Parameter mass transfer

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

For particles with a bidispersed pore structure, the mass-transfer parameter in the LDF approximation (column 2 in Table 16-12) can be approximated by the series-combination of resistances... 

The experimental results imply that the main reaction (eq. 1) is an equilibrium reaction and first order in nitrogen monoxide and iron chelate. The equilibrium constants at various temperatures were determined by modeling the experimental NO absorption profile using the penetration theory for mass transfer. Parameter estimation using well established numerical methods (Newton-Raphson) allowed detrxmination of the equilibrium constant (Fig. 1) as well as the ratio of the diffusion coefficients of Fe"(EDTA) andNO[3]. 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve very slow binding steps. In these cases, the mass-transfer parameter k is replaced... 

Equation (8) is especially useful in determining equilibrium and mass transfer parameters from experimental chromatographic concentration profiles. As shown by Sherwood et al. [37] the peak maximum will occur when... 

For the rhodium-catalyzed hydroformylation of propylene in an aqueous biphasic system. Cents et al. have shown that the accurate knowledge of the mass transfer parameters in the gas-liquid-liquid system is necessary to predict and optimize the production rate [180]. Choudhari et al. enhanced the reaction rate by a factor of 10-50 by using promoter Ugands for the hydroformylation of 1-octene in a biphasic aqueous system [175]. 

Behkish, A., Hydrodynamic and Mass transfer parameters in large-scale slurry bubble column reactors, PhD Thesis, University of Pittsburgh (2004)... 

Note Bubble column mass transfer parameters are difficult to estimate reliably. 9 The above figures are based on results from the sulphite oxidation method at a higher electrolyte concentration than the 0.05M solution to be used in the present example, and therefore the values for and a may be overestimates. 

The task is the determination of the parameters of the reaction model. These reaction model parameters can be rate constants, activation energies, reaction orders or mass-transfer parameters. Additionally, the reaction enthalpies of the different reaction steps have to be... 

Introducing the mass transfer parameter, for the Tafel type reaction, assuming migration is negligible, the local flux will be... 

Figure 12(a) shows the typical distributions in local current for a first order reaction with different values of v 2 and applied dimensionless overpotentials ° for the coupled anode model, including mass transfer parameter y. The values of °, in the range of 0.5 to 16 typically represent overpotentials in the approximate range of 25 to 800 mV. The total current flows fromX = 0 (anode fed plane) to X= 1 (membrane). Current is much higher at the face of the electrode adjacent to the membrane or free electrolyte solution and decreases towards the current collector. An increase in potential increases the local current density and thereby increases the overall variation in current density throughout the electrode. 

Figure 12(b) shows the local current distribution of first and second order reactions and applied over potentials ° for the coupled anode model without the mass transfer parameter y. The figure also shows the effect of a change in the electrode kinetics, in terms of an increase in the reaction order (with respect to reactant concentration) to 2.0, on the current distribution. Essentially a similar variation in current density distribution is produced, to that of a first order reaction, although the influence of mass transport limitations is more severe in terms of reducing the local current densities. 

Table 9. Summary of mass transfer parameters for batch fluoride adsorption...

Furthermore, these characterizations will be completed in determining mass transfer parameters a and Ps, Cconv and Jdiff, respectively, the reflection coefficient and the solute permeability of the membranes, the part of solute mass transfer dedicated to convection and Jam the part of mass transfer dedicated to hydration-diffusion, for two synthetic chlorides and sulphates sodium salts solutions under different concentrations, 10-3 and 10-1 M. 

Nonequilibrium sorption due to mass-transfer limitations (including slow external or internal diffusion) and sorption to two different sorbents have been incorporated into a single ADE to evaluate the conditions under which mass-transfer processes may be important [206]. Simulations with this model, using mass-transfer parameters estimated from empirical correlations, reveal nonequilibrium conditions (i.e., mass-transfer limitations) when groundwater velocities increase (such as those that might occur in a funnel-and-gate system). 

