Exact universal uniqueness criteria for the adiabatic tubular packed bed reactor

Exact, universal a priori bounds and regions of multiplicity for the entire tubular packed bed reactor are developed by application of a technique reported in Chang and Calo, Chem. Engng Sci. 1979 34 285 to a cascade two-phase cell model for an nth order chemical reaction with interphase resistance to mass and heat transport, Le ≠ 1 (or Le = 1) and either lumped parameter catalyst particles or with intraparticle concentration gradients with uniform temperature. Both the more common case of interphase heat transfer greater than interphase mass transfer rate and the inverse case of particle over-temperature have been considered. In all cases it has been shown that the reactor conservation equations can be decoupled at certain points along the bed determined by the Lewis number, and that questions of multiplicity and uniqueness reduce to consideration of a single algebraic equation which is actually a form of the two-phase adiabatic CSTR. Also as for the CSTR, the topology of the adiabatic packed bed reactor is shown to be the simple cusp catastrophe. The application of the resultant criteria is quite simple and represents a practical step in the design procedure for highly exothermic reactions in packed beds. A flow chart of a suggested procedure is included.     

Modelling of adsorption separation of gas mixtures with allowance made for the thermal effects accompanying adsorption: III. Model equations for the non-isothermal kinetics and dynamics of adsorption of multicomponent mixtures

Model equations have been obtained for the non-isothermal kinetics and dynamics of adsorption of multicomponent mixtures allowing for the major features peculiar to the heat and mass exchange inside and outside the porous grains in a porous medium: the essential influence of the interdiffusion of the mixture components; the dependence of the diffusion and interdiffusion coefficients on the mixture component concentrations and temperature; the essential influence of the thermal diffusion and diffusion-thermal effects. It has been shown that the model equations are appropriate for describing the front behaviour of the non-isothermal dynamics of mixture adsorption in the adiabatic and non-adiabatic cases.     

Modelling of adsorption separation of gas mixtures with allowance made for the thermal effects accompanying adsorption: V. Specific patterns of adsorption separation of one substance from a gas mixture in the adiabatic case

The procedure for the elimination of the terms of model equations of non-isothermal adsorption dynamics for multicomponent mixtures that take into account dispersive factors (both the kinetics of mass and heat transfer and longitudinal mixing and longitudinal heat conductance along the adsorber) has been analysed. It is emphasized that the elimination of terms is only valid in the case where conditions ‘F’ (see References 19 and 20) are satisfied. The transformation of the stable frontal patterns into unstable frontal patterns using the Langmuir thermal adsorption equations is shown. The concept of effective thermal diffusion for the adiabatic adsorption of one substance in the mixed kinetic region in the absence of the ‘classical’ thermal diffusion transfer within porous grains of adsorbents is considered. The role and the influence of effective thermal diffusion and diffusion thermal heat and mass transfer on the kinetics and dynamics of adiabatic adsorption have also been analysed. For various thermal models of the adiabatic case simple practical formulae have been obtained for use in calculating the width of heat and mass transfer zones in the real laboratory and in industrial adsorbers.     

Three-dimensional numerical simulation of a circulating fluidized bed reactor for multi-pollutant control

Circulating fluidized bed adsorber (CFBA) technology is regarded as a potentially effective method for simultaneously controlling emissions of sulfur dioxide, fine particulate matter, and trace heavy metals, such as mercury vapor. In order to analyze CFBA systems in detail, a gas mixture/solids mixture model based on the three-dimensional Navier-Stokes equations is developed for particle flow, agglomeration, physical and chemical adsorption in a circulating fluidized bed. The solids mixture consists of two solids, one with components of CaO and CaSO₄, and the other being an activated carbon. The gas mixture is composed of fine particulate matter (PM), sulfur dioxide, mercury vapor, oxygen and inert gas. Source terms representing fine particulate matter agglomeration onto sorbent particles, sulfur dioxide removal through chemical adsorption onto calcined lime, and mercury vapor removal through physical adsorption onto activated carbon are formulated and included into the model. The governing equations are solved using high-resolution upwind-differencing methods, combined with a time-derivative preconditioning method for efficient time-integration. Numerical simulations of bench-scale operation of a prototype CFBA reactor for multi-pollutant control are described.     

A kinetic study of the adsorption and desorption process of two commercial molecular sieves

A mathematical model and its numerical solution is presented to describe adiabatic adsorption—desorption processes in a fixed bed when the mass and heat transfer can be described by external film transfer coefficients only, which is especially interesting in the case of non-uniform, irregular particles. A new method to measure such rates is presented, based on continuous weighing of a through-circulated bed. The measured rates can be checked against the difference in humidity and temperature between the outlet and inlet air in order to minimize errors.The comparison between experimental results and calculations showed that the adsorption process in a bed of molecular sieve pellets can not be described with a constant mass transfer coefficient; the desorption process is better described although not entirely satisfactorily. In the case of a honeycomb molecular sieve, a constant mass transfer coefficient described both the adsorption and desorption processes satisfactorily.     

