Rate-determining mass transfer resistance

Figure 21 Linearized double reciprocal plot of the effective permeability coefficients and corresponding stirring rates to determine the power dependency of the stirring rate and mass transfer resistances for the aqueous boundary layers and the Caco-2 cell monolayer in the Transwell system. 

With the advent of advanced electronics and computerization, electrochemical techniques have evolved rapidly. The most common technologies today are the polarization resistance technique, electrochemical impedance, and Tafel extrapolation. Regardless of the technique used, each relies on the same basic principles in each test, a metallic coupon in an electrolyte is subject to an electrical perturbation. This perturbation is the appUcation of a current from an external source (power supply). This current stimulates the surface corrosion reactions. The voltage (potential) response of the coupon is measured and correlated with the current appUed—a galvanodynamic test. Conversely, the coupon potential is controlled and correlated with the requisite current—a potentiodynamic test. In either case, the resultant current is representative of the rate determining mass transfer or charge transfer rate. This may be related to the corrosion rate. 

To determine the intrinsic reaction rate, all mass transfer resistances have to be excluded by a proper adjustment of the reaction conditions. First we must determine the regime where the gas-liquid mass transfer of hydrogen has no influence on the effective rate. Figure 4.11.20 indicates that the effective rate in the batch reactor is limited by the gas-liquid mass transfer in case of high concentrations of the catalyst and/or high octene concentrations. 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

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... 

The penetration theory has been used to calculate the rate of mass transfer across an interface for conditions where the concentration CAi of solute A in the interfacial layers (y = 0) remained constant throughout the process. When there is no resistance to mass transfer in the other phase, for instance when this consists of pure solute A, there will be no concentration gradient in that phase and the composition at the interface will therefore at all Limes lie the same as the bulk composition. Since the composition of the interfacial layers of the penetration phase is determined by the phase equilibrium relationship, it, too. will remain constant anil the conditions necessary for the penetration theory to apply will hold. If, however, the other phase offers a significant resistance to transfer this condition will not, in general, be fulfilled. 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

Example 11.8 With highly reactive absorbents, the mass transfer resistance in the gas phase can be controlling. Determine the number of trays needed to reduce the CO2 concentration in a methane stream from 5% to 100 ppm (by volume), assuming the liquid mass transfer and reaction steps are fast. A 0.9-m diameter column is to be operated at 8 atm and 50°C with a gas feed rate of 0.2m /s. The trays are bubble caps operated with a 0.1-m liquid level. Literature correlations suggest = 0.002 m/s and A, = 20m per square meter of tray area. 

The diffusivity in gases is about 4 orders of magnitude higher than that in liquids, and in gas-liquid reactions the mass transfer resistance is almost exclusively on the liquid side. High solubility of the gas-phase component in the liquid or very fast chemical reaction at the interface can change that somewhat. The Sh-number does not change very much with reactor design, and the gas-liquid contact area determines the mass transfer rate, that is, bubble size and gas holdup will determine reactor efficiency. 

As can be concluded from this short description of the factors influencing the overall reaction rate in liquid-solid or gas-solid reactions, the structure of the stationary phase is of significant importance. In order to minimize the transport limitations, different types of supports were developed, which will be discussed in the next section. In addition, the amount of enzyme (operative ligand on the surface of solid phase) as well as its activity determine the reaction rate of an enzyme-catalyzed process. Thus, in the following sections we shall briefly describe different types of chromatographic supports, suited to provide both the high surface area required for high enzyme capacity and the lowest possible internal and external mass transfer resistances. 

Case H Infinitely Slow Reaction. Here the mass transfer resistance is negligible, the compositions of A and B are uniform in the liquid, and the rate is determined by chemical kinetics alone. 

Careful reading of papers is required to determine which definition has been used. Measurements of the continuous phase resistance around bubbles frequently use photographic, volumetric, or pressure change techniques to yield instantaneous rates of mass transfer, and thus kA. Here too, both definitions of the Sherwood number, Eqs. (7-43) and (7-45), have been used. 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

The true intrinsic kinetic measurements require (1) negligible heat and mass transfer resistances by the fluids external to the catalyst (2) negligible intraparticle heat and mass transfer resistances and (3) that all catalyst surface be exposed to the reacting species. The choice of the reactor among the ones described in this section depends upon the nature of the reaction system and the type of the required kinetic data. Generally, the best way to determine the conditions where the reaction is controlled by the intrinsic kinetics is to obtain rate per unit catalyst surface area as a function of the stirrer speed. When the reaction is kinetically controlled, the rate will be independent of the stirrer speed. The intraparticle diffusional effects and flow uniformity (item 3, above) are determined by measuring the rates for various particle sizes and the catalyst volume, respectively. If the reaction rate per unit surface area is independent of stirrer speed, particle size, and catalyst volume, the measurements can be considered to be controlled by intrinsic kinetics. It is possible... 

