Design equations for multicomponent gas absorption

The recently developed linearized theory of multicomponent mass transfer^{(1, 2, 3, 4)} is applied to the case of gas absorption in a plate column. Matrix generalizations of the well-known binary design equations are obtained using the diagonalizing procedure of Toor⁽¹⁾. The results demonstrate that the theory provides a general framework for the direct incorporation of diffusional and thermodynamic interaction effects into design procedures for multicomponent systems.     

Breakthrough curves in the cyclic steady state for adsorption systems with concave isotherms

Using numerical procedures, breakthrough curves are calculated as a function of one diffusional and one equilibrium parameter for systems obeying equilibrium isotherms concave to the gas concentration axis. For purposes of demonstration the Langmuir isotherm is chosen. The unfavorable effects of an increasingly concave isotherm in the cyclic steady state are the opposite of the “favorable” effects found by authors who investigated the first adsorption period or who assumed that total desorption is possible in the regeneration phase. These conclusions apply within the range of kinetic parameters studied. The results of technological changes, such as using countercurrent desorption, varying total cycle time or increasing the ratio of desorption to adsorption time are shown.     

Diffusional interference in liquid phase counter-adsorptions

A surface diffusion mocel with diffusional interference has been presented for the analysis of multicomponent adsorption of phenols by activated carbon. Surface diffusion coefficients for multicomponent adsorptions were estimated from the relationship between. the surface diffusion coefficient of each species and the surface coverage. The diffusional interference coefficients, W_ij, was determined from experimental counter-adsorption data. The numerical values of W_ij were in the range of 0.4–0.9, which show that the introduction of diffusional interference is necessary to analyze multicomponent counter-adsorptions properly. The proposed model successfully simulates the behaviour of phenols-activated carbon system in a batch adsorber.     

On the solutions of maxwell-stefan equations for multicomponent film model

Literature dealing with multicomponent mass transfer presents two distinctly different relationships defining diffusion fluxes at a phase boundary in mThe first relationship results from the solution of continuity equations according to the so-called linearized theory of multicomponent mass transfer.According to the first “linearized approach” this influence depends solely on the net total mixture flux, in the second “exact” approach this iTheoretical analysis presented in this paper shows that the influence of finite mass transfer rates on diffusion fluxes can be attriuted only to the neThe difference between the relationships describing diffusion fluxes based on the linearized model and those based on the exact solution is accounted f     

Polymers In Solutions And Blends

Abstract

This review covers the sessions of “Solution Properties” and “Polymer Gels”. The five special subjects have been reviewed; (1) multicomponent solution system, (2) polymer blend, (3) kinetics of emulsion polymerization, (4) micelle, and (5) interaction of polyelectrolyte particles.     

On the necessary conditions of optimality of water utilization systems in process plants with multiple contaminants

This paper presents necessary conditions of optimality for multicomponent water allocation systems in refineries and process plants. We extend the necessary conditions of optimality proved for single component by Savelski and Bagajewicz (Chem. Eng. Sci. 55(21) (2000) 5035). In particular, it is shown that at least one component reaches the maximum concentration at the outlet of a freshwater user process. A necessary condition of monotonicity is also proven. In this particular case, monotonicity only holds for certain components called “key” components.     

Modeling Multicomponent Aerosol Particle Growth By Vapor Condensation

A new “moving-sectional” method is presented to solve the dynamics of multicomponent aerosol particle growth by vapor condensation in a closed system. The method controls numerical diffusion and stiffness by adapting the method of characteristics to a sectional representation of the aerosol. An exact solution for a closed system is presented, and the “moving-sectional” method gives excellent agreement when tested against this solution. Four cases are presented to demonstrate the importance of the solute, Kelvin, and latent heat effects.     

A technique for solution of the equations for fluid—solid reactions with diffusion

The kinetic equations for several types of models for fluid—solid heterogeneous non-catalytic reactions with diffusional limitations have a similar mathematical structure. These coupled nonlinear partial differential equations possess very few analytical solutions, and are even difficult to solve numerically because of the “wave-like” nature of the concentration profiles. A transformation has been formulated that reduces these problems to a single, nonlinear diffusion-reaction equation in a new variable. Then, the multitude of results available for this type of problem can be used. With pseudo-steady-state conditions, the conversion of solid becomes analogous to an “effectiveness factor” in the transformed variable. For slab geometry, especially simple results are obtained, leading to analytical or semi-analytical results.     