DYNAMIC MODELLING OF WATER VAPOR ADSORPTION BY ACTIVATED ALUMINA

Prediction of water vapor adsorption by activated alumina in a packed bed operated adiabatically is accomplished through the use of a simplified mathematical model. The model accounts for the heat and mass convection in the axial direction, and characterizes the heat and mass transfer associated with the adsorption process by a linear driving force. A linear isotherm was applied to approximate the equilibrium relationship of water vapor on activated alumina. Experimental data using Alcoa's commercial activated alumina, obtained from a 6 x 48 inch adiabatic column, were compared with model prediction; and a reasonably good agreement between these two was obtained. @KEYWORDS: Mathematical modeling, Adsorption, Activated alumina, Gas drying, Desiccant, Packed column.     

结炭B-02催化剂烧炭再生本征动力学模型

以工业两段绝热床中运行近4000h的结炭B—02催化剂为研究对象,利用内循环无梯度反应器,求得催化剂烧炭再生本征动力学模型.由于催化剂中的结炭是多核芳烃,因此可简单地以碳氧化和氢氧化的动力学方程表征烧炭再生动力学模型.碳氧化动力学方程为-dN_c/N_Cdt=K_Cp_(O_2)~(0.3)(N_C/N_C)~1.3式中,一段催化剂 K_C=13.37exp[-78.97×10~3/(RT)]二段催化剂 K_C=96.54exp[-89.30×10~3/(RT)]氢氧化动力学方程为-dN_H/N_Hdt=K_H(N_H/N_H)~1.1式中,一段催化剂 K_H=0.48exp[-39.04×10~3/(RT)]二段催化剂 K_H=4.79exp[-52.03×10~3/(RT)]     

Multicomponent ion exchange column dynamics

Simple model equations which consider different rate control mechanisms are formulated for fixed bed multicomponent ion exchange processes. Efficient and accurate numerical methods are developed for solving these equations for liquid phase, solid phase or combined phase control. The algorithms are applicable to both ion exchange and liquid adsorption and are shown to be extendable to a general form of isotherms. The accuracy of the numerical algorithm is evidenced by the fact that the asymptotic limiting equilibrium solutions are closely approached as the dimensionless length parameter is increased, regardless of the rate control mechanism. Numerical examples for ion exchange applications are presented. These examples included multicomponent elution and purification problems. The effect of mass transfer resistance was also examined. Other examples examine the validity of a model reduction assumption and the comparison of equilibrium theory with the results obtained using the present finite mass transfer rate model.     

Application of wave propagation theory to adsorption breakthrough studies of toluene on activated carbon fiber beds

Based on the wave propagation theory, a dynamics model that combines the nonlinear equilibrium isotherm and the linear mass-transfer equation has been developed to predict the breakthrough behaviour of toluene adsorption in a fixed bed packed with activated carbon fibers. The experimental results showed that the constant-pattern wave model using the Langmuir isotherm equation could capture the dynamic behaviour of the adsorption column. Two important parameters, the half breakthrough time (t_1/2) and the volumetric mass-transfer coefficients (k_Gα) in the model were obtained from linear fitting of the model to experimental breakthrough data. k_Gα was found to be insensitive to the initial concentration and increased with the increasing the superficial velocity. It was also observed that t_1/2 decreases with increasing the superficial velocity and the initial concentration, and increases with increasing the bed height. A sensitivity analysis showed that external mass-transfer had a much stronger influence on the breakthrough curve than internal mass-transfer, confirming that the overall mass-transfer for toluene adsorption onto activated carbon fibers in fixed bed is controlled by external mass-transfer.     

Dynamic behaviour of an adiabatic adsorption column—I Analytic solution for irreversible adsorption

A simple theoretical model, based on the rectangular isotherm approximation, is shown to provide a good representation of the dynamic behaviour of an adiabatic adsorption column. The model provides an analytic expression for the dynamic temperature response in terms of the usual kinetic and equilibrium parameters and it is shown that within the constant pattern regime the relationship between the concentration and temperature profiles assumes a very simple form. The magnitude of the temperature rise depends on the relative velocities of thermal and concentration waves as well as the heat of adsorption and sorbate concentration. The maximum temperature rise occurs when the velocities of the temperature and concentration fronts are indentical. Under these conditions there is no temperature plateau and the magnitude of the thermal wave increases continuously as the adsorption front progresses through the bed.Experimental data for the adiabatic adsorption of moisture from an air stream are presented and discussed in relation to the theory.     

Comparison of experimental and predicted breakthrough curves for adiabatic adsorption in fixed bed

Mass and heat transfer in adiabatic fixed bed adsorbers is described by a model which considers resistance to mass and heat transfer simultaneously within the porous adsorbent particles and in the fluid flowing past the pellets. The adsorption equlibrium is described by a temperature dependent Freundlich isotherm.The mathematical model which is given in dimensionless form is solved numerically for different values of the dimensionless parameters.An example of predicted concentration and temperature breakthrough curves for an adiabatic integral bed is given. This prediction is performed solely on the basis of data from an isothermal differential bed. The predicted breakthrough time is within 8% of the experimental value when the dimensionless parameters are assumed constant and within 2% when their concentration and temperature dependence is taken into account.     

