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.     

Effects of non-ideal adsorption equilibria of gas mixtures on column dynamics

A theoretical study has been made for simulating the dynamic behavior of non-ideal gas mixtures in an isothermal fixed-bed adsorber. A mathematical model was developed which takes into account the non-ideality of adsorbable species on the adsorbed phase under equilibrium. The model is based on both the real adsorbed solution theory (RAST), which incorporates the activity coefficients in the multicomponent isotherm equations to account for the deviations from ideality, and the linear driving force (LDF) model for representing diffusion resistance inside the adsorbent particles. To describe the effect of non-ideal adsorption equilibrium of gas mixtures on the breakthrough curves, we considered several model mixtures of binary and ternary components which exhibit non-ideal behavior with azeotropic crossovers in the composition domains at equilibrium. Sample calculations of a fixed-bed adsorption were done with various inlet gas compositions of binary and ternary mixtures, respectively, at a fixed total concentration. From the calculation results, it was shown that the order of breakthrough curves could be changed at a certain value of inlet gas composition ratio. This result implies that the dynamic behaviors of fixed-bed adsorption are greatly influenced by multicomponent equilibrium models. Furthermore, the reversal phenomenon of breakthrough curves could not be simulated by the ideal adsorbed solution theory (IAST).     

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.     

Theoretical basis of adsorption processes for separation of multicomponent mixtures

In this paper different frontal regimes are analysed during adsorptional separation of multicomponent mixtures. Account is taken of the main qualitative characteristics of interphase mass transfer in undefined porous media, consisting of porous grains of different internal structures and the boundary of phase change in physical adsorption.     

Modelling of the adsorption separation of gas mixtures with allowance made for the thermal effects accompanying adsorption: II. Analysis of front behaviour under adsorption elimination of one substance from gas mixture

A classification of various theoretical models for the non-isothermal dynamics of adsorption is presented. It has been shown that the conditions determining a given front behaviour depend on: theoretical models for the kinetics and dynamics of adsorption; the values of heat and mass exchange parameters inside the porous grains and in the porous medium. Formulae have been derived for calculating the values of the quantities characterizing the frontal behaviour in the stage of adsorption (elimination of impurities) and desorption (recovery of the adsorbent).     

Multicomponent adsorption equilibria of highly non-ideal mixtures: The case of chloroaromatic mixtures on zeolite

The adsorption equilibrium behaviour of binary, ternary and quaternary vapour mixtures involving ortho- and para-chlorotoluene, toluene and chlorobenzene on zeolite Ca-X at atmospheric pressure and 230°C has been investigated. Since under these operating conditions the adsorbent surface is saturated and the adsorbed molecules interact strongly with each other, these systems exhibit significant deviations from ideal behaviour. A thermodynamic non-ideal adsorption equilibrium model is presented, which, based only on binary interaction parameters, allows for the prediction of multicomponent equilibrium data. The role of such a model in the simulation of the dynamic behaviour of fixed-bed separation columns is investigated. A surprisingly strong effect of the desorbent on the selectivity of the two isomers is found.     

Generalized linear driving force approximation for adsorption of multicomponent mixtures

This work deals with the development of efficient numerical tools for the solution of diffusion dominated parabolic partial differential equations. This study finds its application in the modeling of the intraparticle mass balance necessary for describing dynamic adsorption processes.The orthogonal collocation method is proposed as the basis for developing generalized linear driving force approximations for adsorption and desorption of multicomponent mixtures in a single particle, independently of the mass transport model adopted. Based on this approach, it was possible to derive some approximations previously obtained from the analytical series of the homogeneous diffusion equation.Orthogonal collocation is also compared to other numerical methods found in the literature, using both the homogeneous diffusion and the dusty-gas mass transport models. The results show that orthogonal collocation is the more consistent approach.     

Review and comparisons of D/R models of equilibrium adsorption of binary mixtures of organic vapors on activated carbons

Published models and options for predicting equilibrium adsorption capacities of multicomponent mixtures using single component Dubinin/Radushkevich isotherm equations and parameters were reviewed. They were then tested for abilities to predict total and component capacities reported for 93 binary adsorbed mixtures. The best model for calculating molar distributions was the Ideal Adsorbed Solution Theory (IAST), which balances spreading pressures. Combined with the IAST, total and component capacities were best calculated using either the Lewis or original Bering equation with the Ideal Adsorbed Solution (Raoult’s Law) assumption.     

