Rate mass transfer controlled

Linear Driving Force Approximation Simplified expressions can also be used for an approximate description of adsorption in terms of rate coefficients for both extrapai ticle and intraparticle mass transfer controlling. As an approximation, the rate of adsorption on a particle can be written as ... 

Before terminating the discussion of external mass transfer limitations on catalytic reaction rates, we should note that in the regime where external mass transfer processes limit the reaction rate, the apparent activation energy of the reaction will be quite different from the intrinsic activation energy of the catalytic reaction. In the limit of complete external mass transfer control, the apparent activation energy of the reaction becomes equal to that of the mass transfer coefficient, typically a kilocalorie or so per gram mole. This decrease in activation energy is obviously... 

Corresponding equations for the two special cases of gas-film mass-transfer control and surface-reaction-rate control may be obtained from these results (they may also be derived individually). The results for the latter case are of the same form as those for reaction-rate control in the SCM (see Table 9.1, for a sphere) with R0 replacing (constant) R (and (variable) R replacing rc in the development). The footnote in Example 9-2 does not apply here (explain why). 

The performance of a reactor for a gas-solid reaction (A(g) + bB(s) -> products) is to be analyzed based on the following model solids in BMF, uniform gas composition, and no overhead loss of solid as a result of entrainment. Calculate the fractional conversion of B (fB) based on the following information and assumptions T = 800 K, pA = 2 bar the particles are cylindrical with a radius of 0.5 mm from a batch-reactor study, the time for 100% conversion of 2-mm particles is 40 min at 600 K and pA = 1 bar. Compare results for /b assuming (a) gas-film (mass-transfer) control (b) surface-reaction control and (c) ash-layer diffusion control. The solid flow rate is 1000 kg min-1, and the solid holdup (WB) in the reactor is 20,000 kg. Assume also that the SCM is valid, and the surface reaction is first-order with respect to A. 

Kinetic experiments and rigorous modelling of the mass-transfer controlled polycondensation reaction have shown that even at low melt viscosities the diffusion of EG in the polymer melt and the mass transfer of EG into the gas phase are the rate-determining steps. Therefore, the generation of a large surface area is essential even in the prepolycondensation step. 

This boundary-layer theory applies to mass-transfer controlled systems where the membrane permeation rate is independent of pressure, for there is no pressure term in the model. In such cases it has been proposed that, as the concentration at the membrane increases, the solute eventually precipitates on the membrane surface. This layer of precipitated solute is known as the gel-layer, and the theory has thus become known as the gel-polarisation model proposed by Micii i i.si 0). Under such conditions C, in equation 8.15 becomes replaced by a constant Cq the concentration of solute in the gel-layer, and ... 

The dimensionless parameter ttd, was first identified by Amon and Denson (1983) and is a measure of whether mass transfer controls the rate of bubble growth (ttd, > 1) or whether momentum transfer controls growth (iron < ) ... 

At 60 minutes only, dc potentiodynamic curves were determined from which the corrosion current was obtained by extrapolation of the anodic Tafel slope to the corrosion potential. The anodic Tafel slope b was generally between 70 to 80 mV whereas the cathodic curve continuously increased to a limiting diffusion current. The curves supported impedance data in indicating the presence of charge transfer and mass transfer control processes. The measurements at 60 minutes indicated a linear relationship between and 0 of slope 21mV. This confirmed that charge transfer impedance could be used to provide a measure of the corrosion rate at intermediate exposure times and these values are summarised in Table 1. 

There have been a number of studies on the rate of dissolution of crystals In agitated tanks (eg.26-31). Predominantly the results Indicate dissolution Is mass transfer controlled. For mass transfer In stirred tanks, among the many studies, that of Levins and Glastonbury (32) Is widely considered. 

A plot of the dissolution rate against driving force, AC, is shown in Figure 13. This shows a linear dependence on undersaturation and a slight dependence on temperature (activation energy of 10 kJ/mole). This indicates that the dissolution is mass transfer controlled. The results can be correlated by... 