Solid-liquid adsorption based on external mass transfer,macropore and micropore diffusion

A mass transfer model has been developed based on external film mass transfer, macropore diffusion and micropore diffusion to explain the adsorption of pollutants from aqueous solutions onto adsorbent particles. A computer program has been developed to facilitate analysis of the model in order that theoretical concentration decay curves may be compared with experimental data. A brief comparison has been made for the adsorption of Acid Blue 25 dye on chitin and phenol on carbon. However, the main purpose of the paper is to show the mathematical development of the model using the basic equations of the branched pore theory developed by Peel et al. (1981, A.I.Ch.E. J.27, 26) and undertake a sensitivity analysis to study the effect of changing the four main parameters, namely, the external film mass transfer coefficient, the surface diffusion coefficient, the branched pore rate coefficient and the fraction of total adsorptive capacity in the macropores.     

Thermal modeling of activated carbon based adsorptive natural gas storage system

A homogeneous, isotropic porous matrix of activated carbon inside a portable steel cylinder is considered as the adsorption bed for natural gas (NG) which is idealized as pure methane for the purpose of simulation. The heat and fluid flow inside the porous adsorption bed are modeled using a volume averaging technique and Darcy-Brinkman formulation. The effective thermal conductivity of the activated carbon-methane system is calculated as a function of uptake according to the Luikov model. Heat generation due to the exothermic process of adsorption is considered. The governing equations are solved using an implicit finite volume method for the given boundary conditions. Three different models of adsorption are considered, namely (i) a no-flow model, (ii) flow model with uniform adsorption and (iii) a flow model with local adsorption. For each of these models, transient temperature profiles in the adsorption bed during the charging process are obtained, and the corresponding mass adsorption potentials are calculated. Parametric studies are performed to investigate the effects of gas inlet temperature and rate of charging on the maximum bed temperature and the time required to fill the cylinder.     

Dynamics of pressurization and blowdown of an adiabatic adsorption bed: 4. Intraparticle diffusion/convection models

The importance of intraparticle mass transfer during pressurization and blowdown steps of PSA processes in an adiabatic adsorption bed was assessed by comparing intraparticle diffusion/ convection and intraparticle diffusion models. Film mass/heat transfer resistances are also considered in the model. The film heat transfer resistance is more important than the heat transfer resistance inside the particle; it can be assumed to be negligible in PSA processes when the temperature variation is not very large, otherwise it leads to serious errors when the adsorption capacity of adsorbents is high and the heat capacity of the system is not high. Intraparticle convection improves the mass transfer inside the particle and leads to faster heat releases into and out of the adsorbents.     

吸附天然气储罐充气过程的数学模拟

对于吸附天然气储罐,结合实际充气过程建立了较简化的一维非绝热模型并进行了数值模拟,以分析比较各种可能缓解充气热效应的措施.对于容积约50L的吸附储罐的模拟计算表明：通过吸附床层自然散热的方法,10min的充气效率为0.76,比绝热过程仅增加0.03;降低气体入口温度不能有效地提高充气效率,而通过气体外循环换热或提高充气压力的方法可有效地提高充气效率.     

A 3-zone model for protein adsorption kinetics in expanded beds

The adsorption behavior of expanded beds is more complex than that of fixed beds, since the adsorbent particle size, local bed voidage and liquid axial dispersion will vary axially with expanded height. Models applicable to fixed beds maybe not adequately describe the hydrodynamic and adsorption behavior in expanded beds. In this paper, a 3-zone model is developed, in which the model equations are written for the bottom zone, middle zone, and top zone of the column, respectively, and the model parameters, such as the adsorbent particle diameter, bed voidage and liquid axial dispersion coefficient, are zonal values. In-bed breakthrough curves are predicted by the 3-zone model, and tested against literature data for lysozyme adsorption on Streamline SP in an expanded bed.Model parametric sensitivity is analyzed. The effects of film mass transfer resistance, liquid axial dispersion and adsorbent axial dispersion on the breakthrough curves are weaker than that of protein intraparticle diffusion resistance for stable expanded beds. Adsorbent particle size axial distribution and bed voidage axial variation significantly affect in-bed breakthrough curves, therefore, model parameters should not be assigned uniform values over the whole column; instead the model should account for the adsorbent particle size axial distribution and bed voidage axial variation.     

Modeling of Water Adsorption in SAPO‐34‐Coated Aluminum Foam

After presenting the most promising continuous adsorption cooling topology for air‐conditioning of a passenger cabin, a transient, 3D model is proposed, based on a modified linear driving force approach, to simulate an adsorption process in a SAPO‐34‐coated open‐celled aluminum foam. The simulation is executed in ANSYS CFX 15.0 and the additional model equations are implemented through the CFX expression language. As a result the influence of the pore diameter onto the system simulation and the mass transport limitation is shown and the sensitivity concerning the pressure in the gas phase adsorption is confirmed.