Mass transfer-based modelling

Xu, Y. and Zhang, Y.P. (2003) An improved mass transfer based model for analyzing VOC emissions from building materials. Atmospheric Environment, 37 (18),... 

Simplified models that do not make a priori assumptions about one or more dominant resistances are often of the 1-D macrohomogeneous type. The 1-D assumption is similar to that in mass transfer-based models. The assumption of macrohomogeneity, based on work by Newman and Tobias [50], has proven useful in battery and fuel cell electrode modelling. It implies that the microstructure of the electrode is homogeneous at the level of the continuum equations governing mass transfer, heat transfer, and current conduction in the electrode (Eqs. (l)-(7) and (33)-(37)). This type of model can exploit solutions available in chemical reaction engineering practice and has been elaborated by several researchers in that field [51-55],... 

The model provides a good approach for the biotransformation system and highlights the main parameters involved. However, prediction of mass transfer effects on the outcome of the process, through evaluation of changes in the mass transfer coefficients, is rather difficult. A similar mass transfer reaction model, but based on the two-film model for mass transfer for a transformation occurring in the bulk aqueous phase as shown in Figure 8.3, could prove quite useful. Each of the films presents a resistance to mass transfer, but concentrations in the two fluids are in equilibrium at the interface, an assumption that holds provided surfactants do not accumulate at the interface and mass transfer rates are extremely high [36]. 

MODELS BASED ON EFFECTIVENESS OF CONTACT, WITH NO EXTERNAL MASS-TRANSFER RESISTANCES (MODELS FOR TRICKLE-BED REACTORS)... 

The mass-transfer efficiencies of various MHF contactors have been studied by many researchers. Dahuron and Cussler [AlChE 34(1), pp. 130-136 (1988)] developed a membrane mass-transfer coefficient model (k ) Yang and Cussler [AIChE /., 32(11), pp. 1910-1916 (1986)] developed a shell-side mass-transfer coefficient model (ks) for flow directed radially into the fibers and Prasad and Sirkar [AIChE /., 34(2), pp. 177-188 (1988)] developed a tube-side mass-transfer coefficient model (k,). Additional studies have been published by Prasad and Sirkar [ Membrane-Based Solvent Extraction, in Membrane Handbook, Ho and Sirkar, eds. (Chapman Hall, 1992)] by Reed, Semmens, and Cussler [ Membrane Contactors, Membrane Separations Technology Principle. and Applications, Noble and Stern, eds. (Elsevier, 1995)] by Qin and Cabral [MChE 43(8), pp. 1975-1988 (1997)] by Baudot, Floury, and Smorenburg [AIChE ]., 47(8), pp. 1780-1793 (2001)] by GonzSlez-Munoz et al. [/. Memhane Sci., 213(1-2), pp. 181-193 (2003) and J. Membrane Sci., 255(1-2), pp. 133-140 (2005)] by Saikia, Dutta, and Dass [/. Membrane Sci., 225(1-2), pp. 1-13 (2003)] by Bocquet et al. [AIChE... 

It should be noted that the bicontinuum models presented by Selim et al. (1976) and Cameron and Klute (1977), which were developed to represent sorption nonequilibrium, are mathematically equivalent in nondimensional form, for the case of linear isotherms, to the first-order mass-transfer bicontinuum model presented by van Genuchten and Wierenga (1976), which was developed to represent transport-related nonequilibrium. This equivalency is beneficial in that it lends a large degree of versatility to the first-order bicontinuum model. However, this equivalency also means that elucidation of nonequilibrium mechanisms is not possible using modeling-based analysis alone. 

The amount of additional information needed to be able directly to take into account heat and mass transfer in Model 4 is high. Using the two-film theory, information on the film thickness is needed, which is usually condensed into correlations for the Sherwood number. That information was not available for Katapak-S so that correlations for similar non-reactive packing had to be adopted for that purpose. Furthermore, information on diffusion coefficients is usually a bottleneck. Experimental data is lacking in most cases. Whereas diffusion coefficients can generally be estimated for gas phases with acceptable accuracy, this does unfortunately not hold for liquid multicomponent systems. For a discussion, see Reid et al. [8] and Taylor and Krishna [9]. These drawbacks, which are commonly encountered in applications of rate-based models to reactive separations, limit our ability to judge their value as deviations between model predictions and experimen-... 

Calculation of the density of deposited layers of sublimate, and of associated variables, as an aid towards the optimization of sublimate condenser design, is discussed by Wintermantel, Holzknecht and Thoma (1987). The starting point of the analysis is the assumption that the growth of sublimate layers is governed mainly by heat and mass transfer the model is based on conditions in the diffusion boundary layer. The main process-determining factors (growth rate, mass transfer, and gas concentration) are accounted for. The derived theoretical relationship is shown to fit experimental data. 

Patience and Chaouki [98] adopted the two-phase model of Brereton et al. [96] to interpret their gas RTD data obtained with a radioactive tracer gas. The two model parameters, crossflow coefficient, k, and (ratio between core and riser cross-sections), were evaluated by fitting the model to the experimental data. They found that the crossflow coefficients varied between 0.03 to 0.1 m/s, and varied from 0.98, at high gas velocities, to 0.5, at low velocities. They attributed gas crossflow between core and annulus by supposing that solids drag gas to the annulus as they condense along the wall and then carry it downward for a certain distance. Solids are reintroduced into the core as they are stripped off the wall and re-entrained into the core gas flow. They developed a correlation for describing this gas mass transfer based on the analogy with wetted wall towers, as ... 

The twin-screw case [11] uses a model based on a series of stagewise units and a semi-infinite mass-transfer diffusion model. 

The difiusion equation taking into account the rate of chemical reaction can be written based on each of the mass transfer diffusion models. 

If the reaction kinetics of the electrode is assumed to be very rapid, mass transfer and ohmic resistance are the dominant resistances. Assuming a reaction zone that coincides with the electrode-electrolyte interface, the diffusion fluxes in stationary operation can be expressed simply in terms of bulk gas partial pressures and gas-phase diffusivities. This is illustrated schematically in Figure 11.8, which compares anode- and cathode-supported cell designs for the simple case of a H2/O2 fuel cell. The decrease in concentration polarisation at the cathode, rjcc- is obvious in the case of an anode-supported cell, while the model shows that concentration polarisation at the anode, tiac is relatively insensitive to anode thickness. The advantage of the mass transfer-based approach is that analytical expressions are obtained for the polarisation behaviour. These are rather simple if activation overpotential is excluded but may still become elaborate in the case of an internally reforming anode where a number of reactions (discussed in Section 11.3) may occur simultaneously within the pores of the anode. 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

The situation is very much poorer for stmctured rather than random packings, in that hardly any data on Hq and have been pubHshed. Based on a mechanistic model for mass transfer, a way to estimate HETP values for stmctured packings in distillation columns has been proposed (91), yet there is a clear need for more experimental data in this area. 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

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