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Mass transfer resistance model

The Brunauer type I is the characteristic shape that arises from uniform micro-porous sorbents such as zeolite molecular sieves. It must be admitted though that there are indeed some deviations from pure Brunauer type I behavior in zeoHtes. From this we derive the concept of the favorable versus an unfavorable isotherm for adsorption. The computation of mass transfer coefficients can be accompHshed through the construction of a multiple mass transfer resistance model. Resistance modehng utilizes the analogy between electrical current flow and transport of molecular species. In electrical current flow voltage difference represents the driving force and current flow represents the transport In mass transport the driving force is typically concentration difference and the flux of the species into the sorbent is resisted by various mechanisms. [Pg.285]

MODELS BASED ON EFFECTIVENESS OF CONTACT, WITH NO EXTERNAL MASS-TRANSFER RESISTANCES (MODELS FOR TRICKLE-BED REACTORS)... [Pg.105]

Figure 5.17 Mass transfer resistance model for defect free (a) as well as for a defect (b) membrane. Figure 5.17 Mass transfer resistance model for defect free (a) as well as for a defect (b) membrane.
A proper resolution of Che status of Che stoichiometric relations in the theory of steady states of catalyst pellets would be very desirable. Stewart s argument and the other fragmentary results presently available suggest they may always be satisfied for a single reaction when the boundary conditions correspond Co a uniform environment with no mass transfer resistance at the surface, regardless of the number of substances in Che mixture, the shape of the pellet, or the particular flux model used. However, this is no more than informed and perhaps wishful speculation. [Pg.149]

The main conclusion to be drawn from these studies is that for most practical purposes the linear rate model provides an adequate approximation and the use of the more cumbersome and computationally time consuming diffusing models is generally not necessary. The Glueckauf approximation provides the required estimate of the effective mass transfer coefficient for a diffusion controlled system. More detailed analysis shows that when more than one mass transfer resistance is significant the overall rate coefficient may be estimated simply from the sum of the resistances (7) ... [Pg.264]

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). [Pg.64]

Correlations of heat and mass-transfer rates are fairly well developed and can be incorporated in models of a reaction process, but the chemical rate data must be determined individually. The most useful rate data are at constant temperature, under conditions where external mass transfer resistance has been avoided, and with small particles... [Pg.2070]

A non-ideal MSMPR model was developed to account for the gas-liquid mass transfer resistance (Yagi, 1986). The reactor is divided into two regions the level of supersaturation in the gas-liquid interfacial region (region I) is higher than that in the main body of bulk liquid (region II), as shown in Figure 8.12. [Pg.236]

As an example, it may be supposed that in phase 1 there is a constant finite resistance to mass transfer which can in effect be represented as a resistance in a laminar film, and in phase 2 the penetration model is applicable. Immediately after surface renewal has taken place, the mass transfer resistance in phase 2 will be negligible and therefore the whole of the concentration driving force will lie across the film in phase 1. The interface compositions will therefore correspond to the bulk value in phase 2 (the penetration phase). As the time of exposure increases, the resistance to mass transfer in phase 2 will progressively increase and an increasing proportion of the total driving force will lie across this phase. Thus the interface composition, initially determined by the bulk composition in phase 2 (the penetration phase) will progressively approach the bulk composition in phase 1 as the time of exposure increases. [Pg.611]

Equation (10.29) is the appropriate reaction rate to use in global models such as Equation (10.1). The reaction rate would be —ka if there were no mass transfer resistance. The effectiveness factor rj accounts for pore diffusion and him resistance so that the effective rate is — 7ka. [Pg.367]

OS 63] ]R 27] ]P 46] Experimental results were compared with a kinetic model taking into account liquid/liquid mass transfer resistance [117]. Calculated and experimental conversions were plotted versus residence time the corresponding dependence of the mass-transfer coefficient k,a is also given as well (Figure 4.78). [Pg.509]

Golay equation 21, 611 gradient (LC) 490 height equivalent to a theoretical plate 11 longitudinal diffusion 16 mass transfer resistance 17 nonlinear chromatography SOS plate model 14 rate theory IS reduced parameters 78, 361, 611... [Pg.509]

A kinetics or reaction model must take into account the various individual processes involved in the overall process. We picture the reaction itself taking place on solid B surface somewhere within the particle, but to arrive at the surface, reactant A must make its way from the bulk-gas phase to the interior of the particle. This suggests the possibility of gas-phase resistances similar to those in a catalyst particle (Figure 8.9) external mass-transfer resistance in the vicinity of the exterior surface of the particle, and interior diffusion resistance through pores of both product formed and unreacted reactant. The situation is illustrated in Figure 9.1 for an isothermal spherical particle of radius A at a particular instant of time, in terms of the general case and two extreme cases. These extreme cases form the bases for relatively simple models, with corresponding concentration profiles for A and B. [Pg.225]

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... [Pg.563]

The reaction is reversible and therefore the products should be removed from the reaction zone to improve conversion. The process was catalyzed by a commercially available poly(styrene-divinyl benzene) support, which played the dual role of catalyst and selective sorbent. The affinity of this resin was the highest for water, followed by ethanol, acetic acid, and finally ethyl acetate. The mathematical analysis was based on an equilibrium dispersive model where mass transfer resistances were neglected. Although many experiments were performed at different fed compositions, we will focus here on the one exhibiting the most complex behavior see Fig. 5. [Pg.186]

