were compared with the obtained results from a one-dimension model. This comparison indicates that one-dimensional model can well predict the HF dynamic adsorption behavior for lab-scale fixed beds. Comparing the experimental breakthrough curves of HF adsorption on NaF pellets with the model results shows the ability and accuracy of the model with maximum 7.82% errors.     

A fundamental approach in liquid phase adsorption kinetics

Liquid-solid adsorption kinetic data are mostly interpreted by a limited number of rate equations, (pseudo-first, pseudo-second order and Elovich). Besides, a fundamental tool in heterogeneous reactions, the Langmuir theory of adsorption, is used almost exclusively to model equilibrium isotherms but, surprisingly, not kinetics. Considering the limited applicability of the mentioned kinetic models, especially in estimating kinetic constants and predicting adsorption mechanism, it seems more reasonable to apply the Langmuir kinetic equation in modeling the liquid phase adsorption. In the diffusion-free regime, by constructing the experimental equilibrium isotherm of a system, one can easily check the validity of the Langmuir model. Afterwards, kinetic constants can be readily calculated and used to predict adsorption performance under different operating conditions. The proposed procedure was tested in the experimental results of cyanide adsorption in activated carbon to verify the applicability of the Langmuir adsorption mechanism and estimate the equilibrium and kinetic constants.     

Multicomponent sorption kinetics of ethane and propane in activated carbon: simultaneous adsorption

Extensive experimental data of binary adsorption kinetics of ethane and propane onto Ajax activated carbon are collected by using a 'differential adsorption bed' over a range of particle sizes and shapes, bulk concentrations and temperatures. A multicomponent model incorporating macropore, surface and micropore diffusion mechanisms recently proposed by Hu and Do (Chem Eng Sci (in press)) is used to predict the binary adsorption dynamic data by using information of single-component isotherms and dynamics. The multicomponent adsorption equilibrium is calculated by using the ideal adsorbed solution theory (IAST), with the single-component isotherm described by a Unilan equation. The model is found to describe the binary adsorption kinetics well and in particular it accurately predicts the degree of the overshoot of the fast-diffusing/less-strongly adsorbed species.     

H1020树脂吸附糖精的动力学和热力学研究

研究了大孔树脂H1020对糖精（邻苯甲酰磺酰亚胺）的吸附性能。在温度为303.15、308.15、313.15和318.15 K条件下分别测定了吸附平衡数据。分别采用了拟一级动力学模型和拟二级动力学模型对实验数据进行模拟,结果表明拟二级动力学方程更适合描述H1020型大孔树脂对糖精的吸附过程。用Langmuir和Freundlich吸附等温方程对实验数据进行拟合,结果表明糖精在大孔树脂H1020上的吸附平衡符合Freundlich吸附等温方程。计算糖精吸附过程的吸附焓变、吸附自由能和吸附熵变,根据吸附热力学值可判断出H1020型大孔树脂对糖精的吸附过程是自发的、放热的物理吸附。     

环己醇、环己酮、二甘醇三组分汽液相平衡研究

用ROSE平衡釜测定了环己醇(1)-环己酮(2)、环己酮(1)-二甘醇(2)、环己醇(1)-二甘醇(2)3对二元系常压下的汽液相平衡数据,并对其进行了热力学一致性检验。用改进的Peng-Rob inson方程计算了气相逸度系数,用W ilson方程和NRTL方程分别计算了液相活度系数,拟合得到了模型参数。通过对实验数据进行关联,取得了较满意的结果:二元系实验数据与模型计算值的平均相对偏差在3%以内,三元系实验数据与模型计算值的平均相对偏差在4%以内。所关联的模型参数可靠,实验取得的相平衡数据可用于化工生产的设计、模拟与优化。     

AB-8大孔树脂对葡萄籽原花青素的吸附过程

研究葡萄籽原花青素粗提液在AB-8大孔树脂上的吸附过程,建立了AB-8大孔树脂吸附原花青素的相平衡方程和动态吸附模型,计算了不同流速、不同进料浓度下的总传质系数、传质区长度及穿透时间。实验结果表明,原花青素静态吸附符合Langmuir吸附等温方程式;AB-8树脂对原花青素的动态吸附属于外扩散控制过程;穿透时间计算值与实验值一致。建立的数学模型可用于指导实际生产操作,为吸附柱的设计提供参考。     

Influence of heat generated on adsorption in bidisperse adsorbents

Sorption behaviour in adsorbate-adsorbent systems can be considerably influenced by adsorption heat generation. General relations for sorption in bidisperse adsorbents, represented by zeolites, are derived. One limiting case is treated analytically assuming mass transport in the interior of the crystallites and heat transport in the zeolite pellets to be fast compared both with mass transport in the intercrystalline space and with the heat dissipation into the surroundings of the zeolite pellets. The first statistical moment of the sorption curve is given and applied to the interpretation of kinetic data in the cyclohexane-13X zeolite system.