Modeling of fixed bed adsorption of phenols on granular activated carbon

Mathematical modeling of liquid phase adsorption of phenols in fixed beds of granular activated carbon was investigated. The model considered the effects of axial diffusion in the fluid, the external film and internal diffusional mass transfer resistances of the particles, and the nonlinear adsorption isotherm of Freundlich. It was shown that the analysis of a complex multicomponent adsorption system could be simplified by converting it into a pseudo single-component adsorption system. This was achieved by lumping the concentrations of the components together as one single parameter, chemical oxygen demand. The resulting model equations were solved using the orthogonal collocation method and third-order semi-implicit Runge-Kutta method combined with a step-size adjustment strategy. Excellent agreement between simulated results and pilot plant data was obtained. Also, the breakthrough profiles revealed the formation of a primary monomolecular layer on the adsorbent surface.     

“Condon” and “non-Condon” Nonlinear Spectroscopy of Polyatomic Molecules in Solutions: Solvation Dynamics Study

A theoretical basis for the solvation dynamics study of complex molecules in solutions by resonance four-photon spectroscopy has been developed. A non-Markovian theory of four-photon spectroscopy of electronic transitions in complex molecules has been generalized for the “non-Condon” tensor case. It has been shown that for definite conditions the cubic susceptibility χ⁽³⁾, describing four-photon interaction, can be expressed as a product of “Condon” and non-Condon parts. The latter describes the mixing effect of different electronic molecular states by nuclear motions (Herzberg-Teller effects). The Condon part depends on the excitation frequency, and the non-Condon one depends on the polarization state of the pump and the probe beams. It has been shown that the Condon resonance transient grating spectroscopy is a good method for the investigation of ultrafast solvation dynamics. The dependence of the non-Condon part of χ⁽³⁾ on the polarizations of the interacting beams permits one to formulate the principles of a new method for the investigation of Herzberg-Teller effects on electronic molecular transitions by transient polarization four-photon spectroscopy.     

Definition von Destillationslinien bei der Trennung von Mehrstoffgemischen

Definition of Distillation Lines in the Separation of Multicomponent Mixtures. In recent years “distillation lines” have been used for the assessment of the separation behaviour of multicomponent mixtures, with these distillation lines being defined differently by different authors. The theory of distillation of multicomponent mixtures shows that it is appropriate to distinguish between residue lines and rectification lines. While the profile of residue lines is determined solely by the thermodynamic phase equilibrium, that of rectification lines also depends upon the mass transfer model used. By analogy with VDI Guideline 2761: “Thermal Separation Processes in Process Engineering”, it is proposed that residue lines and rectification lines are designated by the collective term distillation lines.     

The Kinetics and Equilibrium of Ethanol Adsorption from Aqueous Phase Using Calcined (Na‐1,6‐Hexanediol)‐ZSM‐5

Na‐ZSM‐5, synthesized using 1,6‐hexanediol as the structure directing agent, has been found to have a suitable selectivity and adsorbing capacity for ethanol adsorption from aqueous solutions. In contrast to quaternary ammonium based Na‐ZSM‐5 zeolites, this Na‐ZSM‐5 did not show any catalytic interaction with ethanol during thermal desorption. The dynamics of the adsorption process were investigated using the finite volume “uptake rate” route. The data predicted from the governing relations of the process were correlated with experimental results. The micro‐diffusion coefficient was determined as a function of temperature.The macropore diffusional mass transfer contribution for biporous zeolite particles was found to be negligible.     

