Multicomponent transport model

Both a simplified continuous and discrete model, describing the behaviour of single component mass transport in chromatographic columns with non-linear distribution isotherm, were developed and simulated by Smit et al. Studies of more complex but still relatively simple (multicomponent) transport models have been published (see e.g. ... 

Parameter Correlations for A Multicomponent Transport Model for Chlor-Alkali Membrane Cells," Presention at the 157th Meeting of the Electrochemical Society, St. Louis, Mo. 5-11, 16, 1980, Olin. 

The following three multicomponent transport models have been used to explain the depression of the permeability of a component in a mixture relative to its pure component value (Fig. 21) the Petropoulos model and the competitive sorption model, both of which assume that direct competition for diflfiisive pathways within the glass is negligible, and a more general permeability model in which direct competition can occur between penetrant molecules for both sorption sites and diffusion pathways. All three of the models presented here are based upon the framework of the dual-mode model. It is worth mentioning that the site-distribution model has recently been extended to accoimt for diffusion (98) and that free volume models exist for transport in glassy polymers (99). 

Salem A, Ghoreyshi A A and Jahanshahi M (2006), A multicomponent transport model for dehydration of organic vapors by zeolite membranes . Desalination, 193,35-42. 

Wu Y.S., Zhang K., et al. An efficient parallel-computing scheme for modeling noni-sothermal multiphase flow and multicomponent transport in porous and fractured media. 2002 Advances in Water Resources 25 243-261. 

Chemical mass is redistributed within a groundwater flow regime as a result of three principal transport processes advection, hydrodynamic dispersion, and molecular diffusion (e.g., Bear, 1972 Freeze and Cherry, 1979). Collectively, they are referred to as mass transport. The nature of these processes and how each can be accommodated within a transport model for a multicomponent chemical system are described in the following sections. 

A reactive transport model in a more general sense treats a multicomponent system in which a number of equilibrium and perhaps kinetic reactions occur at the same time. This problem requires more specialized solution techniques, a variety of which have been proposed and implemented (e.g., Yeh and Tripathi, 1989 Steefel and MacQuarrie, 1996). Of the techniques, the operator splitting method is best known and most commonly used. 

Mass transport models for multicomponent systems have been developed where the equilibrium interaction chemistry is solved independently of the mass transport equations which leads to a set of algebraic equations for the chemistry coupled to a set of differential equations for the mass transport. (Cederberg et al., 1985). 

The model described in the previous sections is very complicated and therefore in Part I only isothermal studies will be reported. This limiting situation can be obtained by putting //, = 0 (i = 1,. ..,n) and setting the bulk temperatures equal to To in eq. (16b). In this paper the influence of multicomponent transport phenomena on the mass transfer rate between a gas/vapour and a liquid will be studied in detail for both non-reactive and reactive conditions. It should be stressed that the validity of the model developed in... 

Earlier modeling studies were aimed at predicting the current and temperature distributions, as the nonuniform distributions contribute to stress formation, a major technical challenge associated with the SOFC system. Flow and multicomponent transport were typically simplified in these models that focused on SOFC electrochemistry. Recently, fundamental characteristics of flow and reaction in SOFCs were analyzed using the method of matched asymptotic expansions. " ... 

Numerical simulations were carried out using a multicomponent reactive solute transport model to study the migration of four heavy metals (Cd, Pb, Cu, and Zn ) in a sand/bentonite mixture. The leachate pH has a significant effect on the migration of Cd and Pb but has only limited effect on the mobility of and Zn " (Wu and Li, 1998). 

The most sophisticated models applied to FePRBs to date combine multiple ADEs (i.e., multicomponent transport) with coupled chemical reactions [184,186,208]. These multicomponent reactive transport models were used to simulate the geochemical evolution in FePRBs for the treatment of TCE [184] and for remediating mixtures of Cr(VI) and chlorinated solvents [186,208]. The models are capable of reproducing the spatial distribution of field-observable parameters such as the concentrations of the chlorinated solvents, pH, Eh, alkalinity, Mg2 +, S042-, and N03 ... 

Multicomponent reactive transport models can also be used to estimate the potential for barrier clogging due to secondary mineral formation... 

Wang, Y., and van Capellen, P. (1996) A multicomponent reactive transport model of early diagenesis application to redox cycling in coastal marine sediments. Geochim. Cosmochim. Acta 60, 2993-3014. 

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

At present two models are available for description of pore-transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[4,5] and the Dusty Gas Model (DGM)[6,7]. Both models permit combination of multicomponent transport steps with other rate processes, which proceed simultaneously (catalytic reaction, gas-solid reaction, adsorption, etc). These models are based on the modified Maxwell-Stefan constitutive equation for multicomponent diffusion in pores. One of the experimentally performed transport processes, which can be used for evaluation of transport parameters, is diffusion of simple gases through porous particles packed in a chromatographic column. 

Tebes-Stevens C., Valocchi A. J., VanBriesen J. M., and Rittmann B. E. (1998) Multicomponent transport with coupled geochemical and microbiological reactions model description and example simulations. J. Hydrol. 209, 8-26. 

Mayer K. U., Frind E. O., and Blowes D. W. (2002) Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled reactions. Water Resour. Res. 38, 1174-1195. 

In the five chapters that make up Part II (Chapters 7-11) we consider the estimation of rates of mass and energy transport in multicomponent systems. Multicomponent mass transfer coefficients are defined in Chapter 1, Chapter 8 develops the multicomponent film model, Chapter 9 describes unsteady-state diffusion models, and Chapter 10 considers models based on turbulent eddy diffusion. Chapter 11 shows how the additional complication of simultaneous mass and energy transfer may be handled. 

In recent years the conventional modeling framework has also been adopted for the description of multicomponent transport phenomena during metal alloy solidification [109, 110, 12]. 

Gao H, Butler A, Wheater H, Vesovic V (2001) Chemically reactive multicomponent transport simulation in soil and groundwater. 1. Model development and evaluation. Environ Geol 41 274... 

These results have important implications for surface complexation and reactive transport models as co-precipitation of nanoscale multicomponent phases may be a significant mode of sorption, particularly under conditions where the concentration of metal ions in the aqueous solution is fairly high. Such phases also provide new surfaces on which further sorption of aqueous ions can occur. However, detection of these phases and distinguishing them from the sorbate metal hydroxide phase requires very careful EXAFS analysis and HRTEM studies of sorption samples. 

Further studies on ion-pair formation have to be done for a reliable understanding of ion transport in multicomponent solutions and concentration dependence of transference numbers for nonaqueous electrolyte solutions, solid polymer electrolytes, and associated gels. In transport models for lithium-ion batteries, transference numbers are often introduced as constants entailing inexact results. Although the... 

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