Additional information on hydrodynamics of bubble columns and slurry bubble columns can be obtained from Deckwer (Bubble Column Reactors, Wiley, 1992), Nigam and Schumpe (Three-Phase Sparged Reactors, Gordon and Breach, 1996), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Gianetto and Silveston (Multiphase Chemical Reactors, Hemisphere, 1986). Computational fluid mechanics approaches have also been recently used to estimate mixing and mass-transfer parameters [e.g., see Gupta et al., Chem. Eng. Sci. 56(3) 1117-1125 (2001)]. 

Lehtonen et al. (1998) considered polyesterification of maleic acid with propylene glycol in an experimental batch reactive distillation system. There were two side reactions in addition to the main esterification reaction. The equipment consists of a 4000 ml batch reactor with a one theoretical plate distillation column and a condenser. The reactions took place in the liquid phase of the reactor. By removing the water by distillation, the reaction equilibrium was shifted to the production of more esters. The reaction temperatures were 150-190° C and the catalyst concentrations were varied between 0.01 and 0.1 mol%. The kinetic and mass transfer parameters were estimated via the experiments. These were then used to develop a full-scale dynamic process model for the system. 

Reactor Model. The design of an industrial packed-bed reactor requires a reactor model as well as the chemical and the heat and mass transfer parameters of the catalyst bed - gas stream system. Since these parameters are model-specific, it seemed advisable to employ a continuum model for the reactor calculation. This is the only model to date for which the literature contains consistent data for calculating heat and mass transfer parameters (5,6,7). This model in its... 

The results of the steady-state model for the reactor under the same operating conditions are displayed as the solid lines in Figure 2. The predicted catalyst and gas temperatures are shown at each of the axial collocation points. As discussed earlier, a priori values of kinetic parameters were used ( 1, 2) similarly, heat and mass transfer parameters (which are listed in Table II) were taken from standard correlations (15, 16, 17) or from experimental temperature measurements in the reactor under non-reactive conditions. The agreement with experimental data is encouraging, considering the uncertainty which exists in the catalyst activity and in the heat transfer parameters for beds with such large particles. 

The kinetic parameters reported in Table 1 was applied to calculate the mean value of activity of the catalyst in two industrial reactors to simulate their performance. The mass-transfer parameters of the bubble columnns were calculated using semiempirical equations [5,6], The physical constant values are reported in previous works [1,2]. 

Tracer measurements have indicated that the liquid in the reactor is well mixed on a macroscopic scale. Mass-transfer parameters were determined by... 

Here we examine commonly used mechanically agitated industrial liquid-liquid contactors. Table XVII describes mixing and mass transfer parameters for mechanically agitated liquid-liquid contactors. The most commonly... 

Typical Values of Mixing and Mass-Transfer Parameters in Mechanically Agitated Contactors (Reprinted from Doraiswamy and Sharma. 1984, courtesy of Marcel Dekker, Inc.)... 

The a and b parameters are related to the diffusion coefficient, porosity, mass transfer parameters, etc. If internal diffusion is the main resistance to mass transfer (which is the usual case in preparative chromatography), the dependence on the particle diameter dp is given by24... 

Many processes of gas absorption with chemical reaction are set up at high pressures, result of technical and/or economical requirements. That is, for example, processes of hydrocracking and hydrorefining of heavy oils and processes of oxydation of liquid effluents. However, if many chemical systems are found to determine the mass transfer parameters in an industrial reactor at atmospheric pressure by using the chemical method, they become scarce at elevated pressures. Several physical and chemical methods have been proposed chemical methods present some severe drawbacks, since one has to replace the gas-liquid system of interest by another one, presenting different physical properties (specially a different coalescence behaviour). 

Horstmann and Chase [35] have used the mass transfer parameters determined in stirred tank experiments to simulate the breakthrough curves of affinity chromatography experiments. Numerical methods using different computer packages were carried out to solve the differential equations of the stirred tank adsorption and to predict the performances of a packed bed chromatographic column. 

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