Vapour phase adsorption measurements of c6 hydrocarbon mixtures on synthetic faujasite

A new apparatus is described for measuring pure component isotherms of condensable vapours at temperatures of 25°–150° and pressures up to 600 mm. Facilities are also incorporated into the unit to permit the study of multicomponent adsorption. Without disturbing the adsorption equilibrium, the gas phase can be separated from the adsorbed phase for subsequent analysis by independent methods. With n-hexane, hexene-1, 1,5-hexadiene and benzene on synthetic faujasite at 97°, the pure component isotherms follow the Langmuir equation and the amount adsorbed at saturation has a nearly constant value of 0.23 liq. ml/g. In the adsorption of binary mixtures of benzene and n-hexane at 97°, the separation factor varies strongly with composition and ranges in value from 13 to 52. A maximum factor is observed at intermediate compositions. Hexene-1-n-hexane mixtures under the same conditions give a lower separation factor of 2–3 which is more nearly constant with composition. Data on multicomponent adsorption of other mixtures are also presented.     

Breakthrough behaviour of a binary gas mixture with azeotropic adsorption equilibrium

This contribution reports on the breakthrough behaviour of binary gas mixtures with ideal and non-ideal multicomponent adsorption equilibria. Investigations were carried out on mixtures CO₂/C₂H₄ and C₂H₄/C₂H₆, both adsorbed on molecular sieve 5A (ms5A). The adsorption equilibrium of the system CO₂/C₂H₄/ms5A may exhibit azeotropic behaviour, which subsides with decreasing active pressure (= sum of partial pressures of adsorbable components) or on raising the temperature. In contrast, the system C₂H₄/C₂H₆/ms5A maintains its ideal behaviour also at higher active pressures or lower temperatures. Attempts to calculate the non-ideal adsorption equilibrium from measured single component isotherms have failed when known models were applied. The investigation of the effect of azeotropic equilibrium on the fixed bed adsorption led to intersecting breakthrough curves of the two components. This behaviour is due to a displacement of equilibrium caused by the change in the active pressure and partial pressures, and a superposed temperature effect. This can be shown by calculating the breakthrough curves with the equilibrium model.     

Separation of multicomponent aromatic/aliphatic mixtures by simulated moving bed adsorption: Modeling and experiments

Simulated moving bed (SMB) adsorption has potential for efficient separation of many valuable chemical mixtures, but considerably less attention has been devoted to multicomponent feeds relative to binary mixtures. We take a rigorous experimental and modeling approach to study multicomponent separation of aromatics and aliphatics with a mesoporous silica adsorbent, which is relevant in many petrochemical applications such as separation of reformate and distillate streams. Our approach involves refining multicomponent adsorption, mass transfer, and SMB process parameters based upon detailed experimental inputs, with progressive addition of components. We develop a robust model that quantitatively predicts the influence of key operating parameters such as stream flow rates, desorbent/feed ratio, and switch time on the separation results and concentration profiles. The model is validated as a function of feed complexity by SMB experiments and column concentration profile measurements in a 16-column mini-plant. Furthermore, conditions for clear separation of each mixture are developed.     

The rigid adsorbent lattice fluid model for pure and mixed gas adsorption

The ability of macroscopic models to predict correctly multicomponent systems from pure component isotherms alone remains a major challenge in adsorption engineering. A new fundamental thermodynamic model for multicomponent adsorption of molecules of different size in nanoporous materials is derived from a modified lattice fluid model. Expressions for the fugacity coefficients are derived and the resulting equilibrium relationships are shown to be consistent with a type I adsorption isotherm. Expressions are obtained for the saturation capacity, the Henry law constant and the adsorption energy. The model is applied to silicalite and the parameters for the adsorbent are obtained from crystal properties, the adsorption energy of n-alkanes and Henry law constants for six gases. Model predictions for gas adsorption up to 20 bar are shown to be comparable to empirical adsorption isotherm equations. Extension to binary and quaternary systems shows good a priori predictive capability when compared to experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1304–1314, 2019     

ISOTHERMAL AND NON-ISOTHERMAL MULTICOMPONENT ADSORPTION KINETICS

The model equations in the relaxation form for the multicomponent kinetics of isothermal and non-isothermal adsorption, taking into account all major distinctive features of the interphase heat and mass exchange inside porous grains and at their surface (see points 1 to 4 below) for P (“pore”) and S (“solid”) models of mass transfer within porous grains of the adsorbent, have been obtained.