A general rate model approach for the optimization of the core radius fraction for multicomponent isocratic elution in preparative nonlinear liquid chromatography using cored beads

Cored beads (also known as pellicular, superficially porous, and fused-cored beads or particles) offer advantages over fully porous beads in reduced diffusional mass transfer resistances in particle macropores and separation times in liquid chromatography (LC). They are also used to regulate bead densities. The core of a bead has a relatively small volume and yet presents a large linear distance for diffusional mass transfer inside particle macropores. Using a non-porous inert core, intraparticle diffusional mass transfer resistance can be reduced with a relatively small loss in binding capacities. In multicompnent isocratic elution chromatography, cored beads are a compromise between fully porous beads and non-porous beads. Non-porous beads completely eliminate intraparticle diffusion, providing sharp elution peaks with the shortest retention times. However, they do not provide a sufficient retention time range for peaks to separate in preparative LC because of their limited binding capacities. At the other end, fully porous beads offer the largest retention time differences, but suffering from excessive band broadening. For a particular multicomponent elution system, core radius fraction can be optimized to take the advantages of both fully porous beads and non-porous beads. This work presented a general rate model for cored beads and its numerical solution strategy. The model considered axial dispersion, interfacial mass transfer, intraparticle diffusion, and multicomponent Langmuir isotherm. Computer simulation was used to study the effects of core radius fraction on breakthrough curves and elution peaks. The model was used to optimize the core radius fraction for a preparative ternary elution system as an example case.     

Rigorous modeling of the kinetics of calcium carbonate deposit formation

The complexity of CaCO₃ deposit formation on a flow surface arises from the need to take into account the multicomponent transport of all ionic species involved in the carbonic system. Several semitheoretical and empirical models are available. This article presents a rigorous kinetic model that takes into account the diffusional transport of all species involved in CaCO₃ wall deposition under turbulent flow as well as the kinetics of the CaCO₃ crystallization reaction. Conditions under which high‐ and low‐pH simplified expressions may be used are evaluated. It is shown that the simplified precipitation rate equations provide results within 10% of the rigorous solution when the high‐pH expression is applied for solutions at pH levels above 9.5, and the low‐pH expression is applied for solutions at pH levels below 7.6. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A modified “inside-out” algorithm for simulation of multistage multicomponent separation processes using the UNIFAC group-contribution method

A computational procedure using a modification of Boston and Sullivan's “inside-out” multistage multicomponent separation algorithm (1974) is developed. In order to improve convergence behavior for problems involving mixtures with highly nonideal liquid phases, a two-parameter model is used to describe liquid-phase compositional effects upon the K-factor. The quasi-Newton methods of Mehra et al. (1983) and Nghiem (1983) are applied to solving various sets of solution variables in the proposed algorithm. Activity coefficients are calculated using the UNIQUAC activity-coefficient model (1975) with parameters obtained from the UNIFAC group-contribution method (1975). The computational procedure is applicable to distillation, absorption and reboiled-absorption configurations. The proposed algorithm was implemented in a FORTRAN 77 program and tested on the Honeywell DPS 8/70M computer at the University of Calgary. Inclusion of the liquid-phase model resulted in improved convergence behavior for nonideal systems in which the original “inside-out” method failed to converge.     

Bound rubber and “crepe hardening” in silicone rubber

Some recent results of the research aimed to correlate properties of filled silicone rubber compounds with surface properties of fumed silica fillers are reported. It is shown that the specific interaction between silica surface silanol groups and the siloxane chain of silicone rubber plays the main role in “crepe hardening” and bound rubber formation in compounds. The silanol coverage of silica determines the tightness of polymer–filler network in bound rubber. The experimental data fit Meissner's theory of bound rubber quite well. Remilling of “crepe hardened” compounds was also studied, and the structure of the remilled compounds is proposed. The activation energy of bound rubber formation on mixing was found to be 16.8 kj/mole; this suggests that physical rather than chemical processes are involved in the interaction between silica and silicone rubber.     

Condensation of a binary vapour mixture in the presence of an inert gas

The simultaneous heat and mass transfer process during condensation of a binary vapour mixture in the presence of a non-condensable gas is analysed using matrix formulations of the interfacial mass transfer rate relations. A film model for multicomponent mass transfer based on an exact solution to the Maxwell-Stefan equations is used to calculate the mass transfer coefficients in the ternary vapour phase. With the aid of a computational example involving condensation of methanol and water vapours in the presence of air, it is demonstrated that diffusional interactions can significantly affect condensation rates.