The evaluation of catalyst effectiveness requires a knowledge of the intrinsic chemical reaction rates at various reaction conditions and compositions. These data have to be used for catalyst improvement and for the design and operation of many reactors. The determination of the real reaction rates presents many problems because of the speed, complexity and high exo- or endothermicity of the reactions involved. The measured conversion rate may not represent the true reaction kinetics due to interface and intraparticle heat and mass transfer resistances and nonuniformities in the temperature and concentration profiles in the fluid and catalyst phases in the experimental reactor. Therefore, for the interpretation of experimental data the experiments should preferably be done under reaction conditions, where transport effects can be either eliminated or easily taken into account. In particular, the concentration and temperature distributions in the experimental reactor should preferably be described by plug flow or ideal mixing models. 

In some instances. Equation (14-24) does not hold at the beginning of the electrolysis, because the initial concentration may be so high that the proportionality between the current and the concentration does not hold. Thus, if the source is unable to supply the total voltage -I- iE) at the level of current that can be sustained by the rate of mass transfer, the current is determined initially by the back emf and the electrolytic resistance [Equation (14-1)]. This statement amounts to saying that the cathode potential corresponds to a rising portion of the curve for cathodic current against voltage rather than to a point on the plateau. 

Another synthesis process proposed to receive benefits from operating with monolith catalysts is the conversion of methanol for gasoline production [16,17J. The catalyst used was the ZSM-5 zeolite. However, rather than binding the catalyst onto the wall by use of a washcoat, it was uniformly crystallized on the cordierite honeycomb (62 cells/cm ) wall surfaces (up to 30% by weight), similar to the method described in the patent assigned to Lachman and Patil [18]. The effects of methanol partial pressure on conversion and temperature on hydrocarbon selectivity were determined. Three regimes of mass transfer resistances are experienced in this reaction reactant transfer to the reactor walls within the monolith channels through the laminar flow, diffusion resistance at the surface between zeolite crystals on the walls, and diffusion into the zeolite molecular-size pores to the active sites within the crystals, where the reaction rate limit is anticipated. 

Internal and external mass transfer resistances are important factors affecting the catalyst performance. These are determined mainly by the properties of the fluids in the reaction system, the gas-liquid contact area, which is very high for monolith reactors, and the diffusion lengths, which are short in monoliths. The monolith reactor is expected to provide apparent reaction rates near those of intrinsic kinetics due to its simplicity and the absence of diffusional limitations. The high mass transfer rates obtained in the monolith reactors result in higher catalyst utilization and possibly improved selectivity. 

The kinetics of partial oxidation, ATR, and dry reforming of liquid hydrocarbons have also been reported recently.103,155 Pacheco et al.155 developed and validated a pseudo-homogeneous mathematical model for the ATR of isooctane and the subsequent WGS reaction, based on the reaction kinetics and intraparticle mass transfer resistance. They regressed the kinetic expressions from the literature for partial oxidation and steam reforming reactions to determine the kinetics parameters for the ATR of isooctane on Pt/ceria catalyst. The rate expressions used in the reformer modeling and the parameters of these rate expressions are given in Tables 2.19 and 2.20, respectively. 

Additionally, the parameters of the reaction rate equation have to be determined. Levenspiel (1999) has described different methods that can be applied. For homogeneous-catalyzed reactions the experiments can be done in a stirred tank reactor. If the reaction is catalyzed heterogeneously the use of a fixed bed reactor is recommended. In this case, the mass transfer resistance and the hydrodynamic parameters of the packed bed also have to be taken into account. 

The study of a particular adsorption process requires the knowledge of equilibrium data and adsorption kinetics [4]. Equilibrium data are obtained firom adsorption isotherms and are used to evaluate the capacity of activated carbons to adsorb a particular molecule. They constitute the first experimental information that is generally used as a tool to discriminate among different activated carbons and thereby choose the most appropriate one for a particular application. Statistically, adsorption from dilute solutions is simple because the solvent can be interpreted as primitive, that is to say as a structureless continuum [3]. Therefore, all equations derived firom monolayer gas adsorption remain vafid. Some of these equations, such as the Langmuir and Dubinin—Astakhov, are widely used to determine the adsorption capacity of activated carbons. Batch equilibrium tests are often complemented by kinetics studies, to determine the external mass transfer resistance and the effective diffusion coefficient, and by dynamic column studies. These column studies are used to determine system size requirements, contact time, and carbon usage rates. These parameters can be obtained from the breakthrough curves. In this chapter, I shall deal mainly with equilibrium data in the adsorption of organic solutes. 

The simplest mode of LM operation available is a batch reactor. The LM emulsions containing enzymes or cells are kept agitated in a vessel by using impellers. Periodic samples of external aqueous phase can be taken to monitor the reaction rate it is much more difficult to monitor the conditions in the internal aqueous phase. Impeller speed becomes an important parameter in batch operation, as it determines the size of the emulsion globules and therefore influences the emulsion stability and the mass-transfer resistance (46). 

Equation (10-3) represents the case when diffusion controls the overall process. The rate is determined by k the kinetics of the chemical step at the catalyst surface are unimportant. Equation (10-4) gives the rate when the mass-transfer resistance is negligible with respect to that of the surface step i.e., the kinetics of the surface reaction control the rate. -. 

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