We will now describe the application of the two principal methods for considering mass transport, namely mass-transfer models and diffusion models, to PET polycondensation. Mass-transfer models group the mass-transfer resistances into one mass-transfer coefficient ktj, with a linear concentration term being added to the material balance of the volatile species. Diffusion models employ Fick s concept for molecular diffusion, i.e. J = — D,v ()c,/rdx, with J being the molar flux and D, j being the mutual diffusion coefficient. In this case, the second derivative of the concentration to x, DiFETd2Ci/dx2, is added to the material balance of the volatile species. [Pg.76]

For the semi-batch stirred tank reactor, the model was based on the following assumptions the reactor is well agitated, so no concentration differences appear in the bulk of the liquid gas-liquid and liquid-solid mass transfer resistances can prevail and finally, the liquid phase is in batch, while hydrogen is continuously fed into the reactor. The hydrogen pressure is maintained constant. The liquid and gas volumes inside the reactor vessel can be regarded as constant, since the changes of the fluid properties due to reaction are minor. The total pressure of the gas phase (P) as well as the reactor temperature were continuously monitored and stored on a PC. The partial pressure of hydrogen (pnz) was calculated from the vapour pressure of the solvent (pvp) obtained from Antoine s equation (pvpo) and Raoult s law ... [Pg.190]

Recently, Pacheco et al developed and validated a pseudo-homogeneous mathematical model for ATR of i-Cg and the subsequent WGS reaction, based on the reaction kinetics and intraparticle mass transfer resistance. They regressed kinetic expressions from the literature for POX and SR to determine the kinetic parameters from their i-Cg ATR experimental data using Pt on ceria. [Pg.250]

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]. [Pg.201]

The fact that the two release curves show some separation but not enough to account solely for gas-phase diffusion, indicates that the release is actually governed by mass transfer resistances in both phases. This is in qualitative agreement with the transport model presented above. The quantitative agreement will be demonstrated in the next section. [Pg.86]

A new mathematical model based on moment techniques to describe micro- and macropore diffusion is used to study the mass-transfer resistances of Ci to C4 saturated hydrocarbons in H and Na mordenites between 127° C and 272° C. The intracrystalline diffusion coefficient decreases as the number of carbon atoms increases while the energy of activation increases with the number of carbons. The contribution from individual mass-transfer resistances to the overall mass-transfer processes is estimated. [Pg.392]

A kinetic model was developed based on data obtained over a range of temperatures and hydrogen pressures. The kinetic parameters were expressed as a function of temperature. The kinetic model was applied to the analysis of the trickle-bed data. Predictions of a mathematical model of the trickle-bed reactor were compared with data obtained at two temperatures and a range of pressures. The intraparticle mass transfer resistance was very important. [Pg.105]

The basic approach is to consider the problem in two parts. Firstly, the reaction of a single particle with a plentiful excess of the gaseous reactant is studied. A common technique is to suspend the particle from the arm of a thermobalance in a stream of gas at a carefully controlled temperature the course of the reaction is followed through the change in weight with time. From the results a suitable kinetic model may be developed for the progress of the reaction within a single particle. Included in this model will be a description of any mass transfer resistances associated with the reaction and of how the reaction is affected by concentration of the reactant present in the gas phase. [Pg.182]

The SSMTZ computer program, which uses the LRC coefficients and models for the various mass transfer resistances in the system to predict the shape of the stable portions of the breakthrough curves in the multicomponent system under isothermal conditions. [Pg.75]

Using the computer programs discussed above, it is possible to extract from these breakthrough curves the effective local mass transfer coefficients as a function of CO2 concentration within the stable portion of the wave. These mass transfer coefficients are shown in Figure 15, along with the predicted values with and without the inclusion of the surface diffusion model. It is seen that without the surface diffusion model, very little change in the local mass transfer coefficient is predicted, whereas with surface diffusion effects included, a more than six-fold increase in diffusion rates is predicted over the concentrations measured and the predictions correspond very closely to those actually encountered in the breakthrough runs. Further, the experimentally derived results indicate that, for these runs, the assumption that micropore (intracrystalline) resistances are small relative to overall mass transfer resistance is justified, since the effective mass transfer coefficients for the two (1/8" and 1/4" pellets) runs scale approximately to the inverse of the square of the particle diameter, as would be expected when diffusive resistances in the particle macropores predominate. [Pg.98]


See other pages where Mass transfer resistance model is mentioned: [Pg.1516]    [Pg.236]    [Pg.222]    [Pg.239]    [Pg.241]    [Pg.247]    [Pg.172]    [Pg.597]    [Pg.234]    [Pg.251]    [Pg.253]    [Pg.259]    [Pg.709]    [Pg.318]    [Pg.25]    [Pg.93]    [Pg.218]    [Pg.34]    [Pg.401]    [Pg.152]    [Pg.327]    [Pg.204]    [Pg.206]    [Pg.163]    [Pg.237]   
See also in sourсe #XX -- [ Pg.145 ]

See also in sourсe #XX -- [ Pg.145 ]




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