First for isothermal and non-isothermal kinetics in the mixed kinetics region of mass and heat exchange in the absence natural mutual diffusion and natural thermal-diffusion the essential influence effective mutual diffusion and effective thermal-diffusion is shown.

Recommendations on the use of model equations of adsorption kinetics for describing isothermal and non-isothermal adsorption dynamics of multicomponent mixtures in the inner-diffusion and mixed (outer- and inner-diffusion) kinetic region of heat and mass exchange are made.     

Phoresis of spherical particles in multicomponent gas mixtures

A theory is developed for the drag, thermophoresis, diffusiophoresis and thermodiffusiophoresis of spherical aerosol particles in multicomponent gas mixtures. The theory is based on a kinetic-theory model in which the particles are treated as giant molecules, and covers the full range of particle Knudsen numbers. It is shown how the theory allows results on multicomponent mixtures to be predicted from results on single gases or binary mixtures.     

Surface potential theory of multilayer adsorption from gas mixtures

Methods of calculating equilibria for adsorption of gas mixtures are compared. It is shown that methods proposed earlier by Myers and Prausnitz [14], by Cook and Basmadjian [16], by Lewis [11] and by Arnold [3] are based upon the assumption of an ideal adsorbed solution but differ in their choice of standard states. All of these methods fail for multilayer adsorption because the standard state is undefined.A new surface-potential theory of multilayer adsorption is proposed; it is based upon the formation of an ideal adsorbed solution at high surface coverage where the vapor is close to condensation. The new theory agrees with published experimental data for adsorption isotherms of Types I and II.     

Prediction of multicomponent adsorption equilibrium of gas mixtures including supercritical components

A new model to predict the adsorption equilibrium of mixtures containing supercritical components was presented. The difference in the adsorption mechanism between the supercritical components and the condensable components was accounted for in the new model. Lateral interaction in the adsorbed phase was also considered in the local isotherm. The new model was verified by the experimental data of the mixture CH₄/CO₂/C₂H₆ on activated carbon JX101 collected for 283-313 K and pressures up to . It was also verified with the experimental data published previously in literature. Considerable improvement in the prediction precision was achieved in using the new model to predict the adsorption of mixtures on activated carbon.     

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

Model equations have been obtained for the non-isothermal kinetics and dynamics of adsorption of one substance, allowance being made for all distinctive characteristics of interphase heat and mass transfer in porous grains and in the intergranular space of a porous medium.     

A generalized film model for mass transfer in non-ideal fluid mixtures

Expressions for calculating steady state mass transfer rates in n-component fluid mixtures across planar, cylindrical and spherical interfaces are presented in a common format using matrix formulations. The resulting generalized multicomponent film model for non-ideal fluid mixtures is based on an analytic solution to the Maxwell-Stefan equations.     

Membrane system design for multicomponent gas mixtures via mixed-integer nonlinear programming

An optimal design strategy for membrane networks separating multicomponent gas mixtures based on an approximate permeator model and mixed-integer nonlinear programming (MINLP) is proposed. A permeator system superstructure is used to embed a very large number of possible network configurations and allows the permeator feed-side pressure to be fixed or a design variable. A MINLP design model is developed to minimize the total annual process cost by simultaneous optimization of the permeator configuration and operating conditions. Case studies for the separation of acid gases (CO₂ and H₂S) from crude natural gas mixtures with spiral-wound permeators are presented. Permeator configurations are derived for different number of separation stages for both continuous and discrete membrane areas. The method is sufficiently robust to handle product compositions that vary five orders of magnitude. The proposed approach provides an efficient methodology for preliminary screening of multi-stage membrane separation systems for multicomponent gas mixtures.