Mass transfer controlled by diffusion in the gas phase (ammonia in water) has been studied by Anderson et al. (A5) for horizontal annular flow. In spite of the obvious analogy of this case with countercurrent wetted-wall towers, gas velocities in the cocurrent case exceed these used in any reported wetted-wall-tower investigations. In cocurrent annular flow, smooth liquid films free of ripples are not attainable, and entrainment and deposition of liquid droplets presents an additional transfer mechanism. By measuring solute concentrations of liquid in the film and in entrained drops, as well as flow rates, and by assuming absorption equilibrium between droplets and gas, Anderson et al. were able to separate the two contributing mechanisms of transfer. The agreement of their entrainment values (based on the assumption of transfer equilibrium in the droplets) with those of Wicks and Dukler (W2) was taken as supporting evidence for this supposition. 

Figure 7-9 Reactant concentration profiles around and within a porous catalyst pellet for the cases of reaction control, external mass transfer control, and pore difliision control. Each of these situations leads to different reaclion rate expressions.

For convective crystal dissolution, the dissolution rate is u = (p/p )bD/8. For diffusive crystal dissolution, the dissolution rate is u = diffusive boundary layer thickness as 5 = (Df), the diffusive crystal dissolution rate can be written as u = aD/5, where a is positively related to b through Equation 4-100. Therefore, mass-transfer-controlled crystal dissolution rates (and crystal growth rates, discussed below) are controlled by three parameters the diffusion coefficient D, the boundary layer thickness 5, and the compositional parameter b. The variation and magnitude of these parameters are summarized below. 

According to their analysis, if is zero (practically much lower than 1), then the liquid-film diffusion controls the process rate, while if tfis infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the so-called mechanical parameter represents the ratio of the diffusion resistances (solid and liquid film). The authors did not refer to any assumption concerning the type of isotherm for the derivation of the above-mentioned criterion it is sufficient to be favorable (not only rectangular). They noted that for >1.6, the particle diffusion is more significant, whereas if < 0.14, the external mass transfer controls the adsorption rate. 

Agitated vessels (liquid-solid systems) Below the off-bottom particle suspension state, the total solid-liquid interfacial area is not completely or efficiently utilized. Thus, the mass transfer coefficient strongly depends on the rotational speed below the critical rotational speed needed for complete suspension, and weakly depends on rotational speed above the critical value. With respect to solid-liquid reactions, the rate of the reaction increases only slowly for rotational speed above the critical value for two-phase systems where the sohd-liquid mass transfer controls the whole rate. When the reaction is the ratecontrolling step, the overall rate does not increase at all beyond this critical speed, i.e. when all the surface area is available to reaction. The same holds for gas-liquid-solid systems and the corresponding critical rotational speed. 

Since we know the mass of ozone transferred has to have reacted or left the system, it is relatively easy to determine the reaction rate for slow reactions, which are controlled by chemical kinetics with this method. For kinetic regimes with mass transfer enhancement, the two rates, mass transfer and reaction rate are interdependent. Whether kLa or kD can be determined in such a system and how depends on the regime. Possible methods are similar to those described below in Section B 3.3.3 (see Levenspiel and Godfrey, 1974). 

The mass transfer factor has also been correlated as a function of the Reynolds number only and thus taking account only of hydrodynamic conditions. If e is the voidage of the packed bed and the total volume occupied by all of the catalyst pellets is Vp, then the total reactor volume is Vp/(l - e). Hence the rate of mass transfer of component A per unit volume of reactor is NASx(l - e)/Vp. If we now consider a case in which only external mass transfer controls the overall reaction rate we have ... 

Particle Size and Desorption Rates. Bench-scale reactor studies of the desorption of toluene from single, 2- to 6-mm porous clay partides (14) showed desorption times that increased with the square of the particle radius, suggesting that diffusion controls the rate desorption. Parallel experiments performed in a small, pilot-scale rotary kiln at 300°C showed no effect of day partide size for diameters ranging from 0.4 to 7 mm. Additional single-partide studies with temperature profiles controlled to match those in the pilot-scale kiln had desorption times that were a factor of 2—3 shorter for the range of sizes studied (15). Hence, at the conditions examined, intrapartide mass transfer controlled the rate of desorption when single particles were involved and interpartide mass transfer controlled in a bed of particles in a rotary kiln. These results apply to full-scale kilns. As particle size is increased, intraparticle resistances to heat and mass transfer eventually begin to